Where some form of collusion does occur, as at times it inevitably will, demystifying the collusion has internal repercussions as well. The clarification of patterns of self-mystification (Laing 1965) that this makes it a possibly that being often liberating. It can facilitate a shift on the part of the patient from feeling victimized or helpless, stuck without any options, too freshly experiencing his or her own power and responsibility in relation to multiple choices.
For example, one patient who had difficulty defining where she ended and the other began was invariable in a constant state of anger with others for what she perceived as their not allowing her feelings, as how this operated between us, she realized that no one could control her feelings and that it was her inordinate need for the approval of others that were controlling her. It was her need to control the other, to control the other's reaction to her, that was defining her experience. The result was that she began to feel less threatened and paranoid. She also was able to begin to deal analytically with the unconscious dynamics of her needs for approval and for control, and to focus on her anxieties in a way not possibly earlier.
We must then, ask of ourselves, are the afforded efforts to control the given as the ‘chance' to ‘change', or the given ‘change' to ‘chance'? As a neutral type of the therapist participation proves to be essential to the resolution of the schizophrenic patient's basic ambivalence concerning individuation - his intense conflict, that is, between clinging and a hallucinatory, symbiotic mode of existence, in which he is his whole perceived world, or on the other hand relinquishing this mode of experience and committing himself to object-relatedness and individuality - too becoming, that is, a separate person in a world of other persons. Will (1961) points out that just as ‘In the moves toward closeness the person finds the needed relatedness and identification with another, in the withdrawal (often marked by negativism) he finds the separateness that favours his feelings of being distinct and self-identified, and Burton (1961) says that "In the treatment, the patient's desire for privacy is respected and no encroachment is made. The two conflicting needs war with each other and it is a serious mistake for the therapist to take sides too early." The schizophrenic patient has not as to the experience that commitment too object-relatedness still allows for separateness and privacy, and where SĂ©chehaye (1956) recommends that one "make oneself a substitute for the autistic universe that helped to offer as of a given choice that must rest in the patient's hands." This regarded primeval area of applicability of a general comment by Burton (1961) that "In the psychotherapy of every schizophrenic a point is reached where the patient must be confronted with his choice. . . ." Of Shlien's (1961) comment that "Freedom means the widest scope of choice and openness to experience . . . ."
Only in a therapeutic setting where he finds the freedom to experience both these modes of relatedness with one and the same person can the patient become able to choose between psychosis and emotional maturity. He can settle for this later only in proportion as he realizes that both object-relatedness and symbiosis are essential ingredients of healthy human relatedness - that the choice between these modes amounts not to a once-for-all commitment, but that, to enjoy the gratification of human relatedness he must commit himself to either object-relatedness or symbiotic relatedness, as the chancing needs and possibilities that the basic therapeutics requires and permit.
Such, as to say, the problem is to reconcile our everyday consciousness of us as agents, with the best view of what science tells us that we are. Determinism is one part of the problem. It may be defined as the doctrine that every event has a cause. More precisely, for any event as ‘e', there will be some antecedent state of nature ‘N', and a law of nature. ‘L', such that given to ‘L', ‘N', will be followed by 'e'. Yet if this is true of every event, it is true of events such as my doing something or choosing to do something. So my choosing or doing something is fixed by some antecedent state ‘N' and the laws. Since determinism is universal these in turn are fixed, and so backwards to events, for which I am clearly not responsible (events before my birth, for example). So no events can be voluntary or free, where that means that they come about purely because of free willing them, as when I could have done otherwise. If determinism is true, then there will be antecedent states and laws already determining such events? : How then can I truly be said to be their author, or be responsible for them? Reactions to this problem are commonly classified as: (1) hard determinism. This accepts the conflict and denies that you have real freedom or responsibility. (2) Soft determinism or compatibility. Reactions in this family assert that everything you should want from a notion of freedom is quite compatible with determinism. In particular, even if your action is caused, it can often be true of you that you could have done otherwise if you had chosen, and this may be enough to render you liable to be held responsible or to be blamed if what you did was unacceptable (the fact that previous events will have caused you to choose as doing so and deemed irrelevant on this option). (3) Libertarianism. This is the view that, while compatibilism is inly an evasion, there is a more substantive, real notion of freedom that can yet be preserved in the face of determinism (or of in determinism). While the empirical or phenomenal self is determined and not free, the noumenal or rational self is capable of rational, free action. Nevertheless, since the noumenal self exists outside the categories of space and time, this freedom seems to be of doubtful value. Other libertarian avenues include suggesting that the problem is badly framed, for instance because the definition of determinism breaks down, or postulating a special category of uncaused acts of volition, or suggesting that there are two independent but consistent ways of looking at an agent, the scientific and humanistic. It is only through confusing them that the problem seems urgent. None of these avenues accede to exist by a greater than is less to quantities that seem as not regainfully to employ to any inclusion nontechnical ties. It is an error to confuse determinism and fatalism. Such that, the crux is whether choice, is a process in which different desires, pressures, and attitudes fight it out and eventually result in one decision and action, or whether in attitudinal assertions that there is a ‘self' controlling the conflict, in the name of higher desires, reasons, or mortality? The attempt to add such a extra to the more passive picture (often attributed to Hume), and is a particular target not only of Humean, but also of much feminist and postmodernist writing.
Thus and so, the doctrine that every event has a cause infers to determinism. The usual explanation of this is that for every event, there is some antecedent state, related in such a way that it would break a law of nature for this antecedent state to exist, and as yet the event not to happen. This is a purely metaphysical claim, and carries no implications for whether we can in a principal product the event. The main interest in determinism has been in asserting its implications for ‘free will'. However, quantum physics is essentially indeterministic, yet the view that our actions are subject to quantum indeterminacies hardly encourages a sense of our own responsibility for them.
As such, these reflections are simulated by what might be regarded as naive surprise at the impact of the renewed emphasis on the ‘here-and-now' in our technical work during the last few years, including the early interpretations of the transference. This emphasis has been argued most vigorously by Gill and Muslin (1976) and Gill (1979). It has at times been reacting to, as if it were a technical innovation, and, of course, making it clear, all the same, from the persistence and reiteration that characterize Gill's contributions, that he believes the "resistance to the awareness of transference" to be a critically important and neglected area in psychoanalytic work, this may deserve further emphasis. In Gill's latest contribution of which as before, he concedes that the recall or reconstruction of the past remains useful but that the working out of conflict in the current transference is the more important, i.e., should have priority of attention. In view of the centrality of issues and its interesting place in the development of psychoanalysis, the contributory works of Gill and Muslin (1976). Gill (1979) presents a subtle and searching review and analysis of Freud's evolving views on the interrelationship between the conjoint problems of transference and resistance and the indications for interpretation. Repeating this painstaking work would therefore be superfluous. Our's is for a final purpose to state for reason to posit of itself upon the transference and non-transference interpretation and beyond this, to sketch a tentative certainty to the implications and potentialities of the ‘here-and-now'.
In a sense, the current emphasis may be the historical ‘peaking' of a long and gradual, if fluctuating, development in the history of psychoanalysis. We know that Freud's first re-counted with the transference, the ‘false connection', was its role as a resistance (Breuer and Freud 1893-1895). While Freud's view of this complex phenomenon soon came to include its powerfully affirmative role in the psychoanalytic process, the basis importance of the ‘transference resistance' remained. In the Dynamics of Transference (1912) stated in dramatic figurative terms the indispensable current functions of the transference: "For when all is said and done, destroying anyone in absentia or in effigies is impossible." In fact, to some of us, the two manifestly opposing forces are two sides of the same coin. As, perhaps, the relationship is eve n more intimate, in the sense that the resistance is mobilized in the first place b the existence of (manifest or - often - latent) transference. It is spontaneous protective reaction against loss of love, or punishment, or narcissistic suffering in the unconscious infantile context of the process.
Historically, the effective reinstatement of his personal past into the patient's mental life was thought to be the essential therapeutic vehicle of analysis and thus its operational goal. This was, of course, modified with time, explicitly or in widespread general understanding. The recollection or reconstruction of an experience, however critical its importance, evidently did not (except in relatively few instances) immediately dissolve the imposing edifice of structuralized reaction patterns to which it may have importantly y contributed, this (dissolution) might indeed occur - dramatically - in the case of relatively isolated, encapsulated, and traumatic experiences, but only rarely y in the chronic psychoneuroses whose genesis was usually different and far more complex. Freud's (1914) discovery of the process of ‘working through', along with the emphasis on its importance, was one manifestation of a major process of recognition of the complexity, persuasiveness, and tenacity of the current dynamics of personality, in relation to both genetic and dynamic factors of early or origin. Perhaps Freud's (1937) most vivid figurative recognition of the pseudoparadoxical role of early genetic factors, If not understood as part of a complex continuum, was in his "lamp-fire" critique of the technical implications of Rank's (1924) Trauma of Birth. The term pseudoparadoxical is used because the recovery of the past by recollection or reconstruction - if no longer the sole operational vehicle and goal of psychoanalysis - retains a unique intimate and individual explanatory value, essential to genuine insight into the fundamental issues of personality development and distortion.
When Ferenczi and Rank wrote The Development of Psychoanalysis in 1924, they proposed an enormous emphasis on emotional experience in the analytic process, as opposed to what was thought to be the effectively sterile intellectual investigation the n in vogue. Instead of the speedy reduction of disturbing transference experience by interpretation, these authors, in a sense, advised the elucidation and cultivation of emotional intensities. (As Alexander pointed out in 1925, however, the method was not clear.) These alone could lend a vivid sense of reality and meaningfulness to the basic dynamism of personality incorporated in the transference. Now it is to be masted and marked that in this work, too, there is no ‘repudiation' of the past. Ultimately genetic interpretations were to be made. The intense transference experience, as mentioned, was intended to give body, reality, to the living past. Yet, the ultimate significance of construction was invoked, in the sense of ‘supplying' those memories that might not be spontaneously available. It was felt that the crucial experiences of childhood had usually been promptly repressed and thus not experiences in consciousness in any significant degree. Therapeutic effectiveness of the process was attributed largely to the intensity of emotional experience, than to the depth and ramifications of detained cognitive insight. The fostering in of transference intensity, as, we can infer, was rather by withholding or scantiness of interpretations (as opposed to making facilitating interpretations) and, at times (as specifically stared), by mild confirming responses or attitudes in the affective sphere: These would tend to support the patient's transference affects in interpersonal reality (Ferenczi and Rank 1024).
This is, of course, different from the recent emphasis on ‘early interpretation of the transference (Gill and Muslin 1976), which in a process in the cognitive sphere designed to overcome resistance to awareness of transference and thuds to mobilize the latter as an active participant in the analysis as soon as possible. What they have in common is an undeniable emphasis on current experience, explicitly in the transference. Also, in both tendencies there is an implicit minimization of the vast and rich territories of mind and feeling, which may become available and at times uniquely informative if fewer tendentious attitudes govern the analyst's initial approach. Correspondingly, in both there is the hazard of stimulating resistance of a stubborn, well-rationalized maturity by the sheer tendentious of approachment, and similarly transference tendency pursued assiduously by the analyst.
The question of the moments entering a sense of conviction in the patient (a dynamically indispensable state) is, of course, a complex matter. However, if one is to think that few would doubt that immediate or closely proximal experience (‘today' or ‘yesterday') occasions grater vividness and sense of certainty than isolated recollection or reconstruction of the remote past. Thus the "here-and-now" in analytic work, the immediate cognitive exchange and the important current emotional experiences, and, under favourable conditions, contributes to other elements in the process, i.e., recovery or reconstruction of the past, a quality of vividness deriving from their own immediacy, which can infuse the past with life. Obviously, it is the experience of transference affect that largely engages our attention in this reference. However, we must not ignore the contrapuntal role of the actual adult relationship between patient and analyst. Corresponding is indeed the actual biological constellation that bings the transference itself into being. At the very least, a minimal element of ‘resemblance' to primary figures of the past is a sine quo non for its emergence (Stone 1954).
Nonetheless, this contribution up to and including Gill's, Muslin's (1976) and Gill's (1979) are highly-developed. However, did not introduce alternations in the fundamental conceptions of psychopathology and its essential responses to analytic techniques and process. Yet, there are, of course, varying emphases - namely quantitative - and corresponding positions as to their respective effectiveness. As Strachey states, "there is an approach to actual substantive modification in the keystone position assigned to introjective super-ego change as the essential phenomenons of analytic process - and possibly in the exclusive role assigned to transference interpretations as ‘mutative'.
A related or complementary tendency may be discerned in Gill's (1979) proposal that "analytic situation residues" from the patient's ongoing personal life, insofar as they are judged transferentially significant in free association, is brought into relation with the transference as soon as possible, even if the patient feels no prior awareness of such a relationship. It is as if all significant emotional experience, including extra-analytic experiences, could be viewed as displacement or mechanisms of concealed expression of his transference. That this is very frequently true of even the most trivial-seeming actual allusions to the analytic would, in that, the thoroughly extra-analytic references constitute a more subtle and different problems, ranging from dubiously interpretably minor issues to massive forms of destructive acting out connected with extreme narcissistic resistances and utterly without discernible 'analytic situation residues'. The massive forms are, of course, analytic emergencies, requiring interpretation. Still, such interpretation would usually depend on the awareness of the larger ‘strategic situations (Stone 1973), rather than on a detail of the free association communication (granting the latter's usefulness, if present - and recognizable). However, the fact of the past or the historical as never entirely abandoned or nullified, becoming more even, the role assigned to it may be pale or secondary. That the preponderant emphasis on concealed transference may ultimately, constitute an "actually existing" change in technique and process, with its own intrinsic momentum.
The Ferenczi and Rank technique included, in effect, a deliberate exploitation of the transference resistance, especially in the sense of intense emotional display and discharged. While the polemical emphases of these authors are on (affective) experiences as the sine non of true analytic process - the living through of what was never fully experienced in consciousness in the past (with ultimate translation into ‘memories', i.e., constructions) - the actual techniques (with a few exceptions) are not clearly specified in their book. For a detailed exposition of the techniques learned from Ferenczi, with wholehearted acceptance, as in the paper of De Forest (1942), which includes the deliberate building up of dramatic transference intensities by interpretative withholding and the active participation of the analyst as a reactive individual. Also included is the active directing of all extra-therapeutic experience into the immediate experiential stream if the analysis. The extreme emphasis on affective transference experience became at one time a sort of vogue, appearing almost as an end and measured by the vehemence of the patient's emotional displays. In Gill's own revival of and emphasis on a sound precept of classical techniques (preceded by the 1976 paper of Gill and Muslin), fundamentally different from that of Ferenczi and Rank in its emphasis, one discerns an increment of enthusiasm between the studied, temperate, and well-argued paper of (1979) and the later paper of the same year (1979), which includes similar ideas greatly broadened and extended ti a degree that is, in it's difficultly to accept.
Now, what is it that may actually be worked out in the present - (1) as a prelude to genetic clarification and reduction of the transference neurosis or (2) as a theoretical possibility in its own right without reliance on the explanatory power or specific reductive impact of insight into the past? First some general considerations of whether or not one is an enthusiastic proponent of ‘object relations theory' in any of its elaborate forms, seems self-evident that all major developmental vicissitudes and conflicts have occurred in the context of important relations with important objects and that they or their effects continue to be reflected in current relationships with persons of similar or parallel importance. That we assume that the psychoanalytic situation (and its adjacent ‘ extended family') provides a setting in which such problems may be reproduced in their essentials, both effectively and cognitively.
There is something deductively engaging in the idea that an individual must confront and solve his basic conflicts in their immediate setting in which they arise, regardless of their historical background. Certainly this is true in the patient's (or anyone else's) actual life situation. Some possible and sometimes state corollaries of this view would be that the preponderant resort to the past, whether by recollection or reconstruction, would be largely in the service of resistance, in the sense of a devaluation of the present and a diversion from its ineluctable requirements. It would be as if the United Kingdom and Ireland would undertake to solve the current problems in Ulster essentially by detailed discussion of Cromwell's behaviour a few centuries ago. Granted that the latter might indeed illuminate the historical contribution of some aspects of the current sociopolitical dilemma, there are immediate problems of great complexity and intensity from which the Cromwell discussion might indeed by a diversion, if it were magnified beyond it's clear but very limited contribution, displacing in importance the problematical social-political-economic altercation of the present and the recent clearly accessible and still relevant past. As with so many other issues, Freud himself was the first to note that resort to the past may be involved by the patient to evade pressing and immediate current problems. In conservative technique, it has long been noted that some judicious alternations of focus between past and present, according to the confronting resistances trend, may be necessary (for example, Fenichel 1945). However, it was Horney (1939) who placed the greatest stress on the conflict and the greatest emphasis on the recollection trend as supporting resistance.
Now, from the classical point of view, the emphasis is quite different. The original conflict situation is intrapsychic, within the patient, though obviously engaging his environment and ultimately - most poignantly and productively - his analyst. This culminates in a transference neurosis that reproduces the essential problems of the object relationships and conflicts of his development. Thus, in principle, the vicissitudes of love or hate or fear, etc., do not require, or even admit of, ultimate solution in the immediate reality, perceived and construed as such. The problem is to make the patient aware of the distortions that he has carried into the present and of the defensive modes and mechanisms that have supported them. Obviously, the process (‘tactical') resistances present themselves first for understanding; later there are the ‘strategic' resistances (i.e., those not expressed in manifest disturbances of free association) (Stoner 1973). Insofar as the mobilization of the transference and the transference neurosis is accorded a uniquely central holistic role in all analyses, the ‘resistance to the awareness of transference', becomes a crucial issue, the problem of interpretive timing on which a controversial matter from early. Ultimately the bedrock resistance, the true ‘transference resistance', must be confronted and dissolved or reduced to the greatest possible degree. Such a reduction is construed as largely dependent on the effective reinstatement of the psychological prototype of current transference illusions, with an ensuing sense of the inappropriateness of emotional attitudes in the present and the resultant tendency toward their relinquishment. In a sense, the neurosis is viewed as an anachronistic but compelling investitures of the current scene within unresolved conflict of the past. When successfully reduced, this does appear to have been the accessibly demonstrable phenomenology.
What then may be carried into the analytic situation from the ‘hard-nosed' paradigm of the struggle with every day, current reality, with advantage to the process? We have already made mention, in that the sense of conviction, or ‘sense of reality' - affective and cognitive - which originates in th immediacy of process experience. It is our purpose and expectation that, with appropriate skill and timing, this quality of conviction may become linked too other, fewer immediate phenomena, at least in the sense of more securely felt perceptions, including first the fact of transference and ultimately its accessible genetic origins. What furthers? Insofar as the transference neurosis tends toward organic wholeness, a sort of conflict ‘summary' by condensation, under observation in the immediate present, one may seek and find access in it, not only to the basic conflict mentioned, but to uniquely personal mode of defence and resistance, revealed in dreams, habits of free association, symptomatic acts, parapraxes, and the more direct modes of personal address and interaction that are evident in every analysis. Further, in this view, although not always as transparent as one would wish, this remarkable condensation of effect, impulse, defence, and temporary conflict solution adumbrates more dependably than any other analytic element (or grouping of elements) the essential outlines of the field of obligatory analytic work of a given period of the patient's life. In it is the tightly knotted tangle deprived from the patient's early or prehistoric life enmeshed in him actualities of the analytic situation and his germane and contiguous ongoing life situations.
Also, in the sphere of the "here-and-now," and of extensive importance, is the role of actualities in the analytic situation. Whether in the patent's everyday life or in the analytic relationship, the even-handed, open-minded attention to the patient's emotional experience (especially his suffering or resentment) as to what may be actual, as opposed too ‘neurotic' (i.e., illusory or unwittingly provoked) or specifically transferential, is not only epistemologically deductive for reason that is also a contribution to the affective soundness of the basic analytic relationship and thus of inestimable importance. At the risk of slight - very slight - exaggeration, in that with excepting instances of pathological neurotic submissiveness, as a patient who wholeheartedly accepted the significance his neurotic or transference-motivated attitudes or behaviour if he felt that ‘his reality' was not given just due. Furthermore, even the exploration and evaluation of complicated neurotic behaviour must be exhaustive to the point where a spontaneous urge to look for irrational motivations is practically on the threshold of the patient ‘s awareness. Once, again, one must stress the impact of such a tendency on the total analytic relationship. For, not only are the quality and mood of utilization of interpretations, but ultimately the subtleties of transition from a transference relationship to their realities of the actual relationship depend, on a greater degree than has been made explicit, on the cognitive and emotional aspects of the ongoing experience in the actual sphere. Greenson (1971, 1972. Wexler 1969) devoted several of his last papers to this important subject. The subject, of course, includes the vast spheres of the analyst's character structure and his countertransference. However, more than may be at first apparency, can reside in the sphere of conscious consideration of technique e and attitude in relation to a basic rationale.
However, apart from the immediate function of painstaking discrimination of realities and the impact of this attitude on the total situation, there remains the important question of whether important elements of true analytic process may not be immanent in such trends of inquiry. The vigorous exploration and exposure of distortions in object relations, via the transference or in the affective and behavioural patterns of everyday life, including defence functions, can conceivably catalyse important spontaneous changes in their own right. To further this end, the traditional techniques of psychoanalysis will, of course, be utilized. As an interim phenomenon, however, the patient struggle to deal with distortions, as one might with other error subject to conscious control or pedagogical correction. It is to reasons of conviction that such a tendency may be productive (both as such, and in its intrinsic c capacity to highlight neurotic or conflictive fractions) and has been insufficiently exploited. Nonetheless, there is no reason that the specific dynamic impact of th past is lost or neglected in its ultimate importance, in giving attention to a territory that is, in itself, of a great technical potentiality.
Practitioners and theorists such as Horney (1939) or Sullivan (1953) did not reject the significance of the past, even though its role and proportionate position, both in process and theoretical psychodynamics, was viewed differently. The persisting common features in these views would be a large emphasis on sociological and cultural forces and the focussing of technical emphasis on immediate interpretation transactions.
Granted that various technical recommendations of both dissident and ‘classical' origin, including those on the nature and reduction of the transference, sometimes appear to devaluate the operational importance of the genetic factor, this devaluation is not supported by the clinical experience of most of those that were indeed of closely scrutinizing it as part of the confessio fidei of major deviationists. Certainly, both in theoretical principle and in empirical observation, this essential direction of traditional analytic process remains of fundamental importance. Conceding the power and challenge of cumulative developmental and experiential personality change and the undeniable impact of current factors, it remains true that the uniquely personal, decisive elements in neurosis, apart from constitution, originate in early individual experience. How to mobilize elements into an effectively mutual function is largely a technical problem and - in seeming paradox - relies to a considerable degree on the skilful handling of the "here-and-now." The purposive technical pursuit of the past has not been clinically rewarding. That the ultimate effort to recover an integrated early material in dynamic understanding may not always be successful, especially in severe cases of early pathogenesis is, of course, evident (for example, Jacobson 1971). In such instances, while our preference would be otherwise, we may have to remain largely content with painstaking work in the "here-and-now," illuminated to whatever degree possible by reasonable and sound, if necessarily broad, constructions dealing largely with ego mechanisms than primitive anatomical fantasies. In other events, sometimes after years of painstaking work, even large and challenging characterological behavioural trends that have been viewed, clarified, and interpreted in a variety of current transference, situational (even cultural) references will show striking rottenness in earl y experience, conflict, and conflict solution whose explanatory value then achieves a mutative force that remains uniquely among interpretative manoeuvres or spontaneous insights. To this end, the broader aspects of ‘strategic' resistance (Stone 1973) must be kept in mind, a much subtle element of countertransference and counterresistance.
It would seem proper that at this point of giving to a summation of the current ferment regarding the "here-and-now" of which any number of valuable critique and theoretical and technical suggestions that may help us to improve the analytic effectiveness, it would seem that the emphasis on the "here-and-now" interpreting not only consistently with but also ultimately indispensable for genuine access to the critical dynamism deriving from the individual's early development. Nor is this reflexive, assuming the technical sophistication - inconsistent with the understanding and analysis of continuing developmental problems, character crystallization and the influence of current stresses as such. Adequate attention to the character as a complex interpretational group permits the clear and useful emergence in or the analytic field of significant early material, as defined by the transference neurosis between the technical approaches and that of Gill (1979, 1979), apart from certain larger issues. Whereas Gill would apparently recommend searching out ‘day residues' of probable transference in the patient's responses to the analysis or analyst and in his account of his daily life and offer possible alternative explanations to the patient's direct and simple responses to them as self-evident realities, first relying on the acceptance and exploration of the patient's ‘reality', with the possibility that this will incidently favour the relatively spontaneous precipitation of more readily available transference materials, this general Principle does not, of course, obviate or exclude the other alternatives as something preferable?
Consideration of the interaction between the two adult personalties in the analytic situation requires a mixture of common sense and interest in self-evident (although often ignored) elements, on the one hand, and abstrusely psychological and Metapsychological considerations, on the other.
Thus, if we set aside from immediate consideration questions regarding the ‘real relationship' and accept as a given self-evident fact that the entire psychoanalytic drama occurs (without our question or permission) between two adults in the "here-and-now" the residual is due becomes the management of the transference, which has been a challenging problem since the phenomenon was first described. Let us assume, for purposes of brevity, that few would now adhere to the principle that the transference is to be interpreted only when it becomes a manifest resistance (Freud 1912). It is in fact always a resistance and at the same time a propulsive force (Stone 1962, 1967, 1073). It has long since been recognized that an undue delay of well-founded transference interpretations (regardless of the state of the patient's free association) can seriously hinder progress in analysis, and further, it cas augment the dangers of acting out or neurotic flight from the analysis by the patient. The awareness of such danger has been clearly etched in psychoanalytic consciousness since e Freud's (1905) insight into the end of the Dora case.
Apart from the hazzards inherent in technical default, nonetheless, there has developed over the years with increasing momentum, perhaps in some relations of the increasing stress on the transference neurosis as a nuclear phenomenon of process. The affirmative active address to the transference, i.e., to the analysis - or some by time is the active interpretative bypassing - of the ‘resistances to the awareness of transference
. . . operational emphasis on the countertransference, the tendency - in rational for a proportion - must be regarded as an important integral component of a progressively evolving psychoanalytic method. That individuals vary in their acceptance of technical devotion to this tendency is to be note (as indicated earlier), but its widespread practice by thoughtful analysts cannot be ignored, by the importance of its disregarded note of countransference among analysts, which would tend to restore n earlier emphasis digestedly approach to historical material and avoidance of early or excessive; transference historical material and the avoidance of earlier excessive' transference interpretation.
A few words about our view on th relatively a circumscribed problem of transference interpretation. It is of the belief of longstanding conviction that the economic aspects of transference distribution are critically important, although largely ignored the seeking utilization of this consideration, a broad directional sense, by distinguishing between the potential transference of the analytic situation and those of the typical psychotherapeutic situation (as beyond that, the transference of everyday life. These varying their degree of emergence and their special investment of transference objects with the intensiveness of contact, with the structural emends of deprivation, and with the degree of regressive attention the operation of the rule of abstinence, which is, of course, most highly developed and consistently maintained in the traditional psychoanalytic situation (Stone 1961). Thus although subject to constant infirmed monitoring, the transference can be as medical, at least latently directed ultimately toward the analyst (compared with the cooperated persons in their environment).
Now, under what conditions and with what provisions should the awareness of such transference potentialities be actively mobilized? Obviously, the original precept regarding its emergence as resistance still trued in its implied affirmative aspect but is no longer exclusive. Further, there are, without question, early transference ‘emergences' that must be dealt with by an active interpretive approach: For example, the early rapid and severe transference regression of borderline patients or the less common some timely seriously impeding erotic transference fulminations in neuronic patients. These are special instances in which the indications seem clear and obligatory.
The central situation, nonetheless, is the ‘average' analysis (with apologies!), where the latent transferences tend to remain ego-dystopia, warded off, deploring slowly over periods, and manifesting themselves by a variety of derivative phenomena of variable intensity. Surely, dreams, parapraxes, and trends of free association will reveal basic transference directions very early. However, when should these be interrelated to the patient if he is effectively unaware of them? Again, ‘all things' being equal', an old principle of Freud's suggested for all interpretative interventions (as opposed, for example, to clarification), is applicable: That unconscious elements are interpreted only when the patient evidences a secure positive attachment the analyst. Yet, this would not obtain in the fact of the ‘emergencies' of growing erotic or aggressive intensities, certainly of ‘acting out' is incipient. The disturbing compilations (even in the ‘erotic' sphere) occur most often when basic transferences are ambivalent (largely hostile) or coloured by intense narcissism. Therefore, in relation to Freud's valuable precept, it may be understood that in certain cases, the interpretation of ambivalent hostile transferences may be obligatory prerequisite to the establishment o f the genuinely positive climate that required. In such instances of obligatory intervention, the manifestations that require them are usually quite explicit,
Again, then, what about the relatively uncomplicated case, the chronic neurotic, potentially capable of relatively mature relations to objects? Still, the coping with complications do not seem as in question. There are, a few essential conditions and one cardinal rule. First the patient's sense of reality and his common sense must not be abruptly or excessively tax, lest, in untoward reaction, his constructive imaginative capacities become unavailable. Preliminary explanations and tentative preparatory ‘trail' interventions should be freely employed to accustom him to a new view of the world. The traditional optimum for interpretation (when the patient is on the verge of perceiving its content himself [Freud 1940] is indeed best, although it must sometimes be neglected in favour of an active interpretative approach. Second, the patient's sense that the vicissitudes and exigencies of his actual situation are understood and respected must be maintained
Beyond these considerations, the essential principle is quite simple. If it is assumed that - in the intensive, abstinent, traditional psychoanalytic situation (as differentiated from most psychotherapeutic situations) - the transference (ultimately the transference neurosis) is ‘pointing' toward the unconscious trend is heavily weighted in this direction, there is still a manifest element of movement toward other currently significant objects. Thus, a latent economic problem assumes clinical form: Essentially, the growing magnitude of transference cathexes of the analyst's person, as withdrawn to varying degree from important persons in the environment with whom most of the patient's associations usually deal. There is a point, or a phase, in the evolution of transference in which analytic material (often priori to significant subjective awareness) indicates the rapidly evolving shift from extraanalytic objects to the analyst. In this interval (early in some, later in others) the analyst's interventions, whether in direct substantive form or aimed at resistances to awareness of transference, often become obligatory and certainly most often successful in mobilizing affective emphasis into the "here-and-now" of the analytic situation. The vigorous anticipatory interpretations suggested by some may be helpful in many instances (at least as preparatory manoeuvres) if (1) the analyst is certain of his views, in terms of not only the substance but the quantitative (i.e., economic) situation (2) the patient's state soundly receptive (according to well-established criteria) (3) neither the patient's realities nor his sense of their realities are put to unjustified questions or implicit neglect (4)a sense of proportion regarding the centrality of issues, largely as indicated by the outline of the transference neurosis (of their adumbration), are maintained in a real consideration. This will avoid the superfluous multiplication of transference references that like the massing of scatted genetic interpretations (familiar in the past), can lead to a ‘chaotic situation' resembling that against which Wilhelm Reich (1933) inveighed. This will be more striking with a compliant patient who can as readily become bemused with his transference as with his ‘Oedipus' or his ‘anality.'
Once the affective importance of the transference is established in the analysis, a further (hardly new) question arises, with which some of us have sought to deal in a therapist. Even if some agrees that transference interpretations have a uniquely mutative impact, how exclusively must we concentrate on them? Moreover, to what degree and when are extraanalytic occurrences and relationships of everyday life to be brought into the scope of transference interpretation? With regard to the concentration of transference interpretation alone: a large, complex, and richly informative worlds of psychological experience are obviously attention if the patient ‘s extra therapeutic life is ignored. Further, if the transference situation is unique in an affirmative sense, it is also unique by deficit. To revile at the analyst, for example, is a different experience from reviling at an employer who might ‘fire' the patient or from being snide to a co-worker who might punch him (Stone 1067 and Rangell 1979). Such experiences are also components if the "here-and-now" (granted that the "here"aspect is significantly vitiated), and they do merit attention and understanding in their own right, specially in the sphere of characterology. Certain complex reaction pasterns cannot become accessible in the transference context alone.
At the time of speaking it is true that many spectacular extraanalytic behaviours can, and should be seen as displacements (or ‘acting out') of the analytic transference or in juxtaposed ‘extended family' relation to it, especially where they involve consistent members of an intimate dramatis personae? While such ‘extra-therapeutic' transference interpretations (often clearly Germaine to the conflicts of the transference neurosis) can be indispensable, the confronting vigour and definiteness with which they are advanced (as opposed to tentativeness) must always depend on the security of knowledge of preceding and current unconscious elements that invest the persons involved.
Finally, there are incidents, attitudes, and relationships to persons in the patient's life experience who are not demonstrably involved in the transference neurosis, yet evoke importantly and characteristic responses whose clarification and interpretation may contribute importantly to the patient's self-knowledge of defences, character structure, and allied matters. Nonetheless, such data may occasionally show a vitalizing direct relationship to historical materials. It would not seem necessary or desirable that such material be forced into the analytic transference if the patient does not respond to a tactful tentative trail in this connection, for example, the ‘alternative' suggestion proposed by Gill (1979). For the economic considerations that often obtain, and it may be that certain concurrent transference cluster, not readily related to the mainstream of transference neurosis, retain their own original extra-therapeutic transference investment. In some instances, a closer, more available e relationship to the transference mainstream may appear later and lend itself to such interpretative integration. In so doing, happening is likely if obstinate resistances have not been simulated by unnecessary assault on the patients' sense of immediate reality, or his sense of his actual problems. As for metapsychology, one may recall also that all relationships, following varying degrees of development and conflict vicissitudes, are derived greatly from the original relationship to the primal object (Stone 1967), even if their representations are relatively free of the unique ‘unneutralized' cathexes that characterize active transference (‘transfer' verus ‘transference': Stern 1957).
Caring for a better understanding, to what the concerning change, as seen in the psychotherapy of schizophrenic patient, and particularly in reference to the sense of personal identity, may to this place be clearly vitiated in material that relates to extra-therapeutic experience, whether this is seen ‘in its own right' or as displaced transference. The direct transference experience occurs in relations an individual who knows his own position, i.e., knows ‘both sides' as in no other situation. (Even where there are interposing countertransference. There are at least susceptible to a self-analysis). This can never be true in the analysis of an extra-therapeutic situation, as there is no inevitable cognitive deficit. For this we must try to compensate by exercising maximal judgement, by exploiting what is revealed about the patient himself in sometimes unique situations, and by being sensitive to the growing accuracy of his reporting as the analyst progresses. Epistemologic deficits' are intrinsic in the very nature of analytic work. This is but one important example.
We need to be alert to the respects in which the concepts and technique of our particular science may lend themselves to the repression, in us and our patients, of anxiety concerning change.
Our necessary delineation of the repetitive patterns between the transference and countertransference tends to become so preoccupying as to obscure the circumstance that, as Janet M. Rioch phrases it, "What is curative in the [analytic] process is that in tending to reconstruct in which the analyst that an atmospheric state that obtained in childhood, the patient effectively achieves something new" (Rioch 1943).
Our necessarily high degree of reliance upon verbal communication requires us to be aware of the extent to which grammatical patterns having a tendency to segment and otherwise render static our ever-flowing experience; this has been pointed out by Benjamin (1944); Bertrand Russell (1900), Whorf (1956) and others. The tendency among us to regard prolonged silence for being given to disruptiveness in the analytic process, or evidence per se of the patient's resistance to it, may be due in part to our unconscious realization that profound personalty-change is often best simplified by silent interaction with the patient; therefore, we have an inclination to press forward toward the crystallization of change-inhibiting words.
What is more, our topographical views of the personality a being divisible into the area's id, ego, and superego, are so inclined to shield us from the anxiety-fostering realization that, in a psychoanalytic cure, change is not merely quantitative and partial
as of "Where id was, there shall Ego be," in Freud's dictum, but qualitative and all-pervasive. Apparently such data system in a passage is to provide accompaniment for Freud, as he gives a picture of personality-structure, and of maturation, which leaves the inaccurate but comforting impression that at least a part of us - namely, a part of the id - is free from change. In his paper entitled Thought for the Times on War and Death. In 1915, he said, "the evolution of the mind shows a peculiarity that is present in no other process of development." When a village grows into a town, a child into a man, the village, and the child become submerged in the town and the man. . . . It is in other considerable levels that the accompaniment with the development of the mind . . . the primitive stage [of mental development] can always be re-established; the primitive mind is, in the fullest meaning of the word, imperishable (Freud 1915).
In Introductory Lectures on Psycho-Analysis, he says that "in psychoanalytic treatment. . . . By means of the work of interpretation, which transform what is unconscious into what is conscious, the ego is enlarged at the expense of this unconscious." In the Ego and the Id, he said that, " . . . the ego is that part of the id modified by the direct influence of the external world . . . the pleasure-principle . . . reigns unrestricted by the id. . . . The ego represents what may be called reason and common sense, in contrast to the id, which contains the passions" (Freud 1923).
Glover, in his book on Technique published in 1955, states similarly that, . . ." A successful analysis may have uncovered a good deal of the repressed . . . [and] have mitigated the archaic censoring functions of the superego, but it can scarcely be expected to abolish the id" (Glover 1955).
Favorably to have done something to provide by some measure, conviction, feeling, mind, persuasion, sentiment used to form or be expressed of some modesty about the state of development of our science, and about our own individual therapeutic skills, should not cause us to undertake the all-embracing extent of human personality growth in normal maturation and in a successful psychoanalysis. Presumably we have all encountered a few fortunate instances that have made us wonder whether maturation really leaves any area of the untouched personality, leaves any steel-bound core within which the pleasure principle reigns immutably, or whether, instead, we have a genuine metamorphosis, from a former hateful and self-seeking orientation to a loving and giving orientation, quite as wonderful and thoroughgoing as the metamorphosis of the tadpole into the frog or that of the caterpillar into the butterfly.
Freud himself, in his emphasis upon the ‘negative therapeutic reaction' (1923), the repetition compulsion, and the resistance to analytic insight that he discovered in his work with neurotic patients, has shown the importance, in the neurotic individual, of anxiety concerning change, and he agrees with Jung's statement that ‘a peculiar psychic inertia, hostile to change and progress, is the fundamental condition of neurosis' (Freud 1915). This is, even more true of the psychosis - so much so that only in very recent decades have psychotic patients achieved full recovery through modified psychoanalytic therapy. Also, it has instructively to explore and deal the psychodynamics of schizophrenia as for the anxiety concerning change which one encounters, in a particular intense degree, at work in these patients, and of ones own, inasmuch as for treating them. What the therapy of schizophrenia can teach us of the human being's anxiety concerning change, can broaden and deepen our understanding of the non-psychotic individual also.
Further, we see that during his development years he lacks adequate models, in his parents or other parent-figures, with whom to identify about the acceptance of outer changes and the integration of inner change as personality-maturation throughout adulthood. Alternatively, these are relatively rigid persons who, over the years, either/or tenaciously resist change, if anything becomes progressively constricted, fostering him in the conviction that the change from a child into adult is more loss than gain - that, as one matures, fewer feelings and thoughts are acceptable, until finally one is to attain, or be confined to, the thoroughgoing sterility of adulthood. The sudden, unpredictable changes that puncture his parent's rigidity, due to the eruption of masses of customarily-repressed material in themselves, make them appear to him, for the time being, like totally different persons from their usual selves, and this adds to his experience that personality-change is something that is not to be striving for, but avoided as frighteningly destructive and overwhelming.
We find evidence that he is reacting to, by his parents during his upbringing, predominantly concerning transference and projection, for being the reincarnation of some figure or figures from their own childhood, and the personification of repressed and projected personality-traits in themselves. Thus he is called upon by them, in an often unpredictably changing fashion, to fill various rigid roles in the family, leaving him little opportunity to experience change as something that can occur within himself, as a unique human individual, in a manner beneficial to himself.
When the parents are not relating to him in such a transference fashion they are, it appears, all too often narcissistically absorbed in them. In either instance, the child is left largely in a psychological vacuum, in that he has to cope essentially alone with his own maturing individuality, including the intensely negative emotions produced by the struggle for individuality in such a setting. Because his parents are afraid of the developing individual in him, he too fears this inner self, and his fear of what is heightening parenthetical parents within investing him with powers, based upon the mechanisms of transference and projection that by it's very nature does not understand, powers that he experiences as somehow flowing from himself and yet not an integral part of himself nor within his power to control. As the years bring tragedies to his family, he develops the conviction that he somehow possesses all ill-understood malevolence that is totally responsible for these destructive changes.
In as far as he does discover healthy maturational changes at work in his body and personality, changes that he realizes to be wonderful and priceless, he experiences the poignant accompanying realization that there is no one there to welcome these changes and to share his joy. The parents, if sufficiently free from anxiety to recognize such changes at all, have a tendency to accept them as evidence that their child is rejecting then by growing functionally. Also to be noted, in this connexion, is their lack of trust in him, their lack of assurance that he is elementally good and can be trusted to maturational bases of a good healthy adult. Instead they are alert to find, and warn him against, manifestations in him that can be construed as evidence that he is on a predestined, downward path into an adulthood of criminality, insanity, more at best ineptitude for living.
Moreover, he emergences change not as something within his own power to wield, for the benefit of himself and others but as something imposed from without. This is due not only to structures that the parents place upon his autonomy, but also to the process of increasing repression of his emotions and life as, such that when this latter manifest themselves, they do so in a projected expressive style, for being uncontrollable changed, inflicted upon him from the surrounding world? We see extreme examples of this mechanism later on. In the full-blown schizophrenic person who experiences sexual feelings not as such but as electric shocks sent into him from the outside world, and who experiences anger not as an emerging emotion directorially fittingly as in a way up from within, but a massive and sudden blow coming somehow from the outer world. In fewer extreme instances, in the life of the yet-to-become-schizophrenic youth, he finds repeatedly that when he reaches out to another person, the other suddenly undergoes a change in demeanour, from friendliness to antagonism, in reaction to an unwitting manifestation of the youths' unconscious hostility. The youth himself, if unable to recognize his own hostility, can only be left feeling increased helplessness in face of an unpredictably changeable world of people.
The final incident that occurs before his admission to the hospital, giving him still further reason for anxiety as for change, is his experience of the psychotic symptoms as an overwhelming anxiety-laden and mysterious change. His own anxiety about this frightened away by the seismic disturbance and horror of the members of his family who finds hi ‘changed' by what they see as an unmitigated catastrophe, a nervous or mental ‘breakdown'. Although the therapist can come to see, in retrospect, a potential positive element via this occurrence - namely, the emergence of onetime-repressed insights concerning the true state of affairs involving the patient and his family, none of those participants can integrate so radically changed a picture at that time. Over the preceding years the family members could not tolerate their child's seeing himself and them with the eyes of a normally maturing offspring, and when repressed percepts emerge from repression in him, neither they nor he possesses the requisite ego-strength to accept them as badly needed changes in his picture of himself and of them. Instead, the tumult of depressed percepts foes into the formation of such psychotic phenomena as misidentifications, hallucinations, and delusions in which neither he nor the member of his family can discern the links to reality that we, upon investigation in individual psychotherapy with him, can find in these psychotic phenomena - links, that is, to the state of affairs that has really held sway in the family. Paretically, it should be marked and noted that the psychotic episode often occurs in such ac way as to leave the patient especially fearful of sudden change, for in many instances the de-repressed material emerges suddenly and leads him to damage, in the short space of a few hours or even moments, his life situation so grievously that repair can be affected only very slowly and painfully, over many subsequent months of treatment in the confines of a hospital.
It should be conveyed, in that the regression of the thought-processes, which occurs as one of the features of the developing schizophrenia, results in an experience of the world so kaleidoscopic as to make up still another reason for the individual's anxiety concerning change. That is, as much as he has lost thee capacity to grasp the essentials of a given whole - to the extent that he has regressed to what Goldstein (1946) terms the ‘concrete attitude' - he experiences any change, even if it is only in an insignificant (by mature standards) detail of that which he perceives, as a metamorphosis that leaves him with no sense of continuity between the present perception and that immediately preceding. This thought disorder, various aspects of which have been described also by Angyal (1946), Kasanin (1946), Zucker (1958), and others, is compared by Werner with the modes of thought that are found in members of so-called primitive cultures (and in healthy children of our own culture): . . . in the primitive mentality, particulars often as self-subsisting things that do not necessarily become synthized into larger entities. . . . The natives of the Kilimanjaro region do not have a word for the whole mountain range that they inhabit, only words for its peaks. . . . The same is reported of the aborigines of East Australia. From each twist and turn of a river has a name, but the language does not permit of a single all-embracing differentiation for the whole river. . . . [He] quotes Radin (1927) as saying that for the primitive man: "A mountain is not thought of as a unified whole. It is a continually changing entity' . . . [and, Radin continues, such a man lives in a world that is] ‘dynamic and ever-changing . . . Since he sees the same objects changing in their appearance from day to day, the primitive man regards this phenomenon as definitely depriving them of immutability and self-subsistence' (Werner 1957).
Langer (1942) has called the symbolic-making function ‘one of man's primary activities, like eating, looking, or moving about. It is the fundamental process of his mind', she says, as she terms the need of symbolization ‘a primary need in man, which other creatures probably do not have'. Kubie (1953) terms the symbolizing capacity ‘the unique hallmark of man . . . capacities', and he states that it is in impairment of this capacity to symbolize that all adult psychopathology essentially consists.
As for schizophrenia, we find that since 1911 this disease was described by Bleuler (1911) as involving an impairment of the thinking capacities, and in the thirty years many psychologists and psychiatrists, including Vigotsky (1934) Hanfmann and Kasanin (1942) Goldstein (1946) Norman Cameron (1946) Benjamin (1946) Beck (1946) von Domarus (1946) and Angtal (1946) - to mention but a few - has described various aspects of this thinking disorder. These writers, agreeing that one aspect of the disorder consists in over -concreteness or literalness of thought, have variously described the schizophrenic as unable to think in figurative (including metaphorical) terms, or in abstractions, or in consensually validated concepts and symbols, mor in categorical generalizations. Bateson (1956) described the schizophrenic as using metaphor, but unlabelled metaphor.
Werner (1940) has understood this most accurately matter of regression to a primitive level of thinking, comparable with the found in children and in members of so-called primitive cultures, a level of thinking in which there is a lack of differentiation between the concrete and the metaphorical. Thus we might say that just as the schizophrenic is unable to think in effective, consensually validated metaphor, as too as he is unable to think in terms that are genuinely concrete, free from an animistic forbear of a so-called metaphorical overlay.
The defensive function of the dedifferentiation that in so characterized of schizophrenic experience, and one find that this fragmentation o experience, justly lends itself to the repression of various motions that are too intense, and in particular too complex, for the weak ego to endure, which must be faced as one becomes aware of change as involving continuity rather than total discontinuity.
That is, the deeply schizophrenic patient who, when her beloved therapist makes a unkind or stupid remark, experiences him now for being a different person from the one who was there a moment ago - who experiences that a Bad Therapist has replaced the Good Therapist - is by that spared the complex feeling of disillusionment and hurt, the complex mixture of love and anger and contempt that a healthier patient would feel then. Similarly, if she experiences it in tomorrow's session - or even later in the same session - that another good therapist has now come on the scene. The bad therapist is now totally gone, she will feel none of the guilt and self-reproach that a healthier patient would feel at finding that this therapist, whom she has just now been hated or despising, is after all a person capable of genuine kindness. Likewise, when she experiences a therapist's departure on vacation for being a total deletion of him from her awareness, this bit of discontinuity, or fragmentation, in her subjective experience spars her from feeling the complex mixture of longing, grief, separation-anxiety, rejection, rage and so on, which a less ill patient feels toward a therapist who is absent but of whose existence he continues to be only too keenly aware.
Finally, such repressed emotions as hostility and lust may readily be seen, as these feelings not easy to hear expressed, as, for instance, the woman, who, at the beginning of her therapy, had been encased for years I flint lock paranoid defenses, become able to express her despair by saying that "If I had something to get well for, it would make a difference," her grief, by saying, "The reason I am afraid to be close to people is because I feel so much like crying": Her loneliness, by expressing a wish that she would turn an insect into a person, so then she would have a friend. Her helplessness in face of her ambivalence by saying, to her efforts to communicate with other persons, "I feel just like a little child, at the edge of the Atlantic or Pacific Ocean, trying to build a castle - right next to the water. Something just starts to be gasped [by the other person], and then bang! It has gone - another wave. As joining the mainstream of fellow human beings.
In the compliant charge of bringing forward three hypotheses are to be shown, they're errelated or portray in words as their interconnectivity, are as (1) in the course of a successful psychoanalysis, the analyst goes through a phase of reacting to, and eventually relinquishing, the patient as his oedipal love-object, (2) in normal personality development, the parent reciprocates the child's oedipal love with greater intensity than we have recognized before, and (3) in such normal developments, the passing of the Oedipus complex is at least important a phase in ego-development as in superego-development.
While doing psycho-analysis, time and again patients who have progressed to, or very far toward, a thorough going analysis to cure, become aware of experiential romantic and erotic desires and fantasies. Such fantasizing and emotions have appeared in a usual but of late in the course of treatment, have been preset not briefly but usually for several months, and have subsided only after having experienced a variety of feelings - frustration, separation anxiety, grief and so forth - entirely akin to those that attended as the resolution of an Oedipus complex late in the personal analysis.
Psycho-analysis literature is, in the main. Such as to make one feel more, rather than less, troubled at finding in oneself such feelings toward one's patient. As Lucia Tower (1956) has recently noted, . . . Virtually every writer on the subject of countertransference . . . states unequivocally that no form of erotic reaction to a patient is to be tolerated . . .
Still, in recent years, many writers, such as P. Heimann (1950), M. B. Cohen (1952) and E. Weigert (1952, 1954), have emphasized how much the analyst can learn about the patient from noticing his own feelings, of whatever sort, in the analytic relationship. Weigert (1952), defining countertransference as emphatic identification with the analysand, has stated that . . . "In terminal phases of analyses the resolution of countertransference goes hand in hand with the resolution of transference."
Respectfully, these additional passages are shown in view of countertransference, in the special sense in which defines the analyst for being innate, inevitable ingredients in the psycho-analytic relationship, in particular, the feelings of loss that the analyst experiences with the termination of the analysis. However, case in point, that the particular variety of countertransference with which are under approach is concerned that of the analyst's reacting as a loving and protective parent to the analysand, reacted too as an infant: There are plausible reasons why in the last phase it is especially difficult to achieve and maintain analytic frankness. The end of analysis is an experience of loss that mobilizes all the resistances in the transference (and in the counter-transference too), for a final struggle. . . . Recently, Adelaide Johnson (1951) described the terminal conflict of analysis as fully reliving the Oedipus conflict in which the quest for the genitally gratifying parent is poignantly expressed and the intense grief, anxiety and wrath of its definitive loss are fully reactivated. . . . Unless the patient dares to be exposed to such an ultimate frustration he may cling to the tacit permission that his relation to the analyst will remain his refuge from the hardships of his libidinal cravings to an aim-inhibited, tender attachment to the analyst as an idealized parent, he can get past the conflicts of genital temptation and frustration.
. . . . The resolution of the counter-transference permits the analyst to be emotionally freer and spontaneous with the patient, and this is an additional indication of the approaching end of an analysis.
. . . . When the analyst observes that he can be unrestrained with the patient, when he no longer weighs his words to maintain as cautious objectivity, this empathic countertransference and the transference of the patient are in a process of resolution. The analyst can treat the analysand on terms of equality; he is no longer needed as an auxiliary superego, an unrealistic deity in the clouds of detached neutrality. These are signs that the patient's labour of mourning for infantile attachments nears completion.
In stressing the point, which before an analysis can properly bring to an end, the analyst must have experienced a resolution of his countertransference to the patient for being a deep beloved, and desired, figure not only on this infantile level that Weigert has emphasized valuably, but also on an oedipal-genital level. Weigeret's paper, which helped to formulate the views that are set down, that is, as expressing the total point that a successful psycho-analysis involves the analyst's deeply felt relinquishment of the patient both as a cherished infant, and for being a fellow adult who is responded to at the level of genital love?
The paper by L. E. Tower (1956) comes similarly close to the view that, unlike Weigert, limits the term counter-transference to those phenomena that are transferences of the analyst to the patient. It is much more striking, therefore, that she finds even this classification defined countertransference to be innate to the analytic process: . . . . That there is inevitably, naturally, and often desirable, many countertransference developments in every analysis (some evanescent - some sustained), which is a counterpart of the transference phenomena. Interactions (or transactions) between the transference of the patient and the countertransference of the analyst, going on at unconscious levels, may be - or perhaps are always - of vital significance for the outcome of the treatment. . . .
. . . . Virtually every writer on the subject of countertransference. States unequivocally that no form of erotic reaction to a patient is to be tolerated. This would suggest that temptations in this area are great, and perhaps ubiquitous. This is the one subject about which almost every author is very certain to state his position. Other 'counter-transference' manifestations are not routinely condemned. Therefore, it must be to assume that erotic responses to some extent trouble nearly every analyst. This is an interesting phenomenon and one that call for investigation; nearly all physicians, when they gain enough confidence in their analysts, report erotic feelings and imply toward their patients, but usually do so with a good deal of fear and conflict. . . .
Of our tending purposes, we are to pay close attention to the libidinal resources that are of our applicative theory, in that large amounts of resulting available libido are necessary to tolerate the heavy task of many intensive analyses. While, we deride almost every detectable libidinal investment made by an analyst in a patient . . . various forms of erotic fantasy and erotic countertransference phenomena of a fantasy and of an affective character are in some experiential ubiquitous and presumably normal. Which lead to suspect that in many - perhaps every - intensive analytic treatment there develops something like countertransference structures (perhaps even a 'neurosis') which are essential and inevitable counterparts of the transference neurosis. These countertransference structures may be large or small in their quantitative aspects, but in the total picture they may be of considerable significance for the outcome of the treatment. They function in the manner of a catalytic agent in the treatment process. Their understanding by the analyst may be as important to the final working through of the transference neurosis as is the analyst's intellectual understanding of the transference neurosis itself, perhaps because they are, so to speak, the vehicle for the analyst's emotional understanding of the transference neurosis. Both transference neurosis and countertransference structure seem intimately bound together in a living process and both must be considered continually in the work that is the psychoanalysis. . . .
. . . . Seemingly questionable, is any thorough working through a deep transference neurosis, in the strictest sense, which does not involve some form of emotional upheaval in which both patient and analysts are involved. In other words, there are both a transference neurosis and a corresponding Countertransference 'neurosis' (no matter how small and temporary) which are both analyzed in the treatment situation, with eventual feelings of a new orientation by both one another toward any other but themselves.
Freud, in his description of the Oedipus complex (1900, 1921, 1923), tended largely to give us a picture of the child as having an innate, self-determined tendency to experience, under the conditions of a normal home, feelings of passionate love toward the parent of the opposite sex; we get little hints, from his writings, that in this regard the child enters a mutual relatedness of passionate love with that parent, a relatedness in which the parent's feelings may be of much the same quality and intensity as those in the child (although this relatedness must be very important in the life of the developing child than it is in the life of the mature adult, with his much stronger, more highly differentiated ego and with his having behind him the experience of a successfully resolved oedipal experience during his own maturation).
Nevertheless, in the earliest of his publications concerning the Oedipus complex, namely The Interpretation of Dreams (1900), Freud makes a fuller acknowledgements of the parent's participation in the oedipal phase of the child's life than does in any of his later writings on the subject". . . a child's sexual wishes - if in their embryonic stage they deserve to be so described - awaken very early. . . . A girl's first affection is for her father and boy's first childish desires are for his mother. Accordingly, the father becomes a disturbing rival to the boy and the mother to the girl. The parents too give evidence as a rule of sexual partiality: A natural predilection usually sees to it that a man tends to spoil his little daughters, while his wife takes her sons' part; though both of them, where their judgement is not disturbed by the magic of sex, keep a strict eye upon their children's education. The child is very well aware of this patriality and turns against that one of his parents who is opposed to showing it. Being loved by an adult does not merely bring a child the satisfaction of a special need; it also means that he will get what he wants in every other respect as well. Thus, he will be following his own sexual instinct and while giving fresh strength to the inclination shown by his parents if his choice between them falls in with theirs (1900).
Theodor Reik, in his accounts of his coming to sense something of the depths of possessiveness, jealousy, fury at rivals, and anxiety in the face of impending loss, in himself regarding his two daughters, conveys a much more adequate picture of the emotions that genuinely grip the parent in the oedipal relationship than is conveyed by Freud's sketchy account, as Reik's deeply moving descriptions occupy a chapter in his Listening with the Third Ear (1949), written at the time when his daughters were twelve and six years of age; and a chapter in his The Secret Self (1952), when the oldest daughter was now seventeen.
Returning to a further consideration of the therapist's oedipal-love responses to the patient, it seems that these response flows from four different sources. In actual practice the responses from these four tributaries are probably so commingled in the therapists that it is difficult of impossible fully to distinguish one kind from another; the important thing is that he is maximally open to the recognition of these feelings in himself, no matter what their origin, for he can probably discern, in as far as is possible, from where they flow they signify, therefore, concerning the patient's analysis.
First among these four sources may be mentioned the analyst's feeling-responses to the patient's transference. This, when, as the analysis progresses and the patient enter an experiencing of oedipal love, ongoing, jealousy y, frustration and loss as for the analyst as a parent in the transference, the analyst will experience to at least some degree, response's reciprocally th those of the patient-responses, that is, such for being present within the parent in questions, during the patient's childhood and adolescence, which the parent presumably was not ably to recognize freely and accept within himself. Some writers apply the term 'counter-transference' to such analyst-responese to the patient's transference, unlike others some do not do so.
The second source consists in the countertransference in the classical sense in which this term is most often used: The analyst's responding to the patient about transference-feelings carried over from a figure out of the analyst 's own earlier years, without awareness that his response springs predominantly from this early-life, rather than being based mainly upon the reality of the patient analyst-patient relationship. It is this source, of course, which we wish to reduce to a minimum, by means of thoroughgoing personal analysis and ever-continuing subsequent alertness for indications that our work with a patient has come up against, in us, unanalyzed emotional residues from our past. This source is so very important, in fact, as to make the writing of such a paper as a somewhat precarious venture. Must expect that some readers will charge him with trying to portray, as natural and necessary to the annalistic process generally, certain analyst-responese that in actuality is purely the result of an unworked-through? Oedipus' complex in himself, which are dangerously out of place in his own work with patients that have no place in the well-analysed analyst's experience with his patient.
It can only be surmised that although this source may play an insignificant role in the responses of a well-analysed analyst who has conducted many analyses through to completion - to an intensified inclusion as a thoroughgoing resolution of the patient's Oedipus complex - it is probably to be found, in some measure, in every analyst. This is, it seems that the nature and conflictual feeling-experience in this regard - a fostering of his deepest love toward the fellow human being with whom she participates in such prolonged and deeply personal work, and a simultaneous, unceasing, and rigorous taboo against his behavioural expression of any of the romantic or erotic components of his love - as to require almost any analyst's tending to relegate the deepest intensities of these conflictual feelings to his own unconscious mind, much as were the deepest intensities of his oedipal strivings toward a similar beloved, and similarly unobtainable and rigorously tabooed, parent in particular, and in the hope of the remaining in the analyst's unconscious. That is hoping that this will help analysts - in particular, to a lesser extent-experienced analyst - whereas to some readers awareness, and by that diminution, of this countertransference feeling, as justly dealing with other kinds of countertransference feelings, by such as those wrote by P. Heumann (1950, M. B., Cohen (19520 and E. Weigert (1952?)
A third source is to be found in the appeal that the gratifyingly improving patient makes to the narcissistic residue in the analyst's personality, the Pygmalion in him. He tends to fall in love with this beautifully developing patient, regarded at this narcissistic level as his own creation, just as Pygmalion fell in love with the beautiful statu e of Galatea that he had sculptured. This source, like the second one that we can expect to holds little sways in the well-analysed practitioner of long experience, but it, too, is probably never absent of great experience and professional standing, than we may like to think. Particularly in articles and books that describe the author's new technique or theoretical concept as an outgrowth of the work with a particular patient, or a very few patients, do we see this source very prominently present in many instances.
The fourth source, based on the genuine reality of the analyst-patient situation, consists in the circumstance that nearly becomes, per se, a likeable, admirable and insightfully speaking lovable, human being from whom the analyst will soon become separated. If he is not himself a psychiatrist, the analyst may very likely never see him again. Even if he is a professional colleague, the relationship with him will become in many respects far more superficial, far less intimate, than it has been. This real and unavoidable circumstance of the closing analytic work tends powerfully to arouse within the analyst feelings of painfully frustrated love that deserve to be compared with the feelings of ungratifiable love that both child and parent experience in the oedipal phase of the child's development. Feelings from this source cannot properly be called countertransference. They may flow from the reality of the present circumstances but they may be difficult or impossible e to distinguish fully from countertransference.
There are, then four essentially powerful sources having to promote of the tendency toward the feelings of deep love with romantic and erotic overtones, and with accompanying feelings of jealousy, anxiety, frustration-rage, separation-anxiety, and grief, in the analyst about the patient. These feelings come to him, like all feelings, without tags showing from where they have come, and only if he is open and accepting to their emergence into his awareness does he have a chance to set about finding out their origin and thus their significance in his work with the patient.
Finally, with which the considerations have been presented so far, a few remarks concerning the passing of the Oedipus complex in normal development and in a successful psycho-analysis.
In the Ego and the Id (1923) we find italicized a passage in which Freud stresses that the oedipus phase results in the formation of the superego; we find that he stresses the patient's opposition to ther child's oedipal swosh, and lastly, we see this resultant suprerego to be predominantly a severe and forbidding one: The broad general outcome of the sexual phase dominated by the Oedipus complex may, therefore, be taken to be the forming of a precipitating in the ego . . . This modification of the ego
. . . comforts the other contents of the ego as an ego ideal or super-ego.
. . . . The child's parents, and especially his father, were perceived as the obstacle to verbalizations of his Oedipus wishes, so his infantile ego fortified itself for the carrying out of the repression by building this obstacle within itself. It borrowed the strength to do this, so to seek, from the father, and this loan was an extraordinarily nonentous act. The super-ego retains the character of the father, while the more powerful the Oedipus complex was and the more rapid succumbed to repression (under the influence of authority, religious teachings, schooling and reading), this strictly will be the domination of the super-ego over the ego later on - as conscience or perhaps of an unconscious sense of guilt. . . .
The subject dealt within the subjective matter through which generative pre-oedipal origins are to be found of the superego, on which has been dealt by M. Klein (1955). E. Jacobson (1954) and others, also apart from that subject, a regard for Freud's above-quoted description as more applicable to the child who later becomes neurotic or psychotic, than to the 'normal'; child. Since we can assume that there is virtually a wholly complimentary neurotic difficulty, we may then have in assuming that Freud's formation holds true to some degree in every instance. Still, to the extent that a child's relationships with his parents are healthy, he finds the strength to accept the unrealizibilityy of his oedipal strivings, not mainly through the identification with the forbidding rival-parent, but mainly, as an alternative, the ego-strengthening experiences of finding the beloved parent reciprocate his love - responds to him, that is, for being a worthwhile and loveable individual, for being, a conceivably desirable love-partner - and renounces him only with an accompanying sense of loss on the parent's own part. The renunciation, again, something that is mutual experience for the chid and parent, and is made in deference to a recognizedly greater limiting realty, a reality that includes not only the taboo maintained by the rival-parent, but also the love of the oedipal desired parent toward his or her spouse - a love that undeterred the child's birth and a love to which, in a sense, he owes his very existence?
Out of such an oedipal situation the child emerges, with no matter how deep and painful sense of loss at the recognition that he can never displace the rival-parent and posses the beloved on e in a romantic-and-erotic relationship, in a state differently from the ego-diminished, superego-domination state that Freud described. This child that his love, however unrealized, is reciprocated. Strengthened, too, out of the realization, which his relationship with the beloved parent has helped him to achieve, that he lives in a wold in which any individual's strivings are encompassed by a reality much larger than he: Freud, when he stressed that the oedipal phase normally results mainly in the formations of a forbidding superego, and if it is resulting mainly in enchantments of the ego's ability to test both inner and outer reality.
