An effective fixed-point theorem in intuitionistic diagonalizable algebras

Summary Within the technical frame supplied by the algebraic variety of diagonalizable algebras, defined by R. Magari in [2], we prove the following:LetT be any first-order theory with a predicate Pr satisfying the canonical derivability conditions, including Löb's property. Then any formula inT built up from the propositional variables q, p₁, ..., p_n, using logical connectives and the predicate Pr, has the same fixed-points relative to q (that is, formulas (p₁ ..., p_n) for which for all p₁, ..., p_n T((p₁, ..., p_n), p₁, ..., p_n) (p₁, ..., p_n)) of a formula ^* of the same kind, obtained from in an effective way.Moreover, such ^* is provably equivalent to the formula obtained from substituting with ^* itself all the occurrences of q which are under Pr. In the particular case where q is always under Pr in , ^* is the unique (up to provable equivalence) fixedpoint of .Since this result is proved only assumingPr to be canonical, it can be deduced that Löb's property is, in a sense, equivalent to Gödel's diagonalization lemma.All the results are proved more generally in the intuitionistic case.The algebraization of the theories which express Theor, IXAllatum est die 19 Decembris 1975     

Becoming: A modest proposal

In this paper I attempt a new approach to an old technical term: becoming. I show how the theory that becoming is coming-to-be could be supported by a semantic derivation of the nominalization becoming from its verbal counterpart, by investigating the properties of the present progressive constructions in which becoming as a verbal appears. My theory denies that dates, or qualitative change, play an essential role in the analysis of becoming.     

The logic of linear tolerance

A nonempty sequence T₁,...,T_n of theories is tolerant, if there are consistent theories T ₁ ⁺ ,..., T _n ⁺ such that for each 1 i n, T _i ⁺ is an extension of T_i in the same language and, if i n, T _i ⁺ interprets T _i+1 ⁺ . We consider a propositional language with the modality , the arity of which is not fixed, and axiomatically define in this language the decidable logics TOL and TOL. It is shown that TOL (resp. TOL) yields exactly the schemata of PA-provable (resp. true) arithmetical sentences, if (A₁,..., A_n) is understood as (a formalization of) PA+A₁, ..., PA+A_n is tolerant.     

PROXY FUNCTIONS,TRUTH AND REFERENCE

Quines ontological relativity is related to Tarskis theory of truth in two ways: Quine repudiates term-by-term-correspondence, as does Tarskis rule of truth; and Quines proxy argument in support of relativity finds exact formulation in Tarskis truth definition.Unfortunately, relativity is threatened by the fact that the proxy argument doesnt comply with the rule of truth (Tarskis celebrated condition (T)). Despite Quines express allegiance to (T), use of proxy schemes does not generate all of the true sentences condition (T) requires.A possible adjustment is to drop (T), retain the satisfaction definition and proxy argument, and appeal to the theory of observation and indeterminacy of reference as grounds of relativity. But as we shall see Quines theories of assent to observation sentences and of reference-learning dont square easily with his naturalism. The first attributes intentional attitudes to observers; and the second assumes a holistic context principle and a concept of individuation which do not withstand scrutiny as empirical notions. Both appear to violate Quines behavorist canon.A saving alternative is a theory of term-reference that appears in Roots of Reference and affords a return to behaviorism, and reinstatement of the proxy argument and relativity in a way compatible with Tarskis (T).     

“Anchor-range” results with “same” and “different” responses and similar and dissimilar stimuli

Summary Blocks of pairs of dissimilar (anchor-like) circles were unexpectedly followed by single pairs of similar circles and vice versa. The dissimilar circles were 3 and 10 mm in diameter, and the similar circles were 3 and 5 mm, 5 and 7 mm, and 7 and 10 mm in diameter. In a second experiment, the dissimilar and similar circles did not overlap in size (e.g., they were 1.5 and 5 mm and 7 and 10 mm, respectively). The same responses to the unexpected same pairs of similar circles were faster than the same responses to the identical pairs in the blocks. In contrast, the different responses to the unexpected different pairs of similar circles were slower than the different responses to the identical pairs in the blocks. Similar stimuli accelerate same responses and slow down different responses. So the time results (and the error results as well) suggest that the context of the block dissimilar circles increased the perceived similarity of the unexpected similar circles. These anchor-range results are not explained by Thurstonian theories, which are based on the absolute properties of stimuli. Instead, they imply that the relation between the similar circles in the context of the relation between the dissimilar circles affected performance.     

