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).     

Is “some-other-time” sometimes better than “sometime” for proving partial correctness of programs?

The main result of this paper belongs to the field of the comparative study of program verification methods as well as to the field called nonstandard logics of programs. We compare the program verifying powers of various well-known temporal logics of programs, one of which is the Intermittent Assertions Method, denoted as Bur. Bur is based on one of the simplest modal logics called S5 or sometime-logic. We will see that the minor change in this background modal logic increases the program verifying power of Bur. The change can be described either technically as replacing the reflexive version of S5 with an irreflexive version, or intuitively as using the modality some-other-time instead of sometime. Some insights into the nature of computational induction and its variants are also obtained.This project was supported by the Hungarian National Foundation for Scientific Research, Grant No. 1810.     

On testing hypotheses regarding a class of covariance structures

Let x be ap-component random variable having a multivariate normal distribution with covariance matrix . In this paper, we consider the problem of testing hypotheses of the formH ₀: =b ₁₁ + +b _{m m} , whereb _i 's are unknown scalars, and _i 's are a set of known and simultaneously diagonalizable matrices. This problem has both psychometric and statistical interest, and its basic theory is developed here. Besides, the problem of obtaining likelihood-ratio statistic for testingH ₀ is studied, and the statistic obtained in a special case.     

On the relation provable equivalence and on partitions in effectively inseparable sets

We generalize a well-knownSmullyan's result, by showing that any two sets of the kindC _a = {x/ xa} andC _b = {x/ xb} are effectively inseparable (if I b). Then we investigate logical and recursive consequences of this fact (see Introduction).     

Rules in relevant logic — II: Formula representation

This paper surveys the various forms of Deduction Theorem for a broad range of relevant logics. The logics range from the basic system B of Routley-Meyer through to the system R of relevant implication, and the forms of Deduction Theorem are characterized by the various formula representations of rules that are either unrestricted or restricted in certain ways. The formula representations cover the iterated form,A ₁ .A ₂ . ... .A _n B, the conjunctive form,A ₁&A ₂ & ...A _n B, the combined conjunctive and iterated form, enthymematic version of these three forms, and the classical implicational form,A ₁&A ₂& ...A _n B. The concept of general enthymeme is introduced and the Deduction Theorem is shown to apply for rules essentially derived using Modus Ponens and Adjunction only, with logics containing either (A B)&(B C) .A C orA B .B C .A C.I acknowledge help from anonymous referees for guidance in preparing Part II, and especially for the suggestion that Theorem 9 could be expanded to fully contraction-less logics.     

On objectivity

The following definition of objective is proposed: A statement S is objective if and only if in S all parameters that are relevant to its truth value are made explicit. The objectivity of predicates and relations can be defined in a similar manner. This simple conception of objectivity-which could be called explicitness conception of objectivity-can be found in Hermann Weyl and plays a central part in the natural sciences. There are grades of objectivity depending on the quality and the number of parameters our predicates are relativized to A relativistic Ockham principle has to be recognized: Relativization parameters are not to be multiplied beyond necessity. The explicitness conception of objectivity is accessible to mathematical specifications, is the core of the idea of invariance, has a lot of philosophical applications and leads to precise notions of subjectivity and a precise formulation of the problem of the limits of objectivity.I am grateful to Andreas Bartels, Ulrich Gähde, Mark Helme, Andreas Kamlah, Andreas Kemmerling, Winfred Klink, Toni Koch, Hilary Putnam and Matthias Varga von Kibéd who have, in one way or another, contributed to the present content and form of this paper.     

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.     

Models for stronger normal intuitionistic modal logics

This paper, a sequel to Models for normal intuitionistic modal logics by M. Boi and the author, which dealt with intuitionistic analogues of the modal system K, deals similarly with intuitionistic analogues of systems stronger than K, and, in particular, analogues of S4 and S5. For these prepositional logics Kripke-style models with two accessibility relations, one intuitionistic and the other modal, are given, and soundness and completeness are proved with respect to these models. It is shown how the holding of formulae characteristic for particular logics is equivalent to conditions for the relations of the models. Modalities in these logics are also investigated.This paper presents results of an investigation of intuitionistic modal logic conducted in collaboration with Dr Milan Boi.     

ANOVA and ANCOVA of pre- and post-test,ordinal data

With random assignment to treatments and standard assumptions, either a one-way ANOVA of post-test scores or a two-way, repeated measures ANOVA of pre- and post-test scores provides a legitimate test of the equal treatment effect null hypothesis for latent variable . In an ANCOVA for pre- and post-test variablesX andY which are ordinal measures of and , respectively, random assignment and standard assumptions ensure the legitimacy of inferences about the equality of treatment effects on latent variable . Sample estimates of adjustedY treatment means are ordinal estimators of adjusted post-test means on latent variable .     