All experiences with both neurotic and psychotic patients had shown that, in every individual instance, in as far as the oedipal phase was entered the course of their past elements, it led to ego impairment rather than ego functioning as primarily because the beloved parent had to repress his or her reciprocal desire for the child, chiefly through the mechanism of unconscious denial of the child's importance to the parent. More often than not, in these instancies, that suggested that the parent would unwittingly act out his or her repressed desires in the unduly seductive behaviour toward the child; yet whenever the parents come close to the recognition of such desires within him, he would unpredictably start reacting to the child as unlovable - undesirable.
With many of these parents, appears that, primarily because of the parent's own unresolved Oedipus complex, his marriage proved too unsatisfying, and his emotional relationship to his own culture too tenuous, for him to dare to recognize the strength of his reciprocal feelings toward his child during the latter's oedipal phase of development. The child is reacting too as a little mother or father transference-figure to the parent, a transference-figure toward whom the parent's repressed oedipal love feelings are directed. If the parent had achieved the inner reassurance of a deep and enduring love toward his wife, and a deeply felt relatedness with his culture including the incest taboos to which his culture adheres, he would have been able to participate in as deeply felt, but minimally acted out, relationship with the chid in a way that fostered the healthy resolutions of the child's Oedipus complex. Instead, what usually happens in such instances, in that the child's Oedipus complex remains unresolved because the child stubbornly - and naturally - refuses to accept defeat within these particular family circumstances, whereas the acceptance of oedipal defeat is tantamount to the acceptance of irrevocable personal worthlessness and unlovability.
It seems much clearer, then this former child, now neurotic or psychotic adult, requires from us for the successful resolution to his unresolved Oedipus complex: Not such a repression of desire, acted-out seductiveness, and denial of his own worth as he met in the relationship with his parent, but a maximal awareness on our part of the reciprocal feelings while we develop in response to his oedipal strivings. Our main job remains always, of course, to further the analysis of his transference, but what might be described seems to be the optimal feeling background in the analyst for such analytic work.
Formidably, when applied not to a moderate degree found in the background of the neurotic person but invested with all the weight of actual biological attributes, have much ado with the person's unconscious refusal to relinquish, in adolescence and young adulthood, his or her fantasied infantile omnipotence in exchange for a sexual identity of - in these-described terms - a 'man' or a 'woman'. It would be like having to accept only certain dispensations as well as salvageable sights, if ony to see the whole fabric ruined into the bargin. A person cannot deeply accept an adult sexual identity until he has been able to find that this identity can express all the feeling-potentialities of his comparatively boundless infancy. This implies that he has become able to blend, for example, his infantile - dependent needs into his more adult erotic strivings, than regard these as mutually exclusive in the way that the mother of the future patient or the persons infant frighteningly feels that her lust has been placed in her mothering. Another difficult facet of this situation resides in a patient's youngful conviction, based on his intrafamiliar experiences, which he can win parental love only if he can become or, perhaps, at an unconscious level remain - a girl; accepting her sexuality as a woman is equated with the abandonment of the hope of being loved.
Concerning the warped experiences their persons have and with the oedipal phase of development, calls to our attention of two features. First, the child whose parents are more narcissistic than truly object-related in faced with the basically hopeless challenge of trying to compete with the mother's own narcissistic love for herself, and with the father's similar love for himself, than being presented with a competitive challenge involving separate, flesh-and-blood human beings. Secondly, concerning warped oedipal experiences, in, as far as the parents succeeded in achieving object-relatedness, this has often become only weakly established as a genital level, so that it remains much more prominently at the mother-infant level of ego-development. Thus, the mother, for example, is much more able to love her infant son than her adult husband, and the oedipal competition between husband and son are in terms of who can better become, or remain, the infant whom the mother is capable of loving. When the infant becomes chronologically a young man, having learned that one wins a woman not through genial assertiveness but through regression, he is apt to shy away from entering into true adult genitality, and is tempted to settle for what amounts to 'regressive victory' in the oedipal struggle
We write much about the analyst's or therapist's being able to identify or empathize with the patient for helping in the resolution of the neurotic or psychotic difficulties. Such writings always portray a merely transitory identification, an empathic sensing of the patient's conflicts, an identification that is of essentially communicative value only. However, it should be seen that we inevitably identify with the patient another fashion also, we identify with the healthy elements in him, in a way that entails enduing, constructive additions to our own personality. Patients - above all schizophrenic patients - need and welcome our acknowledgement, simply and undemonstratively, that they have contributed, and are contributing, in some such significant way, to our existence.
Increasing maturity involves increasing ability not merely to embrace change in the world around one, but to realize that one is oneself in a constant state of change. By contrast, the recovering, maturing patiently becomes less and less dependent upon any such sharply delineated, static self-image or even a constellation of such images, the answer to the question, "Who are you?" is almost as small, solid, and well defined as a stone, but is a larger, fluid, richly-laden, and sniffingly outlined as an ocean? As the individual becomes well, he comes to realize that, as Henri Bergson (1944) outs it, "reality is a perpetual growth, a creation pursued without end. . . . A perpetual becoming," and to the extent that he can actively welcome change and let it become part of him, he comes to know that - again in Bergson's phrase - "to exist is to change, to change is too mature, to mature is to go on creating oneself endlessly."
DUBIOSITY
Book Four
UNTIMEOUS DIVINATION
The title presented, has a dramatic quality that does not rest exclusively on the theory of relativity or quantum mechanics. Perhaps, the most startling and potentially revolutionary of implications in human terms is a new perspective on the relationship between mind and the world that is utterly different from that sanctioned by classical physics. René Descartes, for reasons of which was among the first to realize that mind or consciousness in the mechanistic world-view of classical physics appeared to exist in a realm separate and distinct from nature. The prospect was that the realm of the mental is a self-contained and self-referential island universe with no real or necessary connection with the universe itself.
It also tends the belief . . . that all men dance to the tune of an invisible piper. Yet, this may not be so, as whenever a system is really complicated, indeterminacy comes in, not necessarily because of ‘h', the Planck constant, but because to make a prediction so we must know many things that the stray consequences of studying them will disturb the status quo, due to which formidable comminations can never therefore answer-history is not and cannot be determined. The supposed causes may only produce the consequences we expect. This has rarely been more true of those whose thought and action in science and life became interrelated in a way no dramatist would dare to conceive, this itself has some extraordinary qualities if determinacy, which in physics is so reluctant to accept.
A presence awaiting to the future has framed its proposed new understanding of the relationship between mind and world within the larger context of the history of mathematical physics, the origin and extensions of the classical view of the fundamentals of scientific knowledge, and the various ways that physicists have attempted to prevent previous challenges to the efficacy of classical epistemology. There is no basis in contemporary physics or biology for believing in the stark Cartesian division between mind and world that some have moderately described as ‘the disease of the Western mind'. The dialectic orchestrations will serve as background for understanding a new relationship between parts and wholes in physics, with a similar view of that relationship that has emerged in the co-called ‘new biology' and in recent studies of the evolution of a scientific understanding to a more conceptualized representation of ideas, and includes its allied ‘content'.
Descartes, the founder of modern philosophy quickly realized that there appears of nothing in viewing nature that shows possibilities of reconciliation between a full-fledged comparison, as between Plotinus and Whitehead view for which posits of itself outside the scope of concerns, in that the comparability is with the existent idea of ‘God', especially. However, that ‘the primordial nature of God', whom in which is eternal, a consequent of nature, which is in flux, as far as, this difference of thought remains but comprises no bearing on the relationship or either with the quantum theory, as it addresses the actual notion that authenticates the representation of actual entities as processes of self-creation.
Nonetheless, it seems a strong possibility that Plotonic and Whitehead connect upon the issue of the creation of the sensible world may by looking at actual entities as aspects of nature's contemplation. The contemplation of nature is obviously an immensely intricate affair, involving a myriad of possibilities, therefore one can look at actual entities as, in some sense, the basic elements of a vast and expansive process.
We could derive a scientific understanding of these ideas with the aid of precise deduction, as Descartes continued his claim that we could lay the contours of physical reality out in three-dimensional co-ordinates. Following the publication of Isaac Newton's "Principia Mathematica" in 1687, reductionism and mathematical modeling became the most powerful tools of modern science. The dream that we could know and master the entire physical world through the extension and refinement of mathematical theory became the central feature and principals of scientific knowledge.
The radical separation between mind and nature formalized by Descartes served over time to allow scientists to concentrate on developing mathematical descriptions of matter as pure mechanism without any concern about its spiritual dimensions or ontological foundations. Meanwhile, attempts to rationalize, reconcile or eliminate Descartes's merging division between mind and matter became the most central feature of Western intellectual life.
Philosophers like John Locke, Thomas Hobbes, and David Hume tried to articulate some basis for linking the mathematical describable motions of matter with linguistic representations of external reality in the subjective space of mind. Descartes' compatriot Jean-Jacques Rousseau reified nature as the ground of human consciousness in a state of innocence and proclaimed that "Liberty, Equality, Fraternities" are the guiding principles of this consciousness. Rousseau also fabricated the idea of the ‘general will' of the people to achieve these goals and declared that those who do not conform to this will were social deviants.
The Enlightenment idea of ‘deism', which imaged the universe as a clockwork and God as the clockmaker, provided grounds for believing in a divine agency, from which the time of moment the formidable creations also imply, in of which, the exhaustion of all the creative forces of the universe at origins ends, and that the physical substrates of mind were subject to the same natural laws as matter. In that the only means of mediating the gap between mind and matter was pure reason, causally by the traditional Judeo-Christian theism, which had previously been based on both reason and revelation, responded to the challenge of deism by debasing tradionality as a test of faith and embracing the idea that we can know the truths of spiritual reality only through divine revelation. This engendered a conflict between reason and revelation that persists to this day. And laid the foundation for the fierce completion between the mega-narratives of science and religion as frame tales for mediating the relation between mind and matter and the manner in which they should ultimately define the special character of each.
The nineteenth-century Romantics in Germany, England and the United States revived Rousseau's attempt to posit a ground for human consciousness by reifying nature in a different form. Goethe and Friedrich Schelling proposed a natural philosophy premised on ontological Monism ( the idea that adhering manifestations that govern toward evolutionary principles have grounded inside an inseparable spiritual Oneness ) and argued God, man, and nature for the reconciliation of mind and matter with an appeal to sentiment, mystical awareness, and quasi-scientific attempts, as he afforded the efforts of mind and matter, nature became a mindful agency that ‘loves illusion', as it shrouds man in mist, presses him or her heart and punishes those who fail to see the light. Schelling, in his version of cosmic unity, argued that scientific facts were at best partial truths and that the mindful creative spirit that unities mind and matter is progressively moving toward self-realization and ‘undivided wholeness'.
The British version of Romanticism, articulated by figures like William Wordsworth and Samuel Taylor Coleridge, placed more emphasis on the primary of the imagination and the importance of rebellion and heroic vision as the grounds for freedom. As Wordsworth put it, communion with the "incommunicable powers" of the "immortal sea" empowers the mind to release itself from all the material constraints of the laws of nature. The founders of American transcendentalism, Ralph Waldo Emerson and Henry David Theoreau, articulated a version of Romanticism that commensurate with the ideals of American democracy.
The American envisioned a unified spiritual reality that manifested itself as a personal ethos that sanctioned radical individualism and bred aversion to the emergent materialism of the Jacksonian era. They were also more inclined than their European counterpart, as the examples of Thoreau and Whitman attest, to embrace scientific descriptions of nature. However, the Americans also dissolved the distinction between mind and natter with an appeal to ontological monism and alleged that mind could free itself from all the constraint of assuming that by some sorted limitation of matter, in which such states have of them, some mystical awareness.
Since scientists, during the nineteenth century were engrossed with uncovering the workings of external reality and seemingly knew of themselves that these virtually overflowing burdens of nothing, in that were about the physical substrates of human consciousness, the business of examining the distributive contribution in dynamic functionality and structural foundation of mind became the province of social scientists and humanists. Adolphe QuĂ©telet proposed a ‘social physics' that could serve as the basis for a new discipline called sociology, and his contemporary Auguste Comte concluded that a true scientific understanding of the social reality was quite inevitable. Mind, in the view of these figures, was a separate and distinct mechanism subject to the lawful workings of a mechanical social reality.
More formal European philosophers, such as Immanuel Kant, sought to reconcile representations of external reality in mind with the motions of matter-based on the dictates of pure reason. This impulse was also apparent in the utilitarian ethics of Jerry Bentham and John Stuart Mill, in the historical materialism of Karl Marx and Friedrich Engels, and in the pragmatism of Charles Smith, William James and John Dewey. These thinkers were painfully aware, however, of the inability of reason to posit a self-consistent basis for bridging the gap between mind and matter, and each remains obliged to conclude that the realm of the mental exists only in the subjective reality of the individual.
The fatal flaw of pure reason is, of course, the absence of emotion, and purely explanations of the division between subjective reality and external reality, of which had limited appeal outside the community of intellectuals. The figure most responsible for infusing our understanding of the Cartesian dualism with contextual representation of our understanding with emotional content was the death of God theologian Friedrich Nietzsche 1844-1900. After declaring that God and ‘divine will', did not exist, Nietzsche reified the ‘existence' of consciousness in the domain of subjectivity as the ground for individual ‘will' and summarily reducing all previous philosophical attempts to articulate the ‘will to truth'. The dilemma, forth in, had seemed to mean, by the validation, . . . as accredited for doing of science, in that the claim that Nietzsche's earlier versions to the ‘will to truth', disguises the fact that all alleged truths were arbitrarily created in the subjective reality of the individual and are expressed or manifesting the individualism of ‘will'.
In Nietzsche's view, the separation between mind and matter is more absolute and total than previously been imagined. Based on the assumption that there is no really necessary correspondence between linguistic constructions of reality in human subjectivity and external reality, he deuced that we are all locked in ‘a prison house of language'. The prison as he concluded it, was also a ‘space' where the philosopher can examine the ‘innermost desires of his nature' and articulate a new message of individual existence founded on ‘will'.
Those who fail to enact their existence in this space, Nietzsche says, are enticed into sacrificing their individuality on the nonexistent altars of religious beliefs and democratic or socialists' ideals and become, therefore, members of the anonymous and docile crowd. Nietzsche also invalidated the knowledge claims of science in the examination of human subjectivity. Science, he said. Is not exclusive to natural phenomenons and favors reductionistic examination of phenomena at the expense of mind? It also seeks to reduce the separateness and uniqueness of mind with mechanistic descriptions that disallow and basis for the free exercise of individual will.
Nietzsche's emotionally charged defense of intellectual freedom and radial empowerment of mind as the maker and transformer of the collective fictions that shape human reality in a soulless mechanistic universe proved terribly influential on twentieth-century thought. Furthermore, Nietzsche sought to reinforce his view of the subjective character of scientific knowledge by appealing to an epistemological crisis over the foundations of logic and arithmetic that arose during the last three decades of the nineteenth century. Through a curious course of events, attempted by Edmund Husserl 1859-1938, a German mathematician and a principal founder of phenomenology, wherefor to resolve this crisis resulted in a view of the character of consciousness that closely resembled that of Nietzsche.
The best-known disciple of Husserl was Martin Heidegger, and the work of both figures greatly influenced that of the French atheistic existentialist Jean-Paul Sartre. The work of Husserl, Heidegger, and Sartre became foundational to that of the principal architects of philosophical postmodernism, and deconstructionist Jacques Lacan, Roland Barthes, Michel Foucault and Jacques Derrida. It obvious attribution of a direct linkage between the nineteenth-century crisis about the epistemological foundations of mathematical physics and the origin of philosophical postmodernism served to perpetuate the Cartesian two-world dilemma in an even more oppressive form. It also allows us better to understand the origins of cultural ambience and the ways in which they could resolve that conflict.
The mechanistic paradigm of the late n nineteenth century was the one Einstein came to know when he studied physics. Most physicists believed that it represented an eternal truth, but Einstein was open to fresh ideas. Inspired by Mach's critical mind, he demolished the Newtonian ideas of space and time and replaced them with new, "relativistic" notions.
Two theories unveiled and unfolding as their phenomenal yield held by Albert Einstein, attributively appreciated that the special theory of relativity ( 1905 ) and, also the tangling and calculably arranging affordance, as drawn upon the gratifying nature whom by encouraging the finding resolutions upon which the realms of its secreted reservoir in continuous phenomenons, in additional the continuatives as afforded by the efforts by the imagination were made discretely available to any the unsurmountable achievements, as remain obtainably afforded through the excavations underlying the artifactual circumstances that govern all principle ‘forms' or ‘types' in the involving evolutionary principles of the general theory of relativity ( 1915 ). Where the special theory gives a unified account of the laws of mechanics and of electromagnetism, including optics. Before 1905 the purely relative nature of uniform motion had in part been recognized in mechanics, although Newton had considered time to be absolute and postulated absolute space. In electromagnetism the ether was supposed to give an absolute bases respect to which motion could be determined. The Galilean transformation equations represent the set of equations:
= vt
y = y
z = z
t = tThey are used for transforming the parameters of position and motion from an observer at the point ‘O' with co-ordinates ( z, y, z ) to an observer at O with co-ordinates ( , y z ). The axis is chosen to pass through O and O . The times of an event at ‘t' and t in the frames of reference of observers at O and O coincided. ‘V' is the relative velocity of separation of O and O . The equation conforms to Newtonian mechanics as compared with Lorentz transformation equations, it represents a set of equations for transforming the position-motion parameters from an observer at a point O ( , y, z) to an observer at O
( , y , z ), moving compared with one another. The equation replaces the Galilean transformation equation of Newtonian mechanics in reactivity problems. If the x-axes are chosen to pass through O and the time of an event are t and t in the frame of reference of the observers at O and O respectively, where the zeros of their time scales were the instants that O and O supported the equations are:
= ( vt )
y = y
z =z
t = ( t v / c2 ),
Where ‘v' is the relative velocity of separation of O, O , c is the speed of light, and is the function
(1 v2 / c2 )-½.
Newton's laws of motion in his "Principia," Newton ( 1687 ) stated the three fundamental laws of motion, which are the basis of Newtonian mechanics.
The First Law of acknowledgement concerns that all bodies persevere in its state of rest, or uniform motion in a straight line, but in as far as it is compelled, to change that state by forces impressed on it. This may be regarded as a definition of force.
The Second Law to acknowledge is, that the rate of change of linear momentum is propositional to the force applied, and takes place in the straight line in which that force acts. This definition can be regarded as formulating a suitable way by which forces may be measured, that is, by the acceleration they produce,
F = d( mv ) / dt
i.e., F = ma = v( dm / dt ),
Where F = force, m = masses, v = velocity, t = time, and ‘a' = acceleration, from which case, the proceeding majority of quality values were of non-relativistic cases of, dm / dt = 0, i.e., the mass remains constant, and then
F = ma.
The Third Law acknowledges, that forces are caused by the interaction of pairs of bodies. The forces exerted by ‘A' upon ‘B' and the force exerted by ‘B' upon ‘A' are simultaneous, equal in magnitude, opposite in direction and in the same straight line, caused by the same mechanism.
Appreciating the popular statement of this law in terms of significant "action and reaction" leads too much misunderstanding. In particular, any two forces that happen to be equal and opposite if they act on the same body, one force, arbitrarily called "reaction," are supposed to be a consequence of the other and to happen subsequently, as two forces are supposed to oppose each other, causing equilibrium, certain forces such as forces exerted by support or propellants are conventionally called "reaction," causing considerable confusion.
The third law may be illustrated by the following examples. He gravitational force exerted by a body on the earth is equal and opposite to the gravitational force exerted by the earth on the body. The intermolecular repulsive force exerted on the ground by a body resting on it, or hitting it, is equal and opposite to the intermolecular repulsive force exerted on the body by the ground. More general system of mechanics has been given by Einstein in his theory of relativity. This reduces to Newtonian mechanics when all velocities relative to the observer are small compared with those of light.
Einstein rejected the concept of absolute space and time, and made two postulates (i) he laws of nature are the same for all observers n uniform relative motion, and (ii) The speed of light in the same for all such observers, independently of the relative motions of sources and detectors. He showed that these postulates were equivalent to the requirement that co-ordinates of space and time used by different observers should be related by Lorentz transformation equations. The theory has several important consequences.
The transformation of time implies that two events that are simultaneous according to one observer will not necessarily be so according to another in uniform relative motion. This does not affect the construct of its sequence of related events so does not violate any conceptual causation. It will appear to two observers in uniform relative motion that each other's clock runs slowly. This is the phenomenon of ‘time dilation', for example, an observer moving with respect to a radioactive source finds a longer decay time than found by an observer at rest with respect to it, according to:
Tv = T0 / ( 1 v2 / c2 ) ½
Where Tv is the mean life measurement by an observer at relative speed ‘v', and T0 is the mean life maturement by an observer at rest, and ‘c' is the speed of light.
This formula has been verified in innumerable experiments. One consequence is that no body can be accelerated from a speed below ‘c' with respect to any observer to one above ‘c', since this would require infinite energy. Einstein educed that the transfer of energy E by any process entailed the transfer of mass m where E = mc2, hence he concluded that the total energy ‘E' of any system of mass ‘m' would be given by:
E = mc2
The principle of conservation of mass states that in any system is constant. Although conservation of mass was verified in many experiments, the evidence for this was limited. In contrast the great success of theories assuming the conservation of energy established this principle, and Einstein assumed it as an axiom in his theory of relativity. According to this theory the transfer of energy ‘E' by any process entails the transfer of mass m = E/c2./ hence the conservation of energy ensures the conservation of mass.
In Einstein's theory inertial and gravitational masses are assumed to be identical and energy is the total energy of a system. Some confusion often arises because of idiosyncratic terminologies in which the words mass and energies are given different meanings. For example, some particle physicists use "mass" to mean the rest-energy of a particle and "energy" to mean ‘energy other than rest-energy'. This leads to alternate statements of the principle, in which terminology is not generally consistent. Whereas, the law of equivalence of mass and energy such that mass ‘m' and energy ‘E' are related by the equation E = mc2, where ‘c' is the speed of light in a vacuum. Thus, a quantity of energy ‘E' has a mass ‘m' and a mass ‘m' has intrinsic energy ‘E'. The kinetic energy of a particle as determined by an observer with relative speed ‘v' is thus ( m m0 )c2, which tends to the classical value ½mv2 if « C.
Attempts to express quantum theory in terms consistent with the requirements of relativity were begun by Sommerfeld ( 1915 ), eventually. Dirac ( 1928 ) gave a relativistic formulation of the wave mechanics of conserved particles ( fermions ). This explained the concept of spin and the associated magnetic moment, which had been postulated to account for certain details of spectra. The theory led to results of extremely great importance for the theory of standard or elementary particles. The Klein-Gordon equation is the relativistic wave equation for ‘bosons'. It is applicable to bosons of zero spin, such as the ‘pion'. In which case, for example the Klein-Gordon Lagrangian describes a single spin-0, scalar field:
L = ½[ t t y y z z] ½(2 mc / h)22
In this case:
L/ ( ) = ÎĽ
leading to the equation:
L/ = (2 mc/h)22+
and hence the Lagrange equation requires that:
ÎĽ ÎĽ + (2 mc / h)2 2 = 0.
Which is the Klein-Gordon equation describing the evolution in space and time of field ‘'? Individual ‘' excitation of the normal modes of represents particles of spin -0, and mass ‘m'.
A mathematical formulation of the special theory of relativity was given by Minkowski. It is based on the idea that an event is specified by there being a four-dimensional co-ordinates, three of which are spatial co-ordinates and one in a dimensional frame in a time co-ordinates. These continuously of dimensional co-ordinate give to define a four-dimensional space and the motion of a particle can be described by a curve in this space, which is called "Minkowski space-time." In certain formulations of the theory, use is made of a four-dimensional do-ordinate system in which three dimensions represent the spatial co-ordinates , y, z and the fourth dimension are ‘ict', where ‘t' is time, ‘c' is the speed of light and ‘I' is - 1, points in this space are called events. The equivalent to the distance between two points is the interval ( s ) between two events given by Pythagoras law in a space-time as:
s )2 = ij ij i j.
Where'
= 1, y = 2, z = 3 . . . , t = 4 and 11 ( ) 33 ( ) = 1? 44 ( ) = 1:
is componded by the Minkowski metric tensor. The distances between two points are variant under the ‘Lorentz transformation', because the measurements of the positions of the points that are simultaneous according to one observer in uniform motion with respect to the first. By contrast, the interval between two events is invariant.
The equivalents to a vector in the four-dimensional space are consumed by a ‘four vector', in which has three space components and one of time component. For example, the four-vector momentum has a time component proportional to the energy of a particle, the four-vector potential has the space co-ordinates of the magnetic vector potential, while the time co-ordinates corresponds to the electric potential.
The special theory of relativity is concerned with relative motion between non-accelerated frames of reference. The general theory reals with general relative motion between accelerated frames of reference. In accelerated systems of reference, certain fictitious forces are observed, such as the centrifugal and Coriolis forces found in rotating systems. These are known as fictitious forces because they disappear when the observer transforms to a nonaccelerated system. For example, to an observer in a car rounding a bend at constant velocity, objects in the car appear to suffer a force acting outward. To an observer outside the car, this is simply their tendency to continue moving in a straight line. The inertia of the objects is seen to cause a fictitious force and the observer can distinguish between non-inertial ( accelerated ) and inertial
(Nonaccelerated) frames of reference.
A further point is that, to the observer in the car, all the objects are given the same acceleration irrespective of their mass. This implies a connection between the fictitious forces arising from accelerated systems and forces due to gravity, where the acceleration produced is independent of the mass. Near the surface of the earth the acceleration of free fall, ‘g', is measured with respect to a nearby point on the surface. Because of the axial rotation the reference point is accelerated to the centre of the circle of its latitude, hence ‘g' is not quite in magnitude or direction to the acceleration toward the centre of the earth given by the theory of ‘gravitation' in 1687 Newton presented his law of universal gravitation, according to which every particle evokes every other particle with the force, ‘F' given by:
F = Gm1 m2 / 2,
Where m1, m2 is the masses of two particles a distance ‘ ' apart, and ‘G' is the gravitational constant, which, according to modern measurements, has a value
6.672 59 x 10-11 m3 kg -1 s -2.
For extended bodies the forces are found by integrations. Newton showed that the external effect of a spherical symmetric body is the same as if the whole mass were concentrated at the centre. Astronomical bodies are roughly spherically symmetrical so can be treated as point particles to a very good approximation. On this assumption Newton showed that his law was consistent with Kepler's Laws. Until recently, all experiments have confirmed the accuracy of the inverse square law and the independence of the law upon the nature of the substances, but in the past few years evidence has been found against both.
The size of a gravitational field at any point is given by the force exerted on unit mass at that point. The field intensity at a distance ‘ ' from a point mass ‘m' is therefore Gm/ 2, and acts toward ‘m' Gravitational field strength is measured in the newton per kilogram. The gravitational potential ‘V' at that point is the work done in moving a unit mass from infinity to the point against the field, due to a point mass. Importantly, ( a ) Potential at a point distance ‘ ' from the centre of a hollow homogeneous spherical shell of mass ‘m' and outside the shell:
V = Gm/
The potential is the same as if the mass of the shell is assumed concentrated at the centre, ( b ) At any point inside the spherical shell the potential is equal to its value at the surface:
V = Gm/r
Where ‘r' is the radius of the shell, thus there is no resultant force acting at any point inside the shell and since no potential difference acts between any two points. ( c ) potential at a point distance ‘ ' from the centre of a homogeneous solid sphere and outside the sphere is the same as that for a shell;
V = Gm/
(d) At a point inside the sphere, of radius ‘r':
V = Gm( 3r2 2 ) /2r3
The essential property of gravitation is that it causes a change vin motion, in particular the acceleration of free fall ( g ) in the earth's gravitational field. According to the general theory of relativity, gravitational fields change the geometry of spacetime, causing it to become curved. It is this curvature of spacetime, produced by the presence of matter, that controls the natural motions of matter, that controls the natural motions of bodies. General relativity may thus be considered as a theory of gravitation, differences between it and Newtonian gravitation only appearing when the gravitational fields become very strong, as with ‘black holes' and ‘neutron stars', or when very accurate measurements can be made.
Accelerated systems and forces due to gravity, where the acceleration produced are independent of the mass, for example, a person in a sealed container could not easily determine whether he was being driven toward the floor by gravity or if the container were in space and being accelerated upward by a rocket. Observations extended in space and time could distinguish between these alternates, but otherwise they are indistinguishable. His leads to the ‘principle of equivalence', from which it follows that the inertial mass is the same as the gravitational mass. A further principle used in the general theory is that the laws of mechanics are the same in inertial and non-inertial frames of reference.
Still, the equivalence between a gravitational field and the fictitious forces in non-inertial systems can be expressed by using Riemannian space-time, which differs from Minkowski Space-time of the special theory. In special relativity the motion of a particle that is not acted on by any force is represented by a straight line in Minkowski Space-time. In general relativity, using Riemannian Space-time, the motion is represented by a line that is no longer straight, in the Euclidean sense but is the line giving the shortest distance. Such a line is called geodesic. Thus, a space-time is said to be curved. The extent of this curvature is given by the ‘metric tensor' for spacetime, the components of which are solutions to Einstein's ‘field equations'. The fact that gravitational effects occur near masses is introduced by the postulate that the presence of matter produces this curvature of the space-time. This curvature of space-time controls the natural motions of bodies.
The predictions of general relativity only differ from Newton's theory by small amounts and most tests of the theory have been carried out through observations in astronomy. For example, it explains the shift in the perihelion of Mercury, the bending of light or other electromagnetic radiations in the presence of large bodies, and the Einstein Shift. Very close agreements between the predications of general relativity and their accurately measured values have now been obtained.
Reiteratively, assumptions upon which Einstein's special theory of relativity (1905) stretches toward its central position are (i) inertial frameworks are equivalent for the description of all physical phenomena, and (ii) the speed of light in empty space is constant for every observer, regardless of the motion of the observer or the light source, although the second assumption may seem plausible in the light of the Michelson-Morley experiment of 1887, which failed to find any difference in the speed of light in the direction of the earth's rotation or when measured perpendicular ti it, it seems likely that Einstein was not influenced by the experiment, and may not even have known the results. As a consequence of the second postulate, no matter how fast she travels, an observer can never overtake a ray of light, and see it as stationary beside her. However, near her speed approaches to that of light, light still retreats at its classical speed. The consequences are that space, time and mass turn relative to the observer. Measurements composed of quantities in an inertial system moving relative to one's own reveal slow clocks, with the effect increasing as the relative speed of the systems approaches the speed of light. Events deemed simultaneously as measured within one such system will not be simultaneous as measured from the other, forthrightly time and space thus lose their separate identity, and become parts of a single space-time. The special theory also has the famous consequence ( E = mc2 ) of the equivalences of energy and mass.
Einstein's general theory of relativity ( 1916 ) treats of non-inertial systems, i.e., those accelerating relative to each pother. The leading idea is that the laws of motion in an accelerating frame are equivalent to those in a gravitational field. The theory treats gravity not as a Newtonian force acting in an unknown way across distance, but a metrical property of a space-time continuum that is curved in the vicinity of matter. Gravity can be thought of as a field described by the metric tensor at every point. The classic analogy is with a rock sitting on a bed. If a heavy objects where to be thrown across the bed, it is deflected toward the rock not by a mysterious force, but by the deformation of the space, i.e., the depression of the sheet around the object, a called curvilinear trajectory. Interestingly, the general theory lends some credit to a vision of the Newtonian absolute theory of space, in the sense that space itself is regarded as a thing with metrical properties of it's. The search for a unified field theory is the attempt to show that just as gravity is explicable as a consequence of the nature of a space-time, are the other fundamental physical forces: The strong and weak nuclear forces, and the electromagnetic force. The theory of relativity is the most radical challenge to the ‘common sense' view of space and time as fundamentally distinct from each other, with time as an absolute linear flow in which events are fixed in objective relationships.
After adaptive changes in the brains and bodies of hominids made it possible for modern humans to construct a symbolic universe using complex language system, something as quite dramatic and wholly unprecedented occurred. We began to perceive the world through the lenses of symbolic categories, to construct similarities and differences in terms of categorical priorities, and to organize our lives according to themes and narratives. Living in this new symbolic universe, modern humans had a large compulsion to code and recode experiences, to translate everything into representation, and to seek out the deeper hidden and underlying logic that eliminates inconsistencies and ambiguities.
The mega-narrative or frame tale served to legitimate and rationalize the categorical oppositions and terms of relations between the myriad number of constructs in the symbolic universe of modern humans were religion. The use of religious thought for these purposes is quite apparent in the artifacts found in the fossil remains of people living in France and Spain forty thousand years ago. And these artifacts provided the first concrete evidence that a fully developed language system had given birth to an intricate and complex social order.
Both religious and scientific thought seeks to frame or construct reality in terms of origins, primary oppositions, and underlying causes, and this partially explains why fundamental assumptions in the Western metaphysical tradition were eventually incorporated into a view of reality that would later be called scientific. The history of scientific thought reveals that the dialogue between assumptions about the character of spiritual reality in ordinary language and the character of physical reality in mathematical language was intimate and ongoing from the early Greek philosophers to the first scientific revolution in the seventeenth century. But this dialogue did not conclude, as many have argued, with the emergence of positivism in the eighteenth and nineteenth centuries. It was perpetuated in a disguise form in the hidden ontology of classical epistemology -the central issue in the Bohr-Einstein debate.
The assumption that a one-to-one correspondence exists between every element of physical reality and physical theory may serve to bridge the gap between mind and world for those who use physical theories. But it also suggests that the Cartesian division be real and insurmountable in constructions of physical reality based on ordinary language. This explains in no small part why the radical separation between mind and world sanctioned by classical physics and formalized by Descartes ( 1596-1650 ) remains, as philosophical postmodernism attests, one of the most pervasive features of Western intellectual life.
Nietzsche, in an effort to subvert the epistemological authority of scientific knowledge, sought of a legitimate division between mind and world much starker than that originally envisioned by Descartes. What is not widely known, however, is that Nietzsche and other seminal figures in the history of philosophical postmodernism were very much aware of an epistemological crisis in scientific thought than arose much earlier, that occasioned by wave-particle dualism in quantum physics. This crisis resulted from attempts during the last three decades of the nineteenth century to develop a logically self-consistent definition of number and arithmetic that would serve to reinforce the classical view of correspondence between mathematical theory and physical reality. As it turned out, these efforts resulted in paradoxes of recursion and self-reference that threatened to undermine both the efficacy of this correspondence and the privileged character of scientific knowledge.
Nietzsche appealed to this crisis in an effort to reinforce his assumption that, without ontology, all knowledge ( including scientific knowledge ) was grounded only in human consciousness. As the crisis continued, a philosopher trained in higher mathematics and physics, Edmund Husserl 1859-1938, attempted to preserve the classical view of correspondences between mathematical theory and physical reality by deriving the foundation of logic and number from consciousness in ways that would preserve self-consistency and rigour. This afforded effort to ground mathematical physics in human consciousness, or in human subjective reality, was no trivial matter, representing a direct link between these early challenges and the efficacy of classical epistemology and the tradition in philosophical thought that culminated in philosophical postmodernism.
Since Husserl's epistemology, like that of Descartes and Nietzsche, was grounded in human subjectivity, a better understanding of his attempt to preserve the classical view of correspondence not only reveals more about the legacy of Cartesian dualism. It also suggests that the hidden and underlying ontology of classical epistemology was more responsible for the deep division and conflict between the two cultures of humanists-social scientists and scientists-engineers than was previously thought. The central question in this late-nineteenth-century debate over the status of the mathematical description of nature was the following: Is the foundation of number and logic grounded in classical epistemology, or must we assume, in the absence of any ontology, that the rules of number and logic are grounded only in human consciousness? In order to frame this question in the proper context, we should first examine in more detail the intimate and ongoing dialogue between physics and metaphysics in Western thought.
The history of science reveals that scientific knowledge and method did not emerge as full-blown from the minds of the ancient Greek any more than language and culture emerged fully formed in the minds of "Homo sapient's sapient. " Scientific knowledge is an extension of ordinary language into grater levels of abstraction and precision through reliance upon geometric and numerical relationships. We speculate that the seeds of the scientific imagination were planted in ancient Greece, as opposed to Chinese or Babylonian culture, partly because the social, political and an economic climate in Greece was more open to the pursuit of knowledge with marginal cultural utility. Another important factor was that the special character of Homeric religion allowed the Greeks to invent a conceptual framework that would prove useful in future scientific investigation. But it was only after this inheritance from Greek philosophy was wedded to some essential features of Judeo-Christian beliefs about the origin of the cosmos that the paradigm for classical physics emerged.
The philosophical debate that led to conclusions useful to the architects of classical physics can be briefly summarized, such when Thale's fellow Milesian Anaximander claimed that the first substance, although indeterminate, manifested itself in a conflict of oppositions between hot and cold, moist and dry. The idea of nature as a self-regulating balance of forces was subsequently elaborated upon by Heraclitus ( d. after 480 BC ), who asserted that the fundamental substance is strife between opposites, which is itself the unity of the whole. It is, said Heraclitus, the tension between opposites that keeps the whole from simply "passing away."
Parmenides of Elea ( b. c. 515 BC ) argued in turn that the unifying substance is unique and static being. This led to a conclusion about the relationship between ordinary language and external reality that was later incorporated into the view of the relationship between mathematical language and physical reality. Since thinking or naming involves the presence of something, said Parmenides, thought and language must be dependent upon the existence of objects outside the human intellect. Presuming a one-to-one correspondence between word and idea and actual existing things, Parmenides concluded that our ability to think or speak of a thing at various times implies that it exists at all times. Hence the indivisible One does not change, and all perceived change is an illusion.
These assumptions emerged in roughly the form in which they would be used by the creators of classical physics in the thought of the atomists. Leucippus : l. 450-420 BC and Democritus ( c. 460-c. 370 BC ). They reconciled the two dominant and seemingly antithetical concepts of the fundamental character of being-Becoming ( Heraclitus ) and unchanging Being ( Parmenides )-in a remarkable simple and direct way. Being, they said, is present in the invariable substance of the atoms that, through blending and separation, make up the thing of changing or becoming worlds.
The last remaining feature of what would become the paradigm for the first scientific revolution in the seventeenth century is attributed to Pythagoras ( b c. 570 BC ). Like Parmenides, Pythagoras also held that the perceived world is illusory and that there is an exact correspondence between ideas and aspects of external reality. Pythagoras, however, had a different conception of the character of the idea that showed this correspondence. The truth about the fundamental character of the unified and unifying substance, which could be uncovered through reason and contemplation, is, he claimed, mathematical in form.
Pythagoras established and was the cental figure in a school of philosophy, religion and mathematics; He was apparently viewed by his followers as semi-divine. For his followers the regular solids ( symmetrical three-dimensional forms in which all sides are the same regular polygons ) and whole numbers became revered essences of sacred ideas. In contrast with ordinary language, the language of mathematics and geometric forms seemed closed, precise and pure. Providing one understood the axioms and notations, and the meaning conveyed was invariant from one mind to another. The Pythagoreans felt that the language empowered the mind to leap beyond the confusion of sense experience into the realm of immutable and eternal essences. This mystical insight made Pythagoras the figure from antiquity most revered by the creators of classical physics, and it continues to have great appeal for contemporary physicists as they struggle with the epistemological implications of the quantum mechanical description of nature.
Yet, least of mention, progress was made in mathematics, and to a lesser extent in physics, from the time of classical Greek philosophy to the seventeenth century in Europe. In Baghdad, for example, from about A.D. 750 to A.D. 1000, substantial advancement was made in medicine and chemistry, and the relics of Greek science were translated into Arabic, digested, and preserved. Eventually these relics reentered Europe via the Arabic kingdom of Spain and Sicily, and the work of figures like Aristotle universities of France, Italy, and England during the Middle Ages.
For much of this period the Church provided the institutions, like the reaching orders, needed for the rehabilitation of philosophy. But the social, political and an intellectual climate in Europe was not ripe for a revolution in scientific thought until the seventeenth century. Until later in time, lest as far into the nineteenth century, the works of the new class of intellectuals we called scientists, whom of which were more avocations than vocation, and the word scientist do not appear in English until around 1840.
Copernicus (1473-1543 ) would have been described by his contemporaries as an administrator, a diplomat, an avid student of economics and classical literature, and most notable, a highly honoured and placed church dignitaries. Although we named a revolution after him, his devoutly conservative man did not set out to create one. The placement of the Sun at the centre of the universe, which seemed right and necessary to Copernicus, was not a result of making careful astronomical observations. In fact, he made very few observations in the course of developing his theory, and then only to ascertain if his prior conclusions seemed correct. The Copernican system was also not any more useful in making astrological calculations than the accepted model and was, in some ways, much more difficult to implement. What, then, was his motivation for creating the model and his reasons for presuming that the model was correct?
Copernicus felt that the placement of the Sun at the centre of the universe made sense because he viewed the Sun as the symbol of the presence of a supremely intelligent and intelligible God in a man-centred world. He was apparently led to this conclusion in part because the Pythagoreans believed that fire exists at the centre of the cosmos, and Copernicus identified this fire with the fireball of the Sun. the only support that Copernicus could offer for the greater efficacy of his model was that it represented a simpler and more mathematical harmonious model of the sort that the Creator would obviously prefer. The language used by Copernicus in "The Revolution of Heavenly Orbs," illustrates the religious dimension of his scientific thought: "In the midst of all the sun reposes, unmoving. Who, indeed, in this most beautiful temple would place the light-giver in any other part than from where it can illumine all other parts?"
The belief that the mind of God as Divine Architect permeates the working of nature was the guiding principle of the scientific thought of Johannes Kepler ( or Keppler, 1571-1630 ). For this reason, most modern physicists would probably feel some discomfort in reading Kepler's original manuscripts. Physics and metaphysics, astronomy and astrology, geometry and theology commingle with an intensity that might offend those who practice science in the modern sense of that word. Physical laws, wrote Kepler, "lie within the power of understanding of the human mind; God wanted us to perceive them when he created us of His own image, in order . . . that we may take part in His own thoughts. Our knowledge of numbers and quantities is the same as that of God's, at least insofar as we can understand something of it in this mortal life."
Believing, like Newton after him, in the literal truth of the words of the Bible, Kepler concluded that the word of God is also transcribed in the immediacy of observable nature. Kepler's discovery that the motions of the planets around the Sun were elliptical, as opposed perfecting circles, may have made the universe seem a less perfect creation of God on ordinary language. For Kepler, however, the new model placed the Sun, which he also viewed as the emblem of a divine agency, more at the centre of mathematically harmonious universes than the Copernican system allowed. Communing with the perfect mind of God requires as Kepler put it "knowledge of numbers and quantity."
Since Galileo did not use, or even refer to, the planetary laws of Kepler when those laws would have made his defence of the heliocentric universe more credible, his attachment to the god-like circle was probably a more deeply rooted aesthetic and religious ideal. But it was Galileo, even more than Newton, who was responsible for formulating the scientific idealism that quantum mechanics now force us to abandon. In "Dialogue Concerning the Two Great Systems of the World," Galileo said about the following about the followers of Pythagoras: "I know perfectly well that the Pythagoreans had the highest esteem for the science of number and that Plato himself admired the human intellect and believed that it participates in divinity solely because it is able to understand the nature of numbers. And I myself am inclined to make the same judgement."
This article of faith-mathematical and geometrical ideas mirror precisely the essences of physical reality was the basis for the first scientific law of this new science, a constant describing the acceleration of bodies in free fall, could not be confirmed by experiment. The experiments conducted by Galileo in which balls of different sizes and weights were rolled simultaneously down an inclined plane did not, as he frankly admitted, their precise results. And since a vacuum pumps had not yet been invented, there was simply no way that Galileo could subject his law to rigorous experimental proof in the seventeenth century. Galileo believed in the absolute validity of this law in the absence of experimental proof because he also believed that movement could be subjected absolutely to the law of number. What Galileo asserted, as the French historian of science Alexander Koyré put it, was "that the real are in its essence, geometrical and, consequently, subject to rigorous determination and measurement."
The popular image of Isaac Newton ( 1642-1727 ) is that of a supremely rational and dispassionate empirical thinker. Newton, like Einstein, had the ability to concentrate unswervingly on complex theoretical problems until they yielded a solution. But what most consumed his restless intellect were not the laws of physics. In addition to believing, like Galileo that the essences of physical reality could be read in the language of mathematics, Newton also believed, with perhaps even greater intensity than Kepler, in the literal truths of the Bible.
For Newton the mathematical languages of physics and the language of biblical literature were equally valid sources of communion with the eternal writings in the extant documents alone consist of more than a million words in his own hand, and some of his speculations seem quite bizarre by contemporary standards. The Earth, said Newton, will still be inhabited after the day of judgement, and heaven, or the New Jerusalem, must be large enough to accommodate both the quick and the dead. Newton then put his mathematical genius to work and determined the dimensions required to house the population, his rather precise estimate was "the cube root of 12,000 furlongs."
The pint is, that during the first scientific revolution the marriage between mathematical idea and physical reality, or between mind and nature via mathematical theory, was viewed as a sacred union. In our more secular age, the correspondence takes on the appearance of an unexamined article of faith or, to borrow a phrase from William James ( 1842-1910 ), "an altar to an unknown god." Heinrich Hertz, the famous nineteenth-century German physicist, nicely described what there is about the practice of physics that tends to inculcate this belief: "One cannot escape the feeling that these mathematical formulae have an independent existence and intelligence of their own that they are wiser than we, wiser than their discoveries. That we get more out of them than was originally put into them."
While Hertz made this statement without having to contend with the implications of quantum mechanics, the feeling, the described remains the most enticing and exciting aspects of physics. That elegant mathematical formulae provide a framework for understanding the origins and transformations of a cosmos of enormous age and dimensions are a staggering discovery for bidding physicists. Professors of physics do not, of course, tell their students that the study of physical laws in an act of communion with thee perfect mind of God or that these laws have an independent existence outside the minds that discover them. The business of becoming a physicist typically begins, however, with the study of classical or Newtonian dynamics, and this training provides considerable covert reinforcement of the feeling that Hertz described.
Perhaps, the best way to examine the legacy of the dialogue between science and religion in the debate over the implications of quantum non-locality is to examine the source of Einstein's objections tp quantum epistemology in more personal terms. Einstein apparently lost faith in the God portrayed in biblical literature in early adolescence. But, as appropriated, . . . the "Autobiographical Notes" give to suggest that there were aspects that carry over into his understanding of the foundation for scientific knowledge, . . . "Thus I came -despite the fact that I was the son of an entirely irreligious [ Jewish ] Breeden heritage, which is deeply held of its religiosity, which, however, found an abrupt end at the age of 12. Though the reading of popular scientific books I soon reached the conviction that much in the stories of the Bible could not be true. The consequence waw a positively frantic [ orgy ] of freethinking coupled with the impression that youth is intentionally being deceived by the stat through lies that it was a crushing impression. Suspicion against every kind of authority grew out of this experience. . . . It was clear to me that the religious paradise of youth, which was thus lost, was a first attempt ti free myself from the chains of the ‘merely personal'. . . . The mental grasp of this extra-personal world within the frame of the given possibilities swam as highest aim half consciously and half unconsciously before the mind's eye."
What is more, was, suggested Einstein, belief in the word of God as it is revealed in biblical literature that allowed him to dwell in a ‘religious paradise of youth' and to shield himself from the harsh realities of social and political life. In an effort to recover that inner sense of security that was lost after exposure to scientific knowledge, or to become free once again of the ‘merely personal', he committed himself to understanding the ‘extra-personal world within the frame of given possibilities', or as seems obvious, to the study of physics. Although the existence of God as described in the Bible may have been in doubt, the qualities of mind that the architects of classical physics associated with this God were not. This is clear in the comments from which Einstein uses of mathematics, . . . "Nature is the realization of the simplest conceivable mathematical ideas. I am convinced that we can discover, by means of purely mathematical construction, those concepts and those lawful connections between them that furnish the key to the understanding of natural phenomena. Experience remains, of course, the sole criteria of physical utility of a mathematical construction. But the creative principle resides in mathematics. In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed."
This article of faith, first articulated by Kepler, that ‘nature is the realization of the simplest conceivable mathematical ideas' allowed for Einstein to posit the first major law of modern physics much as it allows Galileo to posit the first major law of classical physics. During which time, when the special and then the general theories of relativity had not been confirmed by experiment and many established physicists viewed them as at least minor heresies, Einstein remained entirely confident of their predictions. Ilse Rosenthal-Schneider, who visited Einstein shortly after Eddington's eclipse expedition confirmed a prediction of the general theory ( 1919 ), described Einstein's response to this news: When I was giving expression to my joy that the results coincided with his calculations, he said quite unmoved, "But I knew the theory was correct," and when I asked, what if there had been no confirmation of his prediction, he countered: "Then I would have been sorry for the dear Lord -the theory is correct."
Einstein was not given to making sarcastic or sardonic comments, particularly on matters of religion. These unguarded responses testify to his profound conviction that the language of mathematics allows the human mind access to immaterial and immutable truths existing outside of the mind that conceived them. Although Einstein's belief was far more secular than Galileo's, it retained the same essential ingredients.
What continued in the twenty-three-year-long debate between Einstein and Bohr, least of mention? The primary article drawing upon its faith that contends with those opposing to the merits or limits of a physical theory, at the heart of this debate was the fundamental question, "What is the relationship between the mathematical forms in the human mind called physical theory and physical reality?" Einstein did not believe in a God who spoke in tongues of flame from the mountaintop in ordinary language, and he could not sustain belief in the anthropomorphic God of the West. There is also no suggestion that he embraced ontological monism, or the conception of Being featured in Eastern religious systems, like Taoism, Hinduism, and Buddhism. The closest that Einstein apparently came to affirming the existence of the ‘extra-personal' in the universe was a ‘cosmic religious feeling', which he closely associated with the classical view of scientific epistemology.
The doctrine that Einstein fought to preserve seemed the natural inheritance of physics until the advent of quantum mechanics. Although the mind that constructs reality might be evolving fictions that are not necessarily true or necessary in social and political life, there was, Einstein felt, a way of knowing, purged of deceptions and lies. He was convinced that knowledge of physical reality in physical theory mirrors the preexistent and immutable realm of physical laws. And as Einstein consistently made clear, this knowledge mitigates loneliness and inculcates a sense of order and reason in a cosmos that might appear otherwise bereft of meaning and purpose.
What most disturbed Einstein about quantum mechanics was the fact that this physical theory might not, in experiment or even in principle, mirrors precisely the structure of physical reality. There is, for all the reasons we seem attested of, in that an inherent uncertainty in measurement made, . . . a quantum mechanical process reflects of a pursuit that quantum theory in itself and its contributive dynamic functionalities that there lay the attribution of a completeness of a quantum mechanical theory. Einstein's fearing that it would force us to recognize that this inherent uncertainty applied to all of physics, and, therefore, the ontological bridge between mathematical theory and physical reality -does not exist. And this would mean, as Bohr was among the first to realize, that we must profoundly revive the epistemological foundations of modern science.
The world view of classical physics allowed the physicist to assume that communion with the essences of physical reality via mathematical laws and associated theories was possible, but it made no other provisions for the knowing mind. In our new situation, the status of the knowing mind seems quite different. Modern physics distributively contributed its view toward the universe as an unbroken, undissectable and undivided dynamic whole. "There can hardly be a sharper contrast," said Melic Capek, "than that between the everlasting atoms of classical physics and the vanishing ‘particles' of modern physics as Stapp put it: "Each atom turns out to be nothing but the potentialities in the behaviour pattern of others. What we find, therefore, are not elementary space-time realities, but rather a web of relationships in which no part can stand alone, every part derives its meaning and existence only from its place within the whole"'
The characteristics of particles and quanta are not isolatable, given particle-wave dualism and the incessant exchange of quanta within matter-energy fields. Matter cannot be dissected from the omnipresent sea of energy, nor can we in theory or in fact observe matter from the outside. As Heisenberg put it decades ago, "the cosmos appears to be a complicated tissue of events, in which connection of different kinds alternate or overlay or combine and thereby determine the texture of the whole. This means that a pure reductionist approach to understanding physical reality, which was the goal of classical physics, is no longer appropriate.
While the formalism of quantum physics predicts that correlations between particles over space-like separated regions are possible, it can say nothing about what this strange new relationship between parts ( quanta ) and whole ( cosmos ) was by means an outside formalism. This does not, however, prevent us from considering the implications in philosophical terms, as the philosopher of science Errol Harris noted in thinking about the special character of wholeness in modern physics, a unity without internal content is a blank or empty set and is not recognizable as a whole. A collection of merely externally related parts does not constitute a whole in that the parts will not be "mutually adaptive and complementary to one and another."
Wholeness requires a complementary relationship between unity and differences and is governed by a principle of organization determining the interrelationship between parts. This organizing principle must be universal to a genuine whole and implicit in all parts that constitute the whole, even though the whole is exemplified only in its parts. This principle of order, Harris continued, "is nothing really in and of itself. It is the way parts are organized and not another constituent addition to those that constitute the totality."
In a genuine whole, the relationship between the constituent parts must be ‘internal or immanent' in the parts, as opposed to a mere spurious whole in which parts appear to disclose wholeness due to relationships that are external to the parts. The collection of parts that would allegedly constitute the whole in classical physics is an example of a spurious whole. Parts constitute a genuine whole when the universal principle of order is inside the parts and thereby adjusts each to all that they interlock and become mutually complementary. This not only describes the character of the whole revealed in both relativity theory and quantum mechanics. It is also consistent with the manner in which we have begun to understand the relation between parts and whole in modern biology.
Modern physics also reveals, claims Harris, a complementary relationship between the differences between parts that constituted contentual representations that the universal ordering principle that is immanent in each of the parts. While the whole cannot be finally disclosed in the analysis of the parts, the study of the differences between parts provides insights into the dynamic structure of the whole present in each of the parts. The part can never, nonetheless, be finally isolated from the web of relationships that disclose the interconnections with the whole, and any attempt to do so results in ambiguity.
Much of the ambiguity in attempted to explain the character of wholes in both physics and biology derives from the assumption that order exists between or outside parts. But order in complementary relationships between differences and sameness in any physical event is never external to that event -the connections are immanent in the event. From this perspective, the addition of non-locality to this picture of the dynamic whole is not surprising. The relationship between part, as quantum event apparent in observation or measurement, and the undissectable whole, revealed but not described by the instantaneous, and the undissectable whole, revealed but described by the instantaneous correlations between measurements in space-like separated regions, is another extension of the part-whole complementarity to modern physics.
If the universe is a seamlessly interactive system that evolves to a higher level of complexity, and if the lawful regularities of this universe are emergent properties of this system, we can assume that the cosmos is a singular point of significance as a whole that evinces of the ‘progressive principal order' of complementary relations its parts. Given that this whole exists in some sense within all parts ( quanta ), one can then argue that it operates in self-reflective fashion and is the ground for all emergent complexities. Since human consciousness evinces self-reflective awareness in the human brain and since this brain, like all physical phenomena can be viewed as an emergent property of the whole, it is reasonable to conclude, in philosophical terms at least, that the universe is conscious.
But since the actual character of this seamless whole cannot be represented or reduced to its parts, it lies, quite literally beyond all human representations or descriptions. If one chooses to believe that the universe be a self-reflective and self-organizing whole, this lends no support whatsoever to conceptions of design, meaning, purpose, intent, or plan associated with any mytho-religious or cultural heritage. However, If one does not accept this view of the universe, there is nothing in the scientific descriptions of nature that can be used to refute this position. On the other hand, it is no longer possible to argue that a profound sense of unity with the whole, which has long been understood as the foundation of religious experience, which can be dismissed, undermined or invalidated with appeals to scientific knowledge.
While we have consistently tried to distinguish between scientific knowledge and philosophical speculation based on this knowledge -there is no empirically valid causal linkage between the former and the latter. Those who wish to dismiss the speculative assumptions as its basis to be drawn the obvious freedom of which id firmly grounded in scientific theory and experiments there is, however, in the scientific description of nature, the belief in radical Cartesian division between mind and world sanctioned by classical physics. Seemingly clear, that this separation between mind and world was a macro-level illusion fostered by limited awarenesses of the actual character of physical reality and by mathematical idealization that were extended beyond the realm of their applicability.
Thus, the grounds for objecting to quantum theory, the lack of a one-to-one correspondence between every element of the physical theory and the physical reality it describes, may seem justifiable and reasonable in strictly scientific terms. After all, the completeness of all previous physical theories was measured against the criterion with enormous success. Since it was this success that gave physics the reputation of being able to disclose physical reality with magnificent exactitude, perhaps a more comprehensive quantum theory will emerge to insist on these requirements.
All indications are, however, that no future theory can circumvent quantum indeterminancy, and the success of quantum theory in co-ordinating our experience with nature is eloquent testimony to this conclusion. As Bohr realized, the fact that we live in a quantum universe in which the quantum of action is a given or an unavoidable reality requires a very different criterion for determining the completeness or physical theory. The new measure for a complete physical theory is that it unambiguously confirms our ability to co-ordinate more experience with physical reality.
If a theory does so and continues to do so, which is certainly the case with quantum physics, then the theory must be deemed complete. Quantum physics not only works exceedingly well, it is, in these terms, the most accurate physical theory that has ever existed. When we consider that this physics allows us to predict and measure quantities like the magnetic moment of electrons to the fifteenth decimal place, we realize that accuracy per se is not the real issue. The real issue, as Bohr rightly intuited, is that this complete physical theory effectively undermines the privileged relationship in classical physics between ‘theory' and ‘physical reality'.
In quantum physics, one calculates the probability of an event that can happen in alternative ways by adding the wave function, and then taking the square of the amplitude. In the two-slit experiment, for example, the electron is described by one wave function if it goes through one slit and by another wave function it goes through the other slit. In order to compute the probability of where the electron is going to end on the screen, we add the two wave functions, compute the absolute value of their sum, and square it. Although the recipe in classical probability theory seems similar, it is quite different. In classical physics, we would simply add the probabilities of the two alternate ways and let it go at that. The classical procedure does not work here, because we are not dealing with classical atoms. In quantum physics additional terms arise when the wave functions are added, and the probability is computed in a process known as the ‘superposition principle'.
The superposition principle can be illustrated with an analogy from simple mathematics. Add two numbers and then take the square of their sum. As opposed to just adding the squares of the two numbers. Obviously, ( 2 + 3 )2 is not equal to 22 + 32. The former is 25, and the latter are 13. In the language of quantum probability theory
| 2 | 2 | 1 | 2 + | 2 | 2
Where 1 and 2 are the individual wave functions. On the left-hand side, the superposition principle results in extra terms that cannot be found on the right-hand side. The left-hand side of the above relations is the way a quantum physicist would compute probabilities, and the right0-hand side is the classical analogue. In quantum theory, the right-hand side is realized when we know, for example, which slit through which the electron went. Heisenberg was among the first to compute what would happen in an instance like this. The extra superposition terms contained in the left-hand side of the above relations would not be there, and the peculiar wave-like interference pattern would disappear. The observed pattern on the final screen would, therefore, be what one would expect if electrons were behaving like a bullet, and the final probability would be the sum of the individual probabilities. But when we know which slit the electron went through, this interaction with the system causes the interference pattern to disappear.
In order to give a full account of quantum recipes for computing probabilities, one has to examine what would happen in events that are compound. Compound events are "events that can be broken down into a series of steps, or events that consists of a number of things happening independently." The recipe here calls for multiplying the individual wave functions, and then following the usual quantum recipe of taking the square of the amplitude.
The quantum recipe is | 1 • 2 | 2, and, in this case, it would be the same if we multiplied the individual probabilities, as one would in classical theory. Thus, the recipes of computing results in quantum theory and classical physics can be totally different. The quantum superposition effects are completely non-classical, and there is no mathematical justification per se why the quantum recipes work. What justifies the use of quantum probability theory is the coming thing that justifies the use of quantum physics -it has allowed us in countless experiments to extend our ability to co-ordinate experience with the expansive nature of unity.
A departure from the classical mechanics of Newton involving the principle that certain physical quantities can only assume discrete values. In quantum theory, introduced by Planck (1900), certain conditions are imposed on these quantities to restrict their value; the quantities are then said to be ‘quantized'.
Up to1900, physics was based on Newtonian mechanics. Large-scale systems are usually adequately described, however, several problems could not be solved, in particular, the explanation of the curves of energy against wavelengths for ‘black-body radiation', with their characteristic maximum, as these attemptive efforts were afforded to endeavour upon the base-cases, on which the idea that the enclosure producing the radiation contained a number of ‘standing waves' and that the energy of an oscillator if ‘kT', where ‘k' in the "Boltzmann Constant" and ‘T' the thermodynamic temperature. It is a consequence of classical theory that the energy does not depend on the frequency of the oscillator. This inability to explain the phenomenons has been called the ‘ultraviolet catastrophe'.
Planck tackled the problem by discarding the idea that an oscillator can attain or decrease energy continuously, suggesting that it could only change by some discrete amount, which he called a "quantum." This unit of energy is given by ‘hv' where ‘v' is the frequency and ‘h' is the "Planck Constant," ‘h' has dimensions of energy ‘x' times of action, and was called the "quantum of action.' According to Planck an oscillator could only change its energy by an integral number of quanta, i.e., by hv, 2hv, 3hv, etc. This meant that the radiation in an enclosure has certain discrete energies and by considering the statistical distribution of oscillators with respect to their energies, he was able to derive the "Planck Radiation Formulas." The formulae contrived by Planck, to express the distribution of dynamic energy in the normal spectrum of ‘black-body' radiation. It is usual form is:
8 chd / 5 ( exp[ch / k T] 1,
Which represents the amount of energy per unit volume in the range of wavelengths between and + d ? ‘c' = the speed of light and ‘h' = the Planck constant, as ‘k' = the Boltzmann constant with ‘T' = thermodynamic temperatures.
The idea of quanta of energy was applied to other problems in physics, when in 1905 Einstein explained features of the "Photoelectric Effect" by assuming that light was absorbed in quanta ( photons ). A further advance was made by Bohr ( 1913 ) in his theory of atomic spectra, in which he assumed that the atom can only exist in certain energy states and that light is emitted or absorbed as a result of a change from one state to another. He used the idea that the angular momentum of an orbiting electron could only assume discrete values, ie. , Was quantized? A refinement of Bohr's theory was introduced by Sommerfeld in an attempt to account for fine structure in spectra. Other successes of quantum theory were its explanations of the "Compton Effect" and "Stark Effect." Later developments involved the formulation of a new system of mechanics known as "Quantum Mechanics."
What is more, in furthering to Compton's scattering was to an interaction between a photon of electromagnetic radiation and a free electron, or other charged particles, in which some of the energy of the photon is transferred to the particle. As a result, the wavelength of the photon is increased by amount . Where:
= ( 2h / m0 c ) sin 2 ½.
This is the Compton equation, ‘h' is the Planck constant, m0 the rest mass of the particle, ‘c' the speed of light, and the photon angle between the directions of the incident and scattered photons. The quantity ‘h/m0c' and is known as the "Compton Wavelength," symbol C, which for an electron is equal to 0.002 43 nm.
The outer electrons in all elements and the inner ones in those of low atomic number have ‘binding energies' negligible compared with the quantum energies of all except very soft X- and gamma rays. Thus most electrons in matter are effectively free and at rest and so cause Compton scattering. In the range of quantum energies 105 to 107 electro volts, this effect is commonly the most important process of attenuation of radiation. The scattering electron is ejected from the atom with large kinetic energy and the ionization that it causes plays an important part in the operation of detectors of radiation.
In the "Inverse Compton Effect" there is a gain in energy by low-energy photons as a result of being scattered by free electrons of much higher energy. As a consequence, the electrons lose energy. Whereas, the wavelength of light emitted by atoms is altered by the application of a strong transverse electric field to the source, the spectrum lines being split up into a number of sharply defined components. The displacements are symmetrical about the position of the undisplaced lines, and are prepositional of the undisplaced line, and are propositional to the field strength up to about 100 000 volts per cm ( The Stark Effect).
Adjoined along-side with quantum mechanics, is an unstretching constitution taken advantage of forwarded mathematical physical theories -growing from Planck's "Quantum Theory" and deals with the mechanics of atomic and related systems in terms of quantities that can be measured. The subject development in several mathematical forms, including "Wave Mechanics" ( Schrödinger ) and "Matrix Mechanics" ( Born and Heisenberg ), all of which are equivalent.