A New Representation Theorem for Contranegative Deontic Logic

The logic of an ought operator O is contranegative with respect to an underlying preference relation if it satisfies the property Op & (¬p)(¬q) Oq. Here the condition that is interpolative ((p (pq) q) (q (pq) p)) is shown to be necessary and sufficient for all -contranegative preference relations to satisfy the plausible deontic postulates agglomeration (Op & OqO(p&q)) and disjunctive division (O(p&q) Op Oq).     

The group member's view of inner and outer reality: The Janus phenomenon applied to the group

This paper surveys some theoretical aspects of psychodynamic group treatment from the vantage point of the Janus phenomenon. This focus may provide some clarification in understanding how group therapy facilitates growth, especially in the relationships between inner realities and the realities of the external world. The paper explores and seeks bridges and connections between the dynamics of the group and intrapsychic dynamics. The inner view may be understood as intimately connected with intrapsychic concerns, whereas the issues for patients in groups do, to a degree, concern interpersonal processes in and projections onto the external world. The paper concludes that, thus far, we must accept less than perfect integration of theory and settle for limited domain reasoning (Scheidlinger, 1982). Erlebnis is the term coined by Paul Federn (1952) to refer to subjective experience of the self.     

Derivation of likelihood-ratio tests for Guttman quasi-simplex covariance structures

In this paper, maximum-likelihood estimates have been obtained for covariance matrices which have the Guttman quasi-simplex structure under each of the following null hypotheses: (a) The covariance matrix , can be written asTT + where and are both diagonal matrices with unknown elements andT is a known lower triangular matrix, and (b) the covariance matrix *, is expressible asT*T + I where is an unknown scalar. The linear models from which these covariance structures arise are also stated along with the underlying assumptions. Two likelihood-ratio tests have been constructed, one each for the above null hypotheses, against the alternative hypothesis that the population covariance matrix is simply positive definite and has no particular pattern. A numerical example is provided to illustrate the test procedure. Possible applications of the proposed test are also suggested.Adapted from portions of the author's dissertation under the same title submitted to the Department of Psychology, University of North Carolina, in partial fulfillment of the requirements for the Ph.D. degree. The author wishes to express his gratitude to his thesis chairman Dr. R. Darrell Bock and to his committee members Professors Samarendra Nath Roy, Lyle V. Jones, Thelma G. Thurstone, and Dorothy Adkins. Indebtedness is also acknowledged to Dr. Somesh Das Gupta who was quite helpful during the initial stage of the study.Formerly at the Department of Psychology, Indiana University. The author is grateful both to Indiana University and University of North Carolina for the support extended to him during his doctoral studies.     

Leadership of antireligious propaganda in the Soviet Union

Re-emergent scientific atheism bears the marks of its historical origins in the efforts of Bon-Bruevi and Jaroslavskij. The disciples of the Lenin generation use their fathers somewhat as second-level classics.     

Heidegger's Brightness as a Responsibility of the Therapist in Existential Family Therapy

The author reflects upon the Heideggerian concepts of thrown-ness, death imagery, arrogance and brightness and their usefulness in existential family therapy. The article describes and illustrates with clinical material the process of helping a couple or family to move from an arrogance response to thrownness and death imagery to the response of brightness as attendants of Being. The responsibilities of the therapist in facilitating such a process are also described.Director of the Worthington Logotherapy Institute, co-director of Lantz and Lantz Counseling Associates, and a professor at The Ohio State University. College of Social Work     

Variations in use of the term “or”

Two studies showed that adults' responses to questions involving the term or varied markedly depending upon the type of question presented. When presented with various objects (A's and B's) and asked to circle all things which are A or B subjects tended to circle A's as well as B's, whereas when asked to circle all the A's or B's subjects showed a relatively stronger tendency to circle one or the other. Moreover the nature of the sets of objects (As and Bs) influenced behavior as well. There was also evidence that the effects due to question wording or set type transferred.     

Yes,Virginia, Lemons are Yellow

This paper discusses a number of themes and arguments in The Quest for Reality: Stroud's distinction between philosophical and ordinary questions about reality; the similarity he finds between the view that coloris unreal and the view that it is subjective; his argument against thesecondary quality theory; his argument against the error theory; and the disappointing conclusion of the book.     

Naturalism, scientism and the independence of epistemology

Naturalists seek continuity between epistemology and science. Critics argue this illegitimately expands science into epistemology and commits the fallacy of scientism. Must naturalists commit this fallacy? I defend a conception of naturalized epistemology which upholds the non-identity of epistemic ends, norms, and concepts with scientific evidential ends, norms, and concepts. I argue it enables naturalists to avoid three leading scientistic fallacies: dogmatism, one dimensionalism, and granting science an epistemic monopoly.     

The ‘will to believe’ in science and religion

Conclusion The Will to Believe defines the religious question as forced, living and momentous, but even in this article James asserts that more objective factors are involved. The competing religious hypotheses must both be equally coherent and correspond to experimental data to an equal degree. Otherwise the option is not a live one. If I say to you Be a theosophist or be a Mohammedan, it is probably a dead option, because for you neither hypothesis is likely to be alive. Analogously, in A Pluralistic Universe James is at pains to convince the reader that his own religious hypothesis is just as objective, makes just as much sense, etc. as alternative possibilities: the only thing I emphatically insist upon is that it [pluralistic pantheism] is a fully coordinate hypothesis with monism. This world may, in the last resort, be a block universe; but on the other hand, it may be a universe only strung along, not rounded in and closed. Reality may exist distributively just as it sensibly seems to, after all. On that possibility I do insist. Here, once again, before the will to believe can be employed, the objective factors of competing hypotheses, their equal coherence and correspondence, must be brought out.When reconstructed, James' overall outlook has a qausi Kuhnian taint to it- though obvious differences remain. Much of what goes on in evaluating competing scientific hypotheses is either not forced, or not living, or not momentous, but rather typical, dead, and avoidable, in short very normal. But there are moments in the history of science where the decision between hypotheses might well be forced, living and momentous, and sometimes James comes close to recognizing this.Analogously, a good deal of what goes on in religion is not forced, not living or not momentous - in short it is all too normal. In The Varieties of Religious Experience for example, James proposes to ignore the institutional branch of the religious domain and to concentrate on personal and psychological factors, his reason being that the institutional aspect concentrates on the routine, the normal. Worship and sacrifice, procedures for working on the dispositions of the deity, theology and ceremony and ecclesiastical organization, are the essentials of religion in the institutional branch. Were we to limit our view to it, we should have to define religion as an external art, the art of winning the favor of the gods. and again The word religion, as ordinarily used, is equivocal. A survey of history shows us that, as a rule, religious geniuses attract disciples, and produce groups of sympathizers. When these groups get strong enough to organize themselves, they become ecclesiastical institutions with corporate ambitions of their own. The spirit of politics and the lust of dogmatic rule are then apt to enter and to contaminate the originally innocent thing; so that when we hear the word religion nowadays, we think inevitably of some church or other.Clearly here religion has a normal, i.e. trivial side, just as does science. On the other hand, there are revolutionary moments in religion, such as that of choosing between theism and materialism in Pragmatism, or choosing among theism, monistic pantheism and pluralistic pantheism in A Pluralistic Universe. Such moments involve the will to believe and are clearly more personal than their counterparts in the domain of normal institutionalized religion. Going further, there are no doubt differences of degree between the will to believe decisions in science and the will to believe decisions in religion. These have been explicated in more specific terms by Ian Barbour in his article, Paradigms in Science and Religion. ...each of the subjective features of science... is more evident in the case of religion: (1) the influence of interpretation on data, (2) the resistance of comprehensive theories of falsification, and (3) the absence of rules for choice among paradigms. Each of the corresponding objective features of science is less evident in the case of religion: (1) the presence of common data on which disputants can agree, (2) the cumulative effect of evidence for or against a theory, and (3) the existence of criteria which are not paradigm-dependent. It is clear that in all three respects religion is a more subjective enterprise than science. But in each case there is a difference of degree - not an absolute contrast between an objective science and a subjective religion. Barbour correctly notes that the ...choice is not between religion and science, but between theism, pantheism, and naturalism, let us say, as each is expressed in a particular historical tradition. No basic beliefs are capable of demonstrable proof. James sometimes comes close to recognizing this but his oscillation on the status of the everyday world of common sense, or the perceptual world, causes him not to see the issue clearly. When the animated world of the perceptual is taken as the all inclusive really real, science is viewed as an abstract, second class citizen. But James offers what we would consider a more sophisticated and adequate perspective when he views the world of common sense, having become linguistified, as itself suspicious, and consequently views all three tiers - common sense, scholastic philosophy, and science - as regional ontologies, or language games in Wittgenstein's terminology - and opposes all three to a more primordial or prereflexive level. When James takes this second approach it is easier to see that the basic distinction he began to make in The Will to Believe was between the scientific and religious domain where the will to believe was to be employed, and the domain of ordinary religion and science. Finally this position anticipates his ultimate metaphysical outlook, viz. pure experience as approachable through language on a series of diverse regional levels, but nonetheless not completely describable within language.It is important to recall that in The Varieties of Religious Experience James distinguishes between the science of religions and what he calls living religion: [T] he science of religions may not be an equivalent for living religion; and if we turn to the inner difficulties of such a science, we see that a point comes when she must drop the purely theoretic attitude, and either let her knots remain uncut, or have them cut by active faith. The study of religion, in short is not the activity of religion; the latter is animated, personal, and, we would argue, necessitates a commitment in terms of the will to believe. Once again, however, James hesitates over offering the same two-fold delineation in other areas of science. On the one hand he tells the reader that science-has ended by utterly repudiating the personal point of view. On the other hand, he offers the following comment a few pages later on in a footnote: ...the divorce between scientist facts and religious facts may not necessarily be as eternal as it at first sight seems, nor the personalism and romanticism of the world, as they appeared to primitive thinking, be matters so irrevocably outgrown. The final opinion may, in short, in some manner now impossible to forsee, revert to the more personal style, just as any path of progress may follow a spiral rather than a straight line. If this were so, the rigorously impersonal view of science might one day appear as having been a temporarily useful eccentricity rather than the definitely triumphant position which the sectarian scientist at present so confidently announces it to be. The burden of this paper has been to indicate that when James' two-fold outlook on perception and/or common sense is properly reconstructed, the raproachment between science and religion is not so impossible to forsee.