In quantum mechanics, it is often found that the properties of a physical system, such as its angular moment and energy, can only take discrete values. Where this occurs the property is said to be ‘quantized' and its various possible values are labelled by a set of numbers called quantum numbers. For example, according to Bohr's theory of the atom, an electron moving in a circular orbit could occupy any orbit at any distance from the nucleus but only an orbit for which its angular momentum ( mvr ) was equal to nh/2 , where ‘n' is an integer ( 0, 1, 2, 3, etc. ) and ‘h' is the Planck's constant. Thus the property of angular momentum is quantized and ‘n' is a quantum number that gives its possible values. The Bohr theory has now been superseded by a more sophisticated theory in which the idea of orbits is replaced by regions in which the electron may move, characterized by quantum numbers ‘n', ‘I', and ‘m'.
Properties of [Standard] elementary particles are also described by quantum numbers. For example, an electron has the property known a ‘spin', and can exist in two possible energy states depending on whether this spin set parallel or antiparallel to a certain direction. The two states are conveniently characterized by quantum numbers + ½ and ½. Similarly properties such as charge, isospin, strangeness, parity and hyper-charge are characterized by quantum numbers. In interactions between particles, a particular quantum number may be conserved, I, e., the sum of the quantum numbers of the particles before and after the interaction remains the same. It is the type of interaction -strong, electromagnetic, weak that determines whether the quantum number is conserved.
The energy associated with a quantum state of an atom or other system that is fixed, or determined, by given set quantum numbers. It is one of the various quantum states that can be assumed by an atom under defined conditions. The term is often used to mean the state itself, which is incorrect accorded to: (i) the energy of a given state may be changed by externally applied fields (ii) there may be a number of states of equal energy in the system.
The electrons in an atom can occupy any of an infinite number of bound states with discrete energies. For an isolated atom the energy for a given state is exactly determinate except for the effected of the ‘uncertainty principle'. The ground state with lowest energy has an infinite lifetime hence, the energy, in principle is exactly determinate, the energies of these states are most accurately measured by finding the wavelength of the radiation emitted or absorbed in transitions between them, i.e., from their line spectra. Theories of the atom have been developed to predict these energies by calculation. Due to de Broglie and extended by Schrödinger, Dirac and many others, it ( wave mechanics ) originated in the suggestion that light consists of corpuscles as well as of waves and the consequent suggestion that all [ standard ] elementary particles are associated with waves. Wave mechanics are based on the Schrödinger wave equation describing the wave properties of matter. It relates the energy of a system to wave function, in general, it is found that a system, such as an atom or molecule can only have certain allowed wave functions ( eigenfunction ) and certain allowed energies
(Eigenvalues), in wave mechanics the quantum conditions arise in a natural way from the basic postulates as solutions of the wave equation. The energies of unbound states of positive energy form a continuum. This gives rise to the continuum background to an atomic spectrum as electrons are captured from unbound states. The energy of an atom state can be changed by the "Stark Effect" or the "Zeeman Effect."
The vibrational energies of the molecule also have discrete values, for example, in a diatomic molecule the atom oscillates in the line joining them. There is an equilibrium distance at which the force is zero. The atoms repulse when closer and attract when further apart. The restraining force is nearly prepositional to the displacement hence, the oscillations are simple harmonic. Solution of the Schrödinger wave equation gives the energies of a harmonic oscillation as:
En = ( n + ½ ) h .
Where ‘h' is the Planck constant, is the frequency, and ‘n' is the vibrational quantum number, which can be zero or any positive integer. The lowest possible vibrational energy of an oscillator is not zero but ½ h . This is the cause of zero-point energy. The potential energy of interaction of atoms is described more exactly by the "Morse Equation," which shows that the oscillations are slightly anharmonic. The vibrations of molecules are investigated by the study of ‘band spectra'.
The rotational energy of a molecule is quantized also, according to the Schrödinger equation, a body with the moment of inertial I about the axis of rotation have energies given by:
EJ = h2J ( J + 1 ) / 8 2I.
Where J is the rotational quantum number, which can be zero or a positive integer. Rotational energies originate from band spectra.
The energies of the state of the nucleus are determined from the gamma ray spectrum and from various nuclear reactions. Theory has been less successful in predicting these energies than those of electrons because the interactions of nucleons are very complicated. The energies are very little affected by external influence but the "Mössbauer Effect" has permitted the observations of some minute changes.
In quantum theory, introduced by Max Planck 1858-1947 in 1900, was the first serious scientific departure from Newtonian mechanics. It involved supposing that certain physical quantities can only assume discrete values. In the following two decades it was applied successfully by Einstein and the Danish physicist Neils Bohr (1885-1962). It was superseded by quantum mechanics in the tears following 1924, when the French physicist Louis de Broglie (1892-1987) introduced the idea that a particle may also be regarded as a wave. The Schrödinger wave equation relates the energy of a system to a wave function, the energy of a system to a wave function, the square of the amplitude of the wave is proportional to the probability of a particle being found in a specific position. The wave function expresses the lack of possibly of defining both the position and momentum of a particle, this expression of discrete representation is called as the "uncertainty principle," the allowed wave functions that have described stationary states of a system
Part of the difficulty with the notions involved is that a system may be in an indeterminate state at a time, characterized only by the probability of some result for an observation, but then ‘become' determinate ( the collapse of the wave packet ) when an observation is made such as the position and momentum of a particle if that is to apply to reality itself, than to mere indetermincies of measurement. It is as if there is nothing but a potential for observation or a probability wave before observation is made, but when an observation is made the wave becomes a particle. The ave-particle duality seems to block any way of conceiving of physical reality-in quantum terms. In the famous two-slit experiment, an electron is fired at a screen with two slits, like a tennis ball thrown at a wall with two doors in it. If one puts detectors at each slit, every electron passing the screen is observed to go through exactly one slit. But when the detectors are taken away, the electron acts like a wave process going through both slits and interfering with itself. A particle such an electron is usually thought of as always having an exact position, but its wave is not absolutely zero anywhere, there is therefore a finite probability of it ‘tunnelling through' from one position to emerge at another.
The unquestionable success of quantum mechanics has generated a large philosophical debate about its ultimate intelligibility and it's metaphysical implications. The wave-particle duality is already a departure from ordinary ways of conceiving of tings in space, and its difficulty is compounded by the probabilistic nature of the fundamental states of a system as they are conceived in quantum mechanics. Philosophical options for interpreting quantum mechanics have included variations of the belief that it is at best an incomplete description of a better-behaved classical underlying reality (Einstein), the Copenhagen interpretation according to which there are no objective unobserved events in the micro-world : Bohr and W. K. Heisenberg, 1901-76, an ‘acausal' view of the collapse of the wave packet, J. von Neumann, 1903-57, and a ‘many worlds' interpretation in which time forks perpetually toward innumerable futures, so that different states of the same system exist in different parallel universes ( H. Everett ).
In recent tars the proliferation of subatomic particles, such as there are 36 kinds of quarks alone, in six flavours to look in various directions for unification. One avenue of approach is superstring theory, in which the four-dimensional world is thought of as the upshot of the collapse of a ten-dimensional world, with the four primary physical forces, one of gravity another is electromagnetism and the strong and weak nuclear forces, becoming seen as the result of the fracture of one primary force. While the scientific acceptability of such theories is a matter for physics, their ultimate intelligibility plainly requires some philosophical reflection.
A theory of gravitation that is consistent with quantum mechanics whose subject, still in its infancy, has no completely satisfactory theory. In controventional quantum gravity, the gravitational force is mediated by a massless spin-2 particle, called the ‘graviton'. The internal degrees of freedom of the graviton require hij ( ) represent the deviations from the metric tensor for a flat space. This formulation of general relativity reduces it to a quantum field theory, which has a regrettable tendency to produce infinite for measurable qualitites. However, unlike other quantum field theories, quantum gravity cannot appeal to re-normalization procedures to make sense of these infinites. It has been shown that re-normalization procedures fail for theories, such as quantum gravity, in which the coupling constants have the dimensions of a positive power of length. The coupling constant g= for general relativity is the Planck length,
Lp = ( Gh / c3 )½ 10 35 m.
Super-symmetry has been suggested as a structure that could be free from these pathological infinities. Many theorists believe that an effective superstring field theory may emerge, in which the Einstein field equations are no longer valid and general relativity is required to appar only as low energy limit. The resulting theory may be structurally different from anything that has been considered so far. Super-symmetric string theory ( or superstring ) is an extension of the ideas of Super-symmetry to one-dimensional string-like entities that can interact with each other and scatter according to a precise set of laws. The normal modes of super-strings represent an infinite set of ‘normal' elementary particles whose masses and spins are related in a special way. Thus, the graviton is only one of the string modes-when the string-scattering processes are analysed in terms of their particle content, the low-energy graviton scattering is found to be the same as that computed from Super-symmetric gravity. The graviton mode may still be related to the geometry of the space0time in which the string vibrates, but it remains to be seen whether the other, massive, members of the set of ‘normal' particles also have a geometrical interpretation. The intricacy of this theory stems from the requirement of a space-time of at least ten dimensions to ensure internal consistency. It has been suggested that there are the normal four dimensions, with the extra dimensions being tightly ‘curled up' in a small circle presumably of Planck length size.
In the quantum theory or quantum mechanics of an atom or other system fixed, or determined by a given set of quantum numbers. It is one of the various quantum states that an atom can assume. The conceptual representation of an atom was first introduced by the ancient Greeks, as a tiny indivisible component of matter, developed by Dalton, as the smallest part of an element that can take part in a chemical reaction, and made very much more precisely by theory and excrement in the late-19th and 20th centuries.
Following the discovery of the electron (1897), it was recognized that atoms had structure, since electrons are negatively charged, a neutral atom must have a positive component. The experiments of Geiger and Marsden on the scattering of alpha particles by thin metal foils led Rutherford to propose a model (1912) in which nearly, but all the mass of an atom is concentrated at its centre in a region of positive charge, the nucleus, the radius of the order 10 -15 metre. The electrons occupy the surrounding space to a radius of 10-11 to 10-10 m. Rutherford also proposed that the nucleus have a charge of ‘Ze' and is surrounded by ‘Z' electrons ( Z is the atomic number ). According to classical physics such a system must emit electromagnetic radiation continuously and consequently no permanent atom would be possible. This problem was solved by the development of the quantum theory.
The "Bohr Theory of the Atom," 1913, introduced the concept that an electron in an atom is normally in a state of lower energy, or ground state, in which it remains indefinitely unless disturbed. By absorption of electromagnetic radiation or collision with another particle the atom may be excited -that is an electron is moved into a state of higher energy. Such excited states usually have short lifetimes, typically nanoseconds and the electron returns to the ground state, commonly by emitting one or more quanta of electromagnetic radiation. The original theory was only partially successful in predicting the energies and other properties of the electronic states. Attempts were made to improve the theory by postulating elliptic orbits ( Sommerfeld 1915 ) and electron spin ( Pauli 1925 ) but a satisfactory theory only became possible upon the development of "Wave Mechanics," after 1925.
According to modern theories, an electron does not follow a determinate orbit as envisaged by Bohr, but is in a state described by the solution of a wave equation. This determines the probability that the electron may be located in a given element of volume. Each state is characterized by a set of four quantum numbers, and, according to the Pauli exclusion principle, not more than one electron can be in a given state.
The Pauli exclusion principle states that no two identical ‘fermions' in any system can be in the same quantum state that is have the same set of quantum numbers. The principle was first proposed ( 1925 ) in the form that not more than two electrons in an atom could have the same set of quantum numbers. This hypothesis accounted for the main features of the structure of the atom and for the periodic table. An electron in an atom is characterized by four quantum numbers, n, I, m, and s. A particular atomic orbital, which has fixed values of n, I, and m, can thus contain a maximum of two electrons, since the spin quantum number ‘s' can only be + | or |. In 1928 Sommerfeld applied the principle to the free electrons in solids and his theory has been greatly developed by later associates.
Additionally, an effect occurring when atoms emit or absorb radiation in the presence of a moderately strong magnetic field. Each spectral; Line is split into closely spaced polarized components, when the source is viewed at right angles to the field there are three components, the middle one having the same frequency as the unmodified line, and when the source is viewed parallel to the field there are two components, the undisplaced line being preoccupied. This is the ‘normal' Zeeman Effect. With most spectral lines, however, the anomalous Zeeman effect occurs, where there are a greater number of symmetrically arranged polarized components. In both effects the displacement of the components is a measure of the magnetic field strength. In some cases the components cannot be resolved and the spectral line appears broadened.
The Zeeman effect occurs because the energies of individual electron states depend on their inclination to the direction of the magnetic field, and because quantum energy requirements impose conditions such that the plane of an electron orbit can only set itself at certain definite angles to the applied field. These angles are such that the projection of the total angular momentum on the field direction in an integral multiple of h/2 ( h is the Planck constant ). The Zeeman effect is observed with moderately strong fields where the precession of the orbital angular momentum and the spin angular momentum of the electrons about each other is much faster than the total precession around the field direction. The normal Zeeman effect is observed when the conditions are such that the Landé factor is unity, otherwise the anomalous effect is found. This anomaly was one of the factors contributing to the discovery of electron spin.
Statistics that are concerned with the equilibrium distribution of elementary particles of a particular type among the various quantized energy states. It is assumed that these elementary particles are indistinguishable. The "Pauli Exclusion Principle" is obeyed so that no two identical ‘fermions' can be in the same quantum mechanical state. The exchange of two identical fermions, i.e., two electrons, does not affect the probability of distribution but it does involve a change in the sign of the wave function. The "Fermi-Dirac Distribution Law" gives E the average number of identical fermions in a state of energy E:
E = 1/[e + E/kT + 1],
Where ‘k' is the Boltzmann constant, ‘T' is the thermodynamic temperature and is a quantity depending on temperature and the concentration of particles. For the valences electrons in a solid, ‘ ' takes the form -E1/kT, where E1 is the Fermi level. Whereby, the Fermi level ( or Fermi energy ) E F the value of E is exactly one half. Thus, for a system in equilibrium one half of the states with energy very nearly equal to ‘E' ( if any ) will be occupied. The value of EF varies very slowly with temperatures, tending to E0 as ‘T' tends to absolute zero.
In Bose-Einstein statistics, the Pauli exclusion principle is not obeyed so that any number of identical ‘bosons' can be in the same state. The exchanger of two bosons of the same type affects neither the probability of distribution nor the sign of the wave function. The "Bose-Einstein Distribution Law" gives E the average number of identical bosons in a state of energy E:
E = 1/[e + E/kT - 1].
The formula can be applied to photons, considered as quasi-particles, provided that the quantity , which conserves the number of particles, is zero. Planck's formula for the energy distribution of "Black-Body Radiation" was derived from this law by Bose. At high temperatures and low concentrations both the quantum distribution laws tend to the classical distribution:
E = Ae-E/kT.
Additionally, the property of substances that have a positive magnetic ‘susceptibility', whereby its quantity ÎĽr 1, and where ÎĽr is "Relative Permeability," again, that the electric-quantity presented as r 1, where r is the "Relative Permittivity," all of which has positivity. All of which are caused by the "spins" of electrons, paramagnetic substances having molecules or atoms, in which there are paired electrons and thus, resulting of a "Magnetic Moment." There is also a contribution of the magnetic properties from the orbital motion of the electron, as the relative ‘permeability' of a paramagnetic substance is thus greater than that of a vacuum, i.e., it is slightly greater than unity.
A ‘paramagnetic substance' is regarded as an assembly of magnetic dipoles that have random orientation. In the presence of a field the magnetization is determined by competition between the effect of the field, in tending to align the magnetic dipoles, and the random thermal agitation. In small fields and high temperatures, the magnetization produced is proportional to the field strength, wherefore at low temperatures or high field strengths, a state of saturation is approached. As the temperature rises, the susceptibility falls according to Curie's Law or the Curie-Weiss Law.
Furthering by Curie's Law, the susceptibility ( ) of a paramagnetic substance is unversedly proportional to the ‘thermodynamic temperature' ( T ): = C/T. The constant 'C is called the ‘Curie constant' and is characteristic of the material. This law is explained by assuming that each molecule has an independent magnetic ‘dipole' moment and the tendency of the applied field to align these molecules is opposed by the random moment due to the temperature. A modification of Curie's Law, followed by many paramagnetic substances, where the Curie-Weiss law modifies its applicability in the form
= C/(T ).
The law shows that the susceptibility is proportional to the excess of temperature over a fixed temperature : ‘ ' is known as the Weiss constant and is a temperature characteristic of the material, such as sodium and potassium, also exhibit type of paramagnetic resulting from the magnetic moments of free, or nearly free electrons, in their conduction bands? This is characterized by a very small positive susceptibility and a very slight temperature dependence, and is known as ‘free-electron paramagnetism' or ‘Pauli paramagnetism'.
A property of certain solid substances that having a large positive magnetic susceptibility having capabilities of being magnetized by weak magnetic fields. The chief elements are iron, cobalt, and nickel and many ferromagnetic alloys based on these metals also exist. Justifiably, ferromagnetic materials exhibit magnetic ‘hysteresis', of which formidable combination of decaying within the change of an observed effect in response to a change in the mechanism producing the effect.
(Magnetic) a phenomenon shown by ferromagnetic substances, whereby the magnetic flux through the medium depends not only on the existing magnetizing field, but also on the previous state or states of the substances, the existence of a phenomenon necessitates a dissipation of energy when the substance is subjected to a cycle of magnetic changes, this is known as the magnetic hysteresis loss. The magnetic hysteresis loops were acceding by a curved obtainability from ways of which, in themselves were of plotting the magnetic flux density ‘B', of a ferromagnetic material against the responding value of the magnetizing field 'H', the area to the ‘hysteresis loss' per unit volume in taking the specimen through the prescribed magnetizing cycle. The general forms of the hysteresis loop fore a symmetrical cycle between ‘H' and ‘~ H' and ‘H ~ h, having inclinations that rise to hysteresis.
The magnetic hysteresis loss commands the dissipation of energy as due to magnetic hysteresis, when the magnetic material is subjected to changes, particularly, the cycle changes of magnetization, as having the larger positive magnetic susceptibility, and are capable of being magnetized by weak magnetic fields. Ferro magnetics are able to retain a certain domain of magnetization when the magnetizing field is removed. Those materials that retain a high percentage of their magnetization are said to be hard, and those that lose most of their magnetization are said to be soft, typical examples of hard ferromagnetic are cobalt steel and various alloys of nickel, aluminium and cobalt. Typical soft magnetic materials are silicon steel and soft iron, the coercive force as acknowledged to the reversed magnetic field' that is required to reduce the magnetic ‘flux density' in a substance from its remnant value to zero in characteristic of ferromagnetisms and explains by its presence of domains. A ferromagnetic domain is a region of crystalline matter, whose volume may be 10-12 to 10-8 m3, which contains atoms whose magnetic moments are aligned in the same direction. The domain is thus magnetically saturated and behaves like a magnet with its own magnetic axis and moment. The magnetic moment of the ferrometic atom results from the spin of the electron in an unfilled inner shell of the atom. The formation of a domain depends upon the strong interactions forces (Exchange forces) that are effective in a crystal lattice containing ferrometic atoms.
In an unmagnetized volume of a specimen, the domains are arranged in a random fashion with their magnetic axes pointing in all directions so that the specimen has no resultant magnetic moment. Under the influence of a weak magnetic field, those domains whose magnetic saxes have directions near to that of the field flux at the expense of their neighbours. In this process the atoms of neighbouring domains tend to align in the direction of the field but the strong influence of the growing domain causes their axes to align parallel to its magnetic axis. The growth of these domains leads to a resultant magnetic moment and hence, magnetization of the specimen in the direction of the field, with increasing field strength, the growth of domains proceeds until there is, effectively, only one domain whose magnetic axis appropriates to the field direction. The specimen now exhibits tron magnetization. Further, increasing in field strength cause the final alignment and magnetic saturation in the field direction. This explains the characteristic variation of magnetization with applied strength. The presence of domains in ferromagnetic materials can be demonstrated by use of "Bitter Patterns" or by "Barkhausen Effect."
For ferromagnetic solids there are a change from ferromagnetic to paramagnetic behaviour above a particular temperature and the paramagnetic material then obeyed the Curie-Weiss Law above this temperature, this is the ‘Curie temperature' for the material. Below this temperature the law is not obeyed. Some paramagnetic substances, obey the temperature ‘ C' and do not obey it below, but are not ferromagnetic below this temperature. The value ‘ ' in the Curie-Weiss law can be thought of as a correction to Curie's law reelecting the extent to which the magnetic dipoles interact with each other. In materials exhibiting ‘antiferromagnetism' of which the temperature ‘ ' corresponds to the ‘NĂ©el temperature'.
Without discredited inquisitions, the property of certain materials that have a low positive magnetic susceptibility, as in paramagnetism, and exhibit a temperature dependence similar to that encountered in ferromagnetism. The susceptibility increased with temperatures up to a certain point, called the "NĂ©el Temperature," and then falls with increasing temperatures in accordance with the Curie-Weiss law. The material thus becomes paramagnetic above the NĂ©el temperature, which is analogous to the Curie temperature in the transition from ferromagnetism to paramagnetism. Antiferromagnetism is a property of certain inorganic compounds such as MnO, FeO, FeF2 and MnS. It results from interactions between neighbouring atoms leading and an antiparallel arrangement of adjacent magnetic dipole moments, least of mention. A system of two equal and opposite charges placed at a very short distance apart. The product of either of the charges and the distance between them is known as the ‘electric dipole moments. A small loop carrying a current I behave as a magnetic dipole and is equal to IA, where A being the area of the loop.
The energy associated with a quantum state of an atom or other system that is fixed, or determined by a given set of quantum numbers. It is one of the various quantum states that can be assumed by an atom under defined conditions. The term is often used to mean the state itself, which is incorrect by ways of: (1) the energy of a given state may be changed by externally applied fields, and (2) there may be a number of states of equal energy in the system.
The electrons in an atom can occupy any of an infinite number of bound states with discrete energies. For an isolated atom the energy for a given state is exactly determinate except for the effects of the ‘uncertainty principle'. The ground state with lowest energy has an infinite lifetime, hence the energy is if, in at all as a principle that is exactly determinate. The energies of these states are most accurately measured by finding the wavelength of the radiation emitted or absorbed in transitions between them, i.e., from their line spectra. Theories of the atom have been developed to predict these energies by calculating such a system that emit electromagnetic radiation continuously and consequently no permanent atom would be possible, hence this problem was solved by the developments of quantum theory. An exact calculation of the energies and other particles of the quantum state is only possible for the simplest atom but there are various approximate methods that give useful results as an approximate method of solving a difficult problem, if the equations to be solved, and depart only slightly from those of some problems already solved. For example, the orbit of a single planet round the sun is an ellipse, that the perturbing effect of other planets modifies the orbit slightly in a way calculable by this method. The technique finds considerable application in ‘wave mechanics' and in ‘quantum electrodynamics'. Phenomena that are not amendable to solution by perturbation theory are said to be non-perturbative.
The energies of unbound states of positive total energy form a continuum. This gives rise to the continuos background to an atomic spectrum, as electrons are captured from unbound state, the energy of an atomic state can be changed by the "Stark Effect" or the "Zeeman Effect."
The vibrational energies of molecules also have discrete values, for example, in a diatomic molecule the atoms oscillate in the line joining them. There is an equilibrium distance at which the force is zero, and the atoms deflect when closer and attract when further apart. The restraining force is very nearly proportional to the displacement, hence the oscillations are simple harmonic. Solution of the ‘Schrödinger wave equation' gives the energies of a harmonic oscillation as:
En = ( n + ½ ) hĆ’
Where ‘h' is the Planck constant, Ć’ is the frequency, and ‘n' is the vibrational quantum number, which can be zero or any positive integer. The lowest possible vibrational energy of an oscillator is thus not zero but ½hĆ’. This is the cause of zero-point energy. The potential energy of interaction of atoms is described more exactly by the Morse equation, which shows that the oscillations are slightly anharmonic. The vibrations of molecules are investigated by the study of ‘band spectra'.
The rotational energy of a molecule is quantized also, according to the Schrödinger equation a body with moments of inertia I about the axis of rotation have energies given by:
Ej = h2J(J + 1 )/8 2 I,
Where ‘J' is the rotational quantum number, which can be zero or a positive integer. Rotational energies are found from ‘band spectra'.
The energies of the states of the ‘nucleus' can be determined from the gamma ray spectrum and from various nuclear reactions. Theory has been less successful in predicting these energies than those of electrons in atoms because the interactions of nucleons are very complicated. The energies are very little affected by external influences, but the "Mössbauer Effect" has permitted the observation of some minute changes.
When X-rays are scattered by atomic centres arranged at regular intervals, interference phenomena occur, crystals providing grating of a suitable small interval. The interference effects may be used to provide a spectrum of the beam of X-rays, since, according to "Bragg's Law," the angle of reflection of X-rays from a crystal depends on the wavelength of the rays. For lower-energy X-rays mechanically ruled grating can be used. Each chemical element emits characteristic X-rays in sharply defined groups in more widely separated regions. They are known as the K, L's, M, N. etc., promote lines of any series toward shorter wavelengths as the atomic number of the elements concerned increases. If a parallel beam of X-rays, wavelength , strikes a set of crystal planes it is reflected from the different planes, interferences occurring between X-rays reflect from adjacent planes. Bragg's Law states that constructive interference takes place when the difference in path-lengths, BAC, is equal to an integral number of wavelengths
2d sin = n
where ‘n' is an integer, ‘d' is the interplanar distance, and ‘ ' is the angle between the incident X-ray and the crystal plane. This angle is called the "Bragg's Angle," and a bright spot will be obtained on an interference pattern at this angle. A dark spot will be obtained, however. If be, 2d sin = m . Where ‘m' is half-integral. The structure of a crystal can be determined from a set of interference patterns found at various angles from the different crystal faces.
A concept originally introduced by the ancient Greeks, as a tiny indivisible component of matter, developed by Dalton, as the smallest part of an element that can take part in a chemical reaction, and made experiment in the late-19th and early 20th century. Following the discovery of the electron ( 1897 ), they recognized that atoms had structure, since electrons are negatively charged, a neutral atom must have a positive component. The experiments of Geiger and Marsden on the scattering of alpha particles by thin metal foils led Rutherford to propose a model ( 1912 ) in which nearly all mass of the atom is concentrated at its centre in a region of positive charge, the nucleus is a region of positive charge, the nucleus, radiuses of the order 10-15 metre. The electrons occupy the surrounding space to a radius of 10-11 to 10-10 m. Rutherford also proposed that the nucleus have a charge of Ze is surrounded by ‘Z' electrons ( Z is the atomic number ). According to classical physics such a system must emit electromagnetic radiation continuously and consequently no permanent atom would be possible. This problem was solved by the developments of the "Quantum Theory."
The "Bohr Theory of the Atom" ( 1913 ) introduced the notion that an electron in an atom is normally in a state of lowest energy ( ground state ) in which it remains indefinitely unless disturbed by absorption of electromagnetic radiation or collision with other particle the atom may be excited -that is, electrons moved into a state of higher energy. Such excited states usually have short life spans ( typically nanoseconds ) and the electron returns to the ground state, commonly by emitting one or more ‘quanta' of electromagnetic radiation. The original theory was only partially successful in predicting the energies and other properties of the electronic states. Postulating elliptic orbits made attempts to improve the theory ( Sommerfeld 1915 ) and electron spin ( Pauli 1925 ) but a satisfactory theory only became possible upon the development of "Wave Mechanics" 1925.
According to modern theories, an electron does not follow a determinate orbit as envisaged by Bohr, but is in a state described by the solution of the wave equation. This determines the ‘probability' that the electron may be found in a given element of volume. A set of four quantum numbers has characterized each state, and according to the "Pauli Exclusion Principle," not more than one electron can be in a given state.
An exact calculation of the energies and other properties of the quantum states is possible for the simplest atoms, but various approximate methods give useful results, i.e., as an approximate method of solving a difficult problem if the equations to be solved and depart only slightly from those of some problems already solved. The properties of the innermost electron states of complex atoms are found experimentally by the study of X-ray spectra. The outer electrons are investigated using spectra in the infrared, visible, and ultraviolet. Certain details have been studied using microwaves. As administered by a small difference in energy between the energy levels of the 2 P½ states of hydrogen. In accord with Lamb Shift, these levels would have the same energy according to the wave mechanics of Dirac. The actual shift can be explained by a correction to the energies based on the theory of the interaction of electromagnetic fields with matter, in of which the fields themselves are quantized. Yet, other information may be obtained form magnetism and other chemical properties.
Its appearance potential concludes as, ( 1 )the potential differences through which an electron must be accelerated from rest to produce a given ion from its parent atom or molecule. ( 2 ) This potential difference multiplied bu the electron charge giving the least energy required to produce the ion. A simple ionizing process gives the ‘ionization potential' of the substance, for example:
Ar + e Ar + + 2e.
Higher appearance potentials may be found for multiplying charged ions:
Ar + e Ar + + + 3r.
The number of protons in a nucleus of an atom or the number of electrons resolving around the nucleus is among some concerns of atomic numbers. The atomic number determines the chemical properties of an element and the element's position in the periodic table, because of which the clarification of chemical elements, in tabular form, in the order of their atomic number. The elements show a periodicity of properties, chemically similar recurring in a definite order. The sequence of elements is thus broken into horizontal ‘periods' and vertical ‘groups' the elements in each group showing close chemical analogies, i.e., in valency, chemical properties, etc. all the isotopes of an element have the same atomic number although different isotopes gave mass numbers.
An allowed ‘wave function' of an electron in an atom obtained by a solution of the Schrödinger wave equation. In a hydrogen atom, for example, the electron moves in the electrostatic field of the nucleus and its potential energy is e2, where ‘e' is the electron charge. ‘r' its distance from the nucleus, as a precise orbit cannot be considered as in Bohr's theory of the atom, but the behaviour of the electron is described by its wave function, , which is a mathematical function of its position with respect to the nucleus. The significance of the wave function is that | | 2dt, is the probability of finding the electron in the element of volume ‘dt'.
Solution of Schrödinger's equation for hydrogen atom shows that the electron can only have certain allowed wave functions ( eigenfunction ). Each of these corresponds to a probability distribution in space given by the manner in which | | 2 varies with position. They also have an associated value of energy ‘E'. These allowed wave functions, or orbitals, are characterized by three quantum numbers similar to those characterizing the allowed orbits in the quantum theory of the atom:
‘n', the ‘principle quantum number', can have values of 1, 2, 3, etc. the orbital with n=1 has the lowest energy. The states of the electron with n=1, 2, 3, etc., are called ‘shells' and designated the K, L, M shells, etc.
‘I' the ‘azimuthal quanta number' which for a given value of ‘n' can have values of 0, 1, 2, . . . ( n 1 ). Similarly, the 'M' shell ( n = 3 ) has three sub-shells with I = 0, I = 1, and I = 2. Orbitals with I = 0, 1, 2, and 3 are called s, p, d, and orbitals respectively. The significance of the I quantum number is that it gives the angular momentum of the electron. The orbital annular momentum of an electron is given by
[1(I + 1)(h2 )]
‘m' the ‘magnetic quanta number', which for a given value of ‘I' can have values of; I, (I 1), . . . , 0, . . . (I 1). Thus for ‘p' orbital for which I = 1, there is in fact three different orbitals with m = 1, 0, and 1. These orbitals with the same values of ‘n' and ‘I ‘ but different ‘m' values, have the same energy. The significance of this quantum number is that it shows the number of different levels that would be produced if the atom were subjected to an external magnetic field
According to wave theory the electron may be at any distance from the nucleus, but in fact there is only a reasonable chance of it being within a distance of 5 x 1011 metre. Indeed the maximum probability occurs when r = a0 where a0 is the radius of the first Bohr orbit. It is customary to represent an orbit that there is no arbitrarily decided probability ( say 95% ) of finding them an electron. Notably taken, is that although ‘s' orbitals are spherical ( I = 0 ), orbitals with I > 0, have an angular dependence. Finally. The electron in an atom can have a fourth quantum number, ‘M' characterizing its spin direction. This can be + ½ or ½ and according to the Pauli Exclusion principle, each orbital can hold only two electrons. The fourth quantum numbers lead to an explanation of the periodic table of the elements.
The least distance in a progressive wave between two surfaces with the same phase arises to a wavelength. If ‘v' is the phase speed and ‘v' the frequency, the wavelength is given by v = v . For electromagnetic radiation the phase speed and wavelength in a material medium are equal to their values in a free space divided by the ‘refractive index'. The wavelengths of spectral lines are normally specified for free space.
Optical wavelengths are measure absolutely using interferometers or diffraction gratings, or comparatively using a prism spectrometer. The wavelength can only have an exact value for an infinite waver train if an atomic body emits a quantum in the form of a train of waves of duration the fractional uncertainty of the wavelength, / , is approximately /2c , where ‘c' is the speed in free space. This is associated with the indeterminacy of the energy given by the uncertainty principle
Whereas, a mathematical quantity analogous to the amplitude of a wave that appears in the equation of wave mechanics, particularly the Schrödinger waves equation. The most generally accepted interpretation is that | | 2dV represents the probability that a particle is within the volume element dV. The wavelengths, as a set of waves that represent the behaviour, under appropriate conditions, of a particle, e.g., its diffraction by a particle. The wavelength is given by the "de Broglie Equation." They are sometimes regarded as waves of probability, times the square of their amplitude at a given point represents the probability of finding the particle in unit volume at that point. These waves were predicted by de Broglie in 1924 and observed in 1927 in the Davisson-Germer Experiment. Still, ‘ ' is often a might complex quality.
The analogy between ‘ ' and the amplitude of a wave is purely formal. There is no macroscopic physical quantity with which ‘ ' can be identified, in contrast with, for example, the amplitude of an electromagnetic wave, which is expressed in terms of electric and magnetic field intensities
In general, there are an infinite number of functions satisfying a wave equation but only some of these will satisfy the boundary conditions. ‘ ' must be finite and single-valued at every point, and the spatial derivative must be continuous at an interface? For a particle subject to a law of conservation of numbers, the integral of | | 2dV over all space must remain equal to 1, since this is the probability that it exists somewhere to satisfy this condition the wave equation must be of the first order in (d /dt). Wave functions obtained when these conditions are applied from a set of characteristic functions of the Schrödinger wave equation. These are often called eigenfunctions and correspond to a set of fixed energy values in which the system may exist describe stationary states on the system.
For certain bound states of a system the eigenfunctions do not charge the sign or reversing the co-ordinated axes. These states are said to have even parity. For other states the sign changes on space reversal and the parity is said to be odd.
It's issuing case of eigenvalue problems in physics that take the form:
= ,
Where is come mathematical operation ( multiplication by a number, differentiation, etc.) on a function , which is called the ‘eigenfunction'. is called the ‘eigenvalue', which in a physical system will be identified with an observable quantity, as, too, an atom to other systems that are fixed, or determined, by a given set of quantum numbers? It is one of the various quantum states that can be assumed by an atom
Eigenvalue problems are ubiquitous in classical physics and occur whenever the mathematical description of a physical system yields a series of coupled differential equations. For example, the collective motion of a large number of interacting oscillators may be described by a set of coupled differential equations. Each differential equation describes the motion of one of the oscillators in terms of the positions of all the others. A ‘harmonic' solution may be sought, in which each displacement is assumed as a simple harmonic motion in time. The differential equations then reduce to ‘3N' linear equations with 3N unknowns. Where ‘N' is the number of individual oscillators, each problem is from each one of three degrees of freedom. The whole problem I now easily recast as a ‘matrix' equation of the form:
M = 2 .
Where ‘M' is an N x N matrix called the ‘a dynamic matrix, is an N x 1 column matrix, and 2 of the harmonic solution. The problem is now an eigenvalue problem with eigenfunctions' , where are the normal modes of the system, with corresponding eigenvalues 2. As can be expressed as a column vector, is a vector in some –dimensional vector space. For this reason, is also often called an eigenvector.
When the collection of oscillators is a complicated three-dimensional molecule, the casting of the problem into normal modes s and effective simplification of the system. The symmetry principles of group theory, the symmetry operations in any physical system must be posses the properties of the mathematical group. As the group of rotation, both finite and infinite, are important in the analysis of the symmetry of atoms and molecules, which underlie the quantum theory of angular momentum. Eigenvalue problems arise in the quantum mechanics of atomic arising in the quantum mechanics of atomic or molecular systems yield stationary states corresponding to the normal mode oscillations of either electrons in-an atom or atoms within a molecule. Angular momentum quantum numbers correspond to a labelling system used to classify these normal modes, analysing the transitions between them can lead and theoretically predict of atomic or a molecular spectrum. Whereas, the symmetrical principle of group theory can then be applied, from which allow their classification accordingly. In which, this kind of analysis requires an appreciation of the symmetry properties of the molecules ( rotations, inversions, etc. ) that leave the molecule invariant make up the point group of that molecule. Normal modes sharing the same eigenvalues are said to correspond to the irreducible representations of these molecules' point group. It is among these irreducible representations that one will find the infrared absorption spectrum for the vibrational normal modes of the molecule.
Eigenvalue problems play a particularly important role in quantum mechanics. In quantum mechanics, physically observable as location momentum energy etc., are represented by operations ( differentiations with respect to a variable, multiplication by a variable ), which act on wave functions. Wave functioning differs from classical waves in that they carry no energy. For classical waves, the square modulus of its amplitude measures its energy. For a wave function, the square modulus of its amplitude, at a location represents not energy bu probability, i.e., the probability that a particle -a localized packet of energy will be observed in a detector is placed at that location. The wave function therefore describes the distribution of possible locations of the particle and is perceptible only after many location detectors events have occurred. A measurement of position of a quantum particle may be written symbolically as:
X ( ) = ( ),
Where ( ) is said to be an eigenvector of the location operator and ‘ ' is the eigenvalue, which represents the location. Each ( ) represents amplitude at the location ‘ ', | ( ) |2 is the probability that the particle will be found in an infinitesimal volume at that location. The wave function describing the distribution of all possible locations for the particle is the linear superposition of all ( ) for zero . These principles that hold generally in physics wherever linear phenomena occur. In elasticity, the principle stares that the same strains whether it acts alone accompany each stress or in conjunction with others, it is true so long as the total stress does not exceed the limit of proportionality. In vibrations and wave motion the principle asserts that one set is unaffected by the presence of another set. For example, two sets of ripples on water will pass through one anther without mutual interaction so that, at a particular instant, the resultant distribution at any point traverse by both sets of waves is the sum of the two component disturbances.'
The superposition of two vibrations, y1 and y2, both of frequency , produces a resultant vibration of the same frequency, its amplitude and phase functions of the component amplitudes and phases, that:
y1 = a1 sin(2 t + 1)
y2 = a2 sin(sin(2 t + 2)
Then the resultant vibration, y, is given by:
y1 + y2 = A sin(2 t + ),
Where amplitude A and phase is both functions of a1, a2, 1, and 2.
However, the eigenvalue problems in quantum mechanics therefore represent observable representations as made by possible states ( position, in the case of ) that the quantum system can have to stationary states, of which states that the product of the uncertainty of the resulting value of a component of momentum ( p ) and the uncertainties in the corresponding co-ordinate position ( ) is of the same order of magnitude as the Planck Constant. It produces an accurate measurement of position is possible, as a resultant of the uncertainty principle. Subsequently, measurements of the position acquire a spread themselves, which makes the continuos monitoring of the position impossibly.
As in, classical mechanics may take differential or matrix forms. Both forms have been shown to be equivalent. The differential form of quantum mechanics is called wave mechanics ( Schrödinger ), where the operators are differential operators or multiplications by variables. Eigenfunctions in wave mechanics are wave functions corresponding to stationary wave states that responding to stationary conditions. The matrix forms of quantum mechanics are often matrix mechanics: Born and Heisenberg. Matrices acting of eigenvectors represent the operators.
The relationship between matrix and wave mechanics is similar to the relationship between matrix and differential forms of eigenvalue problems in classical mechanics. The wave functions representing stationary states are really normal modes of the quantum wave. These normal modes may be thought of as vectors that span on a vector space, which have a matrix representation.
Pauli, in 1925, suggested that each electron could exist in two states with the same orbital motion. Uhlenbeck and Goudsmit interpreted these states as due to the spin of the electron about an axis. The electron is assumed to have an intrinsic angular momentum on addition, to any angular momentum due to its orbital motion. This intrinsic angular momentum is called ‘spin' It is quantized in values of
s(s + 1)h/2 ,
Where ‘s' is the ‘spin quantum number' and ‘h' the Planck constant. For an electron the component of spin in a given direction can have values of + ½ and – ½, leading to the two possible states. An electron with spin that is behaviourally likens too small magnetic moments, in which came alongside an intrinsic magnetic moment. A ‘magneton gives of a fundamental constant, whereby the intrinsic magnetic moment of an electron acquires the circulatory current created by the angular momentum ‘p' of an electron moving in its orbital produces a magnetic moment ÎĽ = ep/2m, where ‘e and ‘m' are the charge and mass of the electron, by substituting the quantized relation p = jh/2 (h = the Planck constant; j = magnetic quantum number ), ÎĽ - jh/4 m. When j is taken as unity the quantity eh/4 m is called the Bohr magneton, its value is:
9.274 0780 x 10-24 Am2
Acording to the wave mechanics of Dirac, the magnetic moment associated with the spin of the electron would be exactly one Bohr magnetron, although quantum electrodynamics show that a small difference can v=be expected.
The nuclear magnetron, ‘ÎĽN' is equal to (me/mp)ÎĽB. Where mp is the mass of the proton. The value of ÎĽN is:
5.050 8240 x 10-27 A m2
The magnetic moment of a proton is, in fact, 2.792 85 nuclear magnetos. The two states of different energy result from interactions between the magnetic field due to the electron's spin and that caused by its orbital motion. These are two closely spaced states resulting from the two possible spin directions and these lead to the two limes in the doublet.
In an external magnetic field the angular momentum vector of the electron precesses. For an explicative example, if a body is of a spin, it holds about its axis of symmetry OC ( where O is a fixed point ) and C is rotating round an axis OZ fixed outside the body, the body is said to be precessing round OZ. OZ is the precession axis. A gyroscope precesses due to an applied torque called the precessional torque. If the moment of inertia a body about OC is I and its angular momentum velocity is , a torque ‘K', whose axis is perpendicular to the axis of rotation will produce an angular velocity of precession about an axis perpendicular to both and the torque axis where: = K/I .
It is . . . , wholly orientated of the vector to the field direction are allowed, there is a quantization so that the component of the angular momentum along the direction I restricted of certain values of h/2 . The angular momentum vector has allowed directions such that the component is mS(h2 ), where mS is the magnetic so in quantum number. For a given value of s, mS has the value's, ( s - 1), . . . –s. For example, when s = 1, mS is I, O, and – 1. The electron has a spin of ½ and thus mS is + ½ and – ½. Thus the components of its spin of angular momentum along the field direction are,
± ½(h/2 ). These phenomena are called ‘a space quantization'.
The resultant spin of a number of particles is the vector sum of the spins ( s ) of the individual particles and is given by symbol S. for example, in an atom two electrons with spin of ½ could combine to give a resultant spin of S = ½ + ½ = 1 or a resultant of
S = ½ – ½ =1 or a resultant of S = ½ – ½ =0.
Alternative symbols used for spin is J ( for elementary particles or standard theory ) and I ( for a nucleus ). Most elementary particles have a non-zero spin, which either be integral of half integral. The spin of a nucleus is the resultant of the spin of its constituent's nucleons.
For most generally accepted interpretations is that | |2dV represents the probability that particle is located within the volume element dV, as well, ‘ ' is often a complex quantity. The analogy between ‘ ' and the amplitude of a wave is purely formal. There is no macroscopic physical quantity with which ‘ ' can be identified, in contrast with, for example, the amplitude of an electromagnetic wave, which are expressed in terms of electric and magnetic field intensities. There are an infinite number of functions satisfying a wave equation, but only some of these will satisfy the boundary condition. ‘ ' must be finite and single-valued at each point, and the spatial derivatives must be continuous at an interface? For a particle subject to a law of conservation of numbers; The integral of | |2dV over all space must remain equal to 1, since this is the probability that it exists somewhere. To satisfy this condition the wave equation must be of the first order in (d dt). Wave functions obtained when these conditions are applied form of set of ‘characteristic functions' of the Schrödinger wave equation. These are often called ‘eigenfunctions' and correspond to a set of fixed energy values in which the system may exist, called ‘eigenvalues'. Energy eigenfunctions describe stationary states of a system. For example, bound states of a system the eigenfunctions do not change signs on reversing the co-ordinated axes. These states are said to have ‘even parity'. For other states the sign changes on space reversal and the parity is said to be ‘odd'.
The least distance in a progressive wave between two surfaces with the same phase. If ‘v' is the ‘phase speed' and ‘v' the frequency, the wavelength is given by v = v . For ‘electromagnetic radiation' the phase speed and wavelength in a material medium are equal to their values I free space divided by the ‘refractive index'. The wavelengths are spectral lines are normally specified for free space. Optical wavelengths are measured absolutely using interferometers or diffraction grating, or comparatively using a prism spectrometer.
The wavelength can only have an exact value for an infinite wave train. If an atomic body emits a quantum in the form of a train of waves of duration ‘ ' the fractional uncertainty of the wavelength, / , is approximately /2 c , where ‘c' is the speed of free space. This is associated with the indeterminacy of the energy given by the ‘uncertainty principle'.
A moment of momentum about an axis, represented as Symbol: L, the product of the moment of inertia and angular velocity ( I ) angular momentum is a ‘pseudo vector quality'. It is conserved in an isolated system, as the moment of inertia contains itself of a body about an axis. The sum of the products of the mass of each particle of a body and square of its perpendicular distance from the axis: This addition is replaced by an integration in the case of continuous body. For a rigid body moving about a fixed axis, the laws of motion have the same form as those of rectilinear motion, with moments of inertia replacing mass, angular velocity replacing linear momentum, etc. hence the ‘energy' of a body rotating about a fixed axis with angular velocity is ½I 2, which corresponds to ½mv2 for the kinetic energy of a body mass ‘m' translated with velocity ‘v'.
The linear momentum of a particle ‘p' bears the product of the mass and the velocity of the particle. It is a ‘vector' quality directed through the particle of a body or a system of particles is the vector sum of the linear momentums of the individual particles. If a body of mass ‘M' is translated ( the movement of a body or system in which a way that all points are moved in parallel directions through equal distances ), with a velocity ‘V', it has its mentum as ‘MV', which is the momentum of a particle of mass ‘M' at the centre of gravity of the body. The product of ‘moment of inertia and angular velocity'. Angular momentum is a ‘pseudo vector quality and is conserved in an isolated system, and equal to the linear velocity divided by the radial axes per sec.
If the moment of inertia of a body of mass ‘M' about an axis through the centre of mass is I, the moment of inertia about a parallel axis distance ‘h' from the first axis is I + Mh2. If the radius of gyration is ‘k' about the first axis, it is (k2 + h2 ) about the second. The moment of inertia of a uniform solid body about an axis of symmetry is given by the product of the mass and the sum of squares of the other semi-axes, divided by 3, 4, 5 according to whether the body is rectangular, elliptical or ellipsoidal.
The circle is a special case of the ellipse. The Routh's rule works for a circular or elliptical cylinder or elliptical discs it works for all three axes of symmetry. For example, for a circular disk of the radius ‘an' and mass ‘M', the moment of inertia about an axis through the centre of the disc and lying ( a ) perpendicular to the disc, ( b ) in the plane of the disc is
( a ) ¼M( a2 + a2 ) = ½Ma2
( b ) ¼Ma2.
A formula for calculating moments of inertia I:
I = mass x (a2 /3 + n) + b2 /(3 + n ),
Where n and n are the numbers of principal curvatures of the surface that terminates the semiaxes in question and ‘a' and ‘b's' are the lengths of the semiaxes. Thus, if the body is a rectangular parallelepiped, n = n = 0, and
I = - mass x (a2 / 3 + b2 /3).
If the body is a cylinder then, for an axis through its centre, perpendicular to the cylinder axis, n = 0 and n = 1, it substantiates that if,
I = mass x (a2 / 3 + b2 /4).
If ‘I' is desired about the axis of the cylinder, then n= n = 1 and a = b = r ( the cylinder radius) and; I = mass x ( r2 /2 ).
An array of mathematical concepts, which is similar to a determinant but differ from it in not having a numerical value in the ordinary sense of the term is called a matrix. It obeys the same rules of multiplication, addition. Etc. an array of ‘mn' numbers set out in ‘m' rows and ‘n' columns are a matrix of the order of m x n. the separate numbers are usually called elements, such arrays of numbers, tarted as single entities and manipulated by the rules of matrix algebra, are of use whenever simultaneous equations are found, e.g., changing from one set of Cartesian axes to another set inclined the first: Quantum theory, electrical networks. Matrixes are very prominent in the mathematical expression of quantum mechanics.
A mathematical form of quantum mechanics that was developed by Born and Heisenberg and originally simultaneously with but independently of wave mechanics. It is equivalent to wave mechanics, but in it the wave function of wave mechanics is replaced by ‘vectors' in a seemly space ( Hilbert space ) and observable things of the physical world, such as energy, momentum, co-ordinates, etc., is represented by ‘matrices'.
The theory involves the idea that a maturement on a system disturbs, to some extent, the system itself. With large systems this is of no consequence, and the system this is of no classical mechanics. On the atomic scale, however, the results of the order in which the observations are made. T0atd if ‘p' denotes an observation of a component of momentum and ‘q. An observer of the corresponding co-ordinates pq qp. Here ‘p' and ‘q' are not physical quantities but operators. In matrix mechanics and obey te relationship
pq qp = ih/2
where ‘h' is the Planck constant that equals to 6.626 076 x 10-34 j s. The matrix elements are connected with the transition probability between various states of the system.
A quantity with magnitude and direction. It can be represented by a line whose length is propositional to the magnitude and whose direction is that of the vector, or by three components in rectangular co-ordinate system. Their angle between vectors is 90%, that the product and vector product base a similarity to unit vectors such, are to either be equated to being zero or one.
A true vector, or polar vector, involves the displacement or virtual displacement. Polar vectors include velocity, acceleration, force, electric and magnetic strength. Th deigns of their components are reversed on reversing the co-ordinated axes. Their dimensions include length to an odd power.
A Pseudo vector, or axial vector, involves the orientation of an axis in space. The direction is conventionally obtained in a right-handed system by sighting along the axis so that the rotation appears clockwise, Pseudo-vectors includes angular velocity, vector area and magnetic flux density. The signs of their components are unchanged on reversing the co-ordinated axes. Their dimensions include length to an even power.
Polar vectors and axial vectors obey the same laws of the vector analysis
( a ) Vector addition: If two vectors ‘A' and ‘B' are represented in magnitude and direction by the adjacent sides of a parallelogram, the diagonal represents the vector sun ( A + B ) in magnitude and direction, forces, velocity, etc., combine in this way.
( b ) Vector multiplying: There are two ways of multiplying vectors ( I ) the ‘scalar product' of two vectors equals the product of their magnitudes and the co-sine of the angle between them, and is scalar quantity. It is usually written
A • B ( reads as A dot B )
(ii ) The vector product of two vectors: A and B are defined as a pseudo vector of magnitude AB sin , having a direction perpendicular to the plane containing them. The sense of the product along this perpendicular is defined by the rule: If ‘A' is turned toward ‘B' through the smaller angle, this rotation appears of the vector product. A vector product is usually written
A x B ( reads as A cross B ).
Vectors should be distinguished from scalars by printing the symbols in bold italic letters.
A theo1y that seeks to unite the properties of gravitational, electromagnetic, weak, and strong interactions to predict all their characteristics. At present it is not known whether such a theory can be developed, or whether the physical universe is amenable to a single analysis about the current concepts of physics. There are unsolved problems in using the framework of a relativistic quantum field theory to encompass the four elementary particles. It may be that using extended objects, as superstring and super-symmetric theories, but, still, this will enable a future synthesis for achieving obtainability.
A unified quantum field theory of the electromagnetic, weak and strong interactions, in most models, the known interactions are viewed as a low-energy manifestation of a single unified interaction, the unification taking place at energies (Typically 1015 GeV) very much higher than those currently accessible in particle accelerations. One feature of the Grand Unified Theory is that ‘baryon' number and ‘lepton' number would no-longer be absolutely conserved quantum numbers, with the consequences that such processes as ‘proton decay', for example, the decay of a proton into a positron and a 0, p e+ 0 would be expected to be observed. Predicted lifetimes for proton decay are very long, typically 1035 years. Searchers for proton decay are being undertaken by many groups, using large underground detectors, so far without success.
One of the mutual attractions binding the universe of its owing totality, but independent of electromagnetism, strong and weak nuclear forces of interactive bondages is one of gravitation. Newton showed that the external effect of a spherical symmetric body is the same as if the whole mass were concentrated at the centre. Astronomical bodies are roughly spherically symmetric so can be treated as point particles to a very good approximation. On this assumption Newton showed that his law consistent with Kepler's laws? Until recently, all experiments have confirmed the accuracy of the inverse square law and the independence of the law upon the nature of the substances, but in the past few years evidence has been found against both.
The size of a gravitational field at any point is given by the force exerted on unit mass at that point. The field intensity at a distance ‘ ' from a point mass ‘m' is therefore Gm/ 2, and acts toward ‘m'. Gravitational field strength is measured in ‘newtons' per kilogram. The gravitational potential ‘V' at that point is the work done in moving a unit mass from infinity to the point against the field, due to a point mass.
V = Gm d / 2 = Gm / .
V is a scalar measurement in joules per kilogram. The following special cases are also important ( a ) Potential at a point distance from the centre of a hollow homogeneous spherical shell of mass ‘m' and outside the shell:
V = Gm / .
The potential is the same as if the mass of the shell is assumed concentrated at the centre ( b ) At any point inside the spherical shell the potential is equal to its value at the surface:
V = Gm / r
Where ‘r' is the radius of the shell. Thus, there is no resultant force acting at any point inside the shell, since no potential difference acts between any two points, then ( c ) Potential at a point distance ‘ ' from the centre of a homogeneous solid sphere and outside the spheres the same as that for a shell:
V = Gm /
( d ) At a point inside the sphere, of radius ‘r'.
V = Gm( 3r2 2 ) /2r3.
The essential property of gravitation is that it causes a change in motion, in particular the acceleration of free fall ( g ) in the earth's gravitational field. According to the general theory of relativity, gravitational fields change the geometry of space-timer, causing it to become curved. It is this curvature that is geometrically responsible for an inseparability of the continuum of ‘space-time' and its forbearing product is to a vicinities mass, entrapped by the universality of spacetime, that in ways described by the pressures of their matter, that controls the natural motions of fording bodies. General relativity may thus be considered as a theory of gravitation, differences between it and Newtonian gravitation only appearing when the gravitational fields become very strong, as with ‘black-holes' and ‘neutron stars', or when very accurate measurements can be made.
Another binding characteristic embodied universally is the interaction between elementary particle arising as a consequence of their associated electric and magnetic fields. The electrostatic force between charged particles is an example. This force may be described in terms of the exchange of virtual photons, because of the uncertainty principle it is possible for the law of conservation of mass and energy to be broken by an amount E providing this only occurring for a time such that:
E t h/4 .
This makes it possible for particles to be created for short periods of time where their creation would normally violate conservation laws of energy. These particles are called ‘virtual particles'. For example, in a complete vacuum -which no "real" particle's exist, as pairs of virtual electrons and positron are continuously forming and rapidly disappearing ( in less than 10-23 seconds ). Other conservation laws such as those applying to angular momentum, isospin, etc., cannot be violated even for short periods of time.
Because its strength lies between strong and weak nuclear interactions, the exchanging electromagnetic interaction of particles decaying by electromagnetic interaction, do so with a lifetime shorter than those decaying by weak interaction, but longer than those decaying under the influence of strong interaction. For example, of electromagnetic decay is:
0 + .
This decay process, with a mean lifetime covering 8.4 x 10-17, may be understood as the annihilation of the quark and the antiquark, making up the 0, into a pair of photons. The quantum numbers having to be conserved in electromagnetic interactions are, angular momentum, charge, baryon number, Isospin quantum number I3, strangeness, charm, parity and charge conjugation parity are unduly influenced.
Quanta's electrodynamic descriptions of the photon-mediated electromagnetic interactions have been verified over a great range of distances and have led to highly accurate predictions. Quantum electrodynamics are a ‘gauge theory; as in quantum electrodynamics, the electromagnetic force can be derived by requiring that the equation describing the motion of a charged particle remain unchanged in the course of local symmetry operations. Specifically, if the phase of the wave function, by which charged particle is described is alterable independently, at which point in space, quantum electrodynamics require that the electromagnetic interaction and its mediating photon exist in order to maintain symmetry.
A kind of interaction between elementary particles that is weaker than the strong interaction force by a factor of about 1012. When strong interactions can occur in reactions involving elementary particles, the weak interactions are usually unobserved. However, sometimes strong and electromagnetic interactions are prevented because they would violate the conservation of some quantum number, e.g., strangeness, that has to be conserved in such reactions. When this happens, weak interactions may still occur.
The weak interaction operates over an extremely short range ( about 2 x 10-18 m ) it is mediated by the exchange of a very heavy particle ( a gauge boson ) that may be the charged W+ or W particle ( mass about 80 GeV / c2 ) or the neutral Z0 particles ( mass about 91 GeV / c2 ). The gauge bosons that mediate the weak interactions are analogous to the photon that mediates the electromagnetic interaction. Weak interactions mediated by W particles involve a change in the charge and hence the identity of the reacting particle. The neutral Z0 does not lead to such a change in identity. Both sorts of weak interaction can violate parity.
Most of the long-lived elementary particles decay as a result of weak interactions. For example, the kaon decay K+ ÎĽ+ vÎĽ may be thought of for being due to the annihilation of the u quark and antiquark in the K+ to produce a virtual W+ boson, which then converts into a positive muon and a neutrino. This decay action or and electromagnetic interaction because strangeness is not conserved, Beta decay is the most common example of weak interaction decay. Because it is so weak, particles that can only decay by weak interactions do so relatively slowly, i.e., they have relatively long lifetimes. Other examples of weak interactions include the scattering of the neutrino by other particles and certain very small effects on electrons within the atom.
Understanding of weak interactions is based on the electroweak theory, in which it is proposed that the weak and electromagnetic interactions are different manifestations of a single underlying force, known as the electroweak force. Many of the predictions of the theory have been confirmed experimentally.
A gauge theory, also called quantum flavour dynamics, that provides a unified description of both the electromagnetic and weak interactions. In the Glashow-Weinberg-Salam theory, also known as the standard model, electroweak interactions arise from the exchange of photons and of massive charged W+ and neutral Z0 bosons of spin 1 between quarks and leptons. The extremely massive charged particle, symbol W+ or W , that mediates certain types of weak interaction. The neutral Z-particle, or Z boson, symbol Z0, mediates the other types. Both are gauge bosons. The W- and Z-particles were first detected at CERN ( 1983 ) by studying collisions between protons and antiprotons with total energy 540 GeV in centre-of-mass co-ordinates. The rest masses were determined as about 80 GeV / c2 and 91 GeV / c2 for the W- and Z-particles, respectively, as had been predicted by the electroweak theory.
The interaction strengths of the gauge bosons to quarks and leptons and the masses of the W and Z bosons themselves are predicted by the theory, the Weinberg Angle W, which must be determined by experiment. The Glashow-Weinberg-Salam theory successfully describes all existing data from a wide variety of electroweak processes, such as neutrino-nucleon, neutrino-electron and electron-nucleon scattering. A major success of the model was the direct observation in 1983-84 of the W± and Z0 bosons with the predicted masses of 80 and 91 GeV / c2 in high energy proton-antiproton interactions. The decay modes of the W± and Z0 bosons have been studied in very high pp and e+ e interactions and found to be in good agreement with the Standard model.
The six known types ( or flavours ) of quarks and the six known leptons are grouped into three separate generations of particles as follows:
1st generation: e ve u d
2nd generation: ÎĽ vÎĽ c s
3rd generation: v t b
The second and third generations are essentially copies of the first generation, which contains the electron and the ‘up' and ‘down' quarks making up the proton and neutron, but involve particles of higher mass. Communication between the different generations occurs only in the quark sector and only for interactions involving W± bosons. Studies of Z0 bosons production in very high energy electron-positron interactions has shown that no further generations of quarks and leptons can exist in nature ( an arbitrary number of generations is a priori possible within the standard model ) provided only that any new neutrinos are approximately massless.
The Glashow-Weinberg-Salam model also predicts the existence of a heavy spin 0 particle, not yet observed experimentally, known as the Higgs boson. The spontaneous symmetry-breaking mechanism used to generate non-zero masses for W± and Z bosons in the electroweak theory, whereby the mechanism postulates the existence of two new complex fields, ( ÎĽ) = 1 + I 2 and ( ÎĽ) = 1 + I 2, which are functional distributors to ÎĽ = , y, z and t, and form a doublet ( , ) this doublet of complex fields transforms in the same way as leptons and quarks under electroweak gauge transformations. Such gauge transformations rotate 1, 2, 1, 2 into each other without changing the nature of the physical science.
The vacuum does not share the symmetry of the fields ( , ) and a spontaneous breaking of the vacuum symmetry occurs via the Higgs mechanism. Consequently, the fields and have non-zero values in the vacuum. A particular orientation of 1, 2, 1, 2 may be chosen so that all the components of ( 1 ). This component responds to electroweak fields in a way that is analogous to the response of a plasma to electromagnetic fields. Plasmas oscillate in the presence of electromagnetic waves, however, electromagnetic waves can only propagate at a frequency above the plasma frequency p2 given by the expression:
p2 = ne2 / m
Where ‘n' is the charge number density, ‘e' the electrons charge. ‘m' the electrons mass and ‘ ' is the Permittivity of the plasma. In quantum field theory, this minimum frequency for electromagnetic waves may be thought of as a minimum energy for the existence of a quantum of the electromagnetic field ( a photon ) within the plasma. This minimum energy or mass for the photon, which becomes a field quantum of a finite ranged force. Thus, in its plasma, photons acquire a mass and the electromagnetic interaction has a finite range.
The vacuum field 1 responds to weak fields by giving a mass and finite range to the W± and Z bosons, however, the electromagnetic field is unaffected by the presence of 1 so the photon remains massless. The mass acquired by the weak interaction bosons is proportional to the vacuum of 1 and to the weak charge strength. A quantum of the field 1 is an electrically neutral particle called the Higgs boson. It interacts with all massive particles with a coupling that is proportional to their mass. The standard model does not predict the mass of the Higgs boson, but it is known that it cannot be too heavy ( not much more than about 1000 proton masses ). Since this would lead to complicated self-interaction, such self-interaction is not believed to be present, because the theory does not account for them, but nevertheless successfully predicts the masses of the W± and Z bosons. These of the particle results from the so-called spontaneous symmetry breaking mechanisms, and used to generate non-zero masses for the W± and Z0 bosons and is presumably too massive to have been produced in existing particle accelerators.
We now turn our attentions belonging to the third binding force of unity, in, and of itself, its name implicates a physicality in the belonging nature that holds itself the binding of strong interactions that portray of its owing universality, simply because its universal. Interactions between elementary particles involving the strong interaction force. This force is about one hundred times greater than the electromagnetic force between charged elementary particles. However, it is a short range force -it is only important for particles separated by a distance of less than abut 10-15- and is the force that holds protons and neutrons together in atomic nuclei for ‘soft' interactions between hadrons, where relatively small transfers of momentum are involved, the strong interactions may be described in terms of the exchange of virtual hadrons, just as electromagnetic interactions between charged particles may be described in terms of the exchange of virtual photons. At a more fundamental level, the strong interaction arises as the result of the exchange of gluons between quarks and/and antiquarks as described by quantum chromodynamics.
In the hadron exchange picture, any hadron can act as the exchanged particle provided certain quantum numbers are conserved. These quantum numbers are the total angular momentum, charge, baryon number, Isospin ( both I and I3 ), strangeness, parity, charge conjugation parity, and G-parity. Strong interactions are investigated experimentally by observing how beams of high-energy hadrons are scattered when they collide with other hadrons. Two hadrons colliding at high energy will only remain near to each other for a very short time. However, during the collision they may come sufficiently close to each other for a strong interaction to occur by the exchanger of a virtual particle. As a result of this interaction, the two colliding particles will be deflected ( scattered ) from their original paths. I the virtual hadron exchanged during the interaction carries some quantum numbers from one particle to the other, the particles found after the collision may differ from those before it. Sometimes the number of particles is increased in a collision.
In hadron-hadron interactions, the number of hadrons produced increases approximately logarithmically with the total centre of mass energy, reaching about 50 particles for proton-antiproton collisions at 900 GeV, for example in some of these collisions, two oppositely-directed collimated ‘jets' of hadrons are produced, which are interpreted as due to an underlying interaction involving the exchange of an energetic gluon between, for example, a quark from the proton and an antiquark from the antiproton. The scattered quark and antiquark cannot exist as free particles, but instead ‘fragments' into a large number of hadrons ( mostly pions and kaon ) travelling approximately along the original quark or antiquark direction. This results in collimated jets of hadrons that can be detected experimentally. Studies of this and other similar processes are in good agreement with quantum chromodynamics predictions.
The interaction between elementary particles arising as a consequence of their associated electric and magnetic fields. The electrostatic force between charged particles is an example. This force may be described in terms of the exchange of virtual photons, because its strength lies between strong and weak interactions, particles decaying by electromagnetic interaction do so with a lifetime shorter than those decaying by weak interaction, but longer than those decaying by strong interaction. An example of electromagnetic decay is:
0 + .
This decay process ( mean lifetime 8.4 x 10-17 seconds ) may be understood as the ‘annihilation' of the quark and the antiquark making up the 0, into a pair of photons. The following quantum numbers have to be conserved in electromagnetic interactions: Angular momentum, charm, baryon number, Isospin quantum number I3, strangeness, charm, parity, and charge conjugation parity.
A particle that, as far as is known, is not composed of other simpler particles. Elementary particles represent the most basic constituents of matter and are also the carriers of the fundamental forces between particles, namely the electromagnetic, weak, strong, and gravitational forces. The known elementary particles can be grouped into three classes, leptons, quarks, and gauge bosons, hadrons, such strongly interacting particles as the proton and neutron, which are bound states of quarks and/or antiquarks, are also sometimes called elementary particles.
Leptons undergo electromagnetic and weak interactions, but not strong interactions. Six leptons are known, the negatively charged electron, muon, and tauons plus three associates neutrinos: Ve, vÎĽ and v . The electron is a stable particle but the muon and tau leptons decay through the weak interactions with lifetimes of about 10-8 and 10-13 seconds. Neutrinos are stable neutral leptons, which interact only through the weak interaction.
Corresponding to the leptons are six quarks, namely the up ( u ), charm ( c ) and top ( t ) quarks with electric charge equal to + that of the proton and the down ( d ), strange ( s ), and bottom ( b ) quarks of charge - the proton charge. Quarks have not been observed experimentally as free particles, but reveal their existence only indirectly in high-energy scattering experiments and through patterns observed in the properties of hadrons. They are believed to be permanently confined within hadrons, either in baryons, half integer spin hadrons containing three quarks, or in mesons, integer spin hadrons containing a quark and an antiquark. The proton, for example, is a baryon containing two ‘up' quarks and an ‘anti-down ( d ) quark, while the + is a positively charged meson containing an up quark and an anti-down ( d ) antiquark. The only hadron that is stable as a free particle is the proton. The neutron is unstable when free. Within a nucleus, proton and neutrons are generally both stable but either particle may bear into a transformation into the other, by ‘Beta Decay or Capture'.
Interactions between quarks and leptons are mediated by the exchange of particles known as ‘gauge bosons', specifically the photon for electromagnetic interactions, W± and Z0 bosons for the weak interaction, and eight massless gluons, in the case of the strong integrations.
A class of eigenvalue problems in physics that take the form
= ,
Where ‘ ' is some mathematical operation ( multiplication by a number, differentiation, etc. ) on a function ‘ ', which is called the ‘eigenfunction'. ‘ ' is called the eigenvalue, which in a physical system will be identified with an observable quantity analogous to the amplitude of a wave that appears in the equations of wave mechanics, particularly the Schrödinger wave equation, the most generally accepted interpretation is that | |2dV, representing the probability that a particle is located within the volume element dV, mass in which case a particle of mass ‘m' moving with a velocity ‘v' will, under suitable experimental conditions exhibit the characteristics of a wave of wave length , given by the equation = h/mv, where ‘h' is the Planck constant that equals to 6.626 076 x 10-34 J s.? This equation is the basis of wave mechanics. However, a set of weaves that represent the behaviour, under appropriate conditions, of a particle, e.g., its diffraction by a crystal lattice. The wave length is given by the "de Broglie equation." They are sometimes regarded as waves of probability, since the square of their amplitude at a given point represents the probability of finding the particle in unit volume at that point. These waves were predicted by Broglie in 1924 and in 1927 in the Davisson-Germer experiment.
Eigenvalue problems are ubiquitous in classical physics and occur whenever the mathematical description of a physical system yields a series of coupled differential equations. For example, the collective motion of a large number of interacting oscillators may be described by a set of coupled differential educations. Each differential equation describes the motion of one of the oscillators in terms of the position of all the others. A ‘harmonic' solution may be sought, in which each displacement is assumed to have a ‘simple harmonic motion' in time. The differential equations then reduce to 3N linear equations with 3N unknowns, where ‘N' is the number of individual oscillators, each with three degrees of freedom. The whole problem is now easily recast as a ‘matrix education' of the form:
M = 2
Where ‘M' is an N x N matrix called the ‘dynamical matrix', and is an N x 1 ‘a column matrix, and 2 is the square of an angular frequency of the harmonic solution. The problem is now an eigenvalue problem with eigenfunctions ‘ ' which is the normal mode of the system, with corresponding eigenvalues 2. As ‘ ' can be expressed as a column vector, is a vector in some N-dimensional vector space. For this reason, is often called an eigenvector.
When the collection of oscillators is a complicated three-dimensional molecule, the casting of the problem into normal modes is an effective simplification of the system. The symmetry principles of ‘group theory' can then be applied, which classify normal modes according to their ‘ ' eigenvalues ( frequencies ). This kind of analysis requires an appreciation of the symmetry properties of the molecule. The sets of operations ( rotations, inversions, etc. ) that leave the molecule invariant make up the ‘point group' of that molecule. Normal modes sharing the same ‘ ' eigenvalues are said to correspond to the ‘irreducible representations' of the molecule's point group. It is among these irreducible representations that one will find the infrared absorption spectrum for the vibrational normal modes of the molecule.
Eigenvalue problems play a particularly important role in quantum mechanics. In quantum mechanics, physically observable ( location, momentum, energy, etc. ) are represented by operations ( differentiation with respect to a variable, multiplication by a variable ), which act on wave functions. Wave functions differ from classical waves in that they carry no energy. For classical waves, the square modulus of its amplitude measure its energy. For a wave function, the square modulus of its amplitude ( at a location ) represent not energy but probability, i.e., the probability that a particle -a localized packet of energy will be observed if a detector is placed at that location. The wave function therefore describes the distribution of possible locations of the particle and is perceptible only after many location detection events have occurred. A measurement of position on a quantum particle may be written symbolically as:
X ( ) = ( )
Where ( ) is said to be an eigenvector of the location operator and ‘ ' is the eigenvalue, which represents the location. Each ( ) represents amplitude at the location , | ( ) |2 is the probability that the particle will be located in an infinitesimal volume at that location. The wave function describing the distribution of all possible locations for the particle is the linear super-position of all ( ) for 0 that occur, its principle states that each stress is accompanied by the same strains whether it acts alone or in conjunction with others, it is true so long as the total stress does not exceed the limit of proportionality. Also, in vibrations and wave motion the principle asserts that one set of vibrations or waves are unaffected by the presence of another set. For example, two sets of ripples on water will pass through one another without mutual interactions so that, at a particular instant, the resultant disturbance at any point traversed by both sets of waves is the sum of the two component disturbances.
The eigenvalue problem in quantum mechanics therefore represents the act of measurement. Eigenvectors of an observable presentation were the possible states ( Position, in the case of ) that the quantum system can have. Stationary states of a quantum non-demolition attribute of a quantum system, such as position and momentum, are related by the Heisenberg Uncertainty Principle, which states that the product of the uncertainty of the measured value of a component of momentum ( p ) and the uncertainty in the corresponding co-ordinates of position ( ) is of the same order of magnitude as the Planck constant. Attributes related in this way are called ‘conjugate' attributes. Thus, while an accurate measurement of position is possible, as a result of the uncertainty principle it produces a large momentum spread. Subsequent measurements of the position acquire a spread themselves, which makes the continuous monitoring of the position impossible.
The eigenvalues are the values that observables take on within these quantum states. As in classical mechanics, eigenvalue problems in quantum mechanics may take differential or matrix forms. Both forms have been shown to be equivalent. The differential form of quantum mechanics is called ‘wave mechanics' ( Schrödinger ), where the operators are differential operators or multiplications by variables. Eigenfunctions in wave mechanics are wave functions corresponding to stationary wave states that satisfy some set of boundary conditions. The matrix form of quantum mechanics is often called matrix mechanics ( Born and Heisenberg ). Matrix acting on eigenvectors represents the operators.
The relationship between matrix and wave mechanics is very similar to the relationship between matrix and differential forms of eigenvalue problems in classical mechanics. The wave functions representing stationary states are really normal modes of the quantum wave. These normal modes may be thought of as vectors that span a vector space, which have a matrix representation.
Once, again, the Heisenberg uncertainty relation, or indeterminacy principle of ‘quantum mechanics' that associate the physical properties of particles into pairs such that both together cannot be measured to within more than a certain degree of accuracy. If ‘A' and ‘V' form such a pair is called a conjugate pair, then: A V > k, where ‘k' is a constant and A and V are a variance in the experimental values for the attributes ‘A' and ‘V'. The best-known instance of the equation relates the position and momentum of an electron: p > h, where ‘h' is the Planck constant. This is the Heisenberg uncertainty principle. Still, the usual value given for Planck's constant is 6.6 x 10-27 ergs sec. Since Planck's constant is not zero, mathematical analysis reveals the following: The ‘spread', or uncertainty, in position times the ‘spread', or uncertainty of momentum is greater than, or possibly equal to, the value of the constant or, or accurately, Planck's constant divided by 2 , if we choose to know momentum exactly, then us knowing nothing about position, and vice versa.
The presence of Plank's constant calls that we approach quantum physics a situation in which the mathematical theory does not allow precise prediction of, or exist in exact correspondences with, the physical reality. If nature did not insist on making changes or transitions in precise chunks of Planck's quantum of action, or in multiples of these chunks, there would be no crisis. But whether it is of our own determinacy, such that a cancerous growth in the body of an otherwise perfect knowledge of the physical world or the grounds for believing, in principle at least, in human freedom, one thing appears certain -it is an indelible feature of our understanding of nature.
In order too further explain how fundamental the quantum of action is to our present understanding of the life of nature, let us attempt to do what quantum physics says we cannot do and visualize its role in the simplest of all atoms -the hydrogen atom. It can be thought that standing at the centre of the Sky Dome at roughly where the pitcher's mound is. Place a grain of salt on the mound, and picture a speck of dust moving furiously around the orbital's outskirts of the Sky Dome's fulfilling circle, around which the grain of salt remains referential of the topic. This represents, roughly, the relative size of the nucleus and the distance between electron and nucleus inside the hydrogen atom when imaged in its particle aspect.
In quantum physics, however, the hydrogen atom cannot be visualized with such macro-level analogies. The orbit of the electron is not a circle, in which a planet-like object moves, and each orbit is described in terms of a probability distribution for finding the electron in an average position corresponding to each orbit as opposed to an actual position. Without observation or measurement, the electron could be in some sense anywhere or everywhere within the probability distribution, also, the space between probability distributions is not empty, it is infused with energetic vibrations capable of manifesting itself as the befitting quanta.
The energy levels manifest at certain distances because the transition between orbits occurs in terms of precise units of Planck's constant. If any attentive effects to comply with or measure where the particle-like aspect of the electron is, in that the existence of Planck's constant will always prevent us from knowing precisely all the properties of that electron that we might presume to be they're in the absence of measurement. Also, the two-split experiment, as our presence as observers and what we choose to measure or observe are inextricably linked to the results obtained. Since all complex molecules are built from simpler atoms, what is to be done, is that liken to the hydrogen atom, of which case applies generally to all material substances.
The grounds for objecting to quantum theory, the lack of a one-to-one correspondence between every element of the physical theory and the physical reality it describes, may seem justifiable and reasonable in strict scientific terms. After all, the completeness of all previous physical theories was measured against that criterion with enormous success. Since it was this success that gave physicists the reputation of being able to disclose physical reality with magnificent exactitude, perhaps a more complex quantum theory will emerge by continuing to insist on this requirement.
All indications are, however, that no future theory can circumvent quantum indeterminacy, and the success of quantum theory in co-ordinating our experience with nature is eloquent testimony to this conclusion. As Bohr realized, the fact that we live in a quantum universe in which the quantum of action is a given or an unavoidable reality requires a very different criterion for determining the completeness of physical theory. The new measure for a complete physical theory is that it unambiguously confirms our ability to co-ordinate more experience with physical reality.
If a theory does so and continues to do so, which is certainly the case with quantum physics, then the theory must be deemed complete. Quantum physics not only works exceedingly well, it is, in these terms, the most accurate physical theory that has ever existed. When we consider that this physics allows us to predict and measure quantities like the magnetic moment of electrons to the fifteenth decimal place, we realize that accuracy perse is not the real issue. The real issue, as Bohr rightly intuited, is that this complete physical theory effectively undermines the privileged relationships in classical physics between physical theory and physical reality. Another measure of success in physical theory is also met by quantum physics -eloquence and simplicity. The quantum recipe for computing probabilities given by the wave function is straightforward and can be successfully employed by any undergraduate physics student. Take the square of the wave amplitude and compute the probability of what can be measured or observed with a certain value. Yet there is a profound difference between the recipe for calculating quantum probabilities and the recipe for calculating probabilities in classical physics.
In quantum physics, one calculates the probability of an event that can happen in alternative ways by adding the wave functions, and then taking the square of the amplitude. In the two-split experiment, for example, the electron is described by one wave function if it goes through one slit and by another wave function if it goes through the other slit. In order to compute the probability of where the electron is going to end on the screen, we add the two wave functions, compute the obsolete value of their sum, and square it. Although the recipe in classical probability theory seems similar, it is quite different. In classical physics, one would simply add the probabilities of the two alternative ways and let it go at that. That classical procedure does not work here because we are not dealing with classical atoms in quantum physics additional terms arise when the wave functions are added, and the probability is computed in a process known as the ‘superposition principle'. That the superposition principle can be illustrated with an analogy from simple mathematics. Add two numbers and then take the square of their sum, as opposed to just adding the squares of the two numbers. Obviously, ( 2 + 3 )2 is not equal to 22 + 32. The former is 25, and the latter are 13. In the language of quantum probability theory:
| 1 + 2 |2 | 1 |2 + | 2 |2
Where 1 and 2 are the individual wave functions on the left-hand side, the superposition principle results in extra terms that cannot be found on the right-handed side the left-hand faction of the above relation is the way a quantum physicists would compute probabilities and the right-hand side is the classical analogue. In quantum theory, the right-hand side is realized when we know, for example, which slit through which the electron went. Heisenberg was among the first to compute what would happen in an instance like this. The extra superposition terms contained in the left-hand side of the above relation would not be there, and the peculiar wave-like interference pattern would disappear. The observed pattern on the final screen would, therefore, be what one would expect if electrons were behaving like bullets, and the final probability would be the sum of the individual probabilities. But when we know which slit the electron went through, this interaction with the system causes the interference pattern to disappear.
In order to give a full account of quantum recipes for computing probabilities, one g=has to examine what would happen in events that are compounded. Compound events are events that can be broken down into a series of steps, or events that consist of a number of things happening independently the recipe here calls for multiplying the individual wave functions, and then following the usual quantum recipe of taking the square of the amplitude.
The quantum recipe is | 1 • 2 |2, and, in this case, it would be the same if we multiplied the individual probabilities, as one would in classical theory. Thus the recipes of computing results in quantum theory and classical physics can be totally different from quantum superposition effects are completely non-classical, and there is no mathematical justification to why the quantum recipes work. What justifies the use of quantum probability theory is the same thing that justifies the use of quantum physics -it has allowed us in countless experiments to vastly extend our ability to co-ordinate experience with nature.
The view of probability in the nineteenth century was greatly conditioned and reinforced by classical assumptions about the relationships between physical theory and physical reality. In this century, physicists developed sophisticated statistics to deal with large ensembles of particles before the actual character of these particles was understood. Classical statistics, developed primarily by James C. Maxwell and Ludwig Boltzmann, was used to account for the behaviour of a molecule in a gas and to predict the average speed of a gas molecule in terms of the temperature of the gas.
The presumption was that the statistical average were workable approximations those subsequent physical theories, or better experimental techniques, would disclose with precision and certainty. Since nothing was known about quantum systems, and since quantum indeterminacy is small when dealing with macro-level effects, this presumption was quite reasonable. We know, however, that quantum mechanical effects are present in the behaviour of gasses and that the choice to ignore them is merely a matter of convincing in getting workable or practical resulted. It is, therefore, no longer possible to assume that the statistical averages are merely higher-level approximations for a more exact description.
Perhaps the best-known defence of the classical conception of the relationship between physical theory ands physical reality is the celebrated animal introduced by the Austrian physicist Erin Schrödinger ( 1887-1961 ) in 1935, in a ‘thought experiment' showing the strange nature of the world of quantum mechanics. The cat is thought of as locked in a box with a capsule of cyanide, which will break if a Geiger counter triggers. This will happen if an atom in a radioactive substance in the box decays, and there is a chance of 50% of such an event within an hour. Otherwise, the cat is alive. The problem is that the system is in an indeterminate state. The wave function of the entire system is a ‘superposition' of states, fully described by the probabilities of events occurring when it is eventually measured, and therefore ‘contains equal parts of the living and dead cat'. When we look and see we will find either a breathing cat or a dead cat, but if it is only as we look that the wave packet collapses, quantum mechanic forces us to say that before we looked it was not true that the cat was dead and not true that it was alive, the thought experiment makes vivid the difficulty of conceiving of quantum indetermincies when these are translated to the familiar world of everyday objects.
The "electron," is a stable elementary particle having a negative charge, e, equal to:
1.602 189 25 x 10-19 C
and a rest mass, m0 equal to;
9.109 389 7 x 10-31 kg
equivalent to 0.511 0034 MeV / c2
It has a spin of ½ and obeys Fermi-Dirac Statistics. As it does not have strong interactions, it is classified as a ‘lepton'.
The discovery of the electron was reported in 1897 by Sir J. J. Thomson, following his work on the rays from the cold cathode of a gas-discharge tube, it was soon established that particles with the same charge and mass were obtained from numerous substances by the ‘photoelectric effect', ‘thermionic emission' and ‘beta decay'. Thus, the electron was found to be part of all atoms, molecules, and crystals.
Free electrons are studied in a vacuum or a gas at low pressure, whereby beams are emitted from hot filaments or cold cathodes and are subject to ‘focussing', so that the particles in which an electron beam in, for example, a cathode-ray tube, where in principal methods as ( I ) Electrostatic focussing, the beam is made to converge by the action of electrostatic fields between two or more electrodes at different potentials. The electrodes are commonly cylinders coaxial with the electron tube, and the whole assembly forms an electrostatic electron lens. The focussing effect is usually controlled by varying the potential of one of the electrodes, called the focussing electrode. ( ii ) Electromagnetic focussing, by way that the beam is made to converge by the action of a magnetic field that is produced by the passage of direct current, through a focussing coil. The latter are commonly a coil of short axial length mounted so as to surround the electron tube and to be coaxial with it.
The force FE on an electron or magnetic field of strength E is given by FE = Ee and is in the direction of the field. On moving through a potential difference V, the electron acquires a kinetic energy eV, hence it is possible to obtain beams of electrons of accurately known kinetic energy. In a magnetic field of magnetic flux density ‘B', an electron with speed ‘v' is subject to a force, FB = Bev sin , where is the angle between ‘B' and ‘v'. This force acts at right angles to the plane containing ‘B' and ‘v'.
The mass of any particle increases with speed according to the theory of relativity. If an electron is accelerated from rest through 5kV, the mass is 1% greater than it is at rest. Thus, accountably, must be taken of relativity for calculations on electrons with quite moderate energies.
According to ‘wave mechanics' a particle with momentum ‘mv' exhibits' diffraction and interference phenomena, similar to a wave with wavelength = h/mv, where ‘h' is the Planck constant. For electrons accelerated through a few hundred volts, this gives wavelengths rather less than typical interatomic spacing in crystals. Hence, a crystal can act as a diffraction grating for electron beams.
Owing to the fact that electrons are associated with a wavelength given by = h/mv, where ‘h' is the Planck constant and ( mv ) the momentum of the electron, a beam of electrons suffers diffraction in its passage through crystalline material, similar to that experienced by a beam of X-rays. The diffraction pattern depends on the spacing of the crystal planes, and the phenomenon can be employed to investigate the structure of surface and other films, and under suitable conditions exhibit the characteristics of a wave of the wavelength given by the equation = h/mv, which is the basis of wave mechanics. A set of waves that represent the behaviour, under appropriate conditions, of a particle, e.g., its diffraction by a crystal lattice, that is given the "de Broglie equation." They are sometimes regarded as waves of probability, since the square of their amplitude at a given point represents the probability of finding the particle in unit volume at that point.
The first experiment to demonstrate ‘electron diffraction', and hence the wavelike nature of particles. A narrow pencil of electrons from a hot filament cathode was projected ‘in vacua' onto a nickel crystal. The experiment showed the existence of a definite diffracted beam at one particular angle, which depended on the velocity of the electrons, assuming this to be the Bragg angle, stating that the structure of a crystal can be determined from a set of interference patterns found at various angles from the different crystal faces, least of mention, the wavelength of the electrons was calculated and found to be in agreement with the "de Broglie equation."
At kinetic energies less than a few electro-volts, electrons undergo elastic collision with atoms and molecules, simply because of the large ratio of the masses and the conservation of momentum, only an extremely small transfer of kinetic energy occurs. Thus, the electrons are deflected but not slowed down appreciatively. At slightly higher energies collisions are inelastic. Molecules may be dissociated, and atoms and molecules may be excited or ionized. Thus it is the least energy that causes an ionization
A A+ + e
Where the ION and the electron are far enough apart for their electrostatic interaction to be negligible and no extra kinetic energy removed is that in the outermost orbit, i.e., the level strongly bound electrons. It is also possible to consider removal of electrons from inner orbits, in which their binding energy is greater. As an excited particle or recombining, ions emit electromagnetic radiation mostly in the visible or ultraviolet.
For electron energies of the order of several GeV upwards, X-rays are generated. Electrons of high kinetic energy travel considerable distances through matter, leaving a trail of positive ions and free electrons. The energy is mostly lost in small increments ( about 30 eV ) with only an occasional major interaction causing X-ray emissions. The range increases at higher energies.
The positron -the antiparticle of the electron, I e., an elementary particle with electron mass and positive charge equal to that of the electron. According to the relativistic wave mechanics of Dirac, space contains a continuum of electrons in states of negative energy. These states are normally unobservable, but if sufficient energy can be given, an electron may be raised into a state of positive energy and suggested itself observably. The vacant state of negativity behaves as a positive particle of positive energy, which is observed as a positron.
The simultaneous formation of a positron and an electron from a photon is called ‘pair production', and occurs when the annihilation of gamma-ray photons with an energy of 1.02 MeV passes close to an atomic nucleus, whereby the interaction between the particle and its antiparticle disappear and photons or other elementary particles or antiparticles are so created, as accorded to energy and momentum conservation.
At low energies, an electron and a positron annihilate to produce electromagnetic radiation. Usually the particles have little kinetic energy or momentum in the laboratory system before interaction, hence the total energy of the radiation is nearly 2m0c2, where m0 is the rest mass of an electron. In nearly all cases two photons are generated. Each of 0.511 MeV, in almost exactly opposite directions to conserve momentum. Occasionally, three photons are emitted all in the same plane. Electron-positron annihilation at high energies has been extensively studied in particle accelerators. Generally the annihilation results in the production of a quark, and an antiquark, fort example, e+ e ÎĽ+ ÎĽ or a charged lepton plus an antilepton ( e+e ÎĽ+ÎĽ ). The quarks and antiquarks do not appear as free particles but convert into several hadrons, which can be detected experimentally. As the energy available in the electron-positron interaction increases, quarks and leptons of progressively larger rest mass can be produced. In addition, striking resonances are present, which appear as large increases in the rate at which annihilations occur at particular energies. The I / PSI particle and similar resonances containing an antiquark are produced at an energy of about 3 GeV, for example, giving rise to abundant production of charmed hadrons. Bottom ( b ) quark production occurs at greater energies than about 10 GeV. A resonance at an energy of about 90 GeV, due to the production of the Z0 gauge boson involved in weak interaction is currently under intensive study at the LEP and SLC e+ e colliders. Colliders are the machines for increasing the kinetic energy of charged particles or ions, such as protons or electrons, by accelerating them in an electric field. A magnetic field is used to maintain the particles in the desired direction. The particle can travel in a straight, spiral, or circular paths. At present, the highest energies are obtained in the proton synchrotron.
The Super Proton Synchrotron at CERN ( Geneva ) accelerates protons to 450 GeV. It can also cause proton-antiproton collisions with total kinetic energy, in centre-of-mass co-ordinates of 620 GeV. In the USA the Fermi National Acceleration Laboratory proton synchrotron gives protons and antiprotons of 800 GeV, permitting collisions with total kinetic energy of 1600 GeV. The Large Electron Positron ( LEP ) system at CERN accelerates particles to 60 GeV.
All the aforementioned devices are designed to produce collisions between particles travelling in opposite directions. This gives effectively very much higher energies available for interaction than our possible targets. High-energy nuclear reaction occurs when the particles, either moving in a stationary target collide. The particles created in these reactions are detected by sensitive equipment close to the collision site. New particles, including the tauon, W, and Z particles and requiring enormous energies for their creation, have been detected and their properties determined.
While, still, a ‘nucleon' and ‘anti-nucleon' annihilating at low energy, produce about half a dozen pions, which may be neutral or charged. By definition, mesons are both hadrons and bosons, justly as the pion and kaon are mesons. Mesons have a substructure composed of a quark and an antiquark bound together by the exchange of particles known as gluons.
The conjugate particle or antiparticle that corresponds with another particle of identical mass and spin, but has such quantum numbers as charge ( Q ), baryon number ( B ), strangeness ( S ), charms ( C ), and Isospin ( I3 ) of equal magnitude but opposite sign. Examples of a particle and its antiparticle include the electron and positron, proton and antiproton, the positive and negatively charged pions, and the ‘up' quark and ‘up' antiquark. The antiparticle corresponding to a particle with the symbol ‘a' is usually denoted ‘ '. When a particle and its antiparticle are identical, as with the photon and neutral pion, this is called a ‘self-conjugate particle'.
The critical potential to excitation energy required to change am atom or molecule from one quantum state to another of higher energy, is equal to the difference in energy of the states and is usually the difference in energy between the ground state of the atom and a specified excited state. Which the state of a system, such as an atom or molecule, when it has a higher energy than its ground state.
The ground state contributes the state of a system with the lowest energy. An isolated body will remain indefinitely in it, such that it is possible for a system to have possession of two or more ground states, of equal energy but with different sets of quantum numbers. In the case of atomic hydrogen there are two states for which the quantum numbers n, I, and m are 1, 0, and 0 respectively, while the spin may be + ½ with respect to a defined direction. An allowed wave function of an electron in an atom obtained by a solution of the "Schrödinger wave equation" in which a hydrogen atom, for example, the electron moves in the electrostatic field of the nucleus and its potential energy is e2 / r, where ‘e' is the electron charge and ‘r' its distance from the nucleus. A precise orbit cannot be considered as in Bohr's theory of the atom, but the behaviour of the electron is described by its wave function, , which is a mathematical function of its position with respect to the nucleus. The significance of the wave function is that | |2 dt is the probability of locating the electron in the element of volume dt.
Solution of Schrödinger's equation for the hydrogen atom shows that the electron can only have certain allowed wave functions ( eigenfunctions ). Each of these corresponds to a probability distribution in space given by the manner in which | |2 varies with position. They also have an associated value of the energy ‘E'. These allowed wave functions, or orbitals, are characterized by three quantum numbers similar to those characterized the allowed orbits in the earlier quantum theory of the atom:
‘n', the ‘principal quantum number, can have values of 1, 2, 3, etc. the orbital with n =1 has the lowest energy. The states of the electron with n = 1, 2, 3, etc., are called ‘shells' and designate the K, L, M shells, etc. ‘I', the ‘azimuthal quantum numbers', which for a given value of ‘n' can have values of 0, 1, 2, . . . ( n 1 ). An electron in the ‘L' shell of an atom with n = 2 can occupy two sub-shells of different energy corresponding to
I = 0, I = 1, and I = 2. Orbitals with I = 0, 1, 2 and 3 are called s, p, d, and Ć’ orbitals respectively. The significance of I quantum number is that it gives the angular momentum of the electron. The orbital angular momentum of an electron is given by:
[I( I + 1 )( h/2 ).
‘m', the ‘magnetic quantum number, which for a given value of I can have values,
I, ( I - 1 ), . . . , 0, . . . ( I - 1 ), I. Thus, for a ‘p' orbital for orbits with m = 1, 0, and 1. These orbitals, with the same values of ‘n' and ‘I' but different ‘m' values, have the same energy. The significance of this quantum number is that it indicates the number of different levels that would be produced if the atom were subjected to an external magnetic field.
According to wave theory the electron may be at any distance from the nucleus, but in fact, there is only a reasonable chance of it being within a distance of ~ 5 x 10-11 metre. Indeed the maximum probability occurs when r - a0 where a0 is the radius of the first Bohr orbit. It is customary to represent an orbital by a surface enclosing a volume within which there is an arbitrarily decided probability ( say 95% ) of finding the electron.
Finally, the electron in an atom can have a fourth quantum number MS, characterizing its spin direction. This can be + ½ or ½, and according to the "Pauli Exclusion Principle," each orbital can hold only two electrons. The four quantum numbers lead to an explanation of the periodic table of the elements.
In earlier mention, the concerns referring to the ‘moment' had been to our exchanges to issue as, i.e., the moment of inertia, moment of momentum. The moment of a force about an axis is the product of the perpendicular distance of the axis from the line of action of the force, and the component of the force in the plane perpendicular to the axis. The moment of a system of coplanar forces about an axis perpendicular to the plane containing them is the algebraic sum of the moments of the separate forces about that axis of a anticlockwise moment appear taken controventionally to be positive and clockwise of ones Uncomplementarity. The moment of momentum about an axis, symbol L is the product to the moment of inertia and angular velocity ( I ). Angular momentum is a pseudo-vector quality, as it is connected in an isolated system. It is a scalar and is given a positive or negative sign as in the moment of force. When contending to systems, in which forces and motions do not all lie in one plane, the concept of the moment about a point is needed. The moment of a vector P, e.g., force or momentous pulsivity, from which a point ‘A' is a pseudo-vector M equal to the vector product of r and P, where r is any line joining ‘A' to any point ‘B' on the line of action of P. The vector product M = r x p is independent of the position of ‘B' and the relation between the scalar moment about an axis and the vector moment about which a point on the axis is that the scalar is the component of the vector in the direction of the axis.
The linear momentum of a particle ‘p' is the product of the mass and the velocity of the particle. It is a vector quality directed through the particle in the direction of motion. The linear momentum of a body or of a system of particles is the vector sum of the linear momenta of the individual particle. If a body of mass ‘M' is translated with a velocity ‘V', its momentum is MV, which is the momentum of a particle of mass ‘M' at the centre of gravity of the body. ( 1 ) In any system of mutually interacting or impinging particles, the linear momentum in any fixed direction remains unaltered unless there is an external force acting in that direction. ( 2 ) Similarly, the angular momentum is constant in the case of a system rotating about a fixed axis provided that no external torque is applied.
Subatomic particles fall into two major groups: The elementary particles and the hadrons. An elementary particle is not composed of any smaller particles and therefore represents the most fundamental form of matter. A hadron is composed of panicles, including the major particles called quarks, the most common of the subatomic particles, includes the major constituents of the atom -the electron is an elementary particle, and the proton and the neutron ( hadrons ). An elementary particle with zero charge and a rest mass equal to
1.674 9542 x 10-27 kg,
i.e., 939.5729 MeV / c2.
It is a constituent of every atomic nucleus except that of ordinary hydrogen, free neutrons decay by ‘beta decay' with a mean life of 914 s. the neutron has spin ½, Isospin ½, and positive parity. It is a ‘fermion' and is classified as a ‘hadron' because it has strong interaction.
Neutrons can be ejected from nuclei by high-energy particles or photons, the energy required is usually about 8 MeV, although sometimes it is less. The fission is the most productive source. They are detected using all normal detectors of ionizing radiation because of the production of secondary particles in nuclear reactions. The discovery of the neutron ( Chadwick, 1932 ) involved the detection of the tracks of protons ejected by neutrons by elastic collisions in hydrogenous materials.
Unlike other nuclear particles, neutrons are not repelled by the electric charge of a nucleus so they are very effective in causing nuclear reactions. When there is no ‘threshold energy', the interaction ‘cross sections' become very large at low neutron energies, and the thermal neutrons produced in great numbers by nuclear reactions cause nuclear reactions on a large scale. The capture of neutrons by the ( n, ) process produces large quantities of radioactive materials, both useful nuclides such as 66Co for cancer therapy and undesirable by-products. The least energy required to cause a certain process, in particular a reaction in nuclear or particle physics. It is often important to distinguish between the energies required in the laboratory and in centre-of-mass co-ordinates. In "fission" the splitting of a heavy nucleus of an atom into two or more fragments of comparable size usually as the result of the impact of a neutron on the nucleus. It is normally accompanied by the emission of neutrons or gamma rays. Plutonium, uranium, and thorium are the principle fissionable elements
In nuclear reaction, a reaction between an atonic nucleus and a bombarding particle or photon leading to the creation of a new nucleus and the possible ejection of one or more particles. Nuclear reactions are often represented by enclosing brackets and symbols for the incoming and final nuclides being shown outside the brackets. For example: 14N ( , p )17O.
Energy from nuclear fissions, on the whole, the nucleuses of atoms of moderate size are more tightly held together than the largest nucleus, so that if the nucleus of a heavy atom can be induced to split into two nuclei and moderate mass, there should be considerable release of energy. By Einstein' s law of the conservation of mass and energy, this mass and energy difference is equivalent to the energy released when the nucleons binding differences are equivalent to the energy released when the nucleons bind together. Y=this energy is the binding energy, the graph of binding per nucleon, EB / A increases rapidly up to a mass number of 50-69 ( iron, nickel, etc. ) and then decreases slowly. There are therefore two ways in which energy can be released from a nucleus, both of which can be released from the nucleus, both of which entail a rearrangement of nuclei occurring in the lower as having to curve into form its nuclei, in the upper, higher-energy part of the curve. The fission is the splitting of heavy atoms, such as uranium, into lighter atoms, accompanied by an enormous release of energy. Fusion of light nuclei, such as deuterium and tritium, releases an even greater quantity of energy.
The work that must be done to detach a single particle from a structure of free electrons of an atom or molecule to form a negative ion. The process is sometimes called ‘electron capture, but the term is more usually applied to nuclear processes. As many atoms, molecules and free radicals from stable negative ions by capturing electrons to atoms or molecules to form a negative ion. The electron affinity is the least amount of work that must be done to separate from the ion. It is usually expressed in electro-volts
The uranium isotope 235U will readily accept a neutron but one-seventh of the nuclei stabilized by gamma emissions while six-sevenths split into two parts. Most of the energy released amounts to about 170 MeV, in the form of the kinetic energy of these fission fragments. In addition an averaged of 2.5 neutrons of average energy 2 MeV and some gamma radiation is produced. Further energy is released later by radioactivity of the fission fragments. The total energy released is about 3 x 10-11 joule per atom fissioned, i.e., 6.5 x 1013 joule per kg conserved.
To extract energy in a controlled manner from fissionable nuclei, arrangements must be made for a sufficient proportion of the neutrons released in the fissions to cause further fissions in their turn, so that the process is continuous, the minium mass of a fissile material that will sustain a chain reaction seems confined to nuclear weaponry. Although, a reactor with a large proportion of 235U or plutonium 239Pu in the fuel uses the fast neutrons as they are liberated from the fission, such a rector is called a ‘fast reactor'. Natural uranium contains 0.7% of 235U and if the liberated neutrons can be slowed before they have much chance of meeting the more common 238U atom and then cause another fission. To slow the neutron, a moderator is used containing light atoms to which the neutrons will give kinetic energy by collision. As the neutrons eventually acquire energies appropriate to gas molecules at the temperatures of the moderator, they are then said to be thermal neutrons and the reactor is a thermal reactor.
Then, of course, the Thermal reactors, in typical thermal reactors, the fuel elements are rods embedded as a regular array in which the bulk of the moderator that the typical neutron from a fission process has a good chance of escaping from the relatively thin fuel rod and making many collisions with nuclei in the moderator before again entering a fuel element. Suitable moderators are pure graphite, heavy water ( D2O ), are sometimes used as a coolant, and ordinary water ( H2O ). Very pure materials are essential as some unwanted nuclei capture neutrons readily. The reactor core is surrounded by a reflector made of suitable material to reduce the escape of neutrons from the surface. Each fuel element is encased e. g., in magnesium alloy or stainless steel, to prevent escape of radioactive fission products. The coolant, which may be gaseous or liquid, flows along the channels over the canned fuel elements. There is an emission of gamma rays inherent in the fission process and, many of the fission products are intensely radioactive. To protect personnel, the assembly is surrounded by a massive biological shield, of concrete, with an inner iron thermal shield to protect the concrete from high temperatures caused by absorption of radiation.
To keep the power production steady, control rods are moved in or out of the assembly. These contain material that captures neutrons readily, e.g., cadmium or boron. The power production can be held steady by allowing the currents in suitably placed ionization chambers automatically to modify the settings of the rods. Further absorbent rods, the shut-down rods, are driven into the core to stop the reaction, as in an emergence if the control mechanism fails. To attain high thermodynamic efficiency so that a large proportion of the liberated energy can be used, the heat should be extracted from the reactor core at a high temperature.
In fast reactors no mediator is used, the frequency of collisions between neutrons and fissile atoms being creased by enriching the natural uranium fuel with 239Pu or additional 235U atoms that are fissioned by fast neutrons. The fast neutrons are thus built up a self-sustaining chain reaction. In these reactions the core is usually surrounded by a blanket of natural uranium into which some of the neutrons are allowed to escape. Under suitable conditions some of these neutrons will be captured by 238U atoms forming 239U atoms, which are converted to 239Pu. As more plutonium can be produced than required to enrich the fuel in the core, these are called ‘fast breeder reactors'.
Thus and so, a neutral elementary particle with spin½, that only takes part in weak interactions. The neutrino is a lepton and exists in three types corresponding to the three types of charged leptons, that is, there are the electron neutrinos ( ve ) tauon neutrinos ( vÎĽ ) and tauon neutrinos ( v ). The antiparticle of the neutrino is the antineutrino.
Neutrinos were originally thought to have a zero mass, but recently there have been some advances to an indirect experiment that evince to the contrary. In 1985 a Soviet team reported a measurement for the first time, of a non-zero neutrino mass. The mass measured was extremely small, some 10 000 times smaller than the mass of the electron. However, subsequent attempts to reproduce the Soviet measurement were unsuccessful. More recent ( 1998-99 ), the Super-Kamiokande experiment in Japan has provided indirect evidence for massive neutrinos. The new evidence is based upon studies of neutrinos, which are created when highly energetic cosmic rays bombard the earth's upper atmosphere. By classifying the interaction of these neutrinos according to the type of neutrino involved ( an electron neutrino or muon neutrino ), and counting their relative numbers as a function: An oscillatory behaviour may be shown to occur. Oscillation in this sense is the charging back and forth of the neutrino's type as it travels through space or matter. The Super-Kamiokande result indicates that muon neutrinos are changing into another type of neutrino, e.g., sterile neutrinos. The experiment does not, however, determine directly the masses, though the oscillations suggest very small differences in mass between the oscillating types.
The neutrino was first postulated ( Pauli 1930 )to explain the continuous spectrum of beta rays. It is assumed that there is the same amount of energy available for each beta decay of a particle nuclide and that energy is shared according to a statistical law between the electron and a light neutral particle, now classified as the anti-neutrino, e Later it was shown that the postulated particle would also conserve angular momentum and linear momentum in the beta decays.
In addition to beta decay, the electron neutrino is also associated with, for example, positron decay and electron capture:
22Na 22Ne + e+ + ve
55Fe + e 55Mn + ve
The absorption of anti-neutrinos in matter by the process
2H + e n + e+
was first demonstrated by Reines and Cowan? The muon neutrino is generated in such processes as:
+ ÎĽ+ + vÎĽ
Although the interactions of neutrinos are extremely weak the cross sections increase with energy and reaction can be studied at the enormous energies available with modern accelerators in some forms of ‘grand unification theories', neutrinos are predicted to have a non-zero mass. Nonetheless, no evidences have been found to support this prediction.
The antiparticle of an electron, i.e., an elementary particle with electron mass and positive charge and equal to that of the electron. According to the relativistic wave mechanics of Dirac, space contains a continuum of electrons in states of negative energy. These states are normally unobservable, but if sufficient energy can be given, an electron may be raised into a state of positivity and become observable. The vacant state of negativity seems to behave as a positive particle of positive energy, which is observed as a positron.
A theory of elementary particles based on the idea that the fundamental entities are not point-like particles, but finite lines ( strings ) or closed loops formed by stings. The original idea was that an elementary particle was the result of a standing wave in a string. A considerable amount of theoretical effort has been put into development string theories. In particular, combining the idea of strings with that of super-symmetry, which has led to the idea with which correlation holds strongly with super-strings. This theory may be a more useful route to a unified theory of fundamental interactions than quantum field theory, simply because it's probably by some unvioded infinites that arise when gravitational interactions are introduced into field theories. Thus, superstring theory inevitably leads to particles of spin 2, identified as gravitons. String theory also shows why particles violate parity conservation in weak interactions.
Superstring theories involve the idea of higher dimensional spaces: 10 dimensions for fermions and 26 dimensions for bosons. It has been suggested that there are the normal 4 space-time dimensions, with the extra dimension being tightly ‘curved'. Still, there are no direct experimental evidences for super-strings. They are thought to have a length of about 10-35 m and energies of 1014 GeV, which is well above the energy of any accelerator. An extension of the theory postulates that the fundamental entities are not one-dimensional but two-dimensional, i.e., they are super-membranes.
Allocations often other than what are previous than in time, awaiting the formidable combinations of what precedes the presence to the future, because of which the set of invariance of a system, a symmetry operation on a system is an operation that does not change the system. It is studied mathematically using "Group Theory." Some symmetries are directly physical, for instance the reelections and rotations for molecules and translations in crystal lattices. More abstractively the implicating inclinations toward abstract symmetries involve changing properties, as in the CPT Theorem and the symmetries associated with "Gauge Theory." Gauge theories are now thought to provide the basis for a description in all elementary particle interactions. The electromagnetic particle interactions are described by quantum electrodynamics, which is called Abelian gauge theory
Quantum field theory for which measurable quantities remain unchanged under a ‘group transformation'. All these theories consecutive field transformations do not commute. All non-Abelian gauge theories are based on work proposed by Yang and Mills in 1954, describe the interaction between two quantum fields of fermions. In which particles represented by fields whose normal modes of oscillation are quantized. Elementary particle interactions are described by relativistically invariant theories of quantized fields, ie. , By relativistic quantum field theories. Gauge transformations can take the form of a simple multiplication by a constant phase. Such transformations are called ‘global gauge transformations'. In local gauge transformations, the phase of the fields is alterable by amounts that vary with space and time; i.e.,
ei ( ) ,
Where ( ) is a function of space-time. As, in Abelian gauge theories, consecutive field transformations commute, i.e.,
ei ( ) ei = ei ( ) ei ( ) ,
Where ( ) is another function of space and time. Quantum chromodynamics ( the theory of the strong interaction ) and electroweak and grand unified theories are all non-Abelian. In these theories consecutive field transformations do not commute. All non-Abelian gauge theories are based on work proposed by Yang and Mils, as Einstein's theory of general relativity can also be formulated as a local gauge theory.
A symmetry including both boson and fermions, in theories based on super-symmetry every boson has a corresponding boson. Th boson partners of existing fermions have names formed by prefacing the names of the fermion with an "s" ( e.g., selection, squark, lepton ). The names of the fermion partners of existing bosons are obtained by changing the terminal -on of the boson to -into ( e.g., photons, gluons, and zino ). Although, super-symmetries have not been observed experimentally, they may prove important in the search for a Unified Field Theory of the fundamental interactions.
The quark is a fundamental constituent of hadrons, i.e., of particles that take part in strong interactions. Quarks are never seen as free particles, which is substantiated by lack of experimental evidence for isolated quarks. The explanation given for this phenomenon in gauge theory is known a quantum chromodynamics, by which quarks are described, is that quark interaction become weaker as they come closer together and fall to zero when the distance between them is zero. The converse of this proposition is that the attractive forces between quarks become stronger s they move, as this process has no limited, quarks can never separate from each other. In some theories, it is postulated that at very high-energy temperatures, as might have prevailed in the early universe, quarks can separate, te temperature at which this occurs is called the ‘deconfinement temperatures'. Nevertheless, their existence has been demonstrated in high-energy scattering experiments and by symmetries in the properties of observed hadrons. They are regarded s elementary fermions, with spin ½, baryon number , strangeness 0 or = 1, and charm 0 or + 1. They are classified I six flavours[ up ( u ), charm ( c ) and top ( t ), each with charge the proton charge, down ( d ), strange ( s ) and bottom ( b ), each with the proton charge ]. Each type has an antiquark with reversed signs of charge, baryon number, strangeness, nd charm. The top quark has not been observed experimentally, but there are strong theoretical arguments for its existence.
The fractional charges of quarks are never observed in hadrons, since the quarks form combinations in which the sum of their charges is zero or integral. Hadrons can be either baryons or mesons, essentially, baryons are composed of three quarks while mesons are composed of a quark-antiquark pair. These components are bound together within the hadron by the exchange of particles known as gluons. Gluons are neutral massless gauge bosons, the quantum field theory of electromagnetic interactions discriminate themselves against the gluon as the analogue of the photon and with a quantum number known as ‘colour' replacing that of electric charge. Each quark type ( or flavour ) comes in three colours ( red, blue and green, say ), where colour is simply a convenient label and has no connection with ordinary colour. Unlike the photon in quantum chromodynamics, which is electrically neutral, gluons in quantum chromodynamics carry colour and can therefore interact with themselves. Particles that carry colour are believed not to be able to exist in free particles. Instead, quarks and gluons are permanently confined inside hadrons ( strongly interacting particles, such as the proton and the neutron ).
The gluon self-interaction leads to the property known as ‘asymptotic freedom', in which the interaction strength for th strong interaction decreases as the momentum transfer involved in an interaction increase. This allows perturbation theory to be used and quantitative comparisons to be made with experiment, similar to, but less precise than those possibilities of quantum chromodynamics. Quantum chromodynamics the being tested successfully in high energy muon-nucleon scattering experiments and in proton-antiproton and electron-positron collisions at high energies. Strong evidence for the existence of colour comes from measurements of the interaction rates for e+e hadrons and e+e ÎĽ+ ÎĽ . The relative rate for these two processes is a factor of three larger than would be expected without colour, this factor measures directly the number of colours, i.e., for each quark flavour.
The quarks and antiquarks with zero strangeness and zero charm are the u, d, Ă» and . They form the combinations:
proton ( uud ), antiproton ( )
neutron ( uud ), antineutron ( )
pion: + (u ), ( d ), 0 ( d , u ).
The charge and spin of these particles are the sums of the charge and spin of the component quarks and/or antiquarks.
In the strange baryon, e.g., the and meons, either the quark or antiquark is strange. Similarly, the presence of one or more ‘c' quarks leads to charmed baryons' ‘a' ‘c' or ‘ ' to the charmed mesons. It has been found useful to introduce a further subdivision of quarks, each flavour coming in three colours ( red, green, blue ). Colour as used here serves simply as a convenient label and is unconnected with ordinary colour. A baryon comprises a red, a green, and a blue quark and a meson comprised a red and ant-red, a blue and ant-blue, or a green and
Antigreen quark and antiquark. In analogy with combinations of the three primary colours of light, hadrons carry no net colour, i.e., they are ‘colourless' or ‘white'. Only colourless objects can exist as free particles. The characteristics of the six quark flavours are shown in the table.
The cental feature of quantum field theory, is that the essential reality is a set of fields subject to the rules of special relativity and quantum mechanics, all else is derived as a consequence of the quantum dynamics of those fields. The quantization of fields is essentially an exercise in which we use complex mathematical models to analyse the field in terms of its associated quanta. And material reality as we know it in quantum field theory is constituted by the transformation and organization of fields and their associated quanta. Hence, this reality
Reveals a fundamental complementarity, in which particles are localized in space/time, and fields, which are not. In modern quantum field theory, all matter is composed of six strongly interacting quarks and six weakly interacting leptons. The six quarks are called up, down, charmed, strange, top, and bottom and have different rest masses and functional changes. The up and own quarks combine through the exchange of gluons to form protons and neutrons.
The ‘lepton' belongs to the class of elementary particles, and does not take part in strong interactions. They have no substructure of quarks and are considered indivisible. They are all; fermions, and are categorized into six distinct types, the electron, muon, and tauon, which are all identically charged, but differ in mass, and the three neutrinos, which are all neutral and thought to be massless or nearly so. In their interactions the leptons appear to observe boundaries that define three families, each composed of a charged lepton and its neutrino. The families are distinguished mathematically by three quantum numbers, Ie, IÎĽ, and Iv lepton numbers called ‘lepton numbers. In weak interactions their IeTOT, IÎĽTOT and I for the individual particles are conserved.
In quantum field theory, potential vibrations at each point in the four fields are capable of manifesting themselves in their complemtarity, their expression as individual particles. And the interactions of the fields result from the exchange of quanta that are carriers of the fields. The carriers of the field, known as messenger quanta, are the ‘coloured' gluons for the strong-binding-force, of which the photon for electromagnetism, the intermediate boson for the weak force, and the graviton or gravitation. If we could re-create the energies present in the fist trillionths of trillionths of a second in the life o the universe, these four fields would, according to quantum field theory, become one fundamental field.
The movement toward a unified theory has evolved progressively from super-symmetry to super-gravity to string theory. In string theory the one-dimensional trajectories of particles, illustrated in the Feynman lectures, seem as if, in at all were possible, are replaced by the two-dimensional orbits of a string. In addition to introducing the extra dimension, represented by a smaller diameter of the string, string theory also features another mall but non-zero constant, with which is analogous to Planck's quantum of action. Since the value of the constant is quite small, it can be generally ignored except at extremely small dimensions. But since the constant, like Planck's constant is not zero, this results in departures from ordinary quantum field theory in very small dimensions.
Part of what makes string theory attractive is that it eliminates, or ‘transforms away', the inherent infinities found in the quantum theory of gravity. And if the predictions of this theory are proven valid in repeatable experiments under controlled coeditions, it could allow gravity to be unified with the other three fundamental interactions. But even if string theory leads to this grand unification, it will not alter our understanding of ave-particle duality. While the success of the theory would reinforce our view of the universe as a unified dynamic process, it applies to very small dimensions, and therefore, does not alter our view of wave-particle duality.
While the formalism of quantum physics predicts that correlations between particles over space-like inseparability, of which are possible, it can say nothing about what this strange new relationship between parts ( quanta ) and the whole ( cosmos ) cause to result outside this formalism. This does not, however, prevent us from considering the implications in philosophical terms. As the philosopher of science Errol Harris noted in thinking about the special character of wholeness in modern physics, a unity without internal content is a blank or empty set and is not recognizable as a whole. A collection of merely externally related parts does not constitute a whole in that the parts will not be "mutually adaptive and complementary to one-another."
Wholeness requires a complementary relationship between unity and difference and is governed by a principle of organization determining the interrelationship between parts. This organizing principle must be universal to a genuine whole and implicit in all parts constituting the whole, even the whole is exemplified only in its parts. This principle of order, Harris continued, "is nothing really in and of itself. It is the way he parts are organized, and another constituent additional to those that constitute the totality."
In a genuine whole, the relationship between the constituent parts must be "internal or immanent" ion the parts, as opposed to a more spurious whole in which parts appear to disclose wholeness dur to relationships that are external to the arts. The collection of parts that would allegedly constitute the whole in classical physics is an example of a spurious whole. Parts continue a genuine whole when the universal principle of order is inside the parts and hereby adjusts each to all so that they interlock and become mutually complementary. This not only describes the character of the whole revealed in both relativity theory and quantum mechanics. It is also consistent with the manner in which we have begun to understand the relations between parts and whole in modern biology.
Modern physics also reveals, claimed Harris, complementary relationship between the differences between parts that constitute and the universal ordering principle that are
Immanent in each part. While the whole cannot be finally disclosed in the analysis of the parts, the study of the differences between parts provides insights into the dynamic structure of the whole present in each part. The part can never, however, be finally isolated from the web of relationships that discloses the interconnections with the whole, and any attempt to do so results in ambiguity.
Much of the ambiguity in attempts to explain the character of wholes in both physics and biology derives from the assumption that order exists between or outside parts. Yet order in complementary relationships between difference and sameness in any physical event is never external to that event, and the cognations are immanent in the event. From this perspective, the addition of non-locality to this picture of the distributive constitution in dynamic function of wholeness is not surprising. The relationships between part, as quantum event apparent in observation or measurement, and the undissectable whole, calculate on in but are not described by the instantaneous correlations between measurements in space-like separate regions, is another extension of the part-whole complementarity in modern physics.
If the universe is a seamlessly interactive system that evolves to higher levels of complex and complicating regularities of which ae lawfully emergent in property of systems, we can assume that the cosmos is a single significant whole that evinces progressive order in complementary relations to its parts. Given that this whole exists in some sense within all parts ( quanta ), one can then argue that in operates in self-reflective fashion and is the ground from all emergent plexuities. Since human consciousness evinces self-reflective awareness in te human brain ( well protected between the cranium walls ) and since this brain, like all physical phenomena, can b viewed as an emergent property of the whole, it is unreasonable to conclude, in philosophical terms at least, that the universe is conscious.
Nevertheless, since the actual character of this seamless whole cannot be represented or reduced to its parts, it lies, quite laterally, beyond all human representation or descriptions. If one chooses to believe that the universe be a self-reflective and self-organizing whole, this lends no support whatsoever to conceptual representation of design, meaning, purpose, intent, or plan associated with mytho-religious or cultural heritage. However, if one does not accept this view of the universe, there is noting in the scientific description of nature that can be used to refute this position. On the other hand, it is no longer possible to argue that a profound sense of unity with the whole, which has long been understood as foundation of religious experiences, but can be dismissed, undermined, or invalidated with appeals to scientific knowledge.
While we have consistently tried to distinguish between scientific knowledge and philosophical speculation based on this of what is obtainable, let us be quite clear on one point -there is no empirically valid causal linkage between the former and the latter. Those who wish to dismiss the speculative base on which is obviously free to do as done. However, there is another conclusion to be drawn, in that is firmly grounded in scientific theory and experiment there is no basis in the scientific descriptions of nature for believing in the radical Cartesian division between mind and world sanctioned by classical physics. Clearly, his radical separation between mind and world was a macro-level illusion fostered by limited awareness of the actual character of physical reality nd by mathematical idealizations extended beyond the realms of their applicability.
Nevertheless, the philosophical implications might prove in themselves as a criterial motive in debative consideration to how our proposed new understanding of the relationship between parts and wholes in physical reality might affect the manner in which we deal with some major real-world problems. This will issue to demonstrate why a timely resolution of these problems is critically dependent on a renewed dialogue between members of the cultures of human-social scientists and scientist-engineers. We will also argue that the resolution of these problems could be dependent on a renewed dialogue between science and religion.
As many scholars have demonstrated, the classical paradigm in physics has greatly influenced and conditioned our understanding and management of human systems in economic and political realities. Virtually all models of these realities treat human systems as if they consist of atomized units or parts that interact with one another in terms of laws or forces external to or between the parts. These systems are also viewed as hermetic or closed and, thus, its discreteness, separateness and distinction.
Consider, for example, how the classical paradigm influenced or thinking about economic reality. In the eighteenth and nineteenth centuries, the founders of classical economics -figures like Adam Smith, David Ricardo, and Thomas Malthus conceived of the economy as a closed system in which intersections between parts ( consumer, produces, distributors, etc. ) are controlled by forces external to the parts ( supply and demand ). The central legitimating principle of free market economics, formulated by Adam Smith, is that lawful or law-like forces external to the individual units function as an invisible hand. This invisible hand, said Smith, frees the units to pursue their best interests, moves the economy forward, and in general legislates the behaviour of parts in the best vantages of the whole. ( The resemblance between the invisible hand and Newton's universal law of gravity and between the relations of parts and wholes in classical economics and classical physics should be transparent. )
After roughly 1830, economists shifted the focus to the properties of the invisible hand in the interactions between pats using mathematical models. Within these models, the behaviour of pats in the economy is assumed to be analogous to the awful interactions between pats in classical mechanics. It is, therefore, not surprising that differential calculus was employed to represent economic change in a virtual world in terms of small or marginal shifts in consumption or production. The assumption was that the mathematical description of marginal shifts n the complex web of exchanges between parts ( atomized units and quantities ) and whole ( closed economy ) could reveal the lawful, or law-like, machinations of the closed economic system.
These models later became one of the fundamentals for microeconomics. Microeconomics seek to describe interactions between parts in exact quantifiable measures-such as marginal cost, marginal revenue, marginal utility, and growth of total revenue as indexed against individual units of output. In analogy with classical mechanics, the quantities are viewed as initial conditions that can serve to explain subsequent interactions between parts in the closed system in something like deterministic terms. The combination of classical macro-analysis with micro-analysis resulted in what Thorstein Veblen in 1900 termed neoclassical economics-the model for understanding economic reality that is widely used today
Beginning in the 1939s, the challenge became to subsume the understanding of the interactions between parts in closed economic systems with more sophisticated mathematical models using devices like linear programming, game theory, and new statistical techniques. In spite of the growing mathematical sophistication, these models are based on the same assumptions from classical physics featured in previous neoclassical economic theory-with one exception. They also appeal to the assumption that systems exist in equilibrium or in perturbations from equilibria, and they seek to describe the state of the closed economic system in these terms.
One could argue that the fact that our economic models are assumptions from classical mechanics is not a problem by appealing to the two-domain distinction between micro-level macro-level processes expatiated upon earlier. Since classical mechanic serves us well in our dealings with macro-level phenomena in situations where the speed of light is so large and the quantum of action is so small as to be safely ignored for practical purposes, economic theories based on assumptions from classical mechanics should serve us well in dealing with the macro-level behaviour of economic systems.
The obvious problem, . . . acceded peripherally, . . . nature is relucent to operate in accordance with these assumptions, in that the biosphere, the interaction between parts be intimately related to the hole, no collection of arts is isolated from the whole, and the ability of the whole to regulate the relative abundance of atmospheric gases suggests that the whole of the biota appear to display emergent properties that are more than the sum of its parts. What the current ecological crisis reveals in the abstract virtual world of neoclassical economic theory. The real economies are all human activities associated with the production, distribution, and exchange of tangible goods and commodities and the consumption and use of natural resources, such as arable land and water. Although expanding economic systems in the really economy ae obviously embedded in a web of relationships with the entire biosphere, our measure of healthy economic systems disguises this fact very nicely. Consider, for example, the healthy economic system written in 1996 by Frederick Hu, head of the competitive research team for the World Economic Forum -short of military conquest, economic growth is the only viable means for a country to sustain increases in natural living standards . . . An economy is internationally competitive if it performs strongly in three general areas: Abundant productive inputs from capital, labour, infrastructure and technology, optimal economic policies such as low taxes, little interference, free trade and sound market institutions. Such as the rule of law and protection of property rights.
The prescription for medium-term growth of economies ion countries like Russia, Brazil, and China may seem utterly pragmatic and quite sound. But the virtual economy described is a closed and hermetically sealed system in which the invisible hand of economic forces allegedly results in a health growth economy if impediments to its operation are removed or minimized. It is, of course, often trued that such prescriptions can have the desired results in terms of increases in living standards, and Russia, Brazil and China are seeking to implement them in various ways.
In the real economy, however, these systems are clearly not closed or hermetically sealed: Russia uses carbon-based fuels in production facilities that produce large amounts of carbon dioxide and other gases that contribute to global warming: Brazil is in the process of destroying a rain forest that is critical to species diversity and the maintenance of a relative abundance of atmospheric gases that regulate Earth temperature, and China is seeking to build a first-world economy based on highly polluting old-world industrial plants that burn soft coal. Not to forget, . . . the victual economic systems that the world now seems to regard as the best example of the benefits that can be derived form the workings of the invisible hand, that of the United States, operates in the real economy as one of the primary contributors to the ecological crisis.
In "Consilience," Edward O. Wilson makes to comment, the case that effective and timely solutions to the problem threatening human survival is critically dependent on something like a global revolution in ethical thought and behaviour. But his view of the basis for this revolution is quite different from our own. Wilson claimed that since the foundations for moral reasoning evolved in what he termed ‘gene-culture' evolution, the rules of ethical behaviour re emergent aspects of our genetic inheritance. Based on the assumptions that the behaviour of contemporary hunter-gatherers resembles that of our hunter-gatherers forebears in the Palaeolithic Era, he drew on accounts of Bushman hunter-gatherers living in the centre Kalahari in an effort to demonstrate that ethical behaviour is associated with instincts like bonding, cooperation, and altruism.
Wilson argued that these instincts evolved in our hunter-gatherer accessorial descendabilities, whereby genetic mutation and the ethical behaviour associated with these genetically based instincts provided a survival advantage. He then claimed that since these genes were passed on to subsequent generations of our dependable characteristics, which eventually became pervasive in the human genome, the ethical dimension of human nature has a genetic foundation. When we fully understand the "innate epigenetic rules of moral reasoning," it seems probable that the rules will probably turn out to be an ensemble of many algorithms whose interlocking activities guide the mind across a landscape of nuances moods and choices.
Any reasonable attempt to lay a firm foundation beneath the quagmire of human ethics in all of its myriad and often contradictory formulations is admirable, and Wilson's attempt is more admirable than most. In our view, however, there is little or no prospect that I will prove successful for a number of reasons. Wile te probability for us to discover some linkage between genes and behaviour, seems that the lightened path of human ethical behaviour and ranging advantages of this behaviour is far too complex, not o mention, inconsistently been reduced to a given set classification of "epigenetic ruled of moral reasoning."
Also, moral codes may derive in part from instincts that confer a survival advantage, but when we are t examine these codes, it also seems clear that they are primarily cultural products. This explains why ethical systems are constructed in a bewildering variety of ways in different cultural contexts and why they often sanction or legitimate quite different thoughts and behaviours. Let us not forget that rules f ethical behaviours are quite malleable and have been used to sacredly legitimate human activities such as slavery, colonial conquest, genocide and terrorism. As Cardinal Newman cryptically put it, "Oh how we hate one another for the love of God."
According to Wilson, the "human mind evolved to believe in the gods" and people "need a sacred narrative" to his view are merely human constructs and, therefore, there is no basis for dialogue between the world views of science and religion. "Science for its part, will test relentlessly every assumption about the human condition and in time uncover the bedrock of the moral and religiously sentient. The eventual result of the competition between the two world view, is believed, as I, will be the secularization of the human epic and of religion itself.
Wilson obviously has a right to his opinions, and many will agree with him for their own good reasons, but what is most interesting about his thoughtful attempted to posit a more universal basis for human ethics in that it s based on classical assumptions about the character of both physical and biological realities. While Wilson does not argue that human's behaviour is genetically determined in the strict sense, however, he does allege that there is a causal linkage between genes and behaviour that largely condition this behaviour, he appears to be a firm believer in classical assumption that reductionism can uncover the lawful essences that principally govern the physical aspects attributed to reality, including those associated with the alleged "epigenetic rules of moral reasoning."