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Kenneth Strike on Liberalism,Citizenship and the Private Interest in Schooling

After indicating a number of points of agreement with the argument 0eveloped by Kenneth Strike in his article Liberalism, Citizenship and the Private Interest in Schooling, this article identifies and explores a number of queries and criticisms which arise in relation to that argument. These queries and criticisms relate especially to the nature and extent of the expansiveness involved in Strike's conception of public or common educational influence, and to the implications and justification of the claim that private educational interests enjoy a greater salience and recognition on Strike's view of public or common educational influence than on some alternative views.     

Axiomatization of the De Morgan type rules

In Section 1 we show that the De Morgan type rules (= sequential rules in L(, ) which remain correct if and are interchanged) are finitely based. Section 2 contains a similar result for L(). These results are essentially based on special properties of some equational theories.     

Modal logic with names

We investigate an enrichment of the propositional modal language with a universal modality having semanticsx iff y(y ), and a countable set of names — a special kind of propositional variables ranging over singleton sets of worlds. The obtained language _c proves to have a great expressive power. It is equivalent with respect to modal definability to another enrichment () of, where is an additional modality with the semanticsx iff y(y x y ). Model-theoretic characterizations of modal definability in these languages are obtained. Further we consider deductive systems in _c. Strong completeness of the normal _c-logics is proved with respect to models in which all worlds are named. Every _c-logic axiomatized by formulae containing only names (but not propositional variables) is proved to be strongly frame-complete. Problems concerning transfer of properties ([in]completeness, filtration, finite model property etc.) from to _c are discussed. Finally, further perspectives for names in multimodal environment are briefly sketched.     

Desirable and undesirable masculine and feminine traits in relation to students' dieting tendencies and body image dissatisfaction

Previous research showing greater femininity among overweight persons used measures of masculinity and femininity which have been criticized for conceptual and psychometric reasons. The present study used the Spence-Helmreich measures to examine the interrelationships among socially desirable and socially undesirable instrumental (masculine) and expressive (feminine) traits, body weight, and other attributes of cognitive concern about dieting and weight-related appearance. While body weight was unrelated to these measures of psychological masculinity and femininity, sex differences were found in the relationship of masculinity and femininity to dieting tendencies. dissatisfaction with physical appearance, and achievement motivation in these samples of college undergraduates.     

The concept of a proposition in classical and quantum physics

A proposition is associated in classical mechanics with a subset of phase space, in quantum logic with a projection in Hilbert space, and in both cases with a 2-valued observable or test. A theoretical statement typically assigns a probability to such a pure test. However, since a pure test is an idealization not realizable experimentally, it is necessary — to give such a statement a practical meaning — to describe how it can be approximated by feasible tests. This gives rise to a search for a formal representation of feasible tests, which leads via mixed tests (weighted means of pure tests) to vague tests (convex sets of mixed tests). A model is described in which the latter form a continuous lattice; the pure and mixed tests are the maximal elements and the feasible tests form a basis. Each type of test has its own logic; this is illustrated by the passage from mixed tests to pure tests, which corresponds to the transition from L to classical logic.This work was supported by a grant from the National Research Council of Canada.