Once, again, Wilson's view is apparently nothing that cannot be reduced to scientific understandings or fully disclosed in scientific terms, and this apparency of hope for the future of humanity is that the triumph of scientific thought and method will allow us to achieve the Enlightenments ideal of disclosing the lawful regularities that govern or regulate all aspects of human experience. Hence, science will uncover the "bedrock of moral and religious sentiment, and the entire human epic will be mapped in the secular space of scientific formalism." The intent is not to denigrate Wilson's attentive efforts to posit a more universal basis for the human condition, but is to demonstrate that any attempt to understand or improve upon the behaviour based on appeals to outmoded classical assumptions is unrealistic and outmoded. If the human mind did, in fact, evolve in something like deterministic fashion in gene-culture evolution - and if there were, in fact, innate mechanisms in mind that are both lawful and benevolent. Wilson's program for uncovering these mechanisms could have merit. But for all th reasons that have been posited, classical determinism cannot explain the human condition and its evolutionary principle that govern in their functional dynamics, as Darwinian evolution should be modified to accommodate the complementary relationships between cultural and biological principles that governing evaluations do indeed have in them a strong, and firm grip upon genetical mutations that have attributively been the distribution in the contribution of human interactions with themselves in the finding to self-realizations and undivided wholeness.
Equally important, the classical assumption that the only privileged or valid knowledge is scientific is one of the primary sources of the stark division between the two cultures of humanistic and scientists-engineers, in this view, Wilson is quite correct in assuming that a timely end to the two culture war and a renewer dialogue between members of these cultures is now critically important to human survival. It is also clear, however, that dreams of reason based on the classical paradigm will only serve to perpetuate the two-culture war. Since these dreams are also remnants of an old scientific word view that no longer applies in theory in fact, to the actual character of physical reality, as reality is a probable service to frustrate the solution for which in found of a real world problem.
However, there is a renewed basis for dialogue between the two cultures, it is believed as quite different from that described by Wilson. Since classical epistemology has been displaced, or is the process of being displaced, by the new epistemology of science, the truths of science can no longer be viewed as transcendent ad absolute in the classical sense. The universe more closely resembles a giant organism than a giant machine, and it also displays emergent properties that serve to perpetuate the existence of the whole in both physics and biology that cannot be explained in terms of unrestricted determinism, simple causality, first causes, linear movements and initial conditions. Perhaps the first and most important precondition for renewed dialogue between the two cultural conflicting realizations as Einstein explicated upon its topic as, that a human being is a "part of the whole.' It is this spared awareness that allows for the freedom, or existential choice of self-decision of choosing our free-will and the power to differentiate a direct cars to free ourselves of the "optical illusion"of our present conception of self as a "part limited in space and time" and to widen "our circle of compassion to embrace al living creatures and the whole of nature in its beauty." Yet, one cannot, of course, merely reason oneself into an acceptance of this view, nonetheless, the inherent perceptions of the world are reason that the capacity for what Einstein termed "cosmic religious feedings." Perhaps, our enabling capability for that which is within us to have the obtainable ability to enabling of ours is to experience the self-realization, that of its realness is to sense its proven existence of a sense of elementarily leaving to some sorted conquering sense of universal consciousness, in so given to arise the existence of the universe, which really makes an essential difference to the existence or its penetrative spark of awakening indebtednesses of reciprocality?
Those who have this capacity will hopefully be able to communicate their enhanced scientific understanding of the relations among all aspects, and in part that is our self and the whole that are the universe in ordinary language wit enormous emotional appeal. The task lies before the poets of this renewing reality have nicely been described by Jonas Salk, which "man has come to the threshold of a state of consciousness, regarding his nature and his relationship to the Cosmos, in terms that reflects "reality." By using the processes of Nature and metaphor, to describe the forces by which it operates upon and within Man, we come as close to describing "reality" as we can within te limits of our comprehension. Men will be very uneven in their capacity or such understanding, which, naturally, differs for different ages and cultures, and develops and changes over the course of time. For these reasons it will always be necessary to use metaphorical and mythical provisions as comprehensive guides to living. In this way. Man's afforded efforts by the imagination and intellect can be playing the vital roles embarking upon the survival and his endurable evolution.
It is time, if not, only, concluded from evidence in its suggestive conditional relation, for which the religious imagination and the religious experience to engage upon the complementary truths of science in fitting that silence with meaning, as having to antiquate a continual emphasis, least of mention, that does not mean that those who do not believe in the existence of God or Being, should refrain in any sense from assessing the impletions of the new truths of science. Understanding these implications does not necessitate any ontology, and is in no way diminished by the lack of any ontology. And one is free to recognize a basis for a dialogue between science and religion for the same reason that one is free to deny that this basis exists -there is nothing in our current scientific world view that can prove the existence of God or Being and nothing that legitimate any anthropomorphic conceptions of the nature of God or Being. The question of belief in some ontology yet remains in what it has always been -a question, and the physical universe on the most basic level remains what it always been a riddle. And the ultimate answer to the question and the ultimate meaning of the riddle is, and probably always will be, a matter of personal choice and conviction.
The present time is clearly a time of a major paradigm shift, but consider the last great paradigm shift, the one that resulted in the Newtonian framework. This previous paradigm shift was profoundly problematic for the human spirit, it led to the conviction that we are strangers, freaks of nature, conscious beings in a universe that is almost entirely unconscious, and that, since the universe its strictly deterministic, even the free will we feel in regard to the movements of our bodies is an illusion. Yet it was probably necessary for the Western mind to go through the acceptance of such a paradigm.
The overwhelming success of Newtonian physics led most scientists and most philosophers of the Enlightenment to rely on it exclusively. As far as the quest for knowledge about reality was concerned, they regarded all of the other mode's of expressing human experience, such as accounts of numinous emergences, poetry, art, and so on, as irrelevant. This reliance on science as the only way to the truth about the universe s clearly obsoletes. Science has to give up the illusion of its self-sufficiency and self-sufficiency of human reason. It needs to unite with other modes of knowing, n particular with contemplation, and help each of us move to higher levels of being and toward the Experience of Oneness.
If this is indeed the direction of the emerging world-view, then the paradigm shifts we are presently going through will prove to e nourishing to the human spirit and in correspondences with its deepest conscious or unconscious yearning -the yearning to emerge out of Plato's shadows and into the light of luminosity.
DUBOISITY
Book Five
SYSTEMATIC DELINEATION
Finding to a theory that magnifies the role of decisions, or free selection from among equally possible alternatives, in order to show that what appears to be objective or fixed by nature is in fact an artefact of human convention, similar to conventions of etiquette, or grammar, or law. Thus one might suppose that moral rules owe more to social convention than to anything imposed from outside, or have supposedly inexorable necessities are in fact the shadow of our linguistic conventions. The disadvantage of conventionalism is that it must show that alternative, equally workable conventions could have been adopted, and it is often easy to believe that, for example, if we hold that some ethical norm such as respect for promises or property is conventional, we ought to be able to show that human needs would have been equally well satisfied by a system involving a different norm, and this may be hard to establish.
A convention also suggested by Paul Grice (1913-88) directing participants in conversation to pay heed to an accepted purpose or direction of the exchange. Contributions made without paying this attention are liable to be rejected for other reasons than straightforward falsity: Something rue but unhelpful or inappropriate may meet with puzzlement or rejection. We can nevertheless, infer from the fact that it would be inappropriate to say something in some circumstance that what would be aid, were we to say it, would be false. This inference was frequently and in ordinary language philosophy, it being argued, for example, that since we do not normally say ‘there sees to be a barn there' when there is unmistakably a barn there, it is false that on such occasions there seems to be a barn there.
There are two main views on the nature of theories. According to the ‘received view' theories are partially interpreted axiomatic systems, according to the semantic view, a theory is a collection of models (Suppe, 1974). However, a natural language comes ready interpreted, and the semantic problem is no that of the specification but of understanding the relationship between terms of various categories (names, descriptions, predicates, adverbs . . .) and their meanings. An influential proposal is that this relationship is best understood by attempting to provide a ‘truth definition' for the language, which will involve giving terms and structure of different kinds have on the truth-condition of sentences containing them.
The axiomatic method . . . as, . . . a proposition lid down as one from which we may begin, an assertion that we have taken as fundamental, at least for the branch of enquiry in hand. The axiomatic method is that of defining as a set of such propositions, and the ‘proof procedures' or finding of how a proof ever gets started. Suppose I have as premises (1) p and (2) p q. Can I infer q? Only, it seems, if I am sure of, (3) (p & p q) q. Can I then infer q? Only, it seems, if I am sure that (4) (p & p q) q) q. For each new axiom (N) needing a further axiom (N + 1) telling me that the set so far implies q, and the regress never stops. The usual solution is to treat a system as containing not only axioms, but also rules of reference, allowing movement fro the axiom. The rule ‘modus ponens' allow us to pass from the first two premises to 'q'. Charles Dodgson Lutwidge (1832-98) better known as Lewis Carroll's puzzle shows that it is essential to distinguish two theoretical categories, although there may be choice about which to put in which category.
This type of theory (axiomatic) usually emerges as a body of (supposes) truths that are not nearly organized, making the theory difficult to survey or study a whole. The axiomatic method is an idea for organizing a theory (Hilbert 1970): one tries to select from among the supposed truths a small number from which all others can be seen to be deductively inferable. This makes the theory rather more tractable since, in a sense, all the truths are contained in those few. In a theory so organized, the few truths from which all others are deductively inferred are called axioms. In that, just as algebraic and differential equations, which were used to study mathematical and physical processes, could they be made mathematical objects, so axiomatic theories, like algebraic and differential equations, which are means of representing physical processes and mathematical structures, could be made objects of mathematical investigation.
In the traditional (as in Leibniz, 1704), many philosophers had the conviction that all truths, or all truths about a particular domain, followed from a few principles. These principles were taken to be either metaphysically prior or epistemologically prior or in the fist sense, they were taken to be entities of such a nature that what exists is ‘caused' by them. When the principles were taken as epistemologically prior, that is, as axioms, they were taken to be epistemologically privileged either, e.g., self-evident, not needing to be demonstrated or (again, inclusive ‘or') to be such that all truths do follow from them (by deductive inferences). Gödel (1984) showed that treating axiomatic theories as themselves mathematical objects, that mathematics, and even a small part of mathematics, elementary number theory, could not be axiomatized, that, more precisely, any class of axioms that in such that we could effectively decide, of any proposition, whether or not it was in the class, would be too small to capture all of the truths.
The use of a model to test for the consistency of an axiomatized system is older than modern logic. Descartes's algebraic interpretation of Euclidean geometry provides a way of showing that if the theory of real numbers is consistent, so is the geometry. Similar mapping had been used by mathematicians in the 19th century for example to show that if Euclidean geometry is consistent, so are various non-Euclidean geometries. Model theory is the general study of this kind of procedure: The study of interpretations of formal system. Proof theory studies relations of deductibility as defined purely syntactically, that is, without reference to the intended interpretation of the calculus. More formally, a deductively valid argument starting from true premises, that yields the conclusion between formulae of a system. But once the notion of an interpretation is in place we can ask whether a formal system meets certain conditions. In particular, can it lead us from sentences that are true under some interpretation to ones that are false under the same interpretation? And if a sentence is true under all interpretations, is it also a theorem of the system? We can define a notion of validity (a formula is valid if it is true in all interpretations) and semantic consequence (a formula, written
{A1 . . . An} B, if it is true in all interpretations in which they are true) The central questions for a calculus will be whether all and only its theorems are valid, and whether {A1 . . . An} B, if and only if {A1. . . . An} B. These are the questions of the soundness and completeness of a formal system. For the propositional calculus this turns into the question of whether the proof theory delivers as theorems all and only tautologies. There are many axiomatizations of the propositional calculus that are consistent an complete. Gödel proved in 1929 that first-order predicate calculus is complete: any formula that is true under every interpretation is a theorem of the calculus.
The propositional calculus or logical calculus whose expressions are character representation sentences or propositions, and constants representing operations on those propositions to produce others of higher complexity. The operations include conjunction, disjunction, material implication and negation (although these need not be primitive). Propositional logic was partially anticipated by the Stoics but researched maturity only with the work of Frége, Russell, and Wittgenstein.
The concept introduced by FrĂ©ge of a function taking a number of names as arguments, and delivering one proposition as the value. The idea is that ‘ love's y' is a propositional function, which yields the proposition ‘John loves Mary' from those two arguments (in that order). A propositional function is therefore roughly equivalent to a property or relation. In Principia Mathematica, Russell and Whitehead take propositional functions to be the fundamental function, since the theory of descriptions could be taken as showing that other expressions denoting functions are incomplete symbols.
Keeping in mind, the two classical truth-values that a statement, proposition, or sentence can take. It is supposed in classical (two-valued) logic, that each statement has one of these values, and none has both. A statement is then false if and only if it is not true. The basis of this scheme is that to each statement there corresponds a determinate truth condition, or way the world must be for it to be true, and otherwise false. Statements may be felicitous or infelicitous in other dimensions (polite, misleading, apposite, witty, etc.) but truth is the central normative governing assertion. Considerations of vagueness may introduce greys into a black-and-white scheme. For the issue of whether falsity is the only way of failing to be true.
Formally, it is nonetheless, that any suppressed premise or background framework of thought necessary to make an argument valid, or a position tenable. More formally, a presupposition has been defined as a proposition whose truth is necessary for either the truth or the falsity of another statement. Thus, if ‘p' presupposes ‘q', ‘q' must be true for p to be either true or false. In the theory of knowledge of Robin George Collingwood (1889-1943), any propositions capable of truth or falsity stand on a bed of ‘absolute presuppositions' which are not properly capable of truth or falsity, since a system of thought will contain no way of approaching such a question. It was suggested by Peter Strawson (1919-), in opposition to Russell's theory of ‘definite' descriptions, that ‘there exists a King of France' is a presupposition of ‘the King of France is bald', the latter being neither true, nor false, if there is no King of France. It is, however, a little unclear whether the idea is that no statement at all is made in such a case, or whether a statement i can made, but fails of being one a true and oppose of either true ids false. The former option preserves classical logic, since we can still say that every statement is either true or false, but the latter does not, since in classical logic the law of ‘bivalence' holds, and ensures that nothing at all is presupposed for any proposition to be true or false. The introduction of presupposition therefore means that either a third truth-value is found, ‘intermediate' between truth and falsity, or classical logic is preserved, but it is impossible to tell whether a particular sentence expresses a proposition that is a candidate for truth ad falsity, without knowing more than the formation rules of the language. Each suggestion carries costs, and there is some consensus that at least where definite descriptions are involved, examples like the one given are equally well handed by regarding the overall sentence false when the existence claim fails.
A proposition may be true or false it is said to take the truth-value true, and if the latter the truth-value false. The idea behind the term is the analogy between assigning a propositional variable one or other of these values, as a formula of the propositional calculus, and assigning an object as the value of many other variable. Logics with intermediate values are called many-valued logics. Then, a truth-function of a number of propositions or sentences is a function of them that has a definite truth-value, depends only on the truth-values of the constituents. Thus (p & q) is a combination whose truth-value is true when ‘p' is true and ‘q' is true, and false otherwise, ¬ p is a truth-function of ‘p', false when ‘p' is true and true when ‘p' is false. The way in which the value of the whole is determined by the combinations of values of constituents is presented in a truth table.
In whatever manner, truths of fact cannot be reduced to any identity and our only way of knowing them is a posteriori, by reference to the facts of the empirical world.
A proposition is knowable a priori if it can be known without experience of the specific course of events in the actual world. It may, however, be allowed that some experience is required to acquire the concepts involved in an a priori proposition. Some thing is knowable only a posteriori if it can be known a priori. The distinction given one of the fundamental problem areas of epistemology. The category of a priori propositions is highly controversial, since it is not clear how pure thought, unaided by experience, can give rise to any knowledge at all, and it has always been a concern of empiricism to deny that it can. The two great areas in which it seems to be so are logic and mathematics, so empiricists have commonly tried to show either that these are not areas of real, substantive knowledge, or that in spite of appearances their knowledge that we have in these areas is actually dependent on experience. The former line tries to show sense trivial or analytic, or matters of notation conventions of language. The latter approach is particularly y associated with Quine, who denies any significant slit between propositions traditionally thought of as a priori, and other deeply entrenched beliefs that occur in our overall view of the world.
Another contested category is that of a priori concepts, supposed to be concepts that cannot be ‘derived' from experience, but which are presupposed in any mode of thought about the world, time, substance, causation, number, and self are candidates. The need for such concept s, and the nature of the substantive a prior knowledge to which they give rise, is the central concern of Kant ‘s Critique of Pure Reason.
Likewise, since their denial does not involve a contradiction, there is merely contingent: Their could have been in other ways a hold of the actual world, but not every possible one. Some examples are ‘Caesar crossed the Rubicon' and ‘Leibniz was born in Leipzig', as well as propositions expressing correct scientific generalizations. In Leibniz's view truths of fact rest on the principle of sufficient reason, which is a reason why it is so. This reason is that the actual world (by which he means the total collection of things past, present and future) is better than any other possible world and therefore created by God. The foundation of his thought is the conviction that to each individual there corresponds a complete notion, knowable only to God, from which is deducible all the properties possessed by the individual at each moment in its history. It is contingent that God actualizes te individual that meets such a concept, but his doing so is explicable by the principle of ‘sufficient reason', whereby God had to actualize just that possibility in order for this to be the best of all possible worlds. This thesis is subsequently lampooned by Voltaire (1694-1778), in whom of which was prepared to take refuge in ignorance, as the nature of the soul, or the way to reconcile evil with divine providence.
In defending the principle of sufficient reason sometimes described as the principle that nothing can be so without there being a reason why it is so. But the reason has to be of a particularly potent kind: eventually it has to ground contingent facts in necessities, and in particular in the reason an omnipotent and perfect being would have for actualizing one possibility than another. Among the consequences of the principle is Leibniz's relational doctrine of space, since if space were an infinite box there could be no reason for the world to be at one point in rather than another, and God placing it at any point violate the principle. In Abelard's (1079-1142), as in Leibniz, the principle eventually forces te recognition that the actual world is the best of all possibilities, since anything else would be inconsistent with the creative power that actualizes possibilities.
If truth consists in concept containment, then it seems that all truths are analytic and hence necessary; and if they are all necessary, surely they are all truths of reason. In that not every truth can be reduced to an identity in a finite number of steps; in some instances revealing the connection between subject and predicate concepts would require an infinite analysis, while this may entail that we cannot prove such proposition as a prior, it does not appear to show that proposition could have been false. Intuitively, it seems a better ground for supposing that it is a necessary truth of a special sort. A related question arises from the idea that truths of fact depend on God's decision to create the best world: If it is part of the concept of this world that it is best, how could its existence be other than necessary? An accountable and responsively answered explanation would be so, that any relational question that brakes the norm lay eyes on its existence in the manner other than hypothetical necessities, i.e., it follows from God's decision to create the world, but God had the power to create this world, but God is necessary, so how could he have decided to do anything else? Leibniz says much more about these matters, but it is not clear whether he offers any satisfactory solutions.
The view that the terms in which we think of some area are sufficiently infected with error for it to be better to abandon them than to continue to try to give coherent theories of their use. Eliminativism should be distinguished from scepticism that claims that we cannot know the truth about some area; eliminativism claims rather that there are no truth there to be known, in the terms that we currently think. An eliminativist about theology simply counsels abandoning the terms or discourse of theology, and that will include abandoning worries about the extent of theological knowledge.
Eliminativists in the philosophy of mind counsel abandoning the whole network of terms mind, consciousness, self, qualia that usher in the problems of mind and body. Sometimes the argument for doing this is that we should wait for a supposed future understanding of ourselves, based on cognitive science and better than any our current mental descriptions provide, sometimes it is supposed that physicalism shows that no mental description of ourselves could possibly be true.
Greek scepticism centred on the value of enquiry and questioning, scepticism is now the denial that knowledge or even rational belief is possible, either about some specific subject-matter, e.g., ethics, o r in any atra whatsoever. Classically, scepticism springs from the observation that the best methods in some area seem to fall short of giving us contact with the truth, e.g., there is a gulf between appearance and reality, and in frequency cites the conflicting judgements that our methods deliver, with the result that questions of truth become undecidable.
Sceptical tendencies emerged in the 14th-century writings of Nicholas of Autrecourt. His criticisms of any certainty beyond the immediate deliverance of the senses and basic logic, and in particular of any knowledge of either intellectual or material substances, anticipate the later scepticism of Balye and Hume. The; later distinguishes between Pyrrhonistic and excessive scepticism, which he regarded as unlivable, and the more mitigated scepticism that accepts every day or commonsense beliefs (not as the delivery of reason, but as due more to custom and habit), but is duly wary of the power of reason to give us much more. Mitigated scepticism is thus closer to the attitude fostered by ancient scepticism from Pyrrho through to Sexus Empiricus. Although the phrase ‘Cartesian scepticism' is sometimes used, Descartes himself was not a sceptic, but in the method of doubt, uses a sceptical scenario in order to begin the process of finding a secure mark of knowledge. Descartes himself trusts a category of ‘clear and distinct' ideas, not far removed from the phantasia kataleptikĂ© of the Stoics.
Scepticism should not be confused with relativism, which is a doctrine about the nature of truth, and may be motivated by trying to avoid scepticism. Nor is it identical with eliminativism, which counsels abandoning an area of thought altogether, not because we cannot know the truth, but because there are no truths capable of being framed in the terms we use.
Descartes's theory of knowledge starts with the quest for certainty, for an indubitable starting-point or foundation on the basis alone of which progress is possible. This is eventually found in the celebrated ‘Cogito ergo sum': I think therefore I am. By locating the point of certainty in my own awareness of my own self, Descartes gives a first-person twist to the theory of knowledge that dominated them following centuries in spite of various counter-attacks on behalf of social and public starting-points. The metaphysical associated with this priority are the famous Cartesian dualism, or separation of mind and matter into two different but interacting substances, Descartes rigorously and rightly sees that it takes divine dispensation to certify any relationship between the two realms thus divided, and to prove the reliability of the senses invokes a ‘clear and distinct perception' of highly dubious proofs of the existence of a benevolent deity. This has not met general acceptance: as Hume drily puts it, ‘to have recourse to the veracity of the supreme Being, in order to prove the veracity of our senses, is surely making a very unexpected circuit'.
In his own time Descartes's conception of the entirely separate substance of the mind was recognized to give rise to insoluble problems of the nature of the causal connection between the two. It also gives rise to the problem, insoluble in its own terms, of other minds. Descartes's notorious denial that non-human animals are conscious is a stark illustration of the problem. In his conception of matter Descartes also gives preference to rational cogitation over anything derived from the senses. Since we can conceive of the matter of a ball of wax surviving changes to its sensible qualities, matter is not an empirical concept, but eventually an entirely geometrical one, with extension and motion as its only physical nature. Descartes's thought, as reflected in Leibniz, that the qualities of sense experience have no resemblance to qualities of things, so that knowledge of the external world is essentially knowledge of structure rather than of filling. On this basis Descartes erects a remarkable physics. Since matter is in effect the same as extension there can be no empty space or ‘void', since there is no empty space motion is not a question of occupying previously empty space, but is to be thought of in terms of vortices (like the motion of a liquid).
Although the structure of Descartes's epistemology, theories of mind, and theory of matter have been rejected many times, their relentless exposure of the hardest issues, their exemplary clarity, and even their initial plausibility, all contrives to make him the central point of reference for modern philosophy.
The self conceived as Descartes presents it in the first two Meditations: aware only of its own thoughts, and capable of disembodied existence, neither situated in a space nor surrounded by others. This is the pure self of ‘I-ness' that we are tempted to imagine as a simple unique thing that make up our essential identity. Descartes's view that he could keep hold of this nugget while doubting everything else is criticized by Lichtenberg and Kant, and most subsequent philosophers of mind.
Descartes holds that we do not have any knowledge of any empirical proposition about anything beyond the contents of our own minds. The reason, roughly put, is that there is a legitimate doubt about all such propositions because there is no way to deny justifiably that our senses are being stimulated by some cause (an evil spirit, for example) which is radically different from the objects that we normally think affect our senses.
He also points out, that the senses (sight, hearing, touch, etc., are often unreliable, and ‘it is prudent never to trust entirely those who have deceived us even once', he cited such instances as the straight stick that looks ben t in water, and the square tower that look round from a distance. This argument of illusion, has not, on the whole, impressed commentators, and some of Descartes' contemporaries pointing out that since such errors come to light as a result of further sensory information, it cannot be right to cast wholesale doubt on the evidence of the senses. But Descartes regarded the argument from illusion as only the first stage in softening up process which would ‘lead the mind away from the senses'. He admits that there are some cases of sense-base belief about which doubt would be insane, e.g., the belief that I am sitting here by the fire, wearing a winter dressing gown'.
Descartes was to realize that there was nothing in this view of nature that could explain or provide a foundation for the mental, or from direct experience as distinctly human. In a mechanistic universe, he said, there is no privileged place or function for mind, and the separation between mind and matter is absolute. Descartes was also convinced, that the immaterial essences that gave form and structure to this universe were coded in geometrical and mathematical ideas, and this insight led him to invent algebraic geometry.
A scientific understanding of these ideas could be derived, said Descartes, with the aid of precise deduction, and he also claimed that the contours of physical reality could be laid out in three-dimensional coordinates. Following the publication of Newton's Principia Mathematica in 1687, reductionism and mathematical modelling became the most powerful tools of modern science. And the dream that the entire physical world could be known and mastered through the extension and refinement of mathematical theory became the central feature and guiding principle of scientific knowledge.
Having to its recourse of knowledge, its cental questions include the origin of knowledge, the place of experience in generating knowledge, and the place of reason in doing so, the relationship between knowledge and certainty, and between knowledge and the impossibility of error, the possibility of universal scepticism, and the changing forms of knowledge that arise from new conceptualizations of the world. All of these issues link with other central concerns of philosophy, such as the nature of truth and the natures of experience and meaning.
Foundationalism was associated with the ancient Stoics, and in the modern era with Descartes (1596-1650). Who discovered his foundations in the ‘clear and distinct' ideas of reason? Its main opponent is Coherentism, or the view that a body of propositions mas be known without a foundation in certainty, but by their interlocking strength, than as a crossword puzzle may be known to have been solved correctly even if each answer, taken individually, admits of uncertainty. Difficulties at this point led the logical passivists to abandon the notion of an epistemological foundation altogether, and to flirt with the coherence theory of truth. It is widely accepted that trying to make the connection between thought and experience through basic sentences depends on an untenable ‘myth of the given'.
Still in spite of these concerns, the problem, least of mention, is of defining knowledge in terms of true beliefs plus some favoured relations between the believer and the facts that began with Plato's view in the "Theaetetus," that knowledge is true belief, and some logos. Due of its nonsynthetic epistemology, the enterprising of studying the actual formation of knowledge by human beings, without aspiring to certify those processes as rational, or its proof against ‘scepticism' or even apt to yield the truth. Natural epistemology would therefore blend into the psychology of learning and the study of episodes in the history of science. The scope for ‘external' or philosophical reflection of the kind that might result in scepticism or its refutation is markedly diminished. Despite the fact that the terms of modernity are so distinguished as exponents of the approach include Aristotle, Hume, and J. S. Mills.
The task of the philosopher of a discipline would then be to reveal the correct method and to unmask counterfeits. Although this belief lay behind much positivist philosophy of science, few philosophers now subscribe to it. It places too well a confidence in the possibility of a purely previous ‘first philosophy', or viewpoint beyond that of the work one's way of practitioners, from which their best efforts can be measured as good or bad. These standpoints now seem that too many philosophers to be a fanciefancy, that the more modest of tasks that are actually adopted at various historical stages of investigation into different areas with the aim not so much of criticizing but more of systematization, in the presuppositions of a particular field at a particular tie. There is still a role for local methodological disputes within the community investigators of some phenomenon, with one approach charging that another is unsound or unscientific, but logic and philosophy will not, on the modern view, provide an independent arsenal of weapons for such battles, which indeed often come to seem more like political bids for ascendancy within a discipline.
This is an approach to the theory of knowledge that sees an important connection between the growth of knowledge and biological evolution. An evolutionary epistemologist claims that the development of human knowledge processed through some natural selection process, the best example of which is Darwin's theory of biological natural selection. There is a widespread misconception that evolution proceeds according to some plan or direct, but it has neither, and the role of chance ensures that its future course will be unpredictable. Random variations in individual organisms create tiny differences in their Darwinian fitness. Some individuals have more offsprings than others, and the characteristics that increased their fitness thereby become more prevalent in future generations. Once upon a time, at least a mutation occurred in a human population in tropical Africa that changed the haemoglobin molecule in a way that provided resistance to malaria. This enormous advantage caused the new gene to spread, with the unfortunate consequence that sickle-cell anaemia came to exist.
Chance can influence the outcome at each stage: First, in the creation of genetic mutation, second, in wether the bearer lives long enough to show its effects, thirdly, in chance events that influence the individual's actual reproductive success, and fourth, in whether a gene even if favoured in one generation, is, happenstance, eliminated in the next, and finally in the many unpredictable environmental changes that will undoubtedly occur in the history of any group of organisms. As Harvard biologist Stephen Jay Gould has so vividly expressed that process over again, the outcome would surely be different. Not only might there not be humans, there might not even be anything like mammals.
We will often emphasis the elegance of traits shaped by natural selection, but the common idea that nature creates perfection needs to be analysed carefully. The extent to which evolution achieves perfection depends on exactly what you mean. If you mean "Does natural selections always take the best path for the long-term welfare of a species?" The answer is no. That would require adaption by group selection, and this is, unlikely. If you mean "Does natural selection creates every adaption that would be valuable?" The answer again, is no. For instance, some kinds of South American monkeys can grasp branches with their tails. The trick would surely also be useful to some African species, but, simply because of bad luck, none have it. Some combination of circumstances started some ancestral South American monkeys using their tails in ways that ultimately led to an ability to grab onto branches, while no such development took place in Africa. Mere usefulness of a trait does not necessitate a means in that what will understandably endure phylogenesis or evolution.
This is an approach to the theory of knowledge that sees an important connection between the growth of knowledge and biological evolution. An evolutionary epistemologist claims that the development of human knowledge proceeds through some natural selection process, the best example of which is Darwin's theory of biological natural selection. The three major components of the model of natural selection are variation selection and retention. According to Darwin's theory of natural selection, variations are not pre-designed to do certain functions. Rather, these variations that do useful functions are selected. While those that do not employ of some coordinates in that are regainfully purposed are also, not to any of a selection, as duly influenced of such a selection, that may have responsibilities for the visual aspects of a variational intentionally occurs. In the modern theory of evolution, genetic mutations provide the blind variations: Blind in the sense that variations are not influenced by the effects they would have-the likelihood of a mutation is not correlated with the benefits or liabilities that mutation would confer on the organism, the environment provides the filter of selection, and reproduction provides the retention. Fatnesses are achieved because those organisms with features that make them less adapted for survival do not survive in connection with other organisms in the environment that have features that are better adapted. Evolutionary epistemology applies this blind variation and selective retention model to the growth of scientific knowledge and to human thought processes overall.
The parallel between biological evolution and conceptual or ‘epistemic' evolution can be seen as either literal or analogical. The literal version of evolutionary epistemology deeds biological evolution as the main cause of the growth of knowledge. On this view, called the ‘evolution of cognitive mechanic programs', by Bradie (1986) and the ‘Darwinian approach to epistemology' by Ruse (1986), that growth of knowledge occurs through blind variation and selective retention because biological natural selection itself is the cause of epistemic variation and selection. The most plausible version of the literal view does not hold that all human beliefs are innate but rather than the mental mechanisms that guide the acquisitions of non-innate beliefs are themselves innately and the result of biological natural selection. Ruse, (1986) demands of a version of literal evolutionary epistemology that he links to sociolology (Rescher, 1990).
On the analogical version of evolutionary epistemology, called the ‘evolution of theory's program', by Bradie (1986). The ‘Spenserians approach' (after the nineteenth century philosopher Herbert Spencer) by Ruse (1986), the development of human knowledge is governed by a process analogous to biological natural selection, rather than by an instance of the mechanism itself. This version of evolutionary epistemology, introduced and elaborated by Donald Campbell (1974) as well as Karl Popper, sees the [partial] fit between theories and the world as explained by a mental process of trial and error known as epistemic natural selection.
Both versions of evolutionary epistemology are usually taken to be types of naturalized epistemology, because both take some empirical facts as a starting point for their epistemological project. The literal version of evolutionary epistemology begins by accepting evolutionary theory and a materialist approach to the mind and, from these, constructs an account of knowledge and its developments. In contrast, the metaphorical version does not require the truth of biological evolution: It simply draws on biological evolution as a source for the model of natural selection. For this version of evolutionary epistemology to be true, the model of natural selection need only apply to the growth of knowledge, not to the origin and development of species. Crudely put, evolutionary epistemology of the analogical sort could still be true even if Creationism is the correct theory of the origin of species.
Although they do not begin by assuming evolutionary theory, most analogical evolutionary epistemologists are naturalized epistemologists as well, their empirical assumptions, least of mention, implicitly come from psychology and cognitive science, not evolutionary theory. Sometimes, however, evolutionary epistemology is characterized in a seemingly non-naturalistic fashion. Campbell (1974) says that ‘if one is expanding knowledge beyond what one knows, one has no choice but to explore without the benefit of wisdom', i.e., blindly. This, Campbell admits, makes evolutionary epistemology close to being a tautology (and so not naturalistic). Evolutionary epistemology does assert the analytic claim that when expanding one's knowledge beyond what one knows, one must precessed to something that is already known, but, more interestingly, it also makes the synthetic claim that when expanding one's knowledge beyond what one knows, one must proceed by blind variation and selective retention. This claim is synthetic because it can be empirically falsified. The central claim of evolutionary epistemology is synthetic, not analytic. If the central contradictory, which they are not. Campbell is right that evolutionary epistemology does have the analytic feature he mentions, but he is wrong to think that this is a distinguishing feature, since any plausible epistemology has the same analytic feature (Skagestad, 1978).
Two extraordinary issues lie to awaken the literature that involves questions about ‘realism', i.e., What metaphysical commitment does an evolutionary epistemologist have to make? Progress, i.e., according to evolutionary epistemology, does knowledge develop toward a goal? With respect to realism, many evolutionary epistemologists endorse that is called ‘hypothetical realism', a view that combines a version of epistemological ‘scepticism' and tentative acceptance of metaphysical realism. With respect to progress, the problem is that biological evolution is not goal-directed, but the growth of human knowledge seems to be. Campbell (1974) worries about the potential dis-analogy here but is willing to bite the stone of conscience and admit that epistemic evolution progress toward a goal (truth) while biologic evolution does not. Many another has argued that evolutionary epistemologists must give up the ‘truth-topic' sense of progress because a natural selection model is in essence, is non-teleological, as an alternative, following Kuhn (1970), and embraced in the accompaniment with evolutionary epistemology.
Among the most frequent and serious criticisms levelled against evolutionary epistemology is that the analogical version of the view is false because epistemic variation is not blind (Skagestad, 1978, 613-16, and Ruse, 1986, ch.2 (. Stein and Lipton (1990) have argued, however, that this objection fails because, while epistemic variation is not random, its constraints come from heuristics that, for the most part, are selective retention. Further, Stein and Lipton come to the conclusion that heuristics are analogous to biological pre-adaptions, evolutionary pre-biological pre-adaptions, evolutionary cursors, such as a half-wing, a precursor to a wing, which have some function other than the function of their descendable structures: The function of descendable structures, the function of their descendable character embodied to its structural foundations, is that of the guidelines of epistemic variation is, on this view, not the source of disanalogy, but the source of a more articulated account of the analology.
Many evolutionary epistemologists try to combine the literal and the analogical versions (Bradie, 1986, and Stein and Lipton, 1990), saying that those beliefs and cognitive mechanisms, which are innate results from natural selection of the biological sort and those that are innate results from natural selection of the epistemic sort. This is reasonable as long as the two parts of this hybrid view are kept distinct. An analogical version of evolutionary epistemology with biological variation as its only source of blondeness would be a null theory: This would be the case if all our beliefs are innate or if our non-innate beliefs are not the result of blind variation. An appeal to the legitimate way to produce a hybrid version of evolutionary epistemology since doing so trivializes the theory. For similar reasons, such an appeal will not save an analogical version of evolutionary epistemology from arguments to the effect that epistemic variation is blind (Stein and Lipton, 1990).
Although it is a new approach to theory of knowledge, evolutionary epistemology has attracted much attention, primarily because it represents a serious attempt to flesh out a naturalized epistemology by drawing on several disciplines. In science is relevant to understanding the nature and development of knowledge, then evolutionary theory is among the disciplines worth a look. Insofar as evolutionary epistemology looks there, it is an interesting and potentially fruitful epistemological programme.
What makes a belief justified and what makes a true belief knowledge? Thinking that whether a belief deserves one of these appraisals is natural depends on what caused the depicted branch of knowledge to have the belief. In recent decades a number of epistemologists have pursued this plausible idea with a variety of specific proposals. Some causal theories of knowledge have it that a true belief that ‘p' is knowledge just in case it has the right causal connection to the fact that ‘p'. Such a criterion can be applied only to cases where the fact that ‘p' is a sort that can enter into causal relations, as this seems to exclude mathematically and the necessary facts and perhaps any fact expressed by a universal generalization, and proponents of this sort of criterion have usually supposed that it is limited to perceptual representations where knowledge of particular facts about subjects' environments.
For example, Armstrong (1973), predetermined that a position held by a belief in the form ‘This perceived object is ‘F' is [non-inferential] knowledge if and only if the belief is a completely reliable sign that the perceived object is ‘F', that is, the fact that the object is ‘F' contributed to causing the belief and its doing so depended on properties of the believer such that the laws of nature dictated that, for any subject ‘ ' and perceived object ‘y', if ‘ ' has those properties and believed that ‘y' is ‘F', then ‘y' is ‘F'. (Dretske (1981) offers a rather similar account, in terms of the belief's being caused by a signal received by the perceiver that carries the information that the object is ‘F').
Goldman (1986) has proposed an importantly different causal criterion, namely, that a true belief is knowledge if it is produced by a type of process that is ‘globally' and ‘locally' reliable. Causing true beliefs is sufficiently high is globally reliable if its propensity. Local reliability has to do with whether the process would have produced a similar but false belief in certain counterfactual situations alternative to the actual situation. This way of marking off true beliefs that are knowledge does not require the fact believed to be causally related to the belief, and so it could in principle apply to knowledge of any kind of truth.
Goldman requires the global reliability of the belief-producing process for the justification of a belief, he requires it also for knowledge because justification is required for knowledge. What he requires for knowledge, but does not require for justification is local reliability. His idea is that a justified true belief is knowledge if the type of process that produced it would not have produced it in any relevant counterfactual situation in which it is false. Its purported theory of relevant alternatives can be viewed as an attempt to provide a more satisfactory response to this tension in our thinking about knowledge. It attempts to characterize knowledge in a way that preserves both our belief that knowledge is an absolute concept and our belief that we have knowledge.
According to the theory, we need to qualify rather than deny the absolute character of knowledge. We should view knowledge as absolute, reactive to certain standards (Dretske, 1981 and Cohen, 1988). That is to say, in order to know a proposition, our evidence need not eliminate all the alternatives to that preposition, rather for ‘us', that we can know our evidence eliminates al the relevant alternatives, where the set of relevant alternatives (a proper subset of the set of all alternatives) is determined by some standard. Moreover, according to the relevant alternatives view, and the standards determining that of the alternatives is raised by the sceptic are not relevant. If this is correct, then the fact that our evidence cannot eliminate the sceptic's alternative does not lead to a sceptical result. For knowledge requires only the elimination of the relevant alternatives, so the relevant alternative view preserves in both strands in our thinking about knowledge. Knowledge is an absolute concept, but because the absoluteness is relative to a standard, we can know many things.
The interesting thesis that counts as a causal theory of justification (in the meaning of ‘causal theory' intended here) is that: A belief is justified in case it was produced by a type of process that is ‘globally' reliable, that is, its propensity to produce true beliefs-that can be defined (to a good approximation) As the proportion of the beliefs it produces (or would produce) that is true is sufficiently great.
This proposal will be adequately specified only when we are told (i) how much of the causal history of a belief counts as part of the process that produced it, (ii) which of the many types to which the process belongs is the type for purposes of assessing its reliability, and (iii) relative to why the world or worlds are the reliability of the process type to be assessed the actual world, the closet worlds containing the case being considered, or something else? Let ‘us' look at the answers suggested by Goldman, the leading proponent of a reliabilist account of justification.
(1) Goldman (1979, 1986) takes the relevant belief producing process to include only the proximate causes internal to the believer. So, for instance, when recently I believed that the telephone was ringing the process that produced the belief, for purposes of assessing reliability, includes just the causal chain of neural events from the stimulus in my ear's inward ands other concurrent brain states on which the production of the belief depended: It does not include any events' as the telephone, or the sound waves travelling between it and my ears, or any earlier decisions I made that were responsible for my being within hearing distance of the telephone at that time. It does seem intuitively plausible of a belief depends should be restricted to internal omnes proximate to the belief. Why? Goldman does not tell ‘us'. One answer that some philosophers might give is that it is because a belief's being justified at a given time can depend only on facts directly accessible to the believer's awareness at that time (for, if a believer ought to holds only beliefs that are justified, she can tell at any given time what beliefs would then be justified for her). However, this cannot be Goldman's answer because he wishes to include in the relevantly process neural events that are not directly accessible to consciousness.
(2) Once the reliabilist has told ‘us' how to delimit the process producing a belief, he needs to tell ‘us' which of the many types to which it belongs is the relevant type. Coincide, for example, the process that produces your current belief that you see a book before you. One very broad type to which that process belongs would be specified by ‘coming to a belief as to something one perceives as a result of activation of the nerve endings in some of one's sense-organs'. A constricted type, in which that unvarying processes belong would be specified by ‘coming to a belief as to what one sees as a result of activation of the nerve endings in one's retinas'. A still narrower type would be given by inserting in the last specification a description of a particular pattern of activation of the retina's particular cells. Which of these or other types to which the token process belongs is the relevant type for determining whether the type of process that produced your belief is reliable?
If we select a type that is too broad, as having the same degree of justification various beliefs that intuitively seem to have different degrees of justification. Thus the broadest type we specified for your belief that you see a book before you apply also to perceptual beliefs where the object seen is far away and seen only briefly is less justified. On the other hand, is we are allowed to select a type that is as narrow as we please, then we make it out that an obviously unjustified but true belief is produced by a reliable type of process. For example, suppose I see a blurred shape through the fog far in a field and unjustifiedly, but correctly, believe that it is a sheep: If we include enough details about my retinal image is specifying te type of the visual process that produced that belief, we can specify a type is likely to have only that one instanced and is therefore 100 percent reliable. Goldman conjectures (1986) that the relevant process type is ‘the narrowest type that is casually operative'. Presumably, a feature of the process producing beliefs were causally operatives in producing it just in case some alternative feature instead, but it would not have led to that belief. (We need to say ‘some' here rather than ‘any', because, for example, when I see an oak or pine tree, the particular ‘like-minded' material bodies of my retinal image are causably clearly toward the operatives in producing my belief that what is seen as a tree, even though there are alternative shapes, for example, ‘pineish' or ‘birchness' ones, that would have produced the same belief.)
(3) Should the justification of a belief in a hypothetical, non-actual example turn on the reliability of the belief-producing process in the possible world of the example? That leads to the implausible result in that in a world run by a Cartesian demon-a powerful being who causes the other inhabitants of the world to have rich and coherent sets of perceptual and memory impressions that are all illusory the perceptual and memory beliefs of the other inhabitants are all unjustified, for they are produced by processes that are, in that world, quite unreliable. If we say instead that it is the reliability of the processes in the actual world that matters, we get the equally undesired result that if the actual world is a demon world then our perceptual and memory beliefs are all unjustified.
Goldman's solution (1986) is that the reliability of the process types is to be gauged by their performance in ‘normal' worlds, that is, worlds consistent with ‘our general beliefs about the world . . . ‘about the sorts of objects, events and changes that occur in it'. This gives the intuitively right results for the problem cases just considered, but indicate by inference an implausible proportion of making compensations for alternative tending toward justification. If there are people whose general beliefs about the world are very different from mine, then there may, on this account, be beliefs that I can correctly regard as justified (ones produced by processes that are reliable in what I take to be a normal world) but that they can correctly regard as not justified.
However, these questions about the specifics are dealt with, and there are reasons for questioning the basic idea that the criterion for a belief's being justified is its being produced by a reliable process. Thus and so, doubt about the sufficiency of the reliabilist criterion is prompted by a sort of example that Goldman himself uses for another purpose. Suppose that being in brain-state ‘B' always causes one to believe that one is in brained-state ‘B'. Here the reliability of the belief-producing process is perfect, but ‘we can readily imagine circumstances in which a person goes into grain-state ‘B' and therefore has the belief in question, though this belief is by no means justified' (Goldman, 1979). Doubt about the necessity of the condition arises from the possibility that one might know that one has strong justification for a certain belief and yet that knowledge is not what actually prompts one to believe. For example, I might be well aware that, having read the weather bureau's forecast that it will be much hotter tomorrow. I have ample reason to be confident that it will be hotter tomorrow, but I irrationally refuse to believe it until Wally tells me that he feels in his joints that it will be hotter tomorrow. Here what prompts me to believe dors not justify my belief, but my belief is nevertheless justified by my knowledge of the weather bureau's prediction and of its evidential force: I can advert to any disavowable inference that I ought not to be holding the belief. Indeed, given my justification and that there is nothing untoward about the weather bureau's prediction, my belief, if true, can be counted knowledge. This sorts of example raises doubt whether any causal conditions, are it a reliable process or something else, is necessary for either justification or knowledge.
Philosophers and scientists alike, have often held that the simplicity or parsimony of a theory is one reason, all else being equal, to view it as true. This goes beyond the unproblematic idea that simpler theories are easier to work with and gave greater aesthetic appeal.
One theory is more parsimonious than another when it postulates fewer entities, processes, changes or explanatory principles: The simplicity of a theory depends on essentially the same consecrations, though parsimony and simplicity obviously become the same. Demanding clarification of what makes one theory simpler or more parsimonious is plausible than another before the justification of these methodological maxims can be addressed.
If we set this description problem to one side, the major normative problem is as follows: What reason is there to think that simplicity is a sign of truth? Why should we accept a simpler theory instead of its more complex rivals? Newton and Leibniz thought that the answer was to be found in a substantive fact about nature. In "Principia," Newton laid down as his first Rule of Reasoning in Philosophy that ‘nature does nothing in vain . . . ‘for Nature is pleased with simplicity and affects not the pomp of superfluous causes'. Leibniz hypothesized that the actual world obeys simple laws because God's taste for simplicity influenced his decision about which world to actualize.
The tragedy of the Western mind, described by KoyrĂ©, is a direct consequence of the stark Cartesian division between mind and world. We discovered the ‘certain principles of physical reality', said Descartes, ‘not by the prejudices of the senses, but by the light of reason, and which thus possess so great evidence that we cannot doubt of their truth'. Since the real, or that which actually exists external to ourselves, was in his view only that which could be represented in the quantitative terms of mathematics, Descartes concludes that all quantitative aspects of reality could be traced to the deceitfulness of the senses.
The most fundamental aspect of the Western intellectual tradition is the assumption that there is a fundamental division between the material and the immaterial world or between the realm of matter and the realm of pure mind or spirit. The metaphysical frame-work based on this assumption is known as ontological dualism. As the word dual implies, the framework is predicated on an ontology, or a conception of the nature of God or Being, that assumes reality has two distinct and separable dimensions. The concept of Being as continuous, immutable, and having a prior or separate existence from the world of change dates from the ancient Greek philosopher Parmenides. The same qualities were associated with the God of the Judeo-Christian tradition, and they were considerably amplified by the role played in theology by Platonic and Neoplatonic philosophy.
Nicolas Copernicus, Galileo, Johannes Kepler, and Isaac Newton were all inheritors of a cultural tradition in which ontological dualism was a primary article of faith. Hence the idealization of the mathematical ideal as a source of communion with God, which dates from Pythagoras, provided a metaphysical foundation for the emerging natural sciences. This explains why, the creators of classical physics believed that doing physics was a form of communion with the geometrical and mathematical form's resident in the perfect mind of God. This view would survive in a modified form in what is now known as Einsteinian epistemology and accounts in no small part for the reluctance of many physicists to accept the epistemology associated with the Copenhagen Interpretation.
At the beginning of the nineteenth century, Pierre-Sinon LaPlace, along with a number of other French mathematicians, advanced the view that the science of mechanics constituted a complete view of nature. Since this science, by observing its epistemology, had revealed itself to be the fundamental science, the hypothesis of God was, they concluded, entirely unnecessary.
LaPlace is recognized for eliminating not only the theological component of classical physics but the ‘entire metaphysical component' as well'. The epistemology of science requires, he said, that we proceed by inductive generalizations from observed facts to hypotheses that are ‘tested by observed conformity of the phenomena'. What was unique about LaPlace's view of hypotheses was his insistence that we cannot attribute reality to them. Although concepts like force, mass, motion, cause, and laws are obviously present in classical physics, they exist in LaPlace's view only as quantities. Physics is concerned, he argued, with quantities that we associate as a matter of convenience with concepts, and the truths about nature are only the quantities.
As this view of hypotheses and the truths of nature as quantities were extended in the nineteenth century to a mathematical description of phenomena like heat, light, electricity, and magnetism. LaPlace's assumptions about the actual character of scientific truths seemed correct. This progress suggested that if we could remove all thoughts about the ‘nature of' or the ‘source of' phenomena, the pursuit of strictly quantitative concepts would bring us to a complete description of all aspects of physical reality. Subsequently, figures like Comte, Kirchhoff, Hertz, and PoincarĂ© developed a program for the study of nature hat was quite different from that of the original creators of classical physics.
The seventeenth-century view of physics as a philosophy of nature or as natural philosophy was displaced by the view of physics as an autonomous science that was ‘the science of nature'. This view, which was premised on the doctrine of positivism, promised to subsume all of the nature with a mathematical analysis of entities in motion and claimed that the true understanding of nature was revealed only in the mathematical description. Since the doctrine of positivism assumes that the knowledge we call physics resides only in the mathematical formalism of physical theory, it disallows the prospect that the vision of physical reality revealed in physical theory can have any other meaning. In the history of science, the irony is that positivism, which was intended to banish metaphysical concerns from the domain of science, served to perpetuate a seventeenth-century metaphysical assumption about the relationship between physical reality and physical theory.
Epistemology since Hume and Kant has drawn back from this theological underpinning. Indeed, the very idea that nature is simple (or uniform) has come in for a critique. The view has taken hold that a preference for simple and parsimonious hypotheses is purely methodological: It is constitutive of the attitude we call ‘scientific' and makes no substantive assumption about the way the world is.
A variety of otherwise diverse twentieth-century philosophers of science have attempted, in different ways, to flesh out this position. Two examples must suffice here: Hesse (1969) as, for summaries of other proposals. Popper (1959) holds that scientists should prefer highly falsifiable (improbable) theories: He tries to show that simpler theories are more falsifiable, also Quine (1966), in contrast, sees a virtue in theories that are highly probable, he argues for a general connection between simplicity and high probability.
Both these proposals are global. They attempt to explain why simplicity should be part of the scientific method in a way that spans all scientific subject matters. No assumption about the details of any particular scientific problem serves as a premiss in Popper's or Quine's arguments.
Newton and Leibniz thought that the justification of parsimony and simplicity flows from the hand of God: Popper and Quine try to justify these methodologically median of importance is without assuming anything substantive about the way the world is. In spite of these differences in approach, they have something in common. They assume that all users of parsimony and simplicity in the separate sciences can be encompassed in a single justifying argument. That recent developments in confirmation theory suggest that this assumption should be scrutinized. Good (1983) and Rosenkrantz (1977) has emphasized the role of auxiliary assumptions in mediating the connection between hypotheses and observations. Whether a hypothesis is well supported by some observations, or whether one hypothesis is better supported than another by those observations, crucially depends on empirical background assumptions about the inference problem here. The same view applies to the idea of prior probability (or, prior plausibility). In of a single hypo-physical science if chosen as an alternative to another even though they are equally supported by current observations, this must be due to an empirical background assumption.
Principles of parsimony and simplicity mediate the epistemic connection between hypotheses and observations. Perhaps these principles are able to do this because they are surrogates for an empirical background theory. It is not that there is one background theory presupposed by every appeal to parsimony; This has the quantifier order backwards. Rather, the suggestion is that each parsimony argument is justified only to each degree that it reflects an empirical background theory about the subjective matter. On this theory is brought out into the open, but the principle of parsimony is entirely dispensable (Sober, 1988).
This ‘local' approach to the principles of parsimony and simplicity resurrects the idea that they make sense only if the world is one way rather than another. It rejects the idea that these maxims are purely methodological. How defensible this point of view is, will depend on detailed case studies of scientific hypothesis evaluation and on further developments in the theory of scientific inference.
It is usually not found of one and the same that, an inference is a (perhaps very complex) act of thought by virtue of which act (1) I pass from a set of one or more propositions or statements to a proposition or statement and (2) it appears that the latter are true if the former is or are. This psychological characterization has occurred over a wider summation of literature under more lesser than inessential variations. Desiring a better characterization of inference is natural. Yet attempts to do so by constructing a fuller psychological explanation fail to comprehend the grounds on which inference will be objectively valid-A point elaborately made by Gottlob FrĂ©ge. Attempts to understand the nature of inference through the device of the representation of inference by formal-logical calculations or derivations better (1) leave ‘us' puzzled about the relation of formal-logical derivations to the informal inferences they are supposedly to represent or reconstruct, and (2) leaves ‘us' worried about the sense of such formal derivations. Are these derivations inference? Are not informal inferences needed in order to apply the rules governing the constructions of formal derivations (inferring that this operation is an application of that formal rule)? These are concerns cultivated by, for example, Wittgenstein.
Coming up with an adequate characterization of inference-and even working out what would count as a very adequate characterization here is demandingly by no means nearly some resolved philosophical problem.
The rule of inference, as for raised by Lewis Carroll, the Zeno-like problem of how a ‘proof' ever gets started. Suppose I have as premises (i) ‘p' and (ii) p q. Can I infer ‘q'? Only, it seems, if I am sure of (iii) (p & p q) q. Can I then infer ‘q'? Only, it seems, if I am sure that (iv) (p & p q & (p & p q) q) q. For each new axiom (N) I need a further axiom (N + 1) telling me that the set so far implies ‘q', and the regress never stops. The usual solution is to treat a system as containing not only axioms, but also rules of inference, allowing movement from the axioms. The rule ‘modus ponens' allow ‘us' to pass from the first premise to ‘q'. Carroll's puzzle shows that distinguishing two theoretical categories is essential, although there may be choice about which theses to put in which category.
Traditionally, a proposition that is not a ‘conditional', as with the ‘affirmative' and ‘negative', modern opinion is wary of the distinction, since what appears categorical may vary with the choice of a primitive vocabulary and notation. Apparently categorical propositions may also turn out to be disguised conditionals: ‘X' is intelligent (categorical?) Equivalent, if ‘X' is given a range of tasks, she does them better than many people (conditional?). The problem is not merely one of classification, since deep metaphysical questions arise when facts that seem to be categorical and therefore solid, come to seem by contrast conditional, or purely hypothetical or potential.
Its condition of some classified necessity is so proven sufficient that if ‘p' is a necessary condition of ‘q', then ‘q' cannot be true unless ‘p'; is true? If ‘p' is a sufficient condition, thus steering well is a necessary condition of driving in a satisfactory manner, but it is not sufficient, for one can steer well but drive badly for other reasons. Confusion may result if the distinction is not heeded. For example, the statement that ‘A' causes ‘B' may be interpreted to mean that ‘A' is itself a sufficient condition for ‘B', or that it is only a necessary condition fort ‘B', or perhaps a necessary parts of a total sufficient condition. Lists of conditions to be met for satisfying some administrative or legal requirement frequently attempt to give individually necessary and jointly sufficient sets of conditions.
What is more, that if any proposition of the form ‘if p then q'. The condition hypothesized, ‘p'. Is called the antecedent of the conditionals, and ‘q', the consequent? Various kinds of conditional have been distinguished. Its weakest is that of ‘material implication', merely telling that either ‘not-p', or ‘q'. Stronger conditionals include elements of ‘modality', corresponding to the thought that ‘if p is truer then q must be true'. Ordinary language is very flexible in its use of the conditional form, and there is controversy whether conditionals are better treated semantically, yielding differently finds of conditionals with different meanings, or pragmatically, in which case there should be one basic meaning with surface differences arising from other implicatures.
It follows from the definition of ‘strict implication' that a necessary proposition is strictly implied by any proposition, and that an impossible proposition strictly implies any proposition. If strict implication corresponds to ‘q follows from p', then this means that a necessary proposition follows from anything at all, and anything at all follows from an impossible proposition. This is a problem if we wish to distinguish between valid and invalid arguments with necessary conclusions or impossible premises.
The Humean problem of induction is that if we would suppose that there is some property ‘A' concerning and observational or an experimental situation, and that out of a large number of observed instances of ‘A', some fraction m/n (possibly equal to 1) has also been instances of some logically independent property ‘B'. Suppose further that the background proportionate circumstances not specified in these descriptions has been varied to a substantial degree and that there is no collateral information available concerning the frequency of ‘B's' among ‘A's or concerning causal or nomologically connections between instances of ‘A' and instances of ‘B'.
In this situation, an ‘enumerative' or ‘instantial' induction inference would move rights from the premise, that m/n of observed ‘A's' are ‘B's' to the conclusion that approximately m/n of all ‘A's' are ‘B's. (The usual probability qualification will be assumed to apply to the inference, rather than being part of the conclusion.) Here the class of ‘A's' should be taken to include not only unobserved ‘A's' and future ‘A's', but also possible or hypothetical ‘A's' (an alternative conclusion would concern the probability or likelihood of the adjacently observed ‘A' being a ‘B').
The traditional or Humean problem of induction, often referred to simply as ‘the problem of induction', is the problem of whether and why inferences that fit this schema should be considered rationally acceptable or justified from an epistemic or cognitive standpoint, i.e., whether and why reasoning in this way is likely to lead to true claims about the world. Is there any sort of argument or rationale that can be offered for thinking that conclusions reached in this way are likely to be true in the corresponding premisses is true or even that their chances of truth are significantly enhanced?
Hume's discussion of this issue deals explicitly only with cases where all observed ‘A's' are ‘B's' and his argument applies just as well to the more general case. His conclusion is entirely negative and sceptical: Inductive inferences are not rationally justified, but are instead the result of an essentially a-rational process, custom or habit. Hume (1711-76) challenges the proponent of induction to supply a cogent line of reasoning that leads from an inductive premise to the corresponding conclusion and offers an extremely influential argument in the form of a dilemma (a few times referred to as ‘Hume's fork'), that either our actions are determined, in which case we are not responsible for them, or they are the result of random events, under which case we are also not responsible for them.
Such reasoning would, he argues, have to be either deductively demonstrative reasoning in the concerning relations of ideas or ‘experimental', i.e., empirical, that reasoning concerning matters of fact or existence. It cannot be the former, because all demonstrative reasoning relies on the avoidance of contradiction, and it is not a contradiction to suppose that ‘the course of nature may change', that an order that was observed in the past and not of its continuing against the future: But it cannot be, as the latter, since any empirical argument would appeal to the success of such reasoning about an experience, and the justifiability of generalizing from experience are precisely what is at issue-so that any such appeal would be question-begging. Hence, Hume concludes that there can be no such reasoning (1748).
An alternative version of the problem may be obtained by formulating it with reference to the so-called Principle of Induction, which says roughly that the future will resemble the past or, somewhat better, that unobserved cases will resemble observed cases. An inductive argument may be viewed as enthymematic, with this principle serving as a supposed premiss, in which case the issue is obviously how such a premiss can be justified. Hume's argument is then that no such justification is possible: The principle cannot be justified a prior because having possession of been true in experiences without obviously begging the question is not contradictory to have possession of been true in experiences without obviously begging the question.
The predominant recent responses to the problem of induction, at least in the analytic tradition, in effect accept the main conclusion of Hume's argument, namely, that inductive inferences cannot be justified in the sense of showing that the conclusion of such an inference is likely to be true if the premise is true, and thus attempt to find another sort of justification for induction. Such responses fall into two main categories: (i) Pragmatic justifications or ‘vindications' of induction, mainly developed by Hans Reichenbach (1891-1953), and (ii) ordinary language justifications of induction, whose most important proponent is Frederick, Peter Strawson (1919-). In contrast, some philosophers still attempt to reject Hume's dilemma by arguing either (iii) That, contrary to appearances, induction can be inductively justified without vicious circularity, or (iv) that an anticipatory justification of induction is possible after all. In that:
(1) Reichenbach's view is that induction is best regarded, not as a form of inference, but rather as a ‘method' for arriving at posits regarding, i.e., the proportion of ‘A's' remain additionally of ‘B's'. Such a posit is not a claim asserted to be true, but is instead an intellectual wager analogous to a bet made by a gambler. Understood in this way, the inductive method says that one should posit that the observed proportion is, within some measure of an approximation, the true proportion and then continually correct that initial posit as new information comes in.
The gambler's bet is normally an ‘appraised posit', i.e., he knows the chances or odds that the outcome on which he bets will actually occur. In contrast, the inductive bet is a ‘blind posit': We do not know the chances that it will succeed or even that success is that it will succeed or even that success is possible. What we are gambling on when we make such a bet is the value of a certain proportion in the independent world, which Reichenbach construes as the limit of the observed proportion as the number of cases increases to infinity. Nevertheless, we have no way of knowing that there are even such a limit, and no way of knowing that the proportion of ‘A's' are in addition of ‘B's' converges in the end on some stable value than varying at random. If we cannot know that this limit exists, then we obviously cannot know that we have any definite chance of finding it.
What we can know, according to Reichenbach, is that ‘if' there is a truth of this sort to be found, the inductive method will eventually find it'. That this is so is an analytic consequence of Reichenbach's account of what it is for such a limit to exist. The only way that the inductive method of making an initial posit and then refining it in light of new observations can fail eventually to arrive at the true proportion is if the series of observed proportions never converges on any stable value, which means that there is no truth to be found pertaining the proportion of ‘A's additionally constitute ‘B's'. Thus, induction is justified, not by showing that it will succeed or indeed, that it has any definite likelihood of success, but only by showing that it will succeed if success is possible. Reichenbach's claim is that no more than this can be established for any method, and hence that induction gives ‘us' our best chance for success, our best gamble in a situation where there is no alternative to gambling.
This pragmatic response to the problem of induction faces several serious problems. First, there are indefinitely many other ‘methods' for arriving at posits for which the same sort of defence can be given-methods that yield the same results as the inductive method over time but differ arbitrarily before long. Despite the efforts of others, it is unclear that there is any satisfactory way to exclude such alternatives, in order to avoid the result that any arbitrarily chosen short-term posit is just as reasonable as the inductive posit. Second, even if there is a truth of the requisite sort to be found, the inductive method is only guaranteed to find it or even to come within any specifiable distance of it in the indefinite long run. All the same, any actual application of inductive results always takes place in the presence to the future eventful states in making the relevance of the pragmatic justification to actual practice uncertainly. Third, and most important, it needs to be emphasized that Reichenbach's response to the problem simply accepts the claim of the Humean sceptic that an inductive premise never provides the slightest reason for thinking that the corresponding inductive conclusion is true. Reichenbach himself is quite candid on this point, but this does not alleviate the intuitive implausibility of saying that we have no more reason for thinking that our scientific and commonsense conclusions that result in the induction of it ‘ . . . is true' than, to use Reichenbach's own analogy (1949), a blind man wandering in the mountains who feels an apparent trail with his stick has for thinking that following it will lead him to safety.
An approach to induction resembling Reichenbach's claiming in that those particular inductive conclusions are posits or conjectures, than the conclusions of cogent inferences, is offered by Popper. However, Popper's view is even more overtly sceptical: It amounts to saying that all that can ever be said in favour of the truth of an inductive claim is that the claim has been tested and not yet been shown to be false.
(2) The ordinary language response to the problem of induction has been advocated by many philosophers, none the less, Strawson claims that the question whether induction is justified or reasonable makes sense only if it tacitly involves the demand that inductive reasoning meet the standards appropriate to deductive reasoning, i.e., that the inductive conclusions are shown to follow deductively from the inductive assumption. Such a demand cannot, of course, be met, but only because it is illegitimate: Inductive and deductive reasons are simply fundamentally different kinds of reasoning, each possessing its own autonomous standards, and there is no reason to demand or expect that one of these kinds meet the standards of the other. Whereas, if induction is assessed by inductive standards, the only ones that are appropriate, then it is obviously justified.
The problem here is to understand to what this allegedly obvious justification of an induction amount. In his main discussion of the point (1952), Strawson claims that it is an analytic true statement that believing it a conclusion for which there is strong evidence is reasonable and an analytic truth that inductive evidence of the sort captured by the schema presented earlier constitutes strong evidence for the corresponding inductive conclusion, thus, apparently yielding the analytic conclusion that believing it a conclusion for which there is inductive evidence is reasonable. Nevertheless, he also admits, indeed insists, that the claim that inductive conclusions will be true in the future is contingent, empirical, and may turn out to be false (1952). Thus, the notion of reasonable belief and the correlative notion of strong evidence must apparently be understood in ways that have nothing to do with likelihood of truth, presumably by appeal to the standard of reasonableness and strength of evidence that are accepted by the community and are embodied in ordinary usage.
Understood in this way, Strawson's response to the problem of inductive reasoning does not speak to the central issue raised by Humean scepticism: The issue of whether the conclusions of inductive arguments are likely to be true. It amounts to saying merely that if we reason in this way, we can correctly call ourselves ‘reasonable' and our evidence ‘strong', according to our accepted community standards. Nevertheless, to the undersealing of issue of wether following these standards is a good way to find the truth, the ordinary language response appears to have nothing to say.
(3) The main attempts to show that induction can be justified inductively have concentrated on showing that such as a defence can avoid circularity. Skyrms (1975) formulate, perhaps the clearest version of this general strategy. The basic idea is to distinguish different levels of inductive argument: A first level in which induction is applied to things other than arguments: A second level in which it is applied to arguments at the first level, arguing that they have been observed to succeed so far and hence are likely to succeed in general: A third level in which it is applied in the same way to arguments at the second level, and so on. Circularity is allegedly avoided by treating each of these levels as autonomous and justifying the argument at each level by appeal to an argument at the next level.
One problem with this sort of move is that even if circularity is avoided, the movement to higher and higher levels will clearly eventually fail simply for lack of evidence: A level will reach at which there have been enough successful inductive arguments to provide a basis for inductive justification at the next higher level, and if this is so, then the whole series of justifications collapses. A more fundamental difficulty is that the epistemological significance of the distinction between levels is obscure. If the issue is whether reasoning in accord with the original schema offered above ever provides a good reason for thinking that the conclusion is likely to be true, then it still seems question-begging, even if not flatly circular, to answer this question by appeal to anther argument of the same form.
(4) The idea that induction can be justified on a pure priori basis is in one way the most natural response of all: It alone treats an inductive argument as an independently cogent piece of reasoning whose conclusion can be seen rationally to follow, although perhaps only with probability from its premise. Such an approach has, however, only rarely been advocated (Russell, 19132 and BonJour, 1986), and is widely thought to be clearly and demonstrably hopeless.
Many on the reasons for this pessimistic view depend on general epistemological theses about the possible or nature of anticipatory cognition. Thus if, as Quine alleges, there is no a prior justification of any kind, then obviously a prior justification for induction is ruled out. Or if, as more moderate empiricists have in claiming some preexistent knowledge should be analytic, then again a prevenient justification for induction seems to be precluded, since the claim that if an inductive premise ids truer, then the conclusion is likely to be true does not fit the standard conceptions of ‘analyticity'. A consideration of these matters is beyond the scope of the present spoken exchange.
There are, however, two more specific and quite influential reasons for thinking that an early approach is impossible that can be briefly considered, first, there is the assumption, originating in Hume, but since adopted by very many of others, that a move forward in the defence of induction would have to involve ‘turning induction into deduction', i.e., showing, per impossible, that the inductive conclusion follows deductively from the premise, so that it is a formal contradiction to accept the latter and deny the former. However, it is unclear why a prior approach need be committed to anything this strong. It would be enough if it could be argued that it is deductively unlikely that such a premise is true and corresponding conclusion false.
Second, Reichenbach defends his view that pragmatic justification is the best that is possible by pointing out that a completely chaotic world in which there is simply not true conclusion to be found as to the proportion of ‘A's' in addition that occurs of, but B's' is neither impossible nor unlikely from a purely a prior standpoint, the suggestion being that therefore there can be no a prior reason for thinking that such a conclusion is true. Nevertheless, there is still a substring wayin laying that a chaotic world is a prior neither impossible nor unlikely without any further evidence does not show that such a world os not a prior unlikely and a world containing such-and-such regularity might anticipatorially be somewhat likely in relation to an occurrence of a long-run patten of evidence in which a certain stable proportion of observed ‘A's' are ‘B's' ~. An occurrence, it might be claimed, that would be highly unlikely in a chaotic world (BonJour, 1986).
Goodman's ‘new riddle of induction' purports that we suppose that before some specific time 't' (perhaps the year 2000) we observe a larger number of emeralds (property A) and find them all to be green (property B). We proceed to reason inductively and conclude that all emeralds are green Goodman points out, however, that we could have drawn a quite different conclusion from the same evidence. If we define the term ‘grue' to mean ‘green if examined before 't' and blue examined after t , then all of our observed emeralds will also be gruing. A parallel inductive argument will yield the conclusion that all emeralds are gruing, and hence that all those examined after the year 2000 will be blue. Presumably the first of these concisions is genuinely supported by our observations and the second is not. Nevertheless, the problem is to say why this is so and to impose some further restriction upon inductive reasoning that will permit the first argument and exclude the second.
The obvious alternative suggestion is that ‘grue. Similar predicates do not correspond to genuine, purely qualitative properties in the way that ‘green' and ‘blueness' does, and that this is why inductive arguments involving them are unacceptable. Goodman, however, claims to be unable to make clear sense of this suggestion, pointing out that the relations of formal desirability are perfectly symmetrical: Grue' may be defined in terms if, ‘green' and ‘blue', but ‘green' an equally well be defined in terms of ‘grue' and ‘green' (blue if examined before ‘t' and green if examined after ‘t').
The ‘grued, paradoxes' demonstrate the importance of categorization, in that sometimes it is itemized as ‘gruing', if examined of a presence to the future, before future time ‘t' and ‘green', or not so examined and ‘blue'. Even though all emeralds in our evidence class grue, we ought must infer that all emeralds are gruing. For ‘grue' is unprojectible, and cannot transmit credibility form known to unknown cases. Only projectable predicates are right for induction. Goodman considers entrenchment the key to projectibility having a long history of successful protection, ‘grue' is entrenched, lacking such a history, ‘grue' is not. A hypothesis is projectable, Goodman suggests, only if its predicates (or suitable related ones) are much better entrenched than its rivalrous past successes that do not assume future ones. Induction remains a risky business. The rationale for favouring entrenched predicates is pragmatic. Of the possible projections from our evidence class, the one that fits with past practices enables ‘us' to utilize our cognitive resources best. Its prospects of being true are worse than its competitors' and its cognitive utility is greater.
So, to a better understanding of induction we should then term is most widely used for any process of reasoning that takes ‘us' from empirical premises to empirical conclusions supported by the premises, but not deductively entailed by them. Inductive arguments are therefore kinds of applicative arguments, in which something beyond the content of the premise is inferred as probable or supported by them. Induction is, however, commonly distinguished from arguments to theoretical explanations, which share this applicative character, by being confined to inferences in which he conclusion involves the same properties or relations as the premises. The central example is induction by simple enumeration, where from premises telling that Fa, Fb, Fc . . . ‘where a, b, c's, are all of some kind ‘G', it is inferred that G's from outside the sample, such as future G's, will be ‘F', or perhaps that all G's are ‘F'. In this, which and the other persons deceive them, children may infer that everyone is a deceiver: Different, but similar inferences of a property by some object to the same object's future possession of the same property, or from the constancy of some law-like pattern in events and states of affairs ti its future constancy. All objects we know of attract each other with a force inversely proportional to the square of the distance between them, so perhaps they all do so, and will always do so.
The rational basis of any inference was challenged by Hume, who believed that induction presupposed belie in the uniformity of nature, but that this belief has no defence in reason, and merely reflected a habit or custom of the mind. Hume was not therefore sceptical about the role of reason in either explaining it or justifying it. Trying to answer Hume and to show that there is something rationally compelling about the inference referred to as the problem of induction. It is widely recognized that any rational defence of induction will have to partition well-behaved properties for which the inference is plausible (often called projectable properties) from badly behaved ones, for which it is not. It is also recognized that actual inductive habits are more complex than those of similar enumeration, and that both common sense and science pay attention to such giving factors as variations within the sample giving ‘us' the evidence, the application of ancillary beliefs about the order of nature, and so on.
Nevertheless, the fundamental problem remains that ant experience condition by application show ‘us' only events occurring within a very restricted part of a vast spatial and temporal order about which we then come to believe things.
Uncompounded by its belonging of a confirmation theory finding of the measure to which evidence supports a theory fully formalized confirmation theory would dictate the degree of confidence that a rational investigator might have in a theory, given some-body of evidence. The grandfather of confirmation theory is Gottfried Leibniz (1646-1718), who believed that a logically transparent language of science would be able to resolve all disputes. In the 20th century a fully formal confirmation theory was a main goal of the logical positivist, since without it the central concept of verification by empirical evidence itself remains distressingly unscientific. The principal developments were due to Rudolf Carnap (1891-1970), culminating in his "Logical Foundations of Probability" (1950). Carnap's idea was that the measure necessitated would be the proportion of logically possible states of affairs in which the theory and the evidence both hold, compared ti the number in which the evidence itself holds that the probability of a preposition, relative to some evidence, is a proportion of the range of possibilities under which the proposition is true, compared to the total range of possibilities left by the evidence. The difficulty with the theory lies in identifying sets of possibilities so that they admit of measurement. It therefore demands that we can put a measure on the ‘range' of possibilities consistent with theory and evidence, compared with the range consistent with the evidence alone.
Among the obstacles the enterprise meets, is the fact that while evidence covers only a finite range of data, the hypotheses of science may cover an infinite range. In addition, confirmation proves to vary with the language in which the science is couched, and the Carnapian programme has difficulty in separating genuinely confirming variety of evidence from less compelling repetition of the same experiment. Confirmation also proved to be susceptible to acute paradoxes. Finally, scientific judgement seems to depend on such intangible factors as the problems facing rival theories, and most workers have come to stress instead the historically situated scene of what would appear as a plausible distinction of a scientific knowledge at a given time.
Arose to the paradox of which when a set of apparent incontrovertible premises is given to unacceptable or contradictory conclusions. To solve a paradox will involve showing either that there is a hidden flaw in the premises, or that the reasoning is erroneous, or that the apparently unacceptable conclusion can, in fact, be tolerated. Paradoxes are therefore important in philosophy, for until one is solved it shows that there is something about our reasoning and our concepts that we do not understand. What is more, and somewhat loosely, a paradox is a compelling argument from unacceptable premises to an unacceptable conclusion: More strictly speaking, a paradox is specified to be a sentence that is true if and only if it is false. A characterized objection lesson of it would be: "The displayed sentence is false."
Seeing that this sentence is false if true is easy, and true if false, a paradox, in either of the senses distinguished, presents an important philosophical challenger. Epistemologists are especially concerned with various paradoxes having to do with knowledge and belief. In other words, for example, the Knower paradox is an argument that begins with apparently impeccable premisses about the concepts of knowledge and inference and derives an explicit contradiction. The origin of the reasoning is the ‘surprise examination paradox': A teacher announces that there will be a surprise examination next week. A clever student argues that this is impossible. ‘The test cannot be on Friday, the last day of the week, because it would not be a surprise. We would know the day of the test on Thursday evening. This means we can also rule out Thursday. For after we learn that no test has been given by Wednesday, we would know the test is on Thursday or Friday -and would already know that it s not on Friday and would already know that it is not on Friday by the previous reasoning. The remaining days can be eliminated in the same manner'.
This puzzle has over a dozen variants. The first was probably invented by the Swedish mathematician Lennard Ekbon in 1943. Although the first few commentators regarded the reverse elimination argument as cogent, every writer on the subject since 1950 agrees that the argument is unsound. The controversy has been over the proper diagnosis of the flaw.
Initial analyses of the subject's argument tried to lay the blame on a simple equivocation. Their failure led to more sophisticated diagnoses. The general format has been an assimilation to better-known paradoxes. One tradition casts the surprise examination paradox as a self-referential problem, as fundamentally akin to the Liar, the paradox of the Knower, or Gödel's incompleteness theorem. That in of itself, says enough that Kaplan and Montague (1960) distilled the following ‘self-referential' paradox, the Knower. Consider the sentence:
(S) The negation of this sentence is known (to be true).
Suppose that (S) is true. Then its negation is known and hence true. However, if its negation is true, then (S) must be false. Therefore (s) is false, or what is the name, the negation of (S) is true.
This paradox and its accompanying reasoning are strongly reminiscent of the Lair Paradox that (in one version) begins by considering a sentence ‘This sentence is false' and derives a contradiction. Versions of both arguments using axiomatic formulations of arithmetic and Gödel-numbers to achieve the effect of self-reference yields important meta-theorems about what can be expressed in such systems. Roughly these are to the effect that no predicates definable in the formalized arithmetic can have the properties we demand of truth (Tarski's Theorem) or of knowledge (Montague, 1963).
These meta-theorems still leave ‘us; with the problem that if we suppose that we add of these formalized languages predicates intended to express the concept of knowledge (or truth) and inference - as one mighty does if a logic of these concepts is desired. Then the sentence expressing the leading principles of the Knower Paradox will be true.
Explicitly, the assumption about knowledge and inferences are:
(1) If sentences ‘A' are known, then "a."
(2) (1) is known?
(3) If ‘B' is correctly inferred from ‘A', and ‘A' is known, then ‘B' id known.
To give an absolutely explicit t derivation of the paradox by applying these principles to (S), we must add (contingent) assumptions to the effect that certain inferences have been done. Still, as we go through the argument of the Knower, these inferences are done. Even if we can somehow restrict such principles and construct a consistent formal logic of knowledge and inference, the paradoxical argument as expressed in the natural language still demands some explanation.
The usual proposals for dealing with the Liar often have their analogues for the Knower, e.g., that there is something wrong with a self-reference or that knowledge (or truth) is properly a predicate of propositions and not of sentences. The relies that show that some of these are not adequate are often parallel to those for the Liar paradox. In addition, on e c an try here what seems to be an adequate solution for the Surprise Examination Paradox, namely the observation that ‘new knowledge can drive out knowledge', but this does not seem to work on the Knower (Anderson, 1983).
There are a number of paradoxes of the Liar family. The simplest example is the sentence ‘This sentence is false', which must be false if it is true, and true if it is false. One suggestion is that the sentence fails to say anything, but sentences that fail to say anything are at least not true. In fact case, we consider to sentences ‘This sentence is not true', which, if it fails to say anything is not true, and hence (this kind of reasoning is sometimes called the strengthened Liar). Other versions of the Liar introduce pairs of sentences, as in a slogan on the front of a T-shirt saying ‘This sentence on the back of this T-shirt is false', and one on the back saying ‘The sentence on the front of this T-shirt is true'. It is clear that each sentence individually is well formed, and was it not for the other, might have said something true. So any attempts to dismiss the paradox by sating that the sentence involved are meaningless will face problems.
Even so, the two approaches that have some hope of adequately dealing with this paradox is ‘hierarchy' solutions and ‘truth-value gap' solutions. According to the first, knowledge is structured into ‘levels'. It is argued that there be one-coherent notion expressed by the verb; knows', but rather a whole series of notions: knows0. knows, and so on (perhaps into transfinite), stated ion terms of predicate expressing such ‘ramified' concepts and properly restricted, (1)-(3) lead to no contradictions. The main objections to this procedure are that the meaning of these levels has not been adequately explained and that the idea of such subscripts, even implicit, in a natural language is highly counterintuitive the ‘truth-value gap' solution takes sentences such as (S) to lack truth-value. They are neither true nor false, but they do not express propositions. This defeats a crucial step in the reasoning used in the derivation of the paradoxes. Kripler (1986) has developed this approach in connection with the Liar and Asher and Kamp (1986) has worked out some details of a parallel solution to the Knower. The principal objection is that ‘strengthened' or ‘super' versions of the paradoxes tend to reappear when the solution itself is stated.
Since the paradoxical deduction uses only the properties (1)-(3) and since the argument is formally valid, any notions that satisfy these conditions will lead to a paradox. Thus, Grim (1988) notes that this may be read as ‘is known by an omniscient God' and concludes that there is no coherent single notion of omniscience. Thomason (1980) observes that with some different conditions, analogous reasoning about belief can lead to paradoxical consequence.
Overall, it looks as if we should conclude that knowledge and truth are ultimately intrinsically ‘stratified' concepts. It would seem that wee must simply accept the fact that these (and similar) concepts cannot be assigned of any-one fixed, finite or infinite. Still, the meaning of this idea certainly needs further clarification.
Its paradox arises when a set of apparently incontrovertible premises gives unacceptable or contradictory conclusions, to solve a paradox will involve showing either that there is a hidden flaw in the premises, or that the reasoning is erroneous, or that the apparently unacceptable conclusion can, in fact, be tolerated. Paradoxes are therefore important in philosophy, for until one is solved its show that there is something about our reasoning and our concepts that we do not understand. Famous families of paradoxes include the ‘semantic paradoxes' and ‘Zeno's paradoxes. Art the beginning of the 20th century, paradox and other set-theoretical paradoxes led to the complete overhaul of the foundations of set theory, while the 'Sorites paradox' has lead to the investigations of the semantics of vagueness and fuzzy logics.
It is, however, to what extent can analysis be informative? This is the question that gives a riser to what philosophers has traditionally called ‘the' paradox of analysis. Thus, consider the following proposition:
(1) To be an instance of knowledge is to be an instance of justified true belief not essentially grounded in any falsehood.
(1) if true, illustrates an important type of philosophical analysis. For convenience of exposition, I will assume (1) is a correct analysis. The paradox arises from the fact that if the concept of justified true belief not been essentially grounded in any falsification is the analysand of the concept of knowledge, it would seem that they are the same concept and hence that:
(2) To be an instance of knowledge is to be as an instance of.
knowledge and would have to be the same propositions as (1). But then how can (1) be informative when (2) is not? This is what is called the first paradox of analysis. Classical writings' on analysis suggests a second paradoxical analysis (Moore, 1942).
(3) An analysis of the concept of being a brother is that to be a
brother is to be a male sibling. If (3) is true, it would seem that the concept of being a brother would have to be the same concept as the concept of being a male sibling and tat:
(4) An analysis of the concept of being a brother is that to be a brother is to be a brother
would also have to be true and in fact, would have to be the same proposition as (3?). Yet (3) is true and (4) is false.
Both these paradoxes rest upon the assumptions that analysis is a relation between concepts, than one involving entity of other sorts, such as linguistic expressions, and tat in a true analysis, analysand and analysandum are the same concept. Both these assumptions are explicit in Moore, but some of Moore's remarks hint at a solution to that of another statement of an analysis is a statement partly about the concept involved and partly about the verbal expressions used to express it. He says he thinks a solution of this sort is bound to be right, but fails to suggest one because he cannot see a way in which the analysis can be even partly about the expression (Moore, 1942).
Elsewhere, of such ways, as a solution to the second paradox, to which is explicating (3) as:
(5) An analysis is given by saying that the verbal expression ‘ is a brother' expresses the same concept as is expressed by the conjunction of the verbal expressions ‘ is male' when used to express the concept of being male and ‘ is a sibling' when used to express the concept of being a sibling. (Ackerman, 1990).
An important point about (5) is as follows. Stripped of its philosophical jargon (‘analysis', ‘concept', ‘ is a . . . ‘), (5) seems to state the sort of information generally stated in a definition of the verbal expression ‘brother' in terms of the verbal expressions ‘male' and ‘sibling', where this definition is designed to draw upon listeners' antecedent understanding of the verbal expression ‘male' and ‘sibling', and thus, to tell listeners what the verbal expression ‘brother' really means, instead of merely providing the information that two verbal expressions are synonymous without specifying the meaning of either one. Thus, its solution to the second paradox seems to make the sort of analysis tat gives rise to this paradox matter of specifying the meaning of a verbal expression in terms of separate verbal expressions already understood and saying how the meanings of these separate, already-understood verbal expressions are combined. This corresponds to Moore's intuitive requirement that an analysis should both specify the constituent concepts of the analysandum and tell how they are combined, but is this all there is to philosophical analysis?
To answer this question, we must note that, in addition too there being two paradoxes of analysis, there is two types of analyses that are relevant here. (There are also other types of analysis, such as reformatory analysis, where the analysands are intended to improve on and replace the analysandum. But since reformatory analysis involves no commitment to conceptual identity between analysand and analysandum, reformatory analysis does not generate a paradox of analysis and so will not concern ‘us' here.) One way to recognize the difference between the two types of analysis concerning ‘us' here is to focus on the difference between the two paradoxes. This can be done by means of the FrĂ©ge-inspired sense-individuation condition, which is the condition that two expressions have the same sense if and only if they can be interchangeably ‘salva veritate' whenever used in propositional attitude context. If the expressions for the analysands and the analysandum in (1) met this condition, (1) and (2) would not raise the first paradox, but the second paradox arises regardless of whether the expression for the analysand and the analysandum meet this condition. The second paradox is a matter of the failure of such expressions to be interchangeable salva veritate in sentences involving such contexts as ‘an analysis is given thereof. Thus, a solution (such as the one offered) that is aimed only at such contexts can solve the second paradox. This is clearly false for the first paradox, however, which will apply to all pairs of propositions expressed by sentences in which expressions for pairs of analysands and anslysantia raising the first paradox is interchangeable. For example, consider the following proposition:
(6) Mary knows that some cats tail.
It is possible for John to believe (6) without believing:
(7) Mary has justified true belief, not essentially grounded in any falsehood, that some cats lack tails.
Yet this possibility clearly does not mean that the proposition that Mary knows that some casts lack tails is partly about language.
One approach to the first paradox is to argue that, despite the apparent epistemic inequivalence of (1) and (2), the concept of justified true belief not essentially grounded in any falsehood is still identical with the concept of knowledge (Sosa, 1983). Another approach is to argue that in the sort of analysis raising the first paradox, the analysand and analysandum is concepts that are different but that bear a special epistemic relation to each other. Elsewhere, the development is such an approach and suggestion that this analysand-analysandum relation has the following facets.
(a) The analysand and analysandum are necessarily coextensive, i.e., necessarily every instance of one is an instance of the other.
(b) The analysand and analysandum are knowable theoretical to be coextensive.
© The analysandum is simpler than the analysands a condition whose necessity is recognized in classical writings on analysis, such as, Langford, 1942.
(d) The analysand do not have the analysandum as a constituent.
Condition (d) rules out circularity. But since many valuable quasi-analyses are partly circular, e.g., knowledge is justified true belief supported by known reasons not essentially grounded in any falsehood, it seems best to distinguish between full analysis, from that of (d) is a necessary condition, and partial analysis, for which it is not.
These conditions, while necessary, are clearly insufficient. The basic problem is that they apply too many pairs of concepts that do not seem closely enough related epistemologically to count as analysand and analysandum. , such as the concept of being 6 and the concept of the fourth root of 1296. Accordingly, its solution upon what actually seems epistemologically distinctive about analyses of the sort under consideration, which is a certain way they can be justified. This is by the philosophical example-and-counterexample method, which is in a general term that goes as follows. ‘J' investigates the analysis of K's concept ‘Q' (where ‘K' can but need not be identical to ‘J' by setting ‘K' a series of armchair thought experiments, i.e., presenting ‘K' with a series of simple described hypothetical test cases and asking ‘K' questions of the form ‘If such-and-such where the case would this count as a case of Q? ‘J' then contrasts the descriptions of the cases to which; K' answers affirmatively with the description of the cases to which ‘K' does not, and ‘J' generalizes upon these descriptions to arrive at the concepts (if possible not including the analysandum) and their mode of combination that constitute the analysand of K'‘s concept ‘Q'. Since ‘J' need not be identical with ‘K', there is no requirement that ‘K' himself be able to perform this generalization, to recognize its result as correct, or even to understand he analysand that is its result. This is reminiscent of Walton's observation that one can simply recognize a bird as a swallow without realizing just what feature of the bird (beak, wing configurations, etc.) form the basis of this recognition. (The philosophical significance of this way of recognizing is discussed in Walton, 1972) ‘K' answers the questions based solely on whether the described hypothetical cases just strike him as cases of ‘Q'. ‘J' observes certain strictures in formulating the cases and questions. He makes the cases as simple as possible, to minimize the possibility of confusion and to minimize the likelihood that ‘K' will draw upon his philosophical theories (or quasi-philosophical, a rudimentary notion if he is unsophisticated philosophically) in answering the questions. For this conflicting result, the conflict should ‘other things being equal' be resolved in favour of the simpler case. ‘J' makes the series of described cases wide-ranging and varied, with the aim of having it be a complete series, where a series is complete if and only if no case that is omitted in such that, if included, it would change the analysis arrived at. ‘J' does not, of course, use as a test-case description anything complicated and general enough to express the analysand. There is no requirement that the described hypothetical test cases be formulated only in terms of what can be observed. Moreover, using described hypothetical situations as test cases enables ‘J' to frame the questions in such a way as to rule out extraneous background assumption to a degree, thus, even if ‘K' correctly believes that all and only P's are R's, the question of whether the concepts of P, R, or both enter the analysand of his concept ‘Q' can be investigated by asking him such questions as ‘Suppose (even if it seems preposterous to you) that you were to find out that there was a ‘P' that was not an ‘R'. Would you still consider it a case of Q?
Taking all this into account, the fifth necessary condition for this sort of analysand-analysandum relations is as follows:
(e) If ‘S' is the analysand of ‘Q', the proposition that necessarily all and only instances of ‘S' are instances of ‘Q' can be justified by generalizing from intuition about the correct answers to questions of the sort indicated about a varied and wide-ranging series of simple described hypothetical situations. It so does occur of antinomy, when we are able to argue for, or demonstrate, both a proposition and its contradiction, roughly speaking, a contradiction of a proposition ‘p' is one that can be expressed in form ‘not-p', or, if ‘p' can be expressed in the form ‘not-q', then a contradiction is one that can be expressed in the form ‘q'. Thus, e.g., if ‘p is 2 + 1 = 4, then 2 + 1 4 is the contradictory of ‘p', for
2 + 1 4 can be expressed in the form not (2 + 1 = 4). If ‘p' is 2 + 1 4, then 2 + 1 - 4 is a contradictory of ‘p', since 2 + 1 4 can be expressed in the form not (2 + 1 = 4). This is, mutually, but contradictory propositions can be expressed in the form, ‘r', ‘not-r'. The Principle of Contradiction says that mutually contradictory propositions cannot both be true and cannot both be false. Thus, by this principle, since if ‘p' is true, ‘not-p' is false, no proposition ‘p' can be at once true and false (otherwise both ‘p' and its contradictories would be false?). In particular, for any predicate ‘p' and object ‘ ', it cannot be that ‘p'; is at once true of ‘ ' and false of ? This is the classical formulation of the principle of contradiction, but it is nonetheless, that wherein, we cannot now fault either demonstrates. We would eventually hope to be able ‘to solve the antinomy' by managing, through careful thinking and analysis, eventually to fault either or both demonstrations.
Many paradoxes are as an easy source of antinomies, for example, Zeno gave some famously lets say, logical-cum-mathematical arguments that might be interpreted as demonstrating that motion is impossible. But our eyes as it was, demonstrate motion (exhibit moving things) all the time. Where did Zeno go wrong? Where do our eyes go wrong? If we cannot readily answer at least one of these questions, then we are in antinomy. In the "Critique of Pure Reason," Kant gave demonstrations of the same kind -in the Zeno example they were obviously not the same kind of both, e.g., that the world has a beginning in time and space, and that the world has no beginning in time or space. He argues that both demonstrations are at fault because they proceed on the basis of ‘pure reason' unconditioned by sense experience.
At this point, we display attributes to the theory of experience, as it is not possible to define in an illuminating way, however, we know what experiences are through acquaintances with some of our own, e.g., visual experiences of as afterimage, a feeling of physical nausea or a tactile experience of an abrasive surface (which might be caused by an actual surface -rough or smooth, or which might be part of a dream, or the product of a vivid sensory imagination). The essential feature of experience is it feels a certain way -that there is something that it is like to have it. We may refer to this feature of an experience as its ‘character'.
Another core feature of the sorts of experiences with which this may be of a concern, is that they have representational ‘content'. (Unless otherwise indicated, ‘experience' will be reserved for their ‘contentual representations'.) The most obvious cases of experiences with content are sense experiences of the kind normally involved in perception. We may describe such experiences by mentioning their sensory modalities ad their contents, e.g., a gustatory experience (modality) of chocolate ice cream (content), but do so more commonly by means of perceptual verbs combined with noun phrases specifying their contents, as in ‘Macbeth saw a dagger'. This is, however, ambiguous between the perceptual claim ‘There was a (material) dagger in the world that Macbeth perceived visually' and ‘Macbeth had a visual experience of a dagger' (the reading with which we are concerned, as it is afforded by our imagination, or perhaps, experiencing mentally hallucinogenic imagery).
As in the case of other mental states and events with content, it is important to distinguish between the properties that and experience ‘represents' and the properties that it ‘possesses'. To talk of the representational properties of an experience is to say something about its content, not to attribute those properties to the experience itself. Like every other experience, a visual; experience of a non-shaped square, of which is a mental event, and it is therefore not itself irregular or is it square, even though it represents those properties. It is, perhaps, fleeting, pleasant or unusual, even though it does not represent those properties. An experience may represent a property that it possesses, and it may even do so in virtue of a rapidly changing (complex) experience representing something as changing rapidly. However, this is the exception and not the rule.
Which properties can be [directly] represented in sense experience is subject to debate. Traditionalists include only properties whose presence could not be doubted by a subject having appropriate experiences, e.g., colour and shape in the case of visual experience, and apparent shape, surface texture, hardness, etc., in the case of tactile experience. This view is natural to anyone who has an egocentric, Cartesian perspective in epistemology, and who wishes for pure data in experiences to serve as logically certain foundations for knowledge, especially to the immediate objects of perceptual awareness in or of sense-data, such categorized of colour patches and shapes, which are usually supposed distinct from surfaces of physical objectivity. Qualities of sense-data are supposed to be distinct from physical qualities because their perception is more relative to conditions, more certain, and more immediate, and because sense-data is private and cannot appear other than they are they are objects that change in our perceptual field when conditions of perception change. Physical objects remain constant.
Others who do not think that this wish can be satisfied, and who are more impressed with the role of experience in providing animisms with ecologically significant information about the world around them, claim that sense experiences represent properties, characteristic and kinds that are much richer and much more wide-ranging than the traditional sensory qualities. We do not see only colours and shapes, they tell ‘us', but also earth, water, men, women and fire: We do not smell only odours, but also food and filth. There is no space here to examine the factors relevantly responsible to their choice of situational alternatives. Yet, this suggests that character and content are not really distinct, and there is a close tie between them. For one thing, the relative complexity of the character of sense experience places limitations upon its possible content, e.g., a tactile experience of something touching one's left ear is just too simple to carry the same amount of content as typically convincing to an every day, visual experience. Moreover, the content of a sense experience of a given character depends on the normal causes of appropriately similar experiences, e.g., the sort of gustatory experience that we have when eating chocolate would be not represented as chocolate unless it was normally caused by chocolate. Granting a contingent ties between the character of an experience and its possible causal origins, once, again follows that its possible content is limited by its character.
Character and content are none the less irreducibly different, for the following reasons. (a) There are experiences that completely lack content, e.g., certain bodily pleasures. (b) Not every aspect of the character of an experience with content is relevant to that content, e.g., the unpleasantness of an aural experience of chalk squeaking on a board may have no representational significance. © Experiences in different modalities may overlap in content without a parallel overlap in character, e.g., visual and tactile experiences of circularity feel completely different. (d) The content of an experience with a given character may vary according to the background of the subject, e.g., a certain content ‘singing bird' only after the subject has learned something about birds.
According to the act/object analysis of experience (which is a special case of the act/object analysis of consciousness), every experience involves an object of experience even if it has no material object. Two main lines of argument may be offered in support of this view, one ‘phenomenological' and the other ‘semantic'.
In an outline, the phenomenological argument is as follows. Whenever we have an experience, even if nothing beyond the experience answers to it, we seem to be presented with something through the experience (which is itself diaphanous). The object of the experience is whatever is so presented to ‘us'-is that it is an individual thing, an event, or a state of affairs.
The semantic argument is that objects of experience are required in order to make sense of certain features of our talk about experience, including, in particular, the following. (i) Simple attributions of experience, e.g., ‘Rod is experiencing an oddity that is not really square but in appearance it seems more than likely a square', this seems to be relational. (ii) We appear to refer to objects of experience and to attribute properties to them, e.g., ‘The after-image that John experienced was certainly odd'. (iii) We appear to quantify ov er objects of experience, e.g., ‘Macbeth saw something that his wife did not see'.
The act/object analysis faces several problems concerning the status of objects of experiences. Currently the most common view is that they are sense-data -private mental entities that actually posses the traditional sensory qualities represented by the experiences of which they are the objects. But the very idea of an essentially private entity is suspect. Moreover, since an experience may apparently represent something as having a determinable property, e.g., redness, without representing it as having any subordinate determinate property, e.g., any specific shade of red, a sense-datum may actually have a determinate property subordinate to it. Even more disturbing is that sense-data may have contradictory properties, since experiences can have contradictory contents. A case in point is the waterfall illusion: If you stare at a waterfall for a minute and then immediately fixate on a nearby rock, you are likely to have an experience of the rock's moving upward while it remains in the same place. The sense-data theorist must either deny that there are such experiences or admit contradictory objects.
These problems can be avoided by treating objects of experience as properties. This, however, fails to do justice to the appearances, for experience seems not to present ‘us' with properties embodied in individuals. The view that objects of experience is Meinongian objects accommodate this point. It is also attractive in as far as (1) it allows experiences to represent properties other than traditional sensory qualities, and (2) it allows for the identification of objects of experience and objects of perception in the case of experiences that constitute perception.
According to the act/object analysis of experience, every experience with content involves an object of experience to which the subject is related by an act of awareness (the event of experiencing that object). This is meant to apply not only to perceptions, which have material objects (whatever is perceived), but also to experiences like hallucinations and dream experiences, which do not. Such experiences none the less appear to represent something, and their objects are supposed to be whatever it is that they represent. Act/object theorists may differ on the nature of objects of experience, which have been treated as properties. Meinongian objects (which may not exist or have any form of being), and, more commonly private mental entities with sensory qualities. (The term ‘sense-data' is now usually applied to the latter, but has also been used as a general term for objects of sense experiences, as in the work of G. E. Moore) Act/object theorists may also differ on the relationship between objects of experience and objects of perception. In terms of perception (of which we are ‘indirectly aware') are always distinct from objects of experience (of which we are ‘directly aware'). Meinongian, however, may treat objects of perception as existing objects of experience. But sense-datum theorists must either deny that there are such experiences or admit contradictory objects. Still, most philosophers will feel that the Meinongian's acceptance of impossible objects is too high a price to pay for these benefits.
A general problem for the act/object analysis is that the question of whether two subjects are experiencing one and the same thing (as opposed to having exactly similar experiences) appears to have an answer only on the assumption that the experiences concerned are perceptions with material objects. But in terms of the act/object analysis the question must have an answer even when this condition is not satisfied. (The answer is always negative on the sense-datum theory; it could be positive on other versions of the act/object analysis, depending on the facts of the case.)
In view of the above problems, the case for the act/object analysis should be reassessed. The phenomenological argument is not, on reflection, convincing, for it is easy enough to grant that any experience appears to present ‘us' with an object without accepting that it actually does. The semantic argument is more impressive, but is none the less answerable. The seemingly relational structure of attributions of experience is a challenge dealt with below in connection with the adverbial theory. Apparent reference to and quantification over objects of experience can be handled by analysing them as reference to experiences themselves and quantification over experiences tacitly typed according to content. Thus, ‘The after-image that John experienced was colourfully appealing' becomes ‘John's after-image experience was an experience of colour', and ‘Macbeth saw something that his wife did not see' becomes ‘Macbeth had a visual experience that his wife did not have'.
Pure cognitivism attempts to avoid the problems facing the act/object analysis by reducing experiences to cognitive events or associated disposition, e.g., Susy's experience of a rough surface beneath her hand might be identified with the event of her acquiring the belief that there is a rough surface beneath her hand, or, if she does not acquire this belief, with a disposition to acquire it that has somehow been blocked.
This position has attractions. It does full justice to the cognitive contents of experience, and to the important role of experience as a source of belief acquisition. It would also help clear the way for a naturalistic theory of mind, since there seems to be some prospect of a physicalist/functionalist account of belief and other intentional states. But pure cognitivism is completely undermined by its failure to accommodate the fact that experiences have a felt character that cannot be reduced to their content, as aforementioned.
The adverbial theory is an attempt to undermine the act/object analysis by suggesting a semantic account of attributions of experience that does not require objects of experience. Unfortunately, the oddities of explicit adverbializations of such statements have driven off potential supporters of the theory. Furthermore, the theory remains largely undeveloped, and attempted refutations have traded on this. It may, however, be founded on sound basis intuitions, and there is reason to believe that an effective development of the theory (which is merely hinting at) is possible.
The relevant intuitions are (1) that when we say that someone is experiencing ‘an A', or has an experience ‘of an A', we are using this content-expression to specify the type of thing that the experience is especially apt to fit, (2) that doing this is a matter of saying something about the experience itself (and maybe about the normal causes of like experiences), and (3) that it is no-good of reasons to posit of its position to presuppose that of any involvements, is that its descriptions of an object in which the experience is. Thus the effective role of the content-expression in a statement of experience is to modify the verb it compliments, not to introduce a special type of object.
Perhaps, the most important criticism of the adverbial theory is the ‘many property problem', according to which the theory does not have the resources to distinguish between, e.g.,
(1) Frank has an experience of a brown triangle
and:
(2) Frank has an experience of brown and an experience of a triangle.
Which is entailed by (1) but does not entail it. The act/object analysis can easily accommodate the difference between (1) and (2) by claiming that the truth of (1) requires a single object of experience that is both brown and triangular, while that of the (2) allows for the possibility of two objects of experience, one brown and the other triangular, however, (1) is equivalent to:
(1*) Frank has an experience of something's being both brown and triangular.
And (2) is equivalent to:
(2*) Frank has an experience of something's being brown and an experience of something's being triangular,
and the difference between these can be explained quite simply in terms of logical scope without invoking objects of experience. The Adverbialists may use this to answer the many-property problem by arguing that the phrase ‘a brown triangle' in (1) does the same work as the clause ‘something's being both brown and triangular' in (1*). This is perfectly compatible with the view that it also has the ‘adverbial' function of modifying the verb ‘has an experience of', for it specifies the experience more narrowly just by giving a necessary condition for the satisfaction of the experience (the condition being that there are something both brown and triangular before Frank).
A final position that should be mentioned is the state theory, according to which a sense experience of an ‘A' is an occurrent, non-relational state of the kind that the subject would be in when perceiving an ‘A'. Suitably qualified, this claim is no doubt true, but its significance is subject to debate. Here it is enough to remark that the claim is compatible with both pure cognitivism and the adverbial theory, and that state theorists are probably best advised to adopt adverbials as a means of developing their intuitions.
Yet, clarifying sense-data, if taken literally, is that which is given by the senses. But in response to the question of what exactly is so given, sense-data theories posit private showings in the consciousness of the subject. In the case of vision this would be a kind of inner picture show which itself only indirectly represents aspects of the external world that has in and of itself a worldly representation. The view has been widely rejected as implying that we really only see extremely thin coloured pictures interposed between our mind's eye and reality. Modern approaches to perception tend to reject any conception of the eye as a camera or lense, simply responsible for producing private images, and stress the active life of the subject in and of the world, as the determinant of experience.
Nevertheless, the argument from illusion is of itself the usually intended directive to establish that certain familiar facts about illusion disprove the theory of perception called naĂŻevity or direct realism. There are, however, many different versions of the argument that must be distinguished carefully. Some of these distinctions centre on the content of the premises (the nature of the appeal to illusion); others centre on the interpretation of the conclusion (the kind of direct realism under attack). Let ‘us' set about by distinguishing the importantly different versions of direct realism which one might take to be vulnerable to familiar facts about the possibility of perceptual illusion.
A crude statement of direct realism might go as follows. In perception, we sometimes directly perceive physical objects and their properties, we do not always perceive physical objects by perceiving something ‘else', e.g., a sense-datum. There are, however, difficulties with this formulation of the view, as for one thing a great many philosophers who are ‘not' direct realists would admit that it is a mistake to describe people as actually ‘perceiving' something other than a physical object. In particular, such philosophers might admit, we should never say that we perceive sense-data. To talk that way would be to suppose that we should model our understanding of our relationship to sense-data on our understanding of the ordinary use of perceptual verbs as they describe our relation to and of the physical world, and that is the last thing paradigm sense-datum theorists should want. At least, many of the philosophers who objected to direct realism would prefer to express in what they were of objecting too in terms of a technical (and philosophically controversial) concept such as ‘acquaintance'. Using such a notion, we could define direct realism this way: In ‘veridical' experience we are directly acquainted with parts, e.g., surfaces, or constituents of physical objects. A less cautious verison of the view might drop the reference to veridical experience and claim simply that in all experience we are directly acquainted with parts or constituents of physical objects. The expressions ‘knowledge by acquaintance' and ‘knowledge by description', and the distinction they mark between knowing ‘things' and knowing ‘about' things, are generally associated with Bertrand Russell (1872-1970), that scientific philosophy required analysing many objects of belief as ‘logical constructions' or ‘logical fictions', and the programme of analysis that this inaugurated dominated the subsequent philosophy of logical atomism, and then of other philosophers, Russell's "The Analysis of Mind," the mind itself is treated in a fashion reminiscent of Hume, as no more than the collection of neutral perceptions or sense-data that make up the flux of conscious experience, and that looked at another way that also was to make up the external world (neutral monism), but "An Inquiry into Meaning and Truth" (1940) represents a more empirical approach to the problem. Yet, philosophers have perennially investigated this and related distinctions using varying terminology.
Distinction in our ways of knowing things, highlighted by Russell and forming a central element in his philosophy after the discovery of the theory of ‘definite descriptions'. A thing is known by acquaintance when there is direct experience of it. It is known by description if it can only be described as a thing with such-and-such properties. In everyday parlance, I might know my spouse and children by acquaintance, but know someone as ‘the first person born at sea' only by description. However, for a variety of reasons Russell shrinks the area of things that can be known by acquaintance until eventually only current experience, perhaps my own self, and certain universals or meanings qualify anything else is known only as the thing that has such-and-such qualities.
Because one can interpret the relation of acquaintance or awareness as one that is not ‘epistemic', i.e., not a kind of propositional knowledge, it is important to distinguish the above aforementioned views read as ontological theses from a view one might call ‘epistemological direct realism? In perception we are, on at least some occasions, non-inferentially justified in believing a proposition asserting the existence of a physical object. Since it is that these objects exist independently of any mind that might perceive them, and so it thereby rules out all forms of idealism and phenomenalism, which hold that there are no such independently existing objects. Its being to ‘direct' realism rules out those views defended under the cubic of ‘critical naive realism', or ‘representational realism', in which there is some non-physical intermediary -usually called a ‘sense-datum' or a ‘sense impression' -that must first be perceived or experienced in order to perceive the object that exists independently of this perception. Often the distinction between direct realism and other theories of perception is explained more fully in terms of what is ‘immediately' perceived, than ‘mediately' perceived. What relevance does illusion have for these two forms of direct realism?
The fundamental premise of the arguments is from illusion seems to be the theses that things can appear to be other than they are. Thus, for example, straight sticks when immerged in water looks bent, a penny when viewed from certain perspective appears as an illusory spatial elliptic circularity, when something that is yellow when place under red fluorescent light looks red. In all of these cases, one version of the argument goes, it is implausible to maintain that what we are directly acquainted with is the real nature of the object in question. Indeed, it is hard to see how we can be said to be aware of the really physical object at all. In the above illusions the things we were aware of actually were bent, elliptical and red, respectively. But, by hypothesis, the really physical objects lacked these properties. Thus, we were not aware of the substantial reality of been real as a physical objects or theory.
So far, if the argument is relevant to any of the direct realisms distinguished above, it seems relevant only to the claim that in all sense experience we are directly acquainted with parts or constituents of physical objects. After all, even if in illusion we are not acquainted with physical objects, but their surfaces, or their constituents, why should we conclude anything about the hidden nature of our relations to the physical world in veridical experience?
We are supposed to discover the answer to this question by noticing the similarities between illusory experience and veridical experience and by reflecting on what makes illusion possible at all. Illusion can occur because the nature of the illusory experience is determined, not just by the nature of the object perceived, but also by other conditions, both external and internal as becoming of an inner or as the outer experience. But all of our sensations are subject to these causal influences and it would be gratuitous and arbitrary to select from indefinitely of many and subtly different perceptual experiences some special ones those that get ‘us' in touch with the ‘real' nature of the physical world and its surrounding surfaces. Red fluorescent light affects the way thing's look, but so does sunlight. Water reflects light, but so does air. We have no unmediated access to the external world.
Still, why should we consider that we are aware of something other than a physical object in experience? Why should we not conclude that to be aware of a physical object is just to be appeared to by that object in a certain way? In its best-known form the adverbial theory of something proposes that the grammatical object of a statement attributing an experience to someone be analysed as an adverb. For example,
(A) Rod is experiencing a coloured square.
Is rewritten as?
Rod is experiencing, (coloured square)-ly
This is presented as an alternative to the act/object analysis, according to which the truth of a statement like (A) requires the existence of an object of experience corresponding to its grammatical object. A commitment to t he explicit adverbializations of statements of experience is not, however, essential to adverbialism. The core of the theory consists, rather, in the denial of objects of experience (as opposed ti objects of perception) coupled with the view that the role of the grammatical object in a statement of experience is to characterize more fully te sort of experience that is being attributed to the subject. The claim, then, is that the grammatical object is functioning as a modifier and, in particular, as a modifier of a verb. If it as a special kind of adverb at the semantic level.
At this point, it might be profitable to move from considering the possibility of illusion to considering the possibility of hallucination. Instead of comparing paradigmatic veridical perception with illusion, let ‘us' compare it with complete hallucination. For any experiences or sequence of experiences we take to be veridical, we can imagine qualitatively indistinguishable experiences occurring as part of a hallucination. For those who like their philosophical arguments spiced with a touch of science, we can imagine that our brains were surreptitiously removed in the night, and unbeknown to ‘us' are being stimulated by a neurophysiologist so as to produce the very sensations that we would normally associate with a trip to the Grand Canyon. Currently permit ‘us' into appealing of what we are aware of in this complete hallucination that is obvious that we are not awaken to the sparking awareness of physical objects, their surfaces, or their constituents. Nor can we even construe the experience as one of an object's appearing to ‘us' in a certain way. It is after all a complete hallucination and the objects we take to exist before ‘us' are simply not there. But if we compare hallucinatory experience with the qualitatively indistinguishable veridical experiences, should we most conclude that it would be ‘special' to suppose that in veridical experience we are aware of something radically different from what we are aware of in hallucinatory experience? Again, it might help to reflect on our belief that the immediate cause of hallucinatory experience and veridical experience might be the very same brain event, and it is surely implausible to suppose that the effects of this same cause are radically different -acquaintance with physical objects in the case of veridical experience: Something else in the case of hallucinatory experience.
This version of the argument from hallucination would seem to address straightforwardly the ontological versions of direct realism. The argument is supposed to convince ‘us' that the ontological analysis of sensation in both veridical and hallucinatory experience should give ‘us' the same results, but in the hallucinatory case there is no plausible physical object, constituent of a physical object, or surface of a physical object with which additional premiss we would also get an argument against epistemological direct realism. That premiss is that in a vivid hallucinatory experience we might have precisely the same justification for believing (falsely) what we do about the physical world as we do in the analogous, phenomenological indistinguishable, veridical experience. But our justification for believing that there is a table before ‘us' in the course of a vivid hallucination of a table are surely not non-inferential in character. It certainly is not, if non-inferential justifications are supposedly a consist but yet an unproblematic access to the fact that makes true our belief -by hypothesis the table does not exist. But if the justification that hallucinatory experiences give ‘us' the same as the justification we get from the parallel veridical experience, then we should not describe a veridical experience as giving ‘us non-inferential justification for believing in the existence of physical objects. In both cases we should say that we believe what we do about the physical world on the basis of what we know directly about the character of our experience.
In this brief space, I can only sketch some of the objections that might be raised against arguments from illusion and hallucination. That being said, let us begin with a criticism that accepts most of the presuppositions of the arguments. Even if the possibility of hallucination establishes that in some experience we are not acquainted with constituents of physical objects, it is not clear that it establishes that we are never acquainted with a constituent of physical objects. Suppose, for example, that we decide that in both veridical and hallucinatory experience we are acquainted with sense-data. At least some philosophers have tried to identify physical objects with ‘bundles' of actual and possible sense-data.
To establish inductively that sensations are signs of physical objects one would have to observe a correlation between the occurrence of certain sensations and the existence of certain physical objects. But to observe such a correlation in order to establish a connection, one would need independent access to physical objects and, by hypothesis, this one cannot have. If one further adopts the verificationist's stance that the ability to comprehend is parasitic on the ability to confirm, one can easily be driven to Hume's conclusion:
Let us chance our imagination to the heavens, or to the utmost limits of the universe, we never really advance a step beyond ourselves, nor can conceivable any kind of existence, but those perceptions, which have appear d in that narrow compass. This is the universe of the imagination, nor have we have any idea but what is there Reduced. (Hume, 1739-40, pp. 67-8).
If one reaches such a conclusion but wants to maintain the intelligibility and verifiability of the assertion about the physical world, one can go either the idealistic or the phenomenalistic route.
However, hallucinatory experiences on this view is non-veridical precisely because the sense-data one is acquainted with in hallucination do not bear the appropriate relations to other actual and possible sense-data. But if such a view were plausible one could agree that one is acquainted with the same kind of a thing in veridical and non-veridical experience but insists that there is still a sense in which in veridical experience one is acquainted with constituents of a physical object?
A different sort of objection to the argument from illusion or hallucination concerns its use in drawing conclusions we have not stressed in the above discourses. I, have in mentioning this objection, may to underscore an important feature of the argument. At least some philosophers (Hume, for example) have stressed the rejection of direct realism on the road to an argument for general scepticism with respect to the physical world. Once one abandons epistemological; direct realisms, one has an uphill battle indicating how one can legitimately make the inferences from sensation to physical objects. But philosophers who appeal to the existence of illusion and hallucination to develop an argument for scepticism can be accused of having an epistemically self-defeating argument. One could justifiably infer sceptical conclusions from the existence of illusion and hallucination only if one justifiably believed that such experiences exist, but if one is justified in believing that illusion exists, one must be justified in believing at least, some facts about the physical world (for example, that straight sticks look bent in water). The key point to stress in relying to such arguments is, that strictly speaking, the philosophers in question need only appeal to the ‘possibility' of a vivid illusion and hallucination. Although it would have been psychologically more difficult to come up with arguments from illusion and hallucination if we did not believe that we actually had such experiences, I take it that most philosophers would argue that the possibility of such experiences is enough to establish difficulties with direct realism. Indeed, if one looks carefully at the argument from hallucination discussed earlier, one sees that it nowhere makes any claims about actual cases of hallucinatory experience.
Another reply to the attack on epistemological direct realism focuses on the implausibility of claiming that there is any process of ‘inference' wrapped up in our beliefs about the world and its surrounding surfaces. Even if it is possible to give a phenomenological description of the subjective character of sensation, it requires a special sort of skill that most people lack. Our perceptual beliefs about the physical world are surely direct, at least in the sense that they are unmediated by any sort of conscious inference from premisses describing something other than a physical object. The appropriate reply to this objection, however, is simply to acknowledge the relevant phenomenological fact and point out that from the perceptive of epistemologically direct realism, the philosopher is attacking a claim about the nature of our justification for believing propositions about the physical world. Such philosophers need carry out of any comment at all about the causal genesis of such beliefs.
As mentioned that proponents of the argument from illusion and hallucination have often intended it to establish the existence of sense-data, and many philosophers have attacked the so-called sense-datum inference presupposed in some statements of the argument. When the stick looked bent, the penny looked elliptical and the yellow object looked red, the sense-datum theorist wanted to infer that there was something bent, elliptical and red, respectively. But such an inference is surely suspect. Usually, we do not infer that because something appears to have a certain property, that affairs that affecting something that has that property. When in saying that Jones looks like a doctor, I surely would not want anyone to infer that there must actually be someone there who is a doctor. In assessing this objection, it will be important to distinguish different uses words like ‘appears' and ‘looks'. At least, sometimes to say that something looks ‘F' way and the sense-datum inference from an F ‘appearance' in this sense to an actual ‘F' would be hopeless. However, it also seems that we use the ‘appears'/'looks' terminology to describe the phenomenological character of our experience and the inference might be more plausible when the terms are used this way. Still, it does seem that the arguments from illusion and hallucination will not by themselves constitute strong evidence for sense-datum theory. Even if one concludes that there is something common to both the hallucination of a red thing and a veridical visual experience of a red thing, one need not describe a common constituent as awarenesses of something red. The adverbial theorist would prefer to construe the common experiential state as ‘being appeared too redly', a technical description intended only to convey the idea that the state in question need not be analysed as relational in character. Those who opt for an adverbial theory of sensation need to make good the claim that their artificial adverbs can be given a sense that is not parasitic upon an understanding of the adjectives transformed into verbs. Still, other philosophers might try to reduce the common element in veridical and non-veridical experience to some kind of intentional state. More like belief or judgement. The idea here is that the only thing common to the two experiences is the fact that in both I spontaneously takes there to be present an object of a certain kind.
The selfsame objections can be started within the general framework presupposed by proponents of the arguments from illusion and hallucination. A great many contemporary philosophers, however, uncomfortable with the intelligibility of the concepts needed to make sense of the theories attacked even. Thus, at least, some who object to the argument from illusion do so not because they defend direct realism. Rather they think there is something confused about all this talk of direct awareness or acquaintance. Contemporary Externalists, for example, usually insist that we understand epistemic concepts by appeal: To nomologically connections. On such a view the closest thing to direct knowledge would probably be something by other beliefs. If we understand direct knowledge this way, it is not clar how the phenomena of illusion and hallucination would be relevant to claim that on, at least some occasions our judgements about the physical world are reliably produced by processes that do not take as their input beliefs about something else.
The expressions ‘knowledge by acquaintance' and ‘knowledge by description', and the distinction they mark between knowing ‘things' and knowing ‘about' things, are now generally associated with Bertrand Russell. However, John Grote and Hermann von Helmholtz had earlier and independently to mark the same distinction, and William James adopted Grote's terminology in his investigation of the distinction. Philosophers have perennially investigated this and related distinctions using varying terminology. Grote introduced the distinction by noting that natural languages ‘distinguish between these two applications of the notion of knowledge, the one being of the Greek , nosene, Kennen, connaĂ®tre, the other being ‘wissen', ‘savoir' (Grote, 1865, p. 60). On Grote's account, the distinction is a natter of degree, and there are three sorts of dimensions of variability: Epistemic, causal and semantic.
We know things by experiencing them, and knowledge of acquaintance (Russell changed the preposition to ‘by') is epistemically priori to and has a relatively higher degree of epistemic justification than knowledge about things. Indeed, sensation has ‘the one great value of trueness or freedom from mistake' (1900, p. 206).
A thought (using that term broadly, to mean any mental state) constituting knowledge of acquaintance with a thing is more or less causally proximate to sensations caused by that thing, while a thought constituting knowledge about the thing is more or less distant causally, being separated from the thing and experience of it by processes of attention and inference. At the limit, if a thought is maximally of the acquaintance type, it is the first mental state occurring in a perceptual causal chain originating in the object to which the thought refers, i.e., it is a sensation. The thing's presented to ‘us' in sensation and of which we have knowledge of acquaintance include ordinary objects in the external world, such as the sun.
Grote contrasted the imagistic thoughts involved in knowledge of acquaintance with things, with the judgements involved in knowledge about things, suggesting that the latter but not the former are mentally contentual by a specified state of affairs. Elsewhere, however, he suggested that every thought capable of constituting knowledge of or about a thing involves a form, idea, or what we might call contentual propositional content, referring the thought to its object. Whether contentual or not, thoughts constituting knowledge of acquaintance with a thing are relatively indistinct, although this indistinctness does not imply incommunicably. On the other hand, thoughts constituting distinctly, as a result of ‘the application of notice or attention' to the ‘confusion or chaos' of sensation (1900, pp. 206-7). Grote did not have an explicit theory on reference, the relation by which a thought is ‘of' or ‘about' a specific thing. Nor did he explain how thoughts can be more or less indistinct.
Helmholtz held unequivocally that all thoughts capable of constituting knowledge, whether ‘knowledge that has to do with Notions' (Wissen) or ‘mere familiarity with phenomena' (Kennen), is judgements or, we may say, have conceptual propositional contents. Where Grote saw a difference between distinct and indistinct thoughts, Helmholtz found a difference between precise judgements that are expressible in words and equally precise judgements that, in principle, are not expressible in words, and so are not communicable (Helmholtz, 19620. As happened, James was influenced by Helmholtz and, especially, by Grote. (James, 1975). Taken on the latter's terminology, James agreed with Grote that the distinction between knowledge of acquaintance with things and knowledge about things involves a difference in the degree of vagueness or distinctness of thoughts, though he, too, said little to explain how such differences are possible. At one extreme is knowledge of acquaintance with people and things, and with sensations of colour, flavour, spatial extension, temporal duration, effort and perceptible difference, unaccompanied by knowledge about these things. Such pure knowledge of acquaintance is vague and inexplicit. Movement away from this extreme, by a process of notice and analysis, yields a spectrum of less vague, more explicit thoughts constituting knowledge about things.
All the same, the distinction was not merely a relative one for James, as he was more explicit than Grote in not imputing content to every thought capable of constituting knowledge of or about things. At the extreme where a thought constitutes pure knowledge of acquaintance with a thing, there is a complete absence of conceptual propositional content in the thought, which is a sensation, feeling or precept, of which he renders the thought incommunicable. James' reasons for positing an absolute discontinuity in between pure cognition and preferable knowledge of acquaintance and knowledge at all about things seem to have been that any theory adequate to the facts about reference must allow that some reference is not conventionally mediated, that conceptually unmediated reference is necessary if there are to be judgements at all about things and, especially, if there are to be judgements about relations between things, and that any theory faithful to the common person's ‘sense of life' must allow that some things are directly perceived.
James made a genuine advance over Grote and Helmholtz by analysing the reference relation holding between a thought and of him to specific things of or about which it is knowledge. In fact, he gave two different analyses. On both analyses, a thought constituting knowledge about a thing refers to and is knowledge about ‘a reality, whenever it actually or potentially ends in' a thought constituting knowledge of acquaintance with that thing (1975). The two analyses differ in their treatments of knowledge of acquaintance. On James's first analysis, reference in both sorts of knowledge is mediated by causal chains. A thought constituting pure knowledge of acquaintances with a thing refers to and is knowledge of ‘whatever reality it directly or indirectly operates on and resembles' (1975). The concepts of a thought ‘operating on' a thing or ‘terminating in' another thought are causal, but where Grote found teleology and final causes. On James's later analysis, the reference involved in knowledge of acquaintance with a thing is direct. A thought constituting knowledge of acquaintance with a thing either is that thing, or has that thing as a constituent, and the thing and the experience of it is identical (1975, 1976).
James further agreed with Grote that pure knowledge of acquaintance with things, i.e., sensory experience, is epistemologically priori to knowledge about things. While the epistemic justification involved in knowledge about things rests on the foundation of sensation, all thoughts about things are fallible and their justification is augmented by their mutual coherence. James was unclear about the precise epistemic status of knowledge of acquaintance. At times, thoughts constituting pure knowledge of acquaintance are said to posses ‘absolute veritableness' (1890) and ‘the maximal conceivable truth' (1975), suggesting that such thoughts are genuinely cognitive and that they provide an infallible epistemic foundation. At other times, such thoughts are said not to bear truth-values, suggesting that ‘knowledge' of acquaintance is not genuine knowledge at all, but only a non-cognitive necessary condition of genuine knowledge, knowledge about things (1976). Russell understood James to hold the latter view.
Russell agreed with Grote and James on the following points: First, knowing things involves experiencing them. Second, knowledge of things by acquaintance is epistemically basic and provides an infallible epistemic foundation for knowledge about things. (Like James, Russell vacillated about the epistemic status of knowledge by acquaintance, and it eventually was replaced at the epistemic foundation by the concept of noticing.) Third, knowledge about things is more articulate and explicit than knowledge by acquaintance with things. Fourth, knowledge about things is causally removed from knowledge of things by acquaintance, by processes of reelection, analysis and inference (1911, 1913, 1959).
But, Russell also held that the term ‘experience' must not be used uncritically in philosophy, on account of the ‘vague, fluctuating and ambiguous' meaning of the term in its ordinary use. The precise concept found by Russell ‘in the nucleus of this uncertain patch of meaning' is that of direct occurrent experience of a thing, and he used the term ‘acquaintance' to express this relation, though he used that term technically, and not with all its ordinary meaning (1913). Nor did he undertake to give a constitutive analysis of the relation of acquaintance, though he allowed that it may not be unanalysable, and did characterize it as a generic concept. If the use of the term ‘experience' is restricted to expressing the determinate core of the concept it ordinarily expresses, then we do not experience ordinary objects in the external world, as we commonly think and as Grote and James held we do. In fact, Russell held, one can be acquainted only with one's sense-data, i.e., particular colours, sounds, etc.), one's occurrent mental states, universals, logical forms, and perhaps, oneself.
Russell agreed with James that knowledge of things by acquaintance ‘is essentially simpler than any knowledge of truths, and logically independent of knowledge of truths' (1912, 1929). The mental states involved when one is acquainted with things do not have propositional contents. Russell's reasons here seem to have been similar to James's. Conceptually unmediated reference to particulars necessary for understanding any proposition mentioning a particular, e.g., 1918-19, and, if scepticism about the external world is to be avoided, some particulars must be directly perceived (1911). Russell vacillated about whether or not the absence of propositional content renders knowledge by acquaintance incommunicable.
Russell agreed with James that different accounts should be given of reference as it occurs in knowledge by acquaintance and in knowledge about things, and that in the former case, reference is direct. But Russell objected on a number of grounds to James's causal account of the indirect reference involved in knowledge about things. Russell gave a descriptional rather than a causal analysis of that sort of reference: A thought is about a thing when the content of the thought involves a definite description uniquely satisfied by the thing referred to. Indeed, he preferred to speak of knowledge of things by description, rather than knowledge about things.
Russell advanced beyond Grote and James by explaining how thoughts can be more or less articulate and explicit. If one is acquainted with a complex thing without being aware of or acquainted with its complexity, the knowledge one has by acquaintance with that thing is vague and inexplicit. Reflection and analysis can lead one to distinguish constituent parts of the object of acquaintance and to obtain progressively more comprehensible, explicit, and complete knowledge about it (1913, 1918-19, 1950, 1959).
Apparent facts to be explained about the distinction between knowing things and knowing about things are there. Knowledge about things is essentially propositional knowledge, where the mental states involved refer to specific things. This propositional knowledge can be more or less comprehensive, can be justified inferentially and on the basis of experience, and can be communicated. Knowing things, on the other hand, involves experience of things. This experiential knowledge provides an epistemic basis for knowledge about things, and in some sense is difficult or impossible to communicate, perhaps because it is more or less vague.
If one is unconvinced by James and Russell's reasons for holding that experience of and reference work to things that are at least sometimes direct. It may seem preferable to join Helmholtz in asserting that knowing things and knowing about things both involve propositional attitudes. To do so would at least allow one the advantages of unified accounts of the nature of knowledge (propositional knowledge would be fundamental) and of the nature of reference: Indirect reference would be the only kind. The two kinds of knowledge might yet be importantly different if the mental states involved have different sorts of causal origins in the thinker's cognitive faculties, involve different sorts of propositional attitudes, and differ in other constitutive respects relevant to the relative vagueness and communicability of the mental sates.
In any of cases, perhaps most, Foundationalism is a view concerning the ‘structure' of the system of justified belief possessed by a given individual. Such a system is divided into ‘foundation' and ‘superstructure', so related that beliefs in the latter depend on the former for their justification but not vice versa. However, the view is sometimes stated in terms of the structure of ‘knowledge' than of justified belief. If knowledge is true justified belief (plus, perhaps, some further condition), one may think of knowledge as exhibiting a Foundationalist structure by virtue of the justified belief it involves. In any event, the construing doctrine concerning the primary justification is layed the groundwork as affording the efforts of belief, though in feeling more free, we are to acknowledge the knowledgeable infractions that will from time to time be worthy in showing to its recognition.
The first step toward a more explicit statement of the position is to distinguish between ‘mediate' (indirect) and ‘immediate' (direct) justification of belief. To say that a belief is mediately justified is to any that it s justified by some appropriate relation to other justified beliefs, i.e., by being inferred from other justified beliefs that provide adequate support for it, or, alternatively, by being based on adequate reasons. Thus, if my reason for supposing that you are depressed is that you look listless, speak in an unaccustomedly flat tone of voice, exhibit no interest in things you are usually interested in, etc., then my belief that you are depressed is justified, if, at all, by being adequately supported by my justified belief that you look listless, speak in a flat tone of voice. . . .
A belief is immediately justified, on the other hand, if its justification is of another sort, e.g., if it is justified by being based on experience or if it is ‘self-justified'. Thus my belief that you look listless may not be based on anything else I am justified in believing but just on the cay you look to me. And my belief that 2 + 3 = 5 may be justified not because I infer it from something else, I justifiably believe, but simply because it seems obviously true to me.
In these terms we can put the thesis of Foundationalism by saying that all mediately justified beliefs owe their justification, ultimately to immediately justified beliefs. To get a more detailed idea of what this amounts to it will be useful to consider the most important argument for Foundationalism, the regress argument. Consider a mediately justified belief that ‘p' (we are using lowercase letters as dummies for belief contents). It is, by hypothesis, justified by its relation to one or more other justified beliefs, ‘q' and ‘r'. Now what justifies each of these, e.g., q? If it too is mediately justified that is because it is related accordingly to one or subsequent extra justified beliefs, e.g., ‘s'. By virtue of what is ‘s' justified? If it is mediately justified, the same problem arises at the next stage. To avoid both circularity and an infinite regress, we are forced to suppose that in tracing back this chain we arrive at one or more immediately justified beliefs that stop the regress, since their justification does not depend on any further justified belief.
According to the infinite regress argument for Foundationalism, if every justified belief could be justified only by inferring it from some further justified belief, there would have to be an infinite regress of justifications: Because there can be no such regress, there must be justified beliefs that are not justified by appeal to some further justified belief. Instead, they are non-inferentially or immediately justified, they are basic or foundational, the ground on which all our other justifiable beliefs are to rest.
Variants of this ancient argument have persuaded and continue to persuade many philosophers that the structure of epistemic justification must be foundational. Aristotle recognized that if we are to have knowledge of the conclusion of an argument in the basis of its premisses, we must know the premisses. But if knowledge of a premise always required knowledge of some further proposition, then in order to know the premise we would have to know each proposition in an infinite regress of propositions. Since this is impossible, there must be some propositions that are known, but not by demonstration from further propositions: There must be basic, non-demonstrable knowledge, which grounds the rest of our knowledge.
Foundationalist enthusiasms for regress arguments often overlook the fact that they have also been advanced on behalf of scepticism, relativism, fideisms, conceptualism and Coherentism. Sceptics agree with foundationalist's both that there can be no infinite regress of justifications and that nevertheless, there must be one if every justified belief can be justified only inferentially, by appeal to some further justified belief. But sceptics think all true justification must be inferential in this way -the foundationalist's talk of immediate justification merely overshadows the requiring of any rational justification properly so-called. Sceptics conclude that none of our beliefs is justified. Relativists follow essentially the same pattern of sceptical argument, concluding that our beliefs can only be justified relative to the arbitrary starting assumptions or presuppositions either of an individual or of a form of life.
Regress arguments are not limited to epistemology. In ethics there is Aristotle's regress argument (in "Nichomachean Ethics") for the existence of a single end of rational action. In metaphysics there is Aquinas's regress argument for an unmoved mover: If a mover that it is in motion, there would have to be an infinite sequence of movers each moved by a further mover, since there can be no such sequence, there is an unmoved mover. A related argument has recently been given to show that not every state of affairs can have an explanation or cause of the sort posited by principles of sufficient reason, and such principles are false, for reasons having to do with their own concepts of explanation (Post, 1980; Post, 1987).
The premise of which in presenting Foundationalism as a view concerning the structure ‘that is in fact exhibited' by the justified beliefs of a particular person has sometimes been construed in ways that deviate from each of the phrases that are contained in the previous sentence. Thus, it is sometimes taken to characterise the structure of ‘our knowledge' or ‘scientific knowledge', rather than the structure of the cognitive system of an individual subject. As for the other phrase, Foundationalism is sometimes thought of as concerned with how knowledge (justified belief) is acquired or built up, than with the structure of what a person finds herself with at a certain point. Thus some people think of scientific inquiry as starting with the recordings of observations (immediately justified observational beliefs), and then inductively inferring generalizations. Again, Foundationalism is sometimes thought of not as a description of the finished product or of the mode of acquisition, but rather as a proposal for how the system could be reconstructed, an indication of how it could all be built up from immediately justified foundations. This last would seem to be the kind of Foundationalism we find in Descartes. However, Foundationalism is most usually thought of in contemporary Anglo-American epistemology as an account of the structure actually exhibited by an individual's system of justified belief.
It should also be noted that the term is used with a deplorable looseness in contemporary, literary circles, even in certain corners of the philosophical world, to refer to anything from realism -the view that reality has a definite constitution regardless of how we think of it or what we believe about it to various kinds of ‘absolutism' in ethics, politics, or wherever, and even to the truism that truth is stable (if a proposition is true, it stays true).
Since Foundationalism holds that all mediate justification rests on immediately justified beliefs, we may divide variations in forms of the view into those that have to do with the immediately justified beliefs, the ‘foundations', and those that have to do with the modes of derivation of other beliefs from these, how the ‘superstructure' is built up. The most obvious variation of the first sort has to do with what modes of immediate justification are recognized. Many treatments, both pro and con, are parochially restricted to one form of immediate justification -self-evidence, self-justification (self-warrant), justification by a direct awareness of what the belief is about, or whatever. It is then unwarrantly assumed by critics that disposing of that one form will dispose of Foundationalism generally (Alston, 1989, ch. 3). The emphasis historically has been on beliefs that simply ‘record' what is directly given in experience (Lewis, 1946) and on self-evident propositions (Descartes' ‘clear and distinct perceptions and Locke's ‘Perception of the agreement and disagreement of ideas'). But self-warrant has also recently received a great deal of attention (Alston 1989), and there is also a reliabilist version according to which a belief can be immediately justified just by being acquired by a reliable belief-forming process that does not take other beliefs as inputs (BonJour, 1985, ch. 3).
Foundationalisms also differ as to what further constraints, if any, are put on foundations. Historically, it has been common to require of the foundations of knowledge that they exhibit certain ‘epistemic immunities', as we might put it, immunity from error, refutation or doubt. Thus Descartes, along with many other seventeenth and eighteenth-century philosophers, took it that any knowledge worthy of the name would be based on cognations the truth of which is guaranteed (infallible), that were maximally stable, immune from ever being shown to be mistaken, as incorrigible, and concerning which no reasonable doubt could be raised (indubitable). Hence the search in the "Meditations" for a divine guarantee of our faculty of rational intuition. Criticisms of Foundationalism have often been directed at these constraints: Lehrer, 1974, Will, 1974? Both responded to in Alston, 1989. It is important to realize that a position that is Foundationalist in a distinctive sense can be formulated without imposing any such requirements on foundations.
There are various ways of distinguishing types of Foundationalist epistemology by the use of the variations we have been enumerating. Plantinga (1983), has put forwards an influential innovation of criterial Foundationalism, specified in terms of limitations on the foundations. He construes this as a disjunction of ‘ancient and medieval Foundationalism', which takes foundations to comprise what is self-evidently and ‘evident to he senses', and ‘modern Foundationalism' that replaces ‘evidently to the senses' with ‘incorrigible', which in practice was taken to apply only to beliefs about one's present states of consciousness. Plantinga himself developed this notion in the context of arguing those items outside this territory, in particular certain beliefs about God, could also be immediately justified. A popular recent distinction is between what is variously called ‘strong' or ‘extreme' Foundationalism and ‘moderate', ‘modest' or ‘minimal' Foundationalism, with the distinction depending on whether various epistemic immunities are required of foundations. Finally, its distinction is ‘simple' and ‘iterative' Foundationalism (Alston, 1989), depending on whether it is required of a foundation only that it is immediately justified, or whether it is also required that the higher level belief that the firmer belief is immediately justified is itself immediately justified. Suggesting only that the plausibility of the stronger requirement stems from a ‘level confusion' between beliefs on different levels.
The classic opposition is between Foundationalism and Coherentism. Coherentism denies any immediate justification. It deals with the regress argument by rejecting ‘linear' chains of justification and, in effect, taking the total system of belief to be epistemically primary. A particular belief is justified yo the extent that it is integrated into a coherent system of belief. More recently into a pragmatist like John Dewey has developed a position known as contextualism, which avoids ascribing any overall structure to knowledge. Questions concerning justification can only arise in particular context, defined in terms of assumptions that are simply taken for granted, though they can be questioned in other contexts, where other assumptions will be privileged.
Foundationalism can be attacked both in its commitment to immediate justification and in its claim that all mediately justified beliefs ultimately depend on the former. Though, it is the latter that is the position's weakest point, most of the critical fire has been detected to the former. As pointed out about much of this criticism has been directly against some particular form of immediate justification, ignoring the possibility of other forms. Thus, much anti-foundationalist artillery has been directed at the ‘myth of the given'. The idea that facts or things are ‘given' to consciousness in a pre-conceptual, pre-judgmental mode, and that beliefs can be justified on that basis (Sellars, 1963). The most prominent general argument against immediate justification is a ‘level ascent' argument, according to which whatever is taken ti immediately justified a belief that the putative justifier has in supposing to do so. Hence, since the justification of the higher level belief after all (BonJour, 1985). We lack adequate support for any such higher level requirements for justification, and if it were imposed we would be launched on an infinite undergo regress, for a similar requirement would hold equally for the higher level belief that the original justifier was efficacious.
Coherence is a major player in the theatre of knowledge. There are coherence theories of belief, truth, and justification. These combine in various ways to yield theories of knowledge. We will proceed from belief through justification to truth. Coherence theories of belief are concerned with the content of beliefs. Consider a belief you now have, the beliefs that you are reading a page in a book, so what makes that belief the belief that it is? What makes it the belief that you are reading a page in a book than the belief hat you have a monster in the garden?
One answer is that the belief has a coherent place or role in a system of beliefs. Perception has an influence on belief. You respond to sensory stimuli by believing that you are reading a page in a book rather than believing that you have a centaur in the garden. Belief has an influence on action. You will act differently if you believe that you are reading a page than if you believe something about a centaur. Perspicacity and action undermine the content of belief, however, the same stimuli may produce various beliefs and various beliefs may produce the same action. The role that gives the belief the content it has in the role it plays in a network of relations to the beliefs, the role in inference and implications, for example, I refer different things from believing that I am inferring different things from believing that I am reading a page in a book than from any other beliefs, just as I infer that belief from any other belief, just as I infer that belief from different things than I infer other beliefs from.
The input of perception and the output of an action supplement the centre role of the systematic relations the belief has to other beliefs, but it is the systematic relations that give the belief the specific content it has. They are the fundamental source of the content of beliefs. That is how coherence comes in. A belief has the content that it does because of the way in which it coheres within a system of beliefs (Rosenberg, 1988). We might distinguish weak coherence theories of the content of beliefs from strong coherence theories. Weak coherence theories affirm that coherences are one-determinant of the content of belief. Strong coherence theories of the contents of belief affirm that coherence is the sole determinant of the content of belief.
When we turn from belief to justification, we are in confronting a corresponding group of similarities fashioned by their coherences motifs. What makes one belief justified and another not? The answer is the way it coheres with the background system of beliefs. Again, there is a distinction between weak and strong theories of coherence. Weak theories tell ‘us' that the way in which a belief coheres with a background system of beliefs is one determinant of justification, other typical determinants being perception, memory and intuition. Strong theories, by contrast, tell ‘us' that justification is solely a matter of how a belief coheres with a system of beliefs. There is, however, another distinction that cuts across the distinction between weak and strong coherence theories of justification. It is the distinction between positive and negative coherence theories (Pollock, 1986). A positive coherence theory tells ‘us' that if a belief coheres with a background system of belief, then the belief is justified. A negative coherence theory tells ‘us' that if a belief fails to cohere with a background system of beliefs, then the belief is not justified. We might put this by saying that, according to a positive coherence theory, coherence has the power to produce justification, while according to a negative coherence theory, coherence has only the power to nullify justification.
A strong coherence theory of justification is a combination of a positive and a negative theory that tells ‘us' that a belief is justified if and only if it coheres with a background system of beliefs.
Traditionally, belief has been of epistemological interest in its propositional guise: ‘S' believes that ‘p', where ‘p' is a proposition toward which an agent, ‘S', exhibits an attitude of acceptance. Not all belief is of this sort. If I trust what you say, I believe you. And someone may believe in Mrs. Thatcher, or in a free-market economy, or in God. It is sometimes supposed that all belief is ‘reducible' to propositional belief, belief-that. Thus, my believing you might be thought a matter of my believing, perhaps, that what you say is true, and your belief in free-markets or in God, a matter of your believing that free-market economy's are desirable or that God exists.
It is doubtful, however, that non-propositional believing can, in every case, be reduced in this way. Debate on this point has tended to focus on an apparent distinction between ‘belief-that' and ‘belief-in', and the application of this distinction to belief in God. Some philosophers have followed Aquinas ©. 1225-74), in supposing that to believe in, and God is simply to believe that certain truths hold: That God exists, that he is benevolent, etc. Others (e.g., Hick, 1957) argue that belief-in is a distinctive attitude, one that includes essentially an element of trust. More commonly, belief-in has been taken to involve a combination of propositional belief together with some further attitude.
H.H. Price (1969) defends the claims that there are different sorts of ‘belief-in', some, but not all, reducible to ‘beliefs-that'. If you believe in God, you believe that God exists, that God is good, etc., but, according to Price, your belief involves, in addition, a certain complex pro-attitude toward its object. One might attempt to analyse this further attitude in terms of additional beliefs-that: ‘S' believes in ‘ ' just in case (1) ‘S' believes that ‘ ' exists (and perhaps holds further factual beliefs about ( ): (2)'S' believes that ‘ ' is good or valuable in some respect, and (3) ‘S' believes that 's being good or valuable in this respect is itself is a good thing. An analysis of this sort, however, fails adequately to capture the further affective component of belief-in. Thus, according to Price, if you believe in God, your belief is not merely that certain truths hold, you posses, in addition, an attitude of commitment and trust toward God.
Notoriously, belief-in outruns the evidence for the corresponding belief-that. Does this diminish its rationality? If belief-in presupposes belief-that, it might be thought that the evidential standards for the former must be, at least as high as standards for the latter. And any additional pro-attitude might be thought to require a further layer of justification not required for cases of belief-that.
Some philosophers have argued that, at least for cases in which belief-in is synonymous with faith (or faith-in), evidential thresholds for constituent propositional beliefs are diminished. You may reasonably have faith in God or Mrs. Thatcher, even though beliefs about their respective attitudes, were you to harbour them, would be evidentially substandard.
Belief-in may be, in general, less susceptible to alternations in the face of unfavourable evidence than belief-that. A believer who encounters evidence against God's existence may remain unshaken in his belief, in part because the evidence does not bear on his pro-attitude. So long as this is united with his belief that God exists, the belief may survive epistemic buffeting-and reasonably so in a way that an ordinary propositional belief-that would not.
At least two large sets of questions are properly treated under the heading of epistemological religious beliefs. First, there is a set of broadly theological questions about the relationship between faith and reason, between what one knows by way of reason, broadly construed, and what one knows by way of faith. These theological questions may as we call theological, because, of course, one will find them of interest only if one thinks that in fact there is such a thing as faith, and that we do know something by way of it. Secondly, there is a whole set of questions having to do with whether and to what degree religious beliefs have warrant, or justification, or positive epistemic status. The second, is seemingly as an important set of a theological question is yet spoken of faith.
Epistemology, so we are told, is theory of knowledge: Its aim is to discern and explain that quality or quantity enough of which distinguishes knowledge from mere true belief. We need a name for this quality or quantity, whatever precisely it is, call it ‘warrant'. From this point of view, the epistemology of religious belief should centre on the question whether religious belief has warrant, an if it does, hoe much it has and how it gets it. As a matter of fact, however, epistemological discussion of religious belief, at least since the Enlightenment (and in the Western world, especially the English-speaking Western world) has tended to focus, not on the question whether religious belief has warrant, but whether it is justified. More precisely, it has tended to focus on the question whether those properties enjoyed by theistic belief -the belief that there exists a person like the God of traditional Christianity, Judaism and Islam: An almighty Law Maker, or an all-knowing and most wholly benevolent and a loving spiritual person who has created the living world. The chief question, therefore, has ben whether theistic belief is justified, the same question is often put by asking whether theistic belief is rational or rationally acceptable. Still further, the typical way of addressing this question has been by way of discussing arguments for or and against the existence of God. On the pro side, there are the traditional theistic proofs or arguments: The ontological, cosmological and teleological arguments, using Kant's terms for them. On the other side, the anti-theistic side, the principal argument is the argument from evil, the argument that is not possible or at least probable that there be such a person as God, given all the pain, suffering and evil the world displays. This argument is flanked by subsidiary arguments, such as the claim that the very concept of God is incoherent, because, for example, it is impossible that there are the people without a body, and Freudian and Marxist claims that religious belief arises out of a sort of magnification and projection into the heavens of human attributes we think important.
But why has discussion centred on justification rather than warrant? And precisely what is justification? And why has the discussion of justification of theistic belief focussed so heavily on arguments for and against the existence of God?
As to the first question, we can see why once we see that the dominant epistemological tradition in modern Western philosophy has tended to ‘identify' warrant with justification. On this way of looking at the matter, warrant, that which distinguishes knowledge from mere true belief, just ‘is' justification. Belief theory of knowledge-the theory according to which knowledge is justified true belief has enjoyed the status of orthodoxy. According to this view, knowledge is justified truer belief, therefore any of your beliefs have warrant for you if and only if you are justified in holding it.
But what is justification? What is it to be justified in holding a belief? To get a proper sense of the answer, we must turn to those twin towers of western epistemology. René Descartes and especially, John Locke. The first thing to see is that according to Descartes and Locke, there are epistemic or intellectual duties, or obligations, or requirements. Thus, Locke:
Faith is nothing but a firm assent of the mind, which if it is regulated, A is our duty, cannot be afforded to anything, but upon good reason: And cannot be opposite to it, he that believes, without having any reason for believing, may be in love with his own fanciers: But, seeks neither truth as he ought, nor pats the obedience due his maker, which would have him use those discerning faculties he has given him: To keep him out of mistake and error. He that does this to the best of his power, however, he sometimes lights on truth, is in the right but by chance: And I know not whether the luckiest of the accidents will excuse the irregularity of his proceeding. This, at least is certain, that he must be accountable for whatever mistakes he runs into: Whereas, he that makes use of the light and faculties God has given him, by seeks sincerely to discover truth, by those helps and abilities he has, may have this satisfaction in doing his duty as rational creature, that though he should miss truth, he will not miss the reward of it. For he governs his assent right, and places it as he should, who in any case or matter whatsoever, believes or disbelieves, according as reason directs him. He that does otherwise, transgresses against his own light, and misuses those faculties, which were given him . . . (Essays 4.17.24).
Rational creatures, creatures with reason, creatures capable of believing propositions (and of disbelieving and being agnostic with respect to them), say Locke, have duties and obligation with respect to the regulation of their belief or assent. Now the central core of the notion of justification(as the etymology of the term indicates) this: One is justified in doing something or in believing a certain way, if in doing one is innocent of wrong doing and hence not properly subject to blame or censure. You are justified, therefore, if you have violated no duties or obligations, if you have conformed to the relevant requirements, if you are within your rights. To be justified in believing something, then, is to be within your rights in so believing, to be flouting no duty, to be to satisfy your epistemic duties and obligations. This way of thinking of justification has been the dominant way of thinking about justification: And this way of thinking has many important contemporary representatives. Roderick Chisholm, for example (as distinguished an epistemologist as the twentieth century can boast), in his earlier work explicitly explains justification in terms of epistemic duty (Chisholm, 1977).
The (or, a) main epistemological; questions about religious believe, therefore, has been the question whether or not religious belief in general and theistic belief in particular is justified. And the traditional way to answer that question has been to inquire into the arguments for and against theism. Why this emphasis upon these arguments? An argument is a way of marshalling your propositional evidence-the evidence from other such propositions as likens to believe-for or against a given proposition. And the reason for the emphasis upon argument is the assumption that theistic belief is justified if and only if there is sufficient propositional evidence for it. If there is not' much by way of propositional evidence for theism, then you are not justified in accepting it. Moreover, if you accept theistic belief without having propositional evidence for it, then you are ging contrary to epistemic duty and are therefore unjustified in accepting it. Thus, W.K. William James, trumpets that ‘it is wrong, always everything upon insufficient evidence', his is only the most strident in a vast chorus of only insisting that there is an intellectual duty not to believe in God unless you have propositional evidence for that belief. (A few others in the choir: Sigmund Freud, Brand Blanshard, H.H. Price, Bertrand Russell and Michael Scriven.)
Now how it is that the justification of theistic belief gets identified with there being propositional evidence for it? Justification is a matter of being blameless, of having done one's duty (in this context, one's epistemic duty): What, precisely, has this to do with having propositional evidence?
The answer, once, again, is to be found in Descartes especially Locke. As, justification is the property your beliefs have when, in forming and holding them, you conform to your epistemic duties and obligations. But according to Locke, a central epistemic duty is this: To believe a proposition only to the degree that it is probable with respect to what is certain for you. What propositions are certain for you? First, according to Descartes and Locke, propositions about your own immediate experience, that you have a mild headache, or that it seems to you that you see something red: And second, propositions that are self-evident for you, necessarily true propositions so obvious that you cannot so much as entertain them without seeing that they must be true. (Examples would be simple arithmetical and logical propositions, together with such propositions as that the whole is at least as large as the parts, that red is a colour, and that whatever exists has properties.) Propositions of these two sorts are certain for you, as fort other prepositions. You are justified in believing if and only if when one and only to the degree to which it is probable with respect to what is certain for you. According to Locke, therefore, and according to the whole modern Foundationalist tradition initiated by Locke and Descartes (a tradition that until has recently dominated Western thinking about these topics) there is a duty not to accept a proposition unless it is certain or probable with respect to what is certain.
In the present context, therefore, the central Lockean assumption is that there is an epistemic duty not to accept theistic belief unless it is probable with respect to what is certain for you: As a consequence, theistic belief is justified only if the existence of God is probable with respect to what is certain. Locke does not argue for his proposition, he simply announces it, and epistemological discussion of theistic belief has for the most part followed hin ion making this assumption. This enables ‘us' to see why epistemological discussion of theistic belief has tended to focus on the arguments for and against theism: On the view in question, theistic belief is justified only if it is probable with respect to what is certain, and the way to show that it is probable with respect to what it is certain are to give arguments for it from premises that are certain or, are sufficiently probable with respect to what is certain.
There are at least three important problems with this approach to the epistemology of theistic belief. First, there standards for theistic arguments have traditionally been set absurdly high (and perhaps, part of the responsibility for this must be laid as the door of some who have offered these arguments and claimed that they constitute wholly demonstrative proofs). The idea seems to test. a good theistic argument must start from what is self-evident and proceed majestically by way of self-evidently valid argument forms to its conclusion. It is no wonder that few if any theistic arguments meet that lofty standard -particularly, in view of the fact that almost no philosophical arguments of any sort meet it. (Think of your favourite philosophical argument: Does it really start from premisses that are self-evident and move by ways of self-evident argument forms to its conclusion?)
Secondly, attention has ben mostly confined to three theistic arguments: The traditional arguments, cosmological and teleological arguments, but in fact, there are many more good arguments: Arguments from the nature of proper function, and from the nature of propositions, numbers and sets. These are arguments from intentionality, from counterfactual, from the confluence of epistemic reliability with epistemic justification, from reference, simplicity, intuition and love. There are arguments from colours and flavours, from miracles, play and enjoyment, morality, from beauty and from the meaning of life. This is even a theistic argument from the existence of evil.
But there are a third and deeper problems here. The basic assumption is that theistic belief is justified only if it is or can be shown to be probable with respect to many a body of evidence or proposition -perhaps, those that are self-evident or about one's own mental life, but is this assumption true? The idea is that theistic belief is very much like a scientific hypothesis: It is acceptable if and only if there is an appropriate balance of propositional evidence in favour of it. But why believe a thing like that? Perhaps the theory of relativity or the theory of evolution is like that, such a theory has been devised to explain the phenomena and gets all its warrant from its success in so doing. However, other beliefs, e.g., memory beliefs, feelifelt in other minds is not like that, they are not hypothetical at all, and are not accepted because of their explanatory powers. There are instead, the propositions from which one start in attempting to give evidence for a hypothesis. Now, why assume that theistic belief, belief in God, is in this regard more like a scientific hypothesis than like, say, a memory belief? Why think that the justification of theistic belief depends upon the evidential relation of theistic belief to other things one believes? According to Locke and the beginnings of this tradition, it is because there is a duty not to assent to a proposition unless it is probable with respect to what is certain to you, but is there really any such duty? No one has succeeded in showing that, say, belief in other minds or the belief that there has been a past, is probable with respect to what is certain for ‘us'. Suppose it is not: Does it follow that you are living in epistemic sin if you believe that there are other minds? Or a past?
There are urgent questions about any view according to which one has duties of the sort ‘do not believe ‘p' unless it is probable with respect to what is certain for you; . First, if this is a duty, is it one to which I can conform? My beliefs are for the most part not within my control: Certainly they are not within my direct control. I believe that there has been a past and that there are other people, even if these beliefs are not probable with respect to what is certain forms (and even if I came to know this) I could not give them up. Whether or not I accept such beliefs are not really up to me at all, For I can no more refrain from believing these things than I can refrain from conforming yo the law of gravity. Second, is there really any reason for thinking I have such a duty? Nearly everyone recognizes such duties as that of not engaging in gratuitous cruelty, taking care of one's children and one's aged parents, and the like, but do we also find ourselves recognizing that there is a duty not to believe what is not probable (or, what we cannot see to be probable) with respect to what are certain for ‘us'? It hardly seems so. However, it is hard to see why being justified in believing in God requires that the existence of God be probable with respect to some such body of evidence as the set of propositions certain for you. Perhaps, theistic belief is properly basic, i.e., such that one is perfectly justified in accepting it on the evidential basis of other propositions one believes.
Taking justification in that original etymological fashion, therefore, there is every reason ton doubt that one is justified in holding theistic belief only inf one is justified in holding theistic belief only if one has evidence for it. Of course, the term ‘justification' has under-gone various analogical extensions in the of various philosophers, it has been used to name various properties that are different from justification etymologically so-called, but anagogically related to it. In such a way, the term sometimes used to mean propositional evidence: To say that a belief is justified for someone is to saying that he has propositional evidence (or sufficient propositional evidence) for it. So taken, however, the question whether theistic belief is justified loses some of its interest; for it is not clear (given this use)beliefs that are unjustified in that sense. Perhaps, one also does not have propositional evidence for one's memory beliefs, if so, that would not be a mark against them and would not suggest that there be something wrong holding them.
Another analogically connected way to think about justification (a way to think about justification by the later Chisholm) is to think of it as simply a relation of fitting between a given proposition and one's epistemic vase -which includes the other things one believes, as well as one's experience. Perhaps tat is the way justification is to be thought of, but then, if it is no longer at all obvious that theistic belief has this property of justification if it seems as a probability with respect to many another body of evidence. Perhaps, again, it is like memory beliefs in this regard.
To recapitulate: The dominant Western tradition has been inclined to identify warrant with justification, it has been inclined to take the latter in terms of duty and the fulfilment of obligation, and hence to suppose that there is no epistemic duty not to believe in God unless you have good propositional evidence for the existence of God. Epistemological discussion of theistic belief, as a consequence, as concentrated on the propositional evidence for and against theistic belief, i.e., on arguments for and against theistic belief. But there is excellent reason to doubt that there are epistemic duties of the sort the tradition appeals to here.
And perhaps it was a mistake to identify warrant with justification in the first place. Napoleons have little warrant for him: His problem, however, need not be dereliction of epistemic duty. He is in difficulty, but it is not or necessarily that of failing to fulfill epistemic duty. He may be doing his epistemic best, but he may be doing his epistemic duty in excelsis: But his madness prevents his beliefs from having much by way of warrant. His lack of warrant is not a matter of being unjustified, i.e., failing to fulfill epistemic duty. So warrant and being epistemologically justified by name are not the same things. Another example, suppose (to use the favourite twentieth-century variant of Descartes' evil demon example) I have been captured by Alpha-Centaurian super-scientists, running a cognitive experiment, they remove my brain, and keep it alive in some artificial nutrients, and by virtue of their advanced technology induce in me the beliefs I might otherwise have if I were going about my usual business. Then my beliefs would not have much by way of warrant, but would it be because I was failing to do my epistemic duty? Hardly.
As a result of these and other problems, another, externalist way of thinking about knowledge has appeared in recent epistemology, that a theory of justification is internalized if and only if it requires that all of its factors needed for a belief to be epistemically accessible to that of a person, internal to his cognitive perception, and externalist, if it allows that, at least some of the justifying factors need not be thus accessible, in that they can be external to the believer' s cognitive Perspectives, beyond his ken. However, epistemologists often use the distinction between internalized and externalist theories of epistemic justification without offering any very explicit explanation.
Or perhaps the thing to say, is that it has reappeared, for the dominant sprains in epistemology priori to the Enlightenment were really externalist. According to this externalist way of thinking, warrant does not depend upon satisfaction of duty, or upon anything else to which the Knower has special cognitive access (as he does to what is about his own experience and to whether he is trying his best to do his epistemic duty): It depends instead upon factors ‘external' to the epistemic agent -such factors as whether his beliefs are produced by reliable cognitive mechanisms, or whether they are produced by epistemic faculties functioning properly in-an appropriate epistemic environment.
How will we think about the epistemology of theistic belief in more than is less of an externalist way (which is at once both satisfyingly traditional and agreeably up to date)? I think, that the ontological question whether there is such a person as God is in a way priori to the epistemological question about the warrant of theistic belief. It is natural to think that if in fact we have been created by God, then the cognitive processes that issue in belief in God are indeed realisable belief-producing processes, and if in fact God created ‘us', then no doubt the cognitive faculties that produce belief in God is functioning properly in an epistemologically congenial environment. On the other hand, if there is no such person as God, if theistic belief is an illusion of some sort, then things are much less clear. Then beliefs in God in of the most of basic ways of wishing that never doubt the production by which unrealistic thinking or another cognitive process not aimed at truth. Thus, it will have little or no warrant. And belief in God on the basis of argument would be like belief in false philosophical theories on the basis of argument: Do such beliefs have warrant? Notwithstanding, the custom of discussing the epistemological questions about theistic belief as if they could be profitably discussed independently of the ontological issue as to whether or not theism is true, is misguided. There two issues are intimately intertwined,
Nonetheless, the vacancy left, as today and as days before are an awakening and untold story beginning by some sparking conscious paradigm left by science. That is a central idea by virtue accredited by its epistemology, where in fact, is that justification and knowledge arising from the proper functioning of our intellectual virtues or faculties in an appropriate environment. This particular yet, peculiar idea is captured in the following criterion for justified belief:
(J) ‘S' is justified in believing that ‘p' if and only if of S's believing that ‘p' is the result of S's intellectual virtues or faculties functioning in appropriate environment.
What is an intellectual virtue or faculty? A virtue or faculty in general is a power or ability or competence to achieve some result. An intellectual virtue or faculty, in the sense intended above, is a power or ability or competence to arrive at truths in a particular field, and to avoid believing falsehoods in that field. Examples of human intellectual virtues are sight, hearing, introspection, memory, deduction and induction. More exactly.
(V) A mechanism ‘M' for generating and/or maintaining beliefs is an intellectual virtue if and only if ‘M'‘s' is a competence to believing true propositions and refrain from false believing propositions within a field of propositions ‘F', when one is in a set of circumstances ‘C'.
It is required that we specify a particular field of suggestions or its propositional field for ‘M', since a given cognitive mechanism will be a competence for believing some kind of truths but not others. The faculty of sight, for example, allows ‘us' to determine the colour of objects, but not the sounds that they associatively make. It is also required that we specify a set of circumstances for ‘M', since a given cognitive mechanism will be a competence in some circumstances but not others. For example, the faculty of sight allows ‘us' to determine colours in a well lighten room, but not in a darkened cave or formidable abyss.
According to the aforementioned formulations, what makes a cognitive mechanism an intellectual virtue is that it is reliable in generating true beliefs than false beliefs in the relevant field and in the relevant circumstances. It is correct to say, therefore, that virtue epistemology is a kind of reliabilism. Whereas, genetic reliabilism maintains that justified belief is belief that results from a reliable cognitive process, virtue epistemology makes a restriction on the kind of process which is allowed. Namely, the cognitive processes that are important for justification and knowledge is those that have their basis in an intellectual virtue.
Finally, that the concerning mental faculty reliability point to the importance of an appropriate environment. The idea is that cognitive mechanisms might be reliable in some environments but not in others. Consider an example from Alvin Plantinga. On a planet revolving around Alfa Centauri, cats are invisible to human beings. Moreover, Alfa Centaurian cats emit a type of radiation that causes humans to form the belief that there I a dog barking nearby. Suppose now that you are transported to this Alfa Centaurian planet, a cat walks by, and you form the belief that there is a dog barking nearby. Surely you are not justified in believing this. However, the problem here is not with your intellectual faculties, but with your environment. Although your faculties of perception are reliable on earth, yet are unrealisable on the Alga Centaurian planet, which is an inappropriate environment for those faculties.
The central idea of virtue epistemology, as expressed in (J) above, has a high degree of initial plausibility. By masking the idea of faculties' cental to the reliability if not by the virtue of epistemology, in that it explains quite neatly to why beliefs are caused by perception and memories are often justified, while beliefs caused by unrealistic and superstition are not. Secondly, the theory gives ‘us' a basis for answering certain kinds of scepticism. Specifically, we may agree that if we were brains in a vat, or victims of a Cartesian demon, then we would not have knowledge even in those rare cases where our beliefs turned out true. But virtue epistemology explains that what is important for knowledge is toast our faculties are in fact reliable in the environment in which we are. And so we do have knowledge so long as we are in fact, not victims of a Cartesian demon, or brains in a vat. Finally, Plantinga argues that virtue epistemology deals well with Gettier problems. The idea is that Gettier problems give ‘us' cases of justified belief that is ‘truer by accident'. Virtue epistemology, Plantinga argues, helps ‘us' to understand what it means for a belief to be true by accident, and provides a basis for saying why such cases are not knowledge. Beliefs are rue by accident when they are caused by otherwise reliable faculties functioning in an inappropriate environment. Plantinga develops this line of reasoning in Plantinga (1988).
The Humean problem if induction supposes that there is some property ‘A' pertaining to an observational or experimental situation, and that of ‘A', some fraction m/n (possibly equal to 1) have also been instances of some logically independent property ‘B'. Suppose further that the background circumstances, have been varied to a substantial degree and also that there is no collateral information available concerning the frequency of ‘B's' among ‘A's' or concerning causal nomological connections between instances of ‘A' and instances of ‘B'.
In this situation, an enumerative or instantial inductive inference would move from the premise that m/n of observed ‘A's' are ‘B's' to the conclusion that approximately m/n of all ‘A's' and ‘B's'. (The usual probability qualification will be assumed to apply to the inference, than being part of the conclusion). Hereabouts the class of ‘A's' should be taken to include not only unobservable ‘A's' of future ‘A's', but also possible or hypothetical ‘a's'. (An alternative conclusion would concern the probability or likelihood of the very next observed ‘A' being a ‘B').
The traditional or Humean problem of induction, often refereed to simply as ‘the problem of induction', is the problem of whether and why inferences that fit this schema should be considered rationally acceptable or justified from an epistemic or cognitive standpoint, i.e., whether and why reasoning in this way is likely lead to true claims about the world. Is there any sort of argument or rationale that can be offered for thinking that conclusions reached in this way are likely to be true if the corresponding premiss is true or even that their chances of truth are significantly enhanced?
Hume's discussion of this deals explicitly with cases where all observed ‘A's' ae ‘B's', but his argument applies just as well to the more general casse. His conclusion is entirely negative and sceptical: inductive inferences are not rationally justified, but are instead the result of an essentially a-rational process, custom or habit. Hume challenges the proponent of induction to supply a cogent line of reasoning that leads from an inductive premise to the corresponding conclusion and offers an extremely influential argument in the form of a dilemma, to show that there can be no such reasoning. Such reasoning would, ne argues, have to be either a priori demonstrative reasoning concerning relations of ideas or ‘experimental', i.e., empirical, reasoning concerning mattes of fact to existence. It cannot be the former, because all demonstrative reasoning relies on the avoidance of contradiction, and it is not a contradiction to suppose that ‘the course of nature may change', tat an order that was observed in the past will not continue in the future: but it also cannot be the latter, since any empirical argument would appeal to the success of such reasoning in previous experience, and the justifiability of generalizing from previous experience is precisely what is at issue - s o that any such appeal would be question-begging, so then, there can be no such reasoning.
An alternative version of the problem may be obtained by formulating it with reference to the so-called Principle of Induction, which says roughly that the future will resemble the last or, that unobserved cases will resemble observe cases. An inductive argument may be viewed as enthymematic, with this principle serving as a suppressed premiss, in which case the issue is obviously how such a premise can be justified. Hume's argument is then that no such justification is possible: the principle cannot be justified a priori i t is not contradictory to den y it: it cannot be justified by appeal to its having been true in pervious experience without obviously begging te question.
The predominant recent responses to the problem of induction, at least in the analytic tradition, in effect accept the main conclusion of Hume's argument, viz. That inductive inferences cannot be justified i the sense of showing that the conclusion of such an inference is likely to be truer if the premise is true, and thus attempt to find some other sort of justification for induction.
Bearing upon, and if not taken into account the term ‘induction' is most widely used for any process of reasoning that takes ‘u' from empirical premises to empirical conclusions support b y the premise, but not deductiverly entailed by them. Inductive arguments are therefore kinds of amplicative argument, in which something beyond the content of the premises is inferred as probable or supported by them. Induction is, however, commonly distinguished from arguments to theoretical explanations, which share this amplicative character, by being confined to inference in which the conclusion involves the same properties or relations as the premises. The central example is induction by simple enumeration, where from premiss telling that Fa, Fb, Fc. , where a, b, c, are all of some kind ‘G', i t is inferred ‘G's' from outside the sample, such as future ‘G's' will be ‘F', or perhaps other person deceive them, children may well infer that everyone is a deceiver. Different but similar inferences are those from the past possession of a property by some object to the same object's future possession, or from the constancy of some law-like pattern in events, and states of affairs to its future constancy: all objects we know of attract each the with a fore inversely proportional to the square of the distance between them, so perhaps they all do so, ad always will do so.
The rational basis of any inference was challenged by David Hume (1711-76), who believed that induction of nature, and merely reflected a habit or custom of the mind. Hume was not therefore sceptical about the propriety of processes of induct ion, but sceptical about the tole of reason in either explaining it or justifying it. trying to answer Hume and to show that there is something rationally compelling about the inference is referred to as the problem of induction. It is widely recognized that any rational defence of induction will have to partition well-behaved properties for which the inference is plausible (often called projectable properties) from badly behaved ones for which t is not. It is also recognized that actual inductive habits are more complex than those of simple and science pay attention to such factors as variations within the sample of giving ‘us' the evidence, the application of ancillary beliefs about the order of nature, and so on. Nevertheless, the fundamental problem remains that any experience shows ‘us' only events occurring within a very restricted part of the vast spatial temporal order about which we then come to believe things.
All the same, the classical problem of induction is often phrased in terms of finding some reason to expect that nature is uniform. In Fact, Fiction and Forecast (1954) Goodman showed that we need in addition some reason for preferring some uniformities to others, for without such a selection the uniformity of nature is vacuous. Thus, suppose that all examined emeralds have been green. Uniformity would lead ‘us' to expect that future emeralds will be green as well. But now we define a predicate grue: is grue if and only if is examined before time ‘T' and is green, or is examined after ‘T' and is blue? Let 'T' refer to some time around the present. Then if newly examined emeralds are like previous ones in respect of being grue, they will be blue. We prefer blueness a basis of prediction to gluiness, but why?
Goodman argued that although his new predicate appears to be gerrymandered, and itself involves a reference to a difference, this is just aparohial or language-relative judgement, there being no language-independent standard of similarity to which to appeal. Other philosophers have not been convinced by this degree of linguistic relativism. What remains clear that the possibility of these ‘bent' predicates put a decisive obstacle in face of purely logical and syntactical approaches to problems of ‘confirmation?'.
Nevertheless, in the potential of change we are to think up to the present time but although virtue epistemology has good initial plausibility, we are faced apart by some substantial objections. The first of an objection, which virtue epistemology face is a version of the generality problem. We may understand the problem more clearly if we were to consider the following criterion for justified belief, which results from our explanation of (J):
(J ) ‘S' is justified in believing that ‘p' if and entirely if.
(1) there is a field ‘F' and a set of circumstances ‘C' such that
(a) ‘S' is in ‘C' with respect to the proposition that ‘p', and
(b) ‘S' is in ‘C' with respect to the proposition that ‘p', and
(e) If ‘S' were in ‘C' with respect to a proposition in ‘F'.
Then ‘S' would very likely believe correctly with regard to
that proposition.
The problem arises in how we are to select an appropriate ‘F' and ‘C'. For given any true belief that ‘p', we can always come up with a field ‘F' and a set of circumstances ‘C', such that ‘S' is perfectly reliable in ‘F' and ‘C'. For any true belief that ‘p', let ‘F's' be the field including only the propositions ‘p' and ‘not-p'. Let ‘C' include whatever circumstances there are which causes ‘p's' to be true, together with the circumstanced which causes ‘S' to believe that ‘p'. Clearly, ‘S' is perfectly reliable with respect to propositions in this field in these circumstances. But we do not want to say that all of S's true beliefs are justified for ‘S'. And of course, there is an analogous problem in the other direction of generality. For given any belief that ‘p', we can always specify a field of propositions ‘F' and a set of circumstances ‘C', such that ‘p' is in ‘F', ‘S' is in ‘C', and ‘S' is not reliable with respect to propositions in ‘F' in ‘C'.
Variations of this view have been advanced for both knowledge and justified belief. The first formulation of a reliability account of knowing appeared in a note by F.P. Ramsey (1931), who said that a belief was knowledge if it is true, certain and obtained by a reliable process. P. Unger (1968) suggested that ‘S' knows that ‘p' just in case it is not at all accidental that ‘S' is right about its being the case that ‘p'. D.M. Armstrong (1973) drew an analogy between a thermometer that reliably indicates the temperature and a belief that reliably indicate the truth. Armstrong said that a non-inferential belief qualified as knowledge if the belief has properties that are nominally sufficient for its truth, i.e., guarantee its truth via laws of nature.
Closely allied to the nomic sufficiency account of knowledge, primarily due to F.I. Dretske (19712, 1981), A.I. Goldman (1976, 1986) and R. Nozick (1981). The core of tis approach is that S's belief that ‘p' qualifies as knowledge just in case ‘S' believes ‘p' because of reasons that would not obtain unless ‘p's' being true, or because of a process or method that would not yield belief in ‘p' if ‘p' were not true. For example, ‘S' would not have his current reasons for believing there is a telephone before him, or would not come to believe this, unless there was a telephone before him. Thus, there is a counterfactual reliable guarantor of the belief's being true. A variant of the counterfactual approach says that ‘S' knows that ‘p' only if there is no ‘relevant alterative' situation in which ‘p' is false but ‘S' would still believe that ‘p'.
To a better understanding, this interpretation is to mean that the alterative attempt to accommodate any of an opposing strand in our thinking about knowledge one interpretation is an absolute concept, which is to mean that the justification or evidence one must have in order to know a proposition ‘p' must be sufficient to eliminate all the alternatives to ‘p' (where an alternative to a proposition ‘p' is a proposition incompatible with ‘p'). That is, one's justification or evidence for ‘p' must be sufficient fort one to know that every alternative to ‘p' is false. These elements of our thinking about knowledge are exploited by sceptical argument. These arguments call our attention to alternatives that our evidence cannot eliminate. For example, (Dretske, 1970), when we are at the zoo. We might claim to know that we see a zebra on the basis of certain visual evidence, namely a zebra-like appearance. The sceptic inquires how we know that we are not seeing a clearly disguised mule. While we do have some evidence against the likelihood of such a deception, intuitively it is not strong enough for ‘us' to know that we are not so deceived. By pointing out alternatives of this nature that cannot eliminate, as well as others with more general application (dreams, hallucinations, etc.), the sceptic appears to show that this requirement that our evidence eliminate every alternative is seldom, if ever, met.
The above considerations show that virtue epistemology must say more about the selection of relevant fields and sets of circumstances. Establishing addresses the generality problem by introducing the concept of a design plan for our intellectual faculties. Relevant specifications for fields and sets of circumstances are determined by this plan. One might object that this approach requires the problematic assumption of a Designer of the design plan. But Plantinga disagrees on two counts: He does not think that the assumption is needed, or that it would be problematic. Plantinga discusses relevant material in Plantinga (1986, 1987 and 1988). Ernest Sosa addresses the generality problem by introducing the concept of an epistemic perspective. In order to have reflective knowledge, ‘S' must have a true grasp of the reliability of her faculties, this grasp being itself provided by a ‘faculty of faculties'. Relevant specifications of an ‘F' and ‘C' are determined by this perspective. Alternatively, Sosa has suggested that relevant specifications are determined by the purposes of the epistemic community. The idea is that fields and sets of circumstances are determined by their place in useful generalizations about epistemic agents and their abilities to act as reliable-information sharers.
The second objection which virtue epistemology faces are that (J) and
(J ) are too strong. It is possible for ‘S' to be justified in believing that ‘p', even when S's intellectual faculties are largely unreliable. Suppose, for example, that Jane's beliefs about the world around her are true. It is clear that in this case Jane's faculties of perception are almost wholly unreliable. But we would not want to say that none of Jane's perceptual beliefs are justified. If Jane believes that there is a tree in her yard, and she vases the belief on the usual tree-like experience, then it seems that she is as justified as we would be regarded a substitutable belief.
Sosa addresses the current problem by arguing that justification is relative to an environment ‘E'. Accordingly, ‘S' is justified in believing that ‘p' relative to ‘E', if and only if S's faculties would be reliable in ‘E'. Note that on this account, ‘S' need not actually be in ‘E' in order for ‘S' to be justified in believing some proposition relative to ‘E'. This allows Soda to conclude that Jane has justified belief in the above case. For Jane is justified in her perceptual beliefs relative to our environment, although she is not justified in those beliefs relative to the environment in which they have actualized her.
We have earlier made mention about analyticity, but the true story of analyticity is surprising in many ways. Contrary to received opinion, it was the empiricist Locke rather than the rationalist Kant who had the better information account of this type or deductive proposition. FrĂ©ge and Rudolf Carnap (1891-1970) A German logician positivist whose first major works was "Der logische Aufbau der Welt" (1926, trs, as "The Logical Structure of the World," 1967). Carnap pursued the enterprise of clarifying the structures of mathematics and scientific language (the only legitimate task for scientific philosophy) in "Logische Syntax der Sprache" (1934, trans. As "The Logical Syntax of Language," 1937). Yet, refinements continued with "Meaning and Necessity" (1947), while a general losing of the original ideal of reduction culminated in the great "Logical Foundations of Probability" and the most importantly single work of ‘confirmation theory' in 1950. Other works concern the structure of physics and the concept of entropy.
Both, Frége and Carnap, represented as analyticity's best friends in this century, did as much to undermine it as its worst enemies. Quine (1908-) whose early work was on mathematical logic, and issued in "A System of Logistic" (1934), "Mathematical Logic" (1940) and "Methods of Logic" (1950) it was with this collection of papers a "Logical Point of View" (1953) that his philosophical importance became widely recognized, also, Putman (1926-) his concern in the later period has largely been to deny any serious asymmetry between truth and knowledge as it is obtained in natural science, and as it is obtained in morals and even theology. Books include "Philosophy of logic" (1971), "Representation and Reality" (1988) and "Renewing Philosophy (1992). Collections of his papers include "Mathematics, Master, sand Method" (1975), "Mind, Language, and Reality" (1975), and "Realism and Reason (1983). Both of which represented as having refuted the analytic/synthetic distinction, not only did no such thing, but, in fact, contributed significantly to undoing the damage done by Frége and Carnap. Finally, the epistemological significance of the distinctions is nothing like what it is commonly taken to be.
Locke's account of an analyticity proposition as, for its time, everything that a succinct account of analyticity should be (Locke, 1924, pp. 306-8) he distinguished two kinds of analytic propositions, identified propositions in which we affirm the said terms if itself, e.g., ‘Roses are roses', and predicative propositions in which ‘a part of the complex idea is predicated of the name of the whole', e.g., ‘Roses are flowers' (pp. 306-7). Locke calls such sentences ‘trifling' because a speaker who uses them ‘trifles with words'. A synthetic sentence, in contrast, such as a mathematical theorem, states ‘a truth and conveys with its informative real knowledge'. Correspondingly, Locke distinguishes two kinds of ‘ necessary consequences', analytic entailment where validity depends on the literal containment of the conclusions in the premiss and synthetic entailments where it does not. (Locke did not originate this concept-containment notion of analyticity. It is discussions by Arnaud and Nicole, and it is safe to say it has been around for a very long time (Arnaud, 1964).
Kant's account of analyticity, which received opinion tells ‘us' is the consummate formulation of this notion in modern philosophy, is actually a step backward. What is valid in his account is not novel, and what is novel is not valid. Kant presents Locke's account of concept-containment analyticity, but introduces certain alien features, the most important being his characterizations of most important being his characterization of analytic propositions as propositions whose denials are logical contradictions (Kant, 1783). This characterization suggests that analytic propositions based on Locke's part-whole relation or Kant's explicative copula are a species of logical truth. But the containment of the predicate concept in the subject concept in sentences like ‘Bachelors are unmarried' is a different relation from containment of the consequent in the antecedent in a sentence like ‘If John is a bachelor, then John is a bachelor or Mary read Kant's Critique'. The former is literal containment whereas, the latter are, in general, not. Talk of the ‘containment' of the consequent of a logical truth in the metaphorical, a way of saying ‘logically derivable'.
Kant's conflation of concept containment with logical containment caused him to overlook the issue of whether logical truths are synthetically deductive and the problem of how he can say mathematical truths are synthetically deductive when they cannot be denied without contradiction. Historically. , the conflation set the stage for the disappearance of the Lockean notion. Frége, whom received opinion portrays as second only to Kant among the champions of analyticity, and Carnap, who it portrays as just behind Frége, was jointly responsible for the appearance of concept-containment analyticity.
FrĂ©ge was clear about the difference between concept containment and logical containment, expressing it as like the difference between the containment of ‘beams in a house' the containment of a ‘plant in the seed' (FrĂ©ge, 1853). But he found the former, as Kant formulated it, defective in three ways: It explains analyticity in psychological terms, it does not cover all cases of analytic propositions, and, perhaps, most important for FrĂ©ge's logicism, its notion of containment is ‘unfruitful' as a definition; mechanisms in logic and mathematics (FrĂ©ge, 1853). In an insidious containment between the two notions of containment, FrĂ©ge observes that with logical containment ‘we are not simply talking out of the box again what we have just put inti it'. This definition makes logical containment the basic notion. Analyticity becomes a special case of logical truth, and, even in this special case, the definitions employ the power of definition in logic and mathematics than mere concept combination.
Carnap, attempting to overcome what he saw a shortcoming in FrĂ©ge's account of analyticity, took the remaining step necessary to do away explicitly with Lockean-Kantian analyticity. As Carnap saw things, it was a shortcoming of FrĂ©ge's explanation that it seems to suggest that definitional relations underlying analytic propositions can be extra-logic in some sense, say, in resting on linguistic synonymy. To Carnap, this represented a failure to achieve a uniform formal treatment of analytic propositions and left ‘us' with a dubious distinction between logical and extra-logical vocabulary. Hence, he eliminated the reference to definitions in FrĂ©ge's explanation of analyticity by introducing ‘meaning postulates', e.g., statements such as ( ) ( is a bachelor-is unmarried) (Carnap, 1965). Like standard logical postulate on which they were modelled, meaning postulates express nothing more than constrains on the admissible models with respect to which sentences and deductions are evaluated for truth and validity. Thus, despite their name, its asymptomatic-balance having to pustulate itself by that in what it holds on to not more than to do with meaning than any value-added statements expressing an indispensable truth. In defining analytic propositions as consequences of (an explained set of) logical laws, Carnap explicitly removed the one place in FrĂ©ge's explanation where there might be room for concept containment and with it, the last trace of Locke's distinction between semantic and other ‘necessary consequences'.
Quine, the staunchest critic of analyticity of our time, performed an invaluable service on its behalf-although, one that has come almost completely unappreciated. Quine made two devastating criticism of Carnap's meaning postulate approach that expose it as both irrelevant and vacuous. It is irrelevant because, in using particular words of a language, meaning postulates fail to explicate analyticity for sentences and languages generally, that is, they do not define it for variables ‘S' and ‘L' (Quine, 1953). It is vacuous because, although meaning postulates tell ‘us' what sentences are to count as analytic, they do not tell ‘us' what it is for them to be analytic.
Received opinion gas it that Quine did much more than refute the analytic/synthetic distinction as Carnap tried to draw it. Received opinion has that Quine demonstrated there is no distinction, however, anyone might try to draw it. Nut this, too, is incorrect. To argue for this stronger conclusion, Quine had to show that there is no way to draw the distinction outside logic, in particular theory in linguistic corresponding to Carnap's, Quine's argument had to take an entirely different form. Some inherent feature of linguistics had to be exploited in showing that no theory in this science can deliver the distinction. But the feature Quine chose was a principle of operationalist methodology characteristic of the school of Bloomfieldian linguistics. Quine succeeds in showing that meaning cannot be made objective sense of in linguistics. If making sense of a linguistic concept requires, as that school claims, operationally defining it in terms of substitution procedures that employ only concepts unrelated to that linguistic concept. But Chomsky's revolution in linguistics replaced the Bloomfieldian taxonomic model of grammars with the hypothetico-deductive model of generative linguistics, and, as a consequence, such operational definition was removed as the standard for concepts in linguistics. The standard of theoretical definition that replaced it was far more liberal, allowing the members of as family of linguistic concepts to be defied with respect to one another within a set of axioms that state their systematic interconnections -the entire system being judged by whether its consequences are confirmed by the linguistic facts. Quine's argument does not even address theories of meaning based on this hypothetico-deductive model (Katz, 1988 and 1990).
Putman, the other staunch critic of analyticity, performed a service on behalf of analyticity fully on a par with, and complementary to Quine's, whereas, Quine refuted Carnap's formalization of Frége's conception of analyticity, Putman refuted this very conception itself. Putman put an end to the entire attempt, initiated by Fridge and completed by Carnap, to construe analyticity as a logical concept (Putman, 1962, 1970, 1975a).
However, as with Quine, received opinion has it that Putman did much more. Putman in credited with having devised science fiction cases, from the robot cat case to the twin earth cases, that are counter examples to the traditional theory of meaning. Again, received opinion is incorrect. These cases are only counter examples to FrĂ©ge's version of the traditional theory of meaning. FrĂ©ge's version claims both (1) that senses determines reference, and (2) that there are instances of analyticity, say, typified by ‘cats are animals', and of synonymy, say typified by ‘water' in English and ‘water' in twin earth English. Given (1) and (2), what we call ‘cats' could not be non-animals and what we call ‘water' could not differ from what the earthier twin called ‘water'. But, as Putman's cases show, what we call ‘cats' could be Martian robots and what they call ‘water' could be something other than H2O Hence, the cases are counter examples to FrĂ©ge's version of the theory.
Putman himself takes these examples to refute the traditional theory of meaning per se, because he thinks other versions must also subscribe to both (1) and. (2). He was mistaken in the case of (1). Frége's theory entails (1) because it defines the sense of an expression as the mode of determination of its referent (Fridge, 1952, pp. 56-78). But sense does not have to be defined this way, or in any way that entails (1). / it can be defined as (D).
(D) Sense is that aspect of the grammatical structure of expressions and sentences responsible for their having sense properties and relations like meaningfulness, ambiguity, antonymy, synonymy, redundancy, analyticity and analytic entailment. (Katz, 1972 & 1990).
(Note that this use of sense properties and relations is no more circular than the use of logical properties and relations to define logical form, for example, as that aspect of grammatical structure of sentences on which their logical implications depend.)
(D) makes senses internal to the grammar of a language and reference an external; matter of language use -typically involving extra-linguistic beliefs, Therefore, (D) cuts the strong connection between sense and reference expressed in (1), so that there is no inference from the modal fact that ‘cats' refer to robots to the conclusion that ‘Cats are animals' are not analytic. Likewise, there is no inference from ‘water' referring to different substances on earth and twin earth to the conclusion that our word and theirs are not synonymous. Putman's science fiction cases do not apply to a version of the traditional theory of meaning based on (D).
The success of Putman and Quine's criticism in application to Fridge and Carnap's theory of meaning together with their failure in application to a theory in linguistics based on (D) creates the option of overcoming the shortcomings of the Lockean-Kantian notion of analyticity without switching to a logical notion. this option was explored in the 1960s and 1970s in the course of developing a theory of meaning modelled on the hypothetico-deductive paradigm for grammars introduced in the Chomskyan revolution (Katz, 1972).
This theory automatically avoids FrĂ©ge's criticism of the psychological formulation of Kant's definition because, as an explication of a grammatical notion within linguistics, it is stated as a formal account of the structure of expressions and sentences. The theory also avoids FrĂ©ge's criticism that concept-containment analyticity is not ‘fruitful' enough to encompass truths of logic and mathematics. The criticism rests on the dubious assumption, parts of FrĂ©ge's logicism, that analyticity ‘should' encompass them, (Benacerraf, 1981). But in linguistics where the only concern is the scientific truth about natural concept-containment analyticity encompass truths of logic and mathematics. Moreover, since we are seeking the scientific truth about trifling propositions in natural language, we will eschew relations from logic and mathematics that are too fruitful for the description of such propositions. This is not to deny that we want a notion of necessary truth that goes beyond the trifling, but only to deny that, that notion is the notion of analyticity in natural language.
The remaining FrĂ©gean criticism points to a genuine incompleteness of the traditional account of analyticity. There are analytic relational sentences, for example, Jane walks with those with whom she strolls, 'Jack kills those he himself has murdered', etc., and analytic entailment with existential conclusions, for example, ‘I think', therefore ‘I exist'. The containment in these sentences is just as literal as that in an analytic subject-predicate sentence like ‘Bachelors are unmarried', such are shown to have a theory of meaning construed as a hypothetico-deductive systemisations of sense as defined in (D) overcoming the incompleteness of the traditional account in the case of such relational sentences.
Such a theory of meaning makes the principal concern of semantics the explanation of sense properties and relations like synonymy, an antonymy, redundancy, analyticity, ambiguity, etc. Furthermore, it makes grammatical structure, specifically, senses structure, the basis for explaining them. This leads directly to the discovery of a new level of grammatical structure, and this, in turn, makes possible a proper definition of analyticity. To see this, consider two simple examples. It is a semantic fact that ‘a male bachelor' is redundant and that ‘spinster' is synonymous with ‘woman who never married; . In the case of the redundancy, we have to explain the fact that the sense of the modifier ‘male' is already contained in the sense of its head ‘bachelor'. In the case of the synonymy, we have to explain the fact that the sense of ‘sinister' is identical to the sense of ‘woman who never married' (compositionally formed from the senses of ‘woman', ‘never' and ‘married'). But is so fas as such facts concern relations involving the components of the senses of ‘bachelor' and ‘spinster' and is in as far as these words are syntactic simple, there must be a level of grammatical structure at which syntactic simple are semantically complex. This, in brief, is the route by which we arrive a level of ‘decompositional semantic structure; that is the locus of sense structures masked by syntactically simple words.
Discovery of this new level of grammatical structure was followed by attemptive efforts as afforded to represent the structure of the sense's finds there. Without going into detail of sense representations, it is clear that, once we have the notion of decompositional representation, we can see how to generalize Locke and Kant's informal, subject-predicate account of analyticity to cover relational analytic sentences. Let a simple sentence ‘S' consisted of a - place predicate ‘P' with terms T1 . . . ,. Tn occupying its argument places. Then:
The analysis in case, first, S has a term T1 that consists of a place predicate Q (m > n or m = n) with terms occupying its argument places, and second, P is contained in Q and, for each term TJ. . . . T1 + I ,. . . . , Tn, TJ is contained in the term of Q that occupies the argument place in Q corresponding to the argument place occupied by TJ in P. (Katz, 1972)
To see how (A) works, suppose that ‘stroll' in ‘Jane walks with those whom she strolls' is decompositionally represented as having the same sense as ‘walk idly and in a leisurely way'. The sentence is analytic by (A) because the predicate ‘stroll' (the sense of ‘stroll) and the term ‘Jane' * the sense of ‘Jane' associated with the predicate ‘walk') is contained in the term ‘Jane' (the sense of ‘she herself' associated with the predicate ‘stroll'). The containment in the case of the other terms is automatic.
The fact that (A) itself makes no reference to logical operators or logical laws indicate that analyticity for subject-predicate sentences can be extended to simple relational sentences without treating analytic sentences as instances of logical truths. Further, the source of the incompleteness is no longer explained, as Fridge explained it, as the absence of ‘fruitful' logical apparatus, but is now explained as mistakenly treating what is only a special case of analyticity as if it were the general case. The inclusion of the predicate in the subject is the special case (where n = 1) of the general case of the inclusion of an–place predicate (and its terms) in one of its terms. Noting that the defects by which Quine complained of in connection with Carnap's meaning-postulated explication are absent in (A). (A) contains no words from a natural language. It explicitly uses variable ‘S' and variable ‘L' because it is a definition in linguistic theory. Moreover, (A) tell ‘us' what property is in virtue of which a sentence is analytic, namely, redundant predication, that is, the predication structure of an analytic sentence is already found in the content of its term structure.
Received opinion has been anti-Lockean in holding that necessary consequences in logic and language belong to one and the same species. This seems wrong because the property of redundant predication provides a non-logic explanation of why true statements made in the literal use of analytic sentences are necessarily true. Since the property ensures that the objects of the predication in the use of an analytic sentence are chosen on the basis of the features to be predicated of them, the truth-conditions of the statement are automatically satisfied once its terms take on reference. The difference between such a linguistic source of necessity and the logical and
mathematical sources vindicate Locke's distinction between two kinds of ‘necessary consequence'.
Received opinion concerning analyticity contains another mistake. This is the idea that analyticity is inimical to science, in part, the idea developed as a reaction to certain dubious uses of analyticity such as Frége's attempt to establish logicism and Schlick's, Ayer's and other logical; postivists attempt to deflate claims to metaphysical knowledge by showing that alleged deductive truths are merely empty analytic truths (Schlick, 1948, and Ayer, 1946). In part, it developed as also a response to a number of cases where alleged analytic, and hence, necessary truths, e.g., the law of excluded a seeming next-to-last subsequent to have been taken as open to revision, such cases convinced philosophers like Quine and Putnam that the analytic/synthetic distinction is an obstacle to scientific progress.
The problem, if there is one is one is not analyticity in the concept-containment sense, but the conflation of it with analyticity in the logical sense. This made it seem as if there is a single concept of analyticity that can serve as the grounds for a wide range of deductive truths. But, just as there are two analytic/synthetic distinctions, so there are two concepts of concept. The narrow Lockean/Kantian distinction is based on a narrow notion of expressions on which concepts are senses of expressions in the language. The broad Frégean/Carnap distinction is based on a broad notion of concept on which concepts are conceptions -often scientific one about the nature of the referent (s) of expressions (Katz, 1972) and curiously Putman, 1981). Conflation of these two notions of concepts produced the illusion of a single concept with the content of philosophical, logical and mathematical conceptions , but with the status of linguistic concepts. This encouraged philosophers to think that they were in possession of concepts with the contentual representation to express substantive philosophical claims, e.g., such as Fridge, Schlick and Ayer's, . . . and so on, and with a status that trivializes the task of justifying them by requiring only linguistic grounds for the deductive propositions in question.
Finally, there is an important epistemological implication of separating the broad and narrowed notions of analyticity. Fridge and Carnap took the broad notion of analyticity to provide foundations for necessary and a priority, and, hence, for some form of rationalism, and nearly all rationalistically inclined analytic philosophers followed them in this. Thus, when Quine dispatched the FrĂ©ge-Carnap position on analyticity, it was widely believed that necessary, as a priority, and rationalism had also been despatched, and, as a consequence. Quine had ushered in an ‘empiricism without dogmas' and ‘naturalized epistemology'. But given there is still a notion of analyticity that enables ‘us' to pose the problem of how necessary, synthetic deductive knowledge is possible (moreover, one whose narrowness makes logical and mathematical knowledge part of the problem), Quine did not under-cut the foundations of rationalism. Hence, a serious reappraisal of the new empiricism and naturalized epistemology is, to any the least, is very much in order (Katz, 1990).
In some areas of philosophy and sometimes in things that are less than important we are to find in the deductively/inductive distinction in which has been applied to a wide range of objects, including concepts, propositions, truths and knowledge. Our primary concern will, however, be with the epistemic distinction between deductive and inductive knowledge. The most common way of marking the distinction is by reference to Kant's claim that deductive knowledge is absolutely independent of all experience. It is generally agreed that S's knowledge that ‘p' is independent of experience just in case S's belief that ‘p' is justified independently of experience. Some authors (Butchvarov, 1970, and Pollock, 1974) are, however, in finding this negative characterization of deductive unsatisfactory knowledge and have opted for providing a positive characterisation in terms of the type of justification on which such knowledge is dependent. Finally, others (Putman, 1983 and Chisholm, 1989) have attempted to mark the distinction by introducing concepts such as necessity and rational unrevisability than in terms of the type of justification relevant to deductive knowledge.
One who characterizes deductive knowledge in terms of justification that is independent of experience is faced with the task of articulating the relevant sense of experience, and proponents of the deductive ly cites ‘intuition' or ‘intuitive apprehension' as the source of deductive justification. Furthermore, they maintain that these terms refer to a distinctive type of experience that is both common and familiar to most individuals. Hence, there is a broad sense of experience in which deductive justification is dependent of experience. An initially attractive strategy is to suggest that theoretical justification must be independent of sense experience. But this account is too narrow since memory, for example, is not a form of sense experience, but justification based on memory is presumably not deductive. There appear to remain only two options: Provide a general characterization of the relevant sense of experience or enumerates those sources that are experiential. General characterizations of experience often maintain that experience provides information specific to the actual world while non-experiential sources provide information about all possible worlds. This approach, however, reduces the concept of non-experiential justification to the concept of being justified in believing a necessary truth. Accounts by enumeration have two problems (1) there is some controversy about which sources to include in the list, and (2) there is no guarantee that the list is complete. It is generally agreed that perception and memory should be included. Introspection, however, is problematic, and beliefs about one's conscious states and about the manner in which one is appeared to are plausible regarded as experientially justified. Yet, some, such as Pap (1958), maintain that experiments in imagination are the source of deductive justification. Even if this contention is rejected and deductive justification is characterized as justification independent of the evidence of perception, memory and introspection, it remains possible that there are other sources of justification. If it should be the case that clairvoyance, for example, is a source of justified beliefs, such beliefs would be justified deductively on the enumerative account.
The most common approach to offering a positive characterization of deductive justification is to maintain that in the case of basic deductive propositions, understanding the proposition is sufficient to justify one in believing that it is true. This approach faces two pressing issues. What is it to understand a proposition in the manner that suffices for justification? Proponents of the approach typically distinguish understanding the words used to express a proposition from apprehending the proposition itself and maintain that it is the latter which are relevant to deductive justification. But this move simply shifts the problem to that of specifying what it is to apprehend a proposition. Without a solution to this problem, it is difficult, if possible, to evaluate the account since one cannot be sure that the account since on cannot be sure that the requisite sense of apprehension does not justify paradigmatic inductive propositions as well. Even less is said about the manner in which apprehending a proposition justifies one in believing that it is true. Proponents are often content with the bald assertions that one who understands a basic deductive proposition can thereby ‘see' that it is true. But what requires explanation is how understanding a proposition enable one to see that it is true.
Difficulties in characterizing deductive justification in a term either of independence from experience or of its source have led, out-of-the-ordinary to present the concept of necessity into their accounts, although this appeal takes various forms. Some have employed it as a necessary condition for deductive justification, others have employed it as a sufficient condition, while still others have employed it as both. In claiming that necessity is a criterion of the deductive. Kant held that necessity is a sufficient condition for deductive justification. This claim, however, needs further clarification. There are three theses regarding the relationship between the theoretically and the necessary that can be distinguished: (I) if ‘p' is a necessary proposition and ‘S' is justified in believing that ‘p' is necessary, then S's justification is deductive: (ii) If ‘p' is a necessary proposition and ‘S' is justified in believing that ‘p' is necessarily true, then S's justification is deductive: And (iii) If ‘p' is a necessary proposition and ‘S' is justified in believing that ‘p', then S's justification is deductive. For example, many proponents of deductive contend that all knowledge of a necessary proposition is deductive. (2) and (3) have the shortcoming of setting by stipulation the issue of whether inductive knowledge of necessary propositions is possible. (I) does not have this shortcoming since the recent examples offered in support of this claim by Kriple (1980) and others have been cases where it is alleged that knowledge of the ‘truth value' of necessary propositions is knowable inductive. (i) has the shortcoming, however, of ruling out the possibility of being justified either in believing that a proposition is necessary on the basis of testimony or else sanctioning such justification as deductive. (ii) and (iii), of course, suffer from an analogous problem. These problems are symptomatic of a general shortcoming of the approach: It attempts to provide a sufficient condition for deductive justification solely in terms of the modal status of the proposition believed without making reference to the manner in which it is justified. This shortcoming, however, can be avoided by incorporating necessity as a necessary but not sufficient condition for a prior justification as, for example, in Chisholm (1989). Here there are two theses that must be distinguished: (1) If ‘S' is justified deductively in believing that ‘p', then ‘p' is necessarily true; and (2) If ‘S' is justified deductively in believing that ‘p'. Then ‘p' is a necessary proposition. (1) and (2), however, allows this possibility. A further problem with both (1) and (2) is that it is not clear whether they permit deductively justified beliefs about the modal status of a proposition. For they require that in order for ‘S' to be justified deductively in believing that ‘p' is a necessary preposition it must be necessary that ‘p' is a necessary proposition. But the status of iterated modal propositions is controversial. Finally, (1) and (2) both preclude by stipulation the position advanced by Kripke (1980) and Kitcher (1980) that there is deductive knowledge of contingent propositions.
The concept of rational unrevisability has also been invoked to characterize deductive justification. The precise sense of rational unrevisability has been presented in different ways. Putnam (1983) takes rational unrevisability to be both a necessary and sufficient condition for deductive justification while Kitcher (1980) takes it to be only a necessary condition. There are also two different senses of rational unrevisability that have been associated with the deductive (I) a proposition is weakly unreviable just in case it is rationally unrevisable in light of any future ‘experiential' evidence, and (II) a proposition is strongly unrevisable just in case it is rationally unrevisable in light of any future evidence. Let us consider the plausibility of requiring either form of rational unrevisability as a necessary condition for deductive justification. The view that a proposition is justified deductive only if it is strongly unrevisable entails that if a non-experiential source of justified beliefs is fallible but self-correcting, it is not a deductive source of justification. Casullo (1988) has argued that it vis implausible to maintain that a proposition that is justified non-experientially is ‘not' justified deductively merely because it is revisable in light of further non-experiential evidence. The view that a proposition is justified deductively only if it is weakly unrevisable is not open to this objection since it excludes only fraction in light of experiential evidence. It does, however, face a different problem. To maintain that S's justified belief that ‘p' is justified deductively is to make a claim about the type of evidence that justifies ‘S' in believing that ‘p'. On the other hand, to maintain that S's justified belief that ‘p' is rationally revisable in light of experiential evidence is to make a claim about the type of evidence that can defeat S's justification for believing that ‘p' that a claim about the type of evidence that justifies ‘S' in believing that ‘p'. Hence, it has been argued by Edidin (1984) and Cassel (1988) that to hold that a belief is justified deductively only if it is weakly unrevisable is either to confuse supporting evidence with defeating evidence or to endorse some implausible this about the relationship between the two such as that if evidence of the sort as the kind ‘A' can defeat the justification conferred on S's belief that ‘p' by evidence of kind ‘B' then S's justification for believing that ‘p' is based on evidence of kind ‘A'.
The most influential idea in the theory of meaning in the past hundred years is the thesis that the meaning of an indicative sentence is given by its truth-conditions. On this conception, to understand a sentence is to know its truth-conditions. The conception was first clearly formulated by Fridge, was developed in a distinctive way by the early Wittgenstein, and is a leading idea of Donald Herbert Davidson (1917-), who is also known for rejection of the idea of as conceptual scheme, thought of as something peculiar to one language or one way of looking at the world, arguing that where the possibility of translation stops so dopes the coherence of the idea that there is anything to translate. His [papers are collected in the "Essays on Actions and Events" (1980) and "Inquiries into Truth and Interpretation" (1983). However, the conception has remained so central that those who offer opposing theories characteristically define their position by reference to it.
Wittgenstein's main achievement is a uniform theory of language that yields an explanation of logical truth. A factual sentence achieves sense by dividing the possibilities exhaustively into two groups, those that would make it true and those that would make it false. A truth of logic does not divide the possibilities but comes out true in all of them. It, therefore, lacks sense and says nothing, but it is not nonsense. It is a self-cancellation of sense, necessarily true because it is a tautology, the limiting case of factual discourse, like the figure ‘0' in mathematics. Language takes many forms and even factual discourse does not consist entirely of sentences like ‘The fork is placed to the left of the knife'. However, the first thing that he gave up was the idea that this sentence itself needed further analysis into basic sentences mentioning simple objects with no internal structure. He was to concede, that a descriptive word will often get its meaning partly from its place in a system, and he applied this idea to colour-words, arguing that the essential relations between different colours do not indicate that each colour has an internal structure that needs to be taken apart. On the contrary, analysis of our colour-words would only reveal the same pattern-ranges of incompatible properties-recurring at every level, because that is how we carve up the world.
Indeed, it may even be the case that of our ordinary language is created by moves that we ourselves make. If so, the philosophy of language will lead into the connection between the meaning of a word and the applications of it that its users intend to make. There is also an obvious need for people to understand each other's meanings of their words. There are many links between the philosophy of language and the philosophy of mind and it is not surprising that the impersonal examination of language in the "Tractatus: was replaced by a very different, anthropocentric treatment in "Philosophical Investigations?"
If the logic of our language is created by moves that we ourselves make, various kinds of realisms are threatened. First, the way in which our descriptive language carves up the world will not be forces on ‘us' by the natures of things, and the rules for the application of our words, which feel the external constraints, will really come from within ‘us'. That is a concession to nominalism that is, perhaps, readily made. The idea that logical and mathematical necessity is also generated by what we ourselves accomplish what is more paradoxical. Yet, that is the conclusion of Wittengenstein (1956) and (1976), and here his anthropocentricism has carried less conviction. However, a paradox is not sure of error and it is possible that what is needed here is a more sophisticated concept of objectivity than Platonism provides.
In his later work Wittgenstein brings the great problem of philosophy down to earth and traces them to very ordinary origins. His examination of the concept of ‘following a rule' takes him back to a fundamental question about counting things and sorting them into types: ‘What qualifies as doing the same again? Of a courser, this question as an inconsequential fundamental and would suggest that we forget it and get on with the subject. But Wittgenstein's question is not so easily dismissed. It has the naive profundity of questions that children ask when they are first taught a new subject. Such questions remain unanswered without detriment to their learning, but they point the only way to complete understanding of what is learned.
It is, nevertheless, the meaning of a complex expression in a function of the meaning of its constituents, that is, indeed, that it is just a statement of what it is for an expression to be semantically complex. It is one of the initial attractions of the conception of meaning as truths-conditions that it permits a smooth and satisfying account of the way in which the meaning of a complex expression is a dynamic function of the meaning of its constituents. On the truth-conditional conception, to give the meaning of an expression is to state the contribution it makes to the truth-conditions of sentences in which it occurs. for singular terms-proper names, indexicals, and certain pronoun's -this is done by stating the reference of the term in question.
The truth condition of a statement is the condition the world must meet if the statement is to be true. To know this condition is equivalent to knowing the meaning of the statement. Although, this sounds as if it gives a solid anchorage for meaning, some of the security disappears when it turns out that the truth condition can only be defined by repeating the very same statement, the truth condition of ‘snow is white' is that snow is white, the truth condition of ‘Britain would have capitulated had Hitler invaded' is that Britain would halve capitulated had Hitler invaded. It is disputed whether this element of running-on-the-spot disqualifies truth conditions from playing the central role in a substantive theory of meaning. Truth-conditional theories of meaning are sometimes opposed by the view that to know the meaning of a statement is to be able to users it in a network of inferences.
On the truth-conditional conception, to give the meaning of expressions is to state the contributive function it makes to the dynamic function of sentences in which it occurs. For singular terms-proper names, and certain pronouns, as well are indexicals-this is done by stating the reference of the term in question. For predicates, it is done either by stating the conditions under which the predicate is true of arbitrary objects, or by stating the conditions under which arbitrary atomic sentence containing it is true. The meaning of a sentence-forming operator is given by stating its distributive contribution to the truth-conditions of a complete sentence, as a function of the semantic values of the sentences on which it operates. For an extremely simple, but nonetheless, it is a structured language, we can state the contributions various expressions make to truth conditions as follows:
A1: The referent of ‘London' is London.
A2: The referent of ‘Paris' is Paris.
A3: Any sentence of the form ‘a is beautiful' is true if and only if the referent of ‘a' is beautiful.
A4: Any sentence of the form ‘a is larger than b' is true if and only if the referent of ‘a' is larger than the referent of ‘b'.
A5: Any sentence of the form ‘It is not the case that A' is true if and only if it is not the case that ‘A' is true.
A6: Any sentence of the form "A and B' are true if and only is ‘A' is true and ‘B' is true.
The principle's A2-A6 form a simple theory of truth for a fragment of English. In this theory, it is possible to derive these consequences: That ‘Paris is beautiful' is true if and only if Paris is beautiful (from A2 and A3), which ‘London is larger than Paris and it is not the cases that London is beautiful' is true if and only if London is larger than Paris and it is not the case that London is beautiful (from A1 - As): And in general, for any sentence ‘A' of this simple language, we can derive something of the form ‘A' is true if and only if A'.
The theorist of truth conditions should insist that not every true statement about the reference of an expression be fit to be an axiom in a meaning-giving theory of truth for a language. The axiom:
London' refers to the city in which there was a huge fire in 1666
is a true statement about the reference of ‘London?'. It is a consequence of a theory that substitutes this axiom for A! In our simple truth theory that ‘London is beautiful' is true if and only if the city in which there was a huge fire in 1666 is beautiful. Since a subject can understand the name ‘London' without knowing that last-mentioned truth conditions, this replacement axiom is not fit to be an axiom in a meaning-specifying truth theory. It is, of course, incumbent on a theorist of meaning as truth conditions to state the constraints on the acceptability of axioms in a way that does not presuppose a deductive, non-truth conditional conception of meaning.
Among the many challenges facing the theorist of truth conditions, two are particularly salient and fundamental. First, the theorist has to answer the charge of triviality or vacuity. Second, the theorist must offer an account of what it is for a person's language to be truly descriptive by a semantic theory containing a given semantic axiom.
We can take the charge of triviality first. In more detail, it would run thus: Since the content of a claim that the sentence ‘Paris is beautiful' in which is true of the divisional region, which is no more than the claim that Paris is beautiful, we can trivially describe understanding a sentence, if we wish, as knowing its truth-conditions, but this gives ‘us' no substantive account of understanding whatsoever. Something other than a grasp to truth conditions must provide the substantive account. The charge rests upon what has been called the redundancy theory of truth, the theory that, is somewhat more discriminative. Horwich calls the minimal theory of truth, or deflationary view of truth, as fathered by Fridge and Ramsey. The essential claim is that the predicate' . . . is true' does not have a sense, i.e., expresses no substantive or profound or explanatory concepts that ought be the topic of philosophical enquiry. The approach admits of different versions, but centres on the points (1) that ‘it is true that p' says no more nor less than ‘p' (hence redundancy) (2) that in less direct context, such as ‘everything he said was true', or ‘all logical consequences of true propositions are true', the predicate functions as a device enabling ‘us'; to generalize than as an adjective or predicate describing the thing he said, or the kinds of propositions that follow from true propositions. For example, the second may translate as ‘ ( p, q) (p & p q q) ‘ where there is no use of a notion of truth.
There are technical problems in interpreting all uses of the notion of truth in such ways, but they are not generally felt to be insurmountable. The approach needs to explain away apparently substantive uses of the notion, such a ;science aims at the truth', or ‘truth is a norm governing discourse'. Indeed, postmodernist writing frequently advocates that we must abandon such norms, along with a discredited ‘objective' conception of truth. But perhaps, we can have the norms even when objectivity is problematic, since they can be framed without mention of truth: Science wants it to be so that whenever science holds that ‘p'. Then ‘p'. Discourse is to be regulated by the principle that it is wrong to assert ‘p' when ‘not-p'.
The disquotational theory of truth finds that the simplest formulation is the claim that expressions of the fern ‘S is true' mean the same as expressions of the form 'S'. Some philosophers dislike the idea of sameness of meaning, and if this is disallowed, then the claim is that the two forms are equivalent in any sense of equivalence that matters. That is, it makes no difference whether people say ‘Dogs bark' is true, or whether they say that ‘dogs bark'. In the former representation of what they say the sentence ‘Dogs bark' is mentioned, but in the latter it appears to be used, so the claim that the two are equivalent needs careful formulation and defence. On the face of it someone might know that ‘Dogs bark' is true without knowing what it means, for instance, if one were to find it in a list of acknowledged truths, although he does not understand English, and this is different from knowing that dogs bark. Disquotational theories are usually presented as versions of the redundancy theory of truth.
The minimal theory states that the concept of truth is exhausted by the fact that it conforms to the equivalence principle, the principle that for any proposition ‘p', it is true that ‘p' if and only if ‘p'. Many different philosophical theories of truth will, with suitable qualifications, accept that equivalence principle. The distinguishing feature of the minimal theory is its claim that the equivalence principle exhausts the notion of truths. It is how widely accepted, that both by opponents and supporters of truth conditional theories of meaning, that it is inconsistent to accept both minimal theory of truth and a truth conditional account of meaning (Davidson, 1990, Dummett, 1959 and Horwich, 1990). If the claim that the sentence ‘Paris is beautiful' is true is exhausted by its equivalence to the claim that Paris is beautiful, it is circular to try to explain the sentence's meaning in terms of its truth conditions. The minimal theory of truth has been endorsed by Ramsey, Ayer, the later Wittgenstein, Quine, Strawson, Horwich and-confusingly and inconsistently if be it correct-Fridge himself. But is the minimal theory correct?
The minimal or redundancy theory treats instances of the equivalence principle as definitional of truth for a given sentence. But in fact, it seems that each instance of the equivalence principle can itself be explained. The truths from which such an instance as:
‘London is beautiful' is true if and only if London is beautiful
preserve a right to be interpreted specifically of A1 and A3 above? This would be a pseudo-explanation if the fact that ‘London' refers to ‘London is beautiful' has the truth-condition it does. But that is very implausible: It is, after all, possible to understand the name ‘London' without understanding the predicate ‘is beautiful'. The idea that facts about the reference of particular words can be explanatory of facts about the truth conditions of sentences containing them in no way requires any naturalistic or any other kind of reduction of the notion of reference. Nor is the idea incompatible with the plausible point that singular reference can be attributed at all only to something that is capable of combining with other expressions to form complete sentences. That still leaves room for facts about an expression's having the particular reference it does to be partially explanatory of the particular truth condition possessed by a given sentence containing it. The minimal; theory thus treats as definitional or stimulative something that is in fact open to explanation. What makes this explanation possible is that there is a general notion of truth that has, among the many links that hold it in place, systematic connections with the semantic values of sub-sentential expressions.
A second problem with the minimal theory is that it seems impossible to formulate it without at some point relying implicitly on features and principles involving truths that go beyond anything countenanced by the minimal theory. If the minimal theory treats truth as a predicate of anything linguistic, be it utterances, type-in-a-language, or whatever, then the equivalence schema will not cover all cases, but only those in the theorist's own language. Some account has to be given of truth for sentences of other languages. Speaking of the truth of language-independence propositions or thoughts will only postpone, not avoid, this issue, since at some point principles have to be stated associating these language-independent entities with sentences of particular languages. The defender of the minimalist theory is likely to say that if a sentence ‘S' of a foreign language is best translated by our sentence ‘p', then the foreign sentence ‘S' is true if and only if ‘p'. Now the best translation of a sentence must preserve the concepts expressed in the sentence. Constraints involving a general notion of truth are persuasive in a plausible philosophical theory of concepts. It is, for example, a condition of adequacy on an individualized account of any concept that there exists what is called ‘Determination Theory' for that account-that is, a specification of how the account contributes to fixing the semantic value of that concept, the notion of a concept's semantic value is the notion of something that makes a certain contribution to the truth conditions of thoughts in which the concept occurs. but this is to presuppose, than to elucidate, a general notion of truth.
It is also plausible that there are general constraints on the form of such Determination Theories, constraints that involve truth and which are not derivable from the minimalist's conception. Suppose that concepts are individuated by their possession conditions. A concept is something that is capable of being a constituent of such contentual representational in a way of thinking of something-a particular object, or property, or relation, or another entity. A possession condition may in various says makes a thanker's possession of a particular concept dependent upon his relations to his environment. Many possession conditions will mention the links between a concept and the thinker's perceptual experience. Perceptual experience represents the world for being a certain way. It is arguable that the only satisfactory explanation of what it is for perceptual experience to represent the world in a particular way must refer to the complex relations of the experience to the subject's environment. If this is so, then mention of such experiences in a possession condition will make possession of that condition will make possession of that concept dependent in part upon the environment relations of the thinker. Burge (1979) has also argued from intuitions about particular examples that, even though the thinker's non-environmental properties and relations remain constant, the conceptual content of his mental state can vary if the thinker's social environment is varied. A possession condition which property individuates such a concept must take into account the thinker's social relations, in particular his linguistic relations.
One such plausible general constraint is then the requirement that when a thinker forms beliefs involving a concept in accordance with its possession condition, a semantic value is assigned to the concept in such a way that the belief is true. Some general principles involving truth can indeed, as Horwich has emphasized, be derived from the equivalence schema using minimal logical apparatus. Consider, for instance, the principle that ‘Paris is beautiful and London is beautiful' is true if and only if ‘Paris is beautiful' is true if and only if ‘Paris is beautiful' is true and ‘London is beautiful' is true. This follows logically from the three instances of the equivalence principle: ‘Paris is beautiful and London is beautiful' is rue if and only if Paris is beautiful, and ‘London is beautiful' is true if and only if London is beautiful. But no logical manipulations of the equivalence schemas will allow the deprivation of that general constraint governing possession conditions, truth and the assignment of semantic values. That constraint can have courses be regarded as a further elaboration of the idea that truth is one of the aims of judgement.
We now turn to the other question, ‘What is it for a person's language to be correctly describable by a semantic theory containing a particular axiom, such as the axiom A6 above for conjunction?' This question may be addressed at two depths of generality. At the shallower level, the question may take for granted the person's possession of the concept of conjunction, and be concerned with what has to be true for the axiom correctly to describe his language. At a deeper level, an answer should not duck the issue of what it is to possess the concept. The answers to both questions are of great interest: We will take the lesser level of generality first.
When a person means conjunction by ‘sand', he is not necessarily capable of formulating the axiom A6 explicitly. Even if he can formulate it, his ability to formulate it is not the causal basis of his capacity to hear sentences containing the word ‘and' as meaning something involving conjunction. Nor is it the causal basis of his capacity to mean something involving conjunction by sentences he utters containing the word ‘and'. Is it then right to regard a truth theory as part of an unconscious psychological computation, and to regard understanding a sentence as involving a particular way of depriving a theorem from a truth theory at some level of conscious proceedings? One problem with this is that it is quite implausible that everyone who speaks the same language has to use the same algorithms for computing the meaning of a sentence. In the past thirteen years, thanks particularly to the work of Davies and Evans, a conception has evolved according to which an axiom like A6 is true of a person's language only if there is a common component in the explanation of his understanding of each sentence containing the word ‘and', a common component that explains why each such sentence is understood as meaning something involving conjunction (Davies, 1987). This conception can also be elaborated in computational terms: Suggesting that for an axiom like A6 to be true of a person's language is for the unconscious mechanisms which produce understanding to draw on the information that a sentence of the form ‘A and B' are true if and only if ‘A' is true and ‘B' is true (Peacocke, 1986). Many different algorithms may equally draw n this information. The psychological reality of a semantic theory thus involves, in Marr's (1982) famous classification, something intermediate between his level one, the function computed, and his level two, the algorithm by which it is computed. This conception of the psychological reality of a semantic theory can also be applied to syntactic and phonol logical theories. Theories in semantics, syntax and phonology are not themselves required to specify the particular algorithms that the language user employs. The identification of the particular computational methods employed is a task for psychology. But semantics, syntactic and phonology theories are answerable to psychological data, and are potentially refutable by them-for these linguistic theories do make commitments to the information drawn upon by mechanisms in the language user.
This answer to the question of what it is for an axiom to be true of a person's language clearly takes for granted the person's possession of the concept expressed by the word treated by the axiom. In the example of the axiom A6, the information drawn upon is that sentences of the form ‘A and B' are true if and only if ‘A' is true and ‘B' is true. This informational content employs, as it has to if it is to be adequate, the concept of conjunction used in stating the meaning of sentences containing ‘and'. So the computational answer we have returned needs further elaboration if we are to address the deeper question, which does not want to take for granted possession of the concepts expressed in the language. It is at this point that the theory of linguistic understanding has to draws upon a theory of concepts. It is plausible that the concepts of conjunction are individuated by the following condition for a thinker to possess it.
Finally, this response to the deeper question allows ‘us' to answer two challenges to the conception of meaning as truth-conditions. First, there was the question left hanging earlier, of how the theorist of truth-conditions is to say what makes one axiom of a semantic theory is correctly in that of another, when the two axioms assign the same semantic values, but do so by means of different concepts. Since the different concepts will have different possession conditions, the dovetailing accounts, at the deeper level of what it is for each axiom to be correct for a person's language will be different accounts. Second, there is a challenge repeatedly made by the minimalist theorists of truth, to the effect that the theorist of meaning as truth-conditions should give some non-circular account of what it is to understand a sentence, or to be capable of understanding all sentences containing a given constituent. For each expression in a sentence, the corresponding dovetailing account, together with the possession condition, supplies a non-circular account of what it is to understand any sentence containing that expression. The combined accounts for each of he expressions that comprise a given sentence together constitute a non-circular account of what it is to understand the compete sentences. Taken together, they allow the theorists of meaning as truth-conditions fully to meet the challenge.
A curious view common to that which is expressed by an utterance or sentence: The proposition or claim made about the world. By extension, the content of a predicate or other sub-sentential component is what it contributes to the content of sentences that contain it. The nature of content is the central concern of the philosophy of language, in that mental states have contents: A belief may have the content that the prime minister will resign. A concept is something that is capable of bringing a constituent of such contents. More specifically, a concept is a way of thinking of something-a particular object, or property or relation, or another entity. Such a distinction was held in FrĂ©ge's philosophy of language, explored in "On Concept and Object" (1892). Fridge regarded predicates as incomplete expressions, in the same way as a mathematical expression for a function, such as sines . . . a log . . . , is incomplete. Predicates refer to concepts, which themselves are ‘unsaturated', and cannot be referred to by subject expressions (we thus get the paradox that the concept of a horse is not a concept). Although Fridge recognized the metaphorical nature of the notion of a concept being unsaturated, he was rightly convinced that some such notion is needed to explain the unity of a sentence, and to prevent sentences from being thought of as mere lists of names.
Several different concepts may each be ways of thinking of the same object. A person may think of himself in the first-person way, or think of himself as the spouse of Mary Smith, or as the person located in a certain room now. More generally, a concept ‘c' is distinct from a concept ‘d' if it is possible for a person rationally to believe ‘d is such-and-such'. As words can be combined to form structured sentences, concepts have also been conceived as combinable into structured complex contents. When these complex contents are expressed in English by ‘that . . . 'clauses, as in our opening examples, they will be capable of being true or false, depending on the way the world is.
The general system of concepts with which we organize our thoughts and perceptions are to encourage a conceptual scheme of which the outstanding elements of our every day conceptual formalities include spatial and temporal relations between events and enduring objects, causal relations, other persons, meaning-bearing utterances of others, . . . and so on. To see the world as containing such things is to share this much of our conceptual scheme. A controversial argument of Davidson's urges that we would be unable to interpret speech from a different conceptual scheme as even meaningful, Davidson daringly goes on to argue that since translation proceeds according ti a principle of clarity, and since it must be possible of an omniscient translator to make sense of, ‘us' we can be assured that most of the beliefs formed within the commonsense conceptual framework are true.
Concepts are to be distinguished from a stereotype and from conceptions. The stereotypical spy may be a middle-level official down on his luck and in need of money. None the less, we can come to learn that Anthony Blunt, art historian and Surveyor of the Queen's Pictures, are a spy; we can come to believe that something falls under a concept while positively disbelieving that the same thing falls under the stereotype associated wit the concept. Similarly, a person's conception of a just arrangement for resolving disputes may involve something like contemporary Western legal systems. But whether or not it would be correct, it is quite intelligible for someone to rejects this conception by arguing that it dies not adequately provide for the elements of fairness and respect that are required by the concepts of justice.
Basically, a concept is that which is understood by a term, particularly a predicate. To posses a concept is to be able to deploy a term expressing it in making judgements, in which the ability connection is such things as recognizing when the term applies, and being able to understand the consequences of its application. The term ‘idea' was formally used in the came way, but is avoided because of its associations with subjective matters inferred upon mental imagery in which may be irrelevant ti the possession of a concept. In the semantics of Fridge, a concept is the reference of a predicate, and cannot be referred to by a subjective term, although its recognition of as a concept, in that some such notion is needed to the explanatory justification of which that sentence of unity finds of itself from being thought of as namely categorized lists of itemized priorities.
A theory of a particular concept must be distinguished from a theory of the object or objects it selectively picks the outlying of the theory of the concept under which is partially contingent of the theory of thought and/or epistemology. A theory of the object or objects is part of metaphysics and ontology. Some figures in the history of philosophy-and are open to the accusation of not having fully respected the distinction between the kinds of theory. Descartes appears to have moved from facts about the indubitability of the thought ‘I think', containing the fist-person was of thinking, to conclusions about the nonmaterial nature of the object he himself was. But though the goals of a theory of concepts and a theory of objects are distinct, each theory is required to have an adequate account of its relation to the other theory. A theory if concept is unacceptable if it gives no account of how the concept is capable of picking out the object it evidently does pick out. A theory of objects is unacceptable if it makes it impossible to understand how we could have concepts of those objects.
A fundamental question for philosophy is: What individuates a given concept-that is, what makes it the one it is, rather than any other concept? One answer, which has been developed in great detail, is that it is impossible to give a non-trivial answer to this question (Schiffer, 1987). An alternative approach, addressees the question by starting from the idea that a concept id individuated by the condition that must be satisfied if a thinker is to posses that concept and to be capable of having beliefs and other attitudes whose content contains it as a constituent. So, to take a simple case, one could propose that the logical concept ‘and' is individuated by this condition, it be the unique concept ‘C' to posses that a thinker has to find these forms of inference compelling, without basing them on any further inference or information: From any two premisses ‘A' and ‘B', ACB can be inferred, and from any premiss ACB, each of ‘A' and ‘B' can be inferred. Again, a relatively observational concept such as ‘round' can be individuated in part by stating that the thinker finds specified contents containing it compelling when he has certain kinds of perception, and in part by relating those judgements containing the concept and which are not based on perception to those judgements that are. A statement that individuates a concept by saying what is required for a thinker to posses it can be described as giving the possession condition for the concept.
A possession condition for a particular concept may actually make use of that concept. The possession condition for ‘and' does so. We can also expect to use relatively observational concepts in specifying the kind of experience that have to be mentioned in the possession conditions for relatively observational concepts. What we must avoid is mention of the concept in question as such within the content of the attitudes attributed to the thinker in the possession condition. Otherwise we would be presupposing possession of the concept in an account that was meant to elucidate its possession. In talking of what the thinker finds compelling, the possession conditions can also respect an insight of the later Wittgenstein: That to find her finds it natural to go on in new cases in applying the concept.
Sometimes a family of concepts has this property: It is not possible to master any one of the members of the family without mastering the others. Two of the families that plausibly have this status are these: The family consisting of some simple concepts 0, 1, 2, . . . of the natural numbers and the corresponding concepts of numerical quantifiers there are 0 so-and-so, there is 1 so-and-so, . . . and the family consisting of the concepts ;belief' and ‘desire'. Such families have come to be known as ‘local holism'. A local holism does not prevent the individuation of a concept by its possession condition. Rather, it demands that all the concepts in the family be individuated simultaneously. So one would say something of this form: Belief and desire form the unique pair of concepts C1 and C2 such that for as thinker to posses them are to meet such-and-such condition involving the thinker, C1 and C2. For these and other possession conditions to individuate properly, it is necessary that there be some ranking of the concepts treated. The possession conditions for concepts higher in the ranking must presuppose only possession of concepts at the same or lower levels in the ranking.
A possession conditions may in various way's make a thinker's possession of a particular concept dependent upon his relations to his environment. Many possession conditions will mention the links between a concept and the thinker's perceptual experience. Perceptual experience represents the world as a certain way. It is arguable that the only satisfactory explanation of what it is for perceptual experience to represent the world in a particular way must refer to the complex relations of the experience to the subject's environment. If this is so, then mention of such experiences in a possession condition will make possession of that concept dependent in part upon the environmental relations of the thinker. Burge (1979) has also argued from intuitions about particular examples that, even though the thinker's non-environmental properties and relations remain constant, the conceptual content of his mental state can vary if the thinker's social environment is varied. A possession condition that properly individuates such a concept must take into account the thinker's social relations, in particular his linguistic relations.
Concepts have a normative dimension, a fact strongly emphasized by Kripke. For any judgement whose content involves a given concept, there is a correctness condition for that judgement, a condition that is dependent in part upon the identity of the concept. The normative character of concepts also extends into making the territory of a thinker's reasons for making judgements. A thinker's visual perception can give him good reason for judging ‘That man is bald': It does not by itself give him good reason for judging ‘Rostropovich ids bald', even if the man he sees is Rostropovich. All these normative connections must be explained by a theory of concepts one approach to these matters is to look to the possession condition for the concept, and consider how the referent of a concept is fixed from it, together with the world. One proposal is that the referent of the concept is that object (or property, or function, . . .) which makes the practices of judgement and inference mentioned in the possession condition always lead to true judgements and truth-preserving inferences. This proposal would explain why certain reasons are necessity good reasons for judging given contents. Provided the possession condition permits ‘us' to say what it is about a thinker's previous judgements that masker it the case that he is employing one concept rather than another, this proposal would also have another virtue. It would allow ‘us' to say how the correctness condition is determined for a judgement in which the concept is applied to newly encountered objects. The judgement is correct if the new object has the property that in fact makes the judgmental practices mentioned in the possession condition yield true judgements, or truth-preserving inferences.
These manifesting dissimilations have occasioned the affiliated differences accorded within the distinction as associated with Leibniz, who declares that there are only two kinds of truths-truths of reason and truths of fact. The forms are all either explicit identities, i.e., of the form ‘A is A', ‘AB is B', etc., or they are reducible to this form by successively substituting equivalent terms. Leibniz dubs them ‘truths of reason' because the explicit identities are self-evident deducible truths, whereas the rest can be converted to such by purely rational operations. Because their denial involves a demonstrable contradiction, Leibniz also says that truths of reason ‘rest on the principle of contradiction, or identity' and that they are necessary [propositions, which are true of all possible words. Some examples are ‘All equilateral rectangles are rectangles' and ‘All bachelors are unmarried': The first is already of the form AB is B' and the latter can be reduced to this form by substituting ‘unmarried man' fort ‘bachelor'. Other examples, or so Leibniz believes, are ‘God exists' and the truths of logic, arithmetic and geometry.
Truths of fact, on the other hand, cannot be reduced to an identity and our only way of knowing them is empirically by reference to the facts of the empirical world. Likewise, since their denial does not involve a contradiction, their truth is merely contingent: They could have been otherwise and hold of the actual world, but not of every possible one. Some examples are ‘Caesar crossed the Rubicon' and ‘Leibniz was born in Leipzig', as well as propositions expressing correct scientific generalizations. In Leibniz's view, truths of fact rest on the principle of sufficient reason, which states that nothing can be so unless there is a reason that it is so. This reason is that the actual world (by which he means the total collection of things past, present and future) is better than any other possible worlds and was therefore created by ‘God'.
In defending the principle of sufficient reason, Leibniz runs into serious problems. He believes that in every true proposition, the concept of the predicate is contained in that of the subject. (This holds even for propositions like ‘Caesar crossed the Rubicon': Leibniz thinks anyone who dids not cross the Rubicon, would not have been Caesar). And this containment relationship! Which is eternal and unalterable even by God ~?! Guarantees that every truth has a sufficient reason. If truths consists in concept containment, however, then it seems that all truths are analytic and hence necessary, and if they are all necessary, surely they are all truths of reason. Leibnitz responds that not every truth can be reduced to an identity in a finite number of steps, in some instances revealing the connection between subject and predicate concepts would requite an infinite analysis. But while this may entail that we cannot prove such propositions as deductively manifested, it does not appear to show that the proposition could have been false. Intuitively, it seems a better ground for supposing that it is necessary truth of a special sort. A related question arises from the idea that truths of fact depend on God's decision to create.
the best of all possible worlds: If it is part of the concept of this world that it is best, now could its existence be other than necessary? Leibniz answers that its existence is only hypothetically necessary, i.e., it follows from God's decision to create this world, but God had the power to decide otherwise. Yet God is necessarily good and non-deceiving, so how could he have decided to do anything else? Leibniz says much more about these masters, but it is not clear whether he offers any satisfactory solutions.
Necessary truths are ones that must be true, or whose opposite is impossible. Contingent truths are those that are not necessary and whose opposite is therefore possible. 1-3 below is necessary, 4-6, contingent.
7. It is not the case that it is raining and not raining
8. 2 + 2= 4
9. All bachelors are unmarried.
10. It seldom rains in the Sahara.
11. There are more than four states in the USA.
12. Some bachelors drive Maserati.
Plantinga (1974, p. 2) characterizes the sense of necessity illustrated in 1-3 as ‘broadly logical'. For it includes not only truths of logic, but those of mathematics, set theory, and other quasi-logical ones. Yet it is not so broads as to include matters of causal or natural necessity, such as: Nothing travels faster than the speed of light.
One would like an account of the basis of our distinction and a criterion by which to apply it. Some suppose that necessary truths are those we know as deductively possible. But we lack the criterion for deductive truths, and there are necessary truths we do not know at all, e.g., undiscovered mathematical ones. It would not help to say that necessary truths are one, and it is possible, in the broadly logical sense, to know of a deductive circularity. Finally, Kripke (1972, p.253 v) and Plantinga (1974, p. 8) argues that some contingent truths are knowable by deductive reasoning. Similar problems face the suggestion that necessary truths are the ones we know with the fairest of certainties: We lack a criterion for certainty, there are necessary truths we do not know, and (barring dubious arguments for scepticism) it is reasonable to suppose that we know some contingent truths with certainty.
Leibniz defined a necessary truth as one whose opposite implies a contradiction. Every such proposition, he held, is either an explicit identity, i.e., of the form ‘A is A', ‘AB is B', etc.) or is reducible to an identity by successively substituting equivalent terms. (thus, 3 above might be so reduced by substituting ‘unmarried man'; for ‘bachelor'.) This has several advantages over the ideas of the previous paragraph. First, it explicated the notion of necessity and possibility and seems to provide a criterion we can apply. Second, because explicit identities are self-evident a deductive propositions, the theory implies that all necessary truths are knowable deductively, but it does not entail that wee actually know all of them, nor does it define ‘knowable' in a circular way. Third, it implies that necessary truths are knowable with certainty, but does not preclude our having certain knowledge of contingent truths by means other than a reduction.
Nevertheless, this view is also problematic, and Leibniz's examples of reductions are too sparse to prove a claim about all necessary truths. Some of his reductions, moreover, are deficient: Fridge has pointed out, for example, that his proof of ‘2 + 2 = 4' presupposes the principle of association and so does not depend on the principle of identity. More generally, it has been shown that arithmetic cannot be reduced to logic, but requires the resources of set theory as well. Finally, there are other necessary propositions, e.g., ‘Nothing can be red and green all over', which do not seem to be reducible to identities and which Leibniz does not show how to reduce.
Leibniz and others have thought of truths as a property of propositions, where the latter are conceived as things that may be expressed by, but are distinct from, linguistic items like statements. On another approach, truth is a property of linguistic entities, and the basis of necessary truth in convention. Thus A.J. Ayer, for example,. Argued that the only necessary truths are analytic statements and that the latter rest entirely on our commitment to use words in certain ways.
The slogan ‘the meaning of a statement is its method of verification' expresses the empirical verification's theory of meaning. It is more than the general criterion of meaningfulness if and only if it is empirically verifiable. If says in addition what the meaning of a sentence is: It is all those observations that would confirm or disconfirmed the sentence. Sentences that would be verified or falsified by all the same observations are empirically equivalent or have the same meaning. A sentence is said to be cognitively meaningful if and only if it can be verified or falsified in experience. This is not meant to require that the sentence be conclusively verified or falsified, since universal scientific laws or hypotheses (which are supposed to pass the test) are not logically deducible from any amount of actually observed evidence.
When one predicate's necessary truth of a preposition one speaks of modality de dicto. For one ascribes the modal property, necessary truth, to a dictum, namely, whatever proposition is taken as necessary. A venerable tradition, however, distinguishes this from necessary de re, wherein one predicates necessary or essential possession of some property to an on object. For example, the statement ‘4 is necessarily greater than 2' might be used to predicate of the object, 4, the property, being necessarily greater than 2. That objects have some of their properties necessarily, or essentially, and others only contingently, or accidentally, are a main part of the doctrine called ;essentialism'. Thus, an essentials might say that Socrates had the property of being bald accidentally, but that of being self-identical, or perhaps of being human, essentially. Although essentialism has been vigorously attacked in recent years, most particularly by Quine, it also has able contemporary proponents, such as Plantinga.
Modal necessity as seen by many philosophers whom have traditionally held that every proposition has a modal status as well as a truth value. Every proposition is either necessary or contingent as well as either true or false. The issue of knowledge of the modal status of propositions has received much attention because of its intimate relationship to the issue of deductive reasoning. For example, no propositions of the theoretic content that all knowledge of necessary propositions is deductively knowledgeable. Others reject this claim by citing Kripke's (1980) alleged cases of necessary theoretical propositions. Such contentions are often inconclusive, for they fail to take into account the following tripartite distinction: ‘S' knows the general modal status of ‘p' just in case ‘S' knows that ‘p' is a necessary proposition or ‘S' knows the truth that ‘p' is a contingent proposition. ‘S' knows the truth value of ‘p' just in case ‘S' knows that ‘p' is true or ‘S' knows that ‘p' is false. ‘S' knows the specific modal status of ‘p' just in case ‘S' knows that ‘p' is necessarily true or ‘S' knows that ‘p' is necessarily false or ‘S' knows that ‘p' is contingently true or ‘S' knows that ‘p' is contingently false. It does not follow from the fact that knowledge of the general modal status of a proposition is a deductively reasoned distinctive modal status is also given to theoretical principles. Nor des it follow from the fact that knowledge of a specific modal status of a proposition is theoretically given as to the knowledge of its general modal status that also is deductive.
The certainties involving reason and a truth of fact are much in distinction by associative measures given through Leibniz, who declares that there are only two kinds of truths-truths of reason and truths of fact. The former are all either explicit identities, i.e., of the form ‘A is A', ‘AB is B', etc., or they are reducible to this form by successively substituting equivalent terms. Leibniz dubs them ‘truths of reason' because the explicit identities are self-evident theoretical truth, whereas the rest can be converted to such by purely rational operations. Because their denial involves a demonstrable contradiction, Leibniz also says that truths of reason ‘rest on the principle of contraction, or identity' and that they are necessary propositions, which are true of all possible worlds. Some examples are that All bachelors are unmarried': The first is already of the form ‘AB is B' and the latter can be reduced to this form by substituting ‘unmarried man' for ‘bachelor'. Other examples, or so Leibniz believes, are ‘God exists' and the truth of logic, arithmetic and geometry.
Truths of fact, on the other hand, cannot be reduced to an identity and our only way of knowing hem os a theoretical manifestations, or by reference to the fact of the empirical world. Likewise, since their denial does not involve as contradiction, their truth is merely contingent: They could have been otherwise and hold of the actual world, but not of every possible one. Some examples are ‘Caesar crossed the Rubicon' and ‘Leibniz was born in Leipzig', as well as propositions expressing correct scientific generalizations. In Leibniz's view, truths of fact rest on the principle of sufficient reason, which states that nothing can be so unless thee is a reason that it is so. This reason is that the actual world (by which he means the total collection of things past, present and future) is better than any other possible world and was therefore created by God.
In defending the principle of sufficient reason, Leibniz runs into serious problems. He believes that in every true proposition, the concept of the predicate is contained in that of the subject. (This hols even for propositions like ‘Caesar crossed the Rubicon': Leibniz thinks anyone who did not cross the Rubicon would not have been Caesar) And this containment relationship-that is eternal and unalterable even by God-guarantees that every truth has a sufficient reason. If truth consists in concept containment, however, then it seems that all truths are analytic and hence necessary, and if they are all necessary, surely they are all truths of reason. Leibniz responds that not evert truth can be reduced to an identity in a finite number of steps: In some instances revealing the connection between subject and predicate concepts would require an infinite analysis. But while this may entail that we cannot prove such propositions as deductively probable, it does not appear to show that the proposition could have been false. Intuitively, it seems a better ground for supposing that it is a necessary truth of a special sort. A related question arises from the idea that truths of fact depend on God's decision to create the best world, if it is part of the concept of this world that it is best, how could its existence be other than necessary? Leibniz answers that its existence is only hypothetically necessary, i.e., it follows from God's decision to create this world, but God is necessarily good, so how could he have decided to do anything else? Leibniz says much more about the matters, but it is not clear whether he offers any satisfactory solutions.
The modality of a proposition is the way in which it is true or false. The most important division is between propositions true of necessity, and those true asa things are: Necessary as opposed to contingent propositions. Other qualifiers sometimes called ‘modal' include the tense indicators ‘It will be the case that p' or It was the case that p', and there are affinities between the ‘deontic indicators', as, ;it ought to be the case that p' or ‘it is permissible that p', and the logical modalities as a logic that study the notions of necessity and possibility. Modal logic was of a great importance historically, particularly in the light of various doctrines concerning the necessary properties of the deity, but was not a central topic of modern logic in its golden period at the beginning of the 20th century. It was,
- however, revived by C. I. Lewis, by adding to a propositional or predicate calculus two operators, and (sometimes written N and M), meaning necessarily and possibly, respectively. These like p p and p p will be wanted. Controversial theses include p p (if a proposition is necessary, it is necessarily necessary, characteristic of the system known as S4) and p p (if a proposition is possible, it is necessarily possible, characteristic of the system known as S5). The classical ‘modal theory' for modal logic, due to Kripke and the Swedish logician Stig Kanger, involves valuing propositions not as true or false ‘simplicitiers', but as true or false art possible worlds, with necessity then corresponding to truth in all worlds, and possibly to truths in some world.
The doctrine advocated by David Lewis, which different ‘possible worlds' are to be thought of as existing exactly as this one does. Thinking in terms of possibilities is thinking of real worlds where things are different, this view has been charged with misrepresenting it as some insurmountably unseeing to why it is good to save the child from drowning, since there is still a possible world in which she (or her counterpart) drowned, and from the standpoint of the universe it should make no difference that world is actual. Critics asio charge either that the notion fails to fit with a coherent theory of how we know about possible worlds, or with a coherent theory about possible worlds, or with a coherent theory of why we are interested in them, but Lewis denies that any other way of interpreting modal statements is tenable.
Thus and so, the ‘standard analysis' of propositional knowledge, suggested by Plato and Kant among others, implies that if one has a justified true belief that ‘p', then one knows that ‘p'. The belief condition ‘p' believes that ‘p', the truth condition requires that any known proposition be true. And the justification condition requires that any known proposition be adequately justified, warranted or evidentially supported. Plato appears to be considering the tripartite definition in the "Theaetetus" (201c-202d), and to be endorsing its jointly sufficient conditions for knowledge in the "Meno" (97e-98a). This definition has come to be called ‘the standard analysis' of knowledge, and has received a serious challenge from Edmund Gettier's counterexamples in 1963. Gettier published two counterexamples to this implication of the standard analysis. In essence, they are:
(1) Smith and Jones have applied for the same job. Smith is justified in believing that (a) Jones will get the job, and that (b) Jones has ten coins in his pocket. On the basis of (a) and (b) Smith infers, and thus is justified in believing, that ©) the person who will get the job has ten coins in his pocket. At it turns out, Smith himself will get the job, and he also happens to have ten coins in his pocket. So, although Smith is justified in believing the true proposition ©), Smith does not know ©).
(2) Smith is justified in believing the false proposition that (a) Smith owns a Ford. On the basis of (a) Smith infers, and thus is justified in believing, that (b) either Jones owns a Ford or Brown is in Barcelona. As it turns out, Brown or in Barcelona, and so (b) is true. So although Smith is justified in believing the true proposition (b). Smith does not know (b).
Gettier's counterexamples are thus cases where one has justified true belief that ‘p', but lacks knowledge that ‘p'. The Gettier problem is the problem of finding a modification of, or an alterative to, the standard justified-true-belief analysis of knowledge that avoids counterexamples like Gettier's. Some philosophers have suggested that Gettier style counterexamples are defective owing to their reliance on the false principle that false propositions can justify one's belief in other propositions. But there are examples much like Gettier's that do not depend on this allegedly false principle. Here is one example inspired by Keith and Richard Feldman:
(3) Suppose Smith knows the following proposition, ‘m': Jones, whom Smith has always found to be reliable and whom Smith, has no reason to distrust now, has told Smith, his office-mate, that ‘p': He, Jones owns a Ford. Suppose also that Jones has told Smith that ‘p' only because of a state of hypnosis Jones is in, and that ‘p' is true only because, unknown to himself, Jones has won a Ford in a lottery since entering the state of hypnosis. And suppose further that Smith deduces from ‘m' its existential generalization, ‘q': There is someone, whom Smith has always found to be reliable and whom Smith has no reason to distrust now, who has told Smith, his office-mate, that he owns a Ford. Smith, then, knows that ‘q', since he has correctly deduced ‘q' from ‘m', which he also knows. But suppose also that on the basis of his knowledge that ‘q'. Smith believes that ‘r': Someone in the office owns a Ford. Under these conditions, Smith has justified true belief that ‘r', knows his evidence for ‘r', but does not know that ‘r'.
Gettier-style examples of this sort have proven especially difficult for attempts to analyse the concept of propositional knowledge. The history of attempted solutions to the Gettier problem is complex and open-ended. It has not produced consensus on any solution. Many philosophers hold, in light of Gettier-style examples, that propositional knowledge requires a fourth condition, beyond the justification, truth and belief conditions. Although no particular fourth condition enjoys widespread endorsement, there are some prominent general proposals in circulation. One sort of proposed modification, the so-called ‘defeasibility analysis', requires that the justification appropriate to knowledge be ‘undefeated' in the general sense that some appropriate subjunctive conditional concerning genuine defeaters of justification be true of that justification. One straightforward defeasibility fourth condition, for instance, requires of Smith's knowing that ‘p' that there be no true proposition ‘q', such that if ‘q' became justified for Smith, ‘p' would no longer be justified for Smith (Pappas and Swain, 1978). A different prominent modification requires that the actual justification for a true belief qualifying as knowledge not depend I a specified way on any falsehood (Armstrong, 1973). The details proposed to elaborate such approaches have met with considerable controversy.
The fourth condition of evidential truth-sustenance may be a speculative solution to the Gettier problem. More specifically, for a person, ‘S', to have knowledge that ‘p' on justifying evidence ‘e', ‘e' must be truth-sustained in this sense for every true proposition ‘t' that, when conjoined with ‘e', undermines S's justification for ‘p' on ‘e', there is a true proposition, ‘t', that, when conjoined with ‘e' & ‘t', restores the justification of ‘p' for ‘S' in a way that ‘S' is actually justified in believing that ‘p'. The gist of this resolving evolution, put roughly, is that propositional knowledge requires justified true belief that is sustained by the collective totality of truths. Herein, is to argue in Knowledge and Evidence, that Gettier-style examples as (1)-(3), but various others as well.
Three features that proposed this solution merit emphasis. First, it avoids a subjunctive conditional in its fourth condition, and so escapes some difficult problems facing the use of such a conditional in an analysis of knowledge. Second, it allows for non-deductive justifying evidence as a component of propositional knowledge. An adequacy condition on an analysis of knowledge is that it does not restrict justifying evidence to relations of deductive support. Third, its proposed solution is sufficiently flexible to handle cases describable as follows:
(4) Smith has a justified true belief that ‘p', but there is a true proposition, ‘t', which undermines Smith's justification for ‘p' when conjoined with it, and which is such that it is either physically or humanly impossible for Smith to be justified in believing that ‘t'.
Examples represented by (4) suggest that we should countenance varying strengths in notions of propositional knowledge. These strengths are determined by accessibility qualifications on the set of relevant knowledge-precluding underminers. A very demanding concept of knowledge assumes that it need only be logically possible for a Knower to believe a knowledge-precluding underminer. Less demanding concepts assume that it must be physically or humanly possible for a Knower to believe knowledge-precluding underminers. But even such less demanding concepts of knowledge need to rely on a notion of truth-sustained evidence if they are to survive a threatening range of Gettier-style examples. Given to some resolution that it needs be that the forth condition for a notion of knowledge is not a function simply of the evidence a Knower actually possesses.
The higher controversial aftermath of Gettier's original counterexamples has left some philosophers doubted of the real philosophical significance of the Gettier problem. Such doubt, however, seems misplaced. One fundamental branch of epistemology seeks understanding of the nature of propositional knowledge. And our understanding exactly what prepositional knowledge is essentially involves our having a Gettier-resistant analysis of such knowledge. If our analysis is not Gettier-resistant, we will lack an exact understanding of what propositional knowledge is. It is epistemologically important, therefore, to have a defensible solution to the Gettier problem, however, demanding such a solution is.
Propositional knowledge (PK) is the type of knowing whose instance are labelled by means of a phrase expressing some proposition, e.g., in English a phrase of the form ‘that h', where some complete declarative sentence is instantial for ‘h'.
Theories of ‘PK' differ over whether the proposition that ‘h' is involved in a more intimate fashion, such as serving as a way of picking out a proposition attitude required for knowing, e.g., believing that ‘h', accepting that ‘h' or being sure that ‘h'. For instance, the tripartite analysis or standard analysis, treats ‘PK' as consisting in having a justified, true belief that ‘h' , the belief condition requires that anyone who knows that ‘h' believes that ‘h', the truth condition requires that any known proposition be true, in contrast, some regarded theories do so consider and treat ‘PK' as the possession of specific abilities, capabilities, or powers, and that view the proposition that ‘h' as needed to be expressed only in order to label a specific instance of ‘PK'.
Although most theories of Propositional knowledge (PK) purport to analyse it, philosophers disagree about the goal of a philosophical analysis. Theories of ‘PK' may differ over whether they aim to cover all species of ‘PK' and, if they do not have this goal, over whether they aim to reveal any unifying link between the species that they investigate, e.g., empirical knowledge, and other species of knowing.
Very many accounts of ‘PK' have been inspired by the quest to add a fourth condition to the tripartite analysis so as to avoid Gettier-type counterexamples to it, whereby a fourth condition of evidential truth-sustenance for every true proposition when conjoined with a regaining justification, which may require the justified true belief that is sustained by the collective totality of truths that an adequacy condition of propositional knowledge not restrict justified evidences in relation of deductive support, such that we should countenance varying strengths in notions of propositional knowledge. Restoratively, these strengths are determined by accessibility qualifications on the set of relevant knowledge-precluding underminers. A very demanding concept of knowledge assumes that it need only be logically possible for a Knower to believe a knowledge-precluding undeterminers, and less demanding concepts that it must physically or humanly possible for a Knower to believe knowledge-precluding undeterminers. But even such demanding concepts of knowledge need to rely on a notion of truth-sustaining evidence if they are to survive a threatening range of Gettier-style examples. As the needed fourth condition for a notion of knowledge is not a function simply of the evidence a Knower actually possesses. One fundamental source of epistemology seeks understanding of the nature of propositional knowledge, and our understanding exactly what propositional knowledge is essentially involves our having a Gettier-resistant analysis of such knowledge. If our analysis is not Gettier-resistant, we will lack an exact understanding of what propositional knowledge is. It is epistemologically important, therefore, to have a defensible solution to the Gettier problem, however, demanding such a solution is. And by the resulting need to deal with other counterexamples provoked by these new analyses.
Keith Lehrer (1965) originated a Gettier-type example that has been a fertile source of important variants. It is the case of Mr Notgot, who is in one's office and has provided some evidence, ‘e', in response to all of which one forms a justified belief that Mr. Notgot is in the office and owns a Ford, thanks to which one arrives at the justified belief that ‘h': ‘Someone in the office owns a Ford'. In the example, ‘e' consists of such things as Mr. Notgot's presently showing one a certificate of Ford ownership while claiming to own a Ford and having been reliable in the past. Yet, Mr Notgot has just been shamming, and the only reason that it is true that ‘h1' is because, unbeknown to oneself, a different person in the office owns a Ford.
Variants on this example continue to challenge efforts to analyse species of ‘PK'. For instance, Alan Goldman (1988) has proposed that when one has empirical knowledge that ‘h', when the state of affairs (call it h*) expressed by the proposition that ‘h' figures prominently in an explanation of the occurrence of one's believing that ‘h', where explanation is taken to involve one of a variety of probability relations concerning ‘h*' , and the belief state. But this account runs foul of a variant on the Notgot case akin to one that Lehrer (1979) has described. In Lehrer's variant, Mr Notgot has manifested a compulsion to trick people into justified believing truths yet falling short of knowledge by means of concocting Gettierized evidence for those truths. It we make the trickster's neuroses highly specific ti the type of information contained in the proposition that ‘h', we obtain a variant satisfying Goldman's requirement That the occurrences of ‘h*' significantly raises the probability of one's believing that ‘h'. (Lehrer himself (1990, pp. 103-4) has criticized Goldman by questioning whether, when one has ordinary perceptual knowledge that abn object is present, the presence of the object is what explains one's believing it to be present.)
In grappling with Gettier-type examples, some analyses proscribe specific relations between falsehoods and the evidence or grounds that justify one's believing. A simple restriction of this type requires that one's reasoning to the belief that ‘h' does not crucially depend upon any false lemma (such as the false proposition that Mr Notgot is in the office and owns a Ford). However, Gettier-type examples have been constructed where one does not reason through and false belief, e.g., a variant of the Notgot case where one arrives at belief that ‘h', by basing it upon a true existential generalization of one's evidence: ‘There is someone in the office who has provided evidence e', in response to similar cases, Sosa (1991) has proposed that for ‘PK' the ‘basis' for the justification of one's belief that ‘h' must not involve one's being justified in believing or in ‘presupposing' any falsehood, even if one's reasoning to the belief does not employ that falsehood as a lemma. Alternatively, Roderick Chisholm (1989) requires that if there is something that makes the proposition that ‘h' evident for one and yet makes something else that is false evident for one, then the proposition that ‘h' is implied by a conjunction of propositions, each of which is evident for one and is such that something that makes it evident for one makes no falsehood evident for one. Other types of analyses are concerned with the role of falsehoods within the justification of the proposition that ‘h' (Versus the justification of one's believing that ‘h'). Such a theory may require that one's evidence bearing on this justification not already contain falsehoods. Or it may require that no falsehoods are involved at specific places in a special explanatory structure relating to the justification of the proposition that ‘h' (Shope, 1983.).
A frequently pursued line of research concerning a fourth condition of knowing seeks what is called a ‘defeasibility' analysis of ‘PK." Early versions characterized defeasibility by means of subjunctive conditionals of the form, ‘If ‘A' were the case then ‘B' would be the case'. But more recently the label has been applied to conditions about evidential or justificational relations that are not themselves characterized in terms of conditionals. Early versions of defeasibility theories advanced conditionals where ‘A' is a hypothetical situation concerning one's acquisition of a specified sort of epistemic status for specified propositions, e.g., one's acquiring justified belief in some further evidence or truths, and ‘B'; concerned, for instance, the continued justified status of the proposition that ‘h' or of one's believing that ‘h'.
A unifying thread connecting the conditional and non-conditional approaches to defeasibility may lie in the following facts: (1) What is a reason for being in a propositional attitude is in part a consideration , instances of the thought of which have the power to affect relevant processes of propositional attitude formation? : (2) Philosophers have often hoped to analyse power ascriptions by means of conditional statements: And (3) Arguments portraying evidential or justificational relations are abstractions from those processes of propositional attitude maintenance and formation that manifest rationality. So even when some circumstance, ‘R', is a reason for believing or accepting that ‘h', another circumstance, ‘K' may present an occasion from being present for a rational manifestation of the relevant power of the thought of ‘R' and it will not be a good argument to base a conclusion that ‘h' on the premiss that ‘R' and ‘K' obtain. Whether ‘K' does play this interfering, ‘defeating'. Role will depend upon the total relevant situation.
Accordingly, one of the most sophisticated defeasibility accounts, which has been proposed by John Pollock (1986), requires that in order to know that ‘h', one must believe that ‘h' on the basis of an argument whose force is not defeated in the above way, given the total set of circumstances described by all truths. More specifically, Pollock defines defeat as a situation where (1) one believes that ‘p' and it is logically possible for one to become justified in believing that ‘h' by believing that 'p', and (2) on e actually has a further set of beliefs, ‘S' logically has a further set of beliefs, ‘S', logically consistent with the proposition that ‘h', such that it is not logically possible for one to become justified in believing that ‘h' by believing it ion the basis of holding the set of beliefs that is the union of ‘S' with the belief that ‘p' (Pollock, 1986, pp. 36, 38). Furthermore, Pollock requires for ‘PK' that the rational presupposition in favour of one's believing that ‘h' created by one's believing that ‘p' is undefeated by the set of all truths, including considerations that one does not actually believe. Pollock offers no definition of what this requirements means. But he may intend roughly the following: There ‘T' is the set of all true propositions: (I) one believes that ‘p' and it is logically possible for one to become justified in believing that ‘h'; by believing that ‘p'. And (II) there are logically possible situations in which one becomes justified in believing that ‘h' on the bass of having the belief that ‘p' and the beliefs in ‘T'. Thus, in the Notgot example, since ‘T' includes the proposition that Mr. Notgot does own a Ford, one lack's knowledge because condition (II) is not satisfied.
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