A notorious affair called exportation

In Quantifiers and Propositional Attitudes, Quine held (a) that the rule of exportation is always admissible, and (b) that there is a significant distinction between a believes-true (Ex)Fx and (Ex) a believes-true F of x. An argument of Hintikka's, also urged by Sleigh, persuaded him that these two intuitions are incompatible; and he consequently repudiated the rule of exportation. Hintikka and Kaplan propose to restrict exportation and quantifying in to favoured contexts — Hintikka to contexts where the believer knows who or what the person or thing in question is; Kaplan to contexts where the believer possesses a vivid name of the person or thing in question. The bulk of this paper is taken up with criticisms of these proposals. Its ultimate purpose, however, is to motivate an alternative approach, which imposes no restrictions on exportation or quantifying in, but repudiates Quine's other intuition: this is the approach taken in my A Logical Form for the Propositional Attitudes.This paper is based on my doctoral dissertation (Rockefeller University, 1977). I wish to thank Susan Haack for her help in turning a draft into the present version.     

Are Knowledge Claims Indexical?

David Lewis, Stewart Cohen, and Keith DeRose have proposed that sentences of the form S knows P are indexical, and therefore differ in truth value from one context to another.¹ On their indexical contextualism, the truth value of S knows P is determined by whether S meets the epistemic standards of the speakers context. I will not be concerned with relational forms of contextualism, according to which the truth value of S knows P is determined by the standards of the subject Ss context, regardless of the standards applying to the speaker making the knowledge claim. Relational contextualism is a form of normative relativism. Indexical contextualism is a semantic theory. When the subject is the speaker, as when S is the first person pronoun I, the two forms of contextualism coincide. But otherwise, they diverge. I critically examine the principal arguments for indexicalism, detail linguistic evidence against it, and suggest a pragmatic alternative.     

Algebraic aspects of deduction theorems

The first known statements of the deduction theorems for the first-order predicate calculus and the classical sentential logic are due to Herbrand [8] and Tarski [14], respectively. The present paper contains an analysis of closure spaces associated with those sentential logics which admit various deduction theorems. For purely algebraic reasons it is convenient to view deduction theorems in a more general form: given a sentential logic C (identified with a structural consequence operation) in a sentential language I, a quite arbitrary set P of formulas of I built up with at most two distinct sentential variables p and q is called a uniform deduction theorem scheme for C if it satisfies the following condition: for every set X of formulas of I and for any formulas and , C(X{{a}}) iff P(, ) AC(X). [P(, ) denotes the set of formulas which result by the simultaneous substitution of for p and for q in all formulas in P]. The above definition encompasses many particular formulations of theorems considered in the literature to be deduction theorems. Theorem 1.3 gives necessary and sufficient conditions for a logic to have a uniform deduction theorem scheme. Then, given a sentential logic C with a uniform deduction theorem scheme, the lattices of deductive filters on the algebras A similar to the language of C are investigated. It is shown that the join-semilattice of finitely generated (= compact) deductive filters on each algebra A is dually Brouwerian.A part of this paper was presented in abstracted form in Bulletin of the Section of Logic, Vol. 12, No. 3 (1983), pp. 111–116, and in The Journal of Symbolic Logic.     

Distributive justice in Aristotle's ethics and politics

Conclusion The symbolism introduced earlier provides a convenient vehicle for examining the status and consistency of Aristotle's three diverse justifications and for explaining how he means to avoid Protagorean relativism without embracing Platonic absolutism.When the variables x and y are allowed to range over the groups of free men in a given polis as well as over individual free men, the formula for the Aristotelian conception of justice expresses the major premiss of Aristotle's three justifications: (1) (_x)(_y) (P(x)·W(x)/P(y)·W(y)=V(T(x))/V(T(y)))Democracy is justified by adding a minor premiss to the effect that as a group the many (m) are superior (>) in virtue and wealth to the few best men (f): ⁸⁵ (2_d) (P(m) · W(m)) > (P(f) · W(f)) (3_d) V(T(m))>V(T(f))Absolute kingship is justified when a godlike man (g) appears in a polis who is incommensurably superior () in virtue and wealth to all the remaining free men (r): (2_k) (P(g) · W(g)) (P(r) · W(r)) (3_k) V(T(g)) V(T(r))True aristocracy requires a more complex justification, which was symbolized in Section 4.These justifications are compatible with each other since they apply to different situations. The polises where democracy and true aristocracy are justified contain no godlike men, and the polis in which democracy is justified differs from that in which true aristocracy is justified in containing a large group of free men who individually have little virtue (Pol. III.11.1281b23-25, 1282a25-26).Each of the justifications is a valid deductive argument. Aristotle affirms the major premiss they share on the basis of a twofold appeal to nature. The principle of distributive justice, the concept as distinguished from the various conceptions of distributive justice, is itself according to nature (Pol. VII.3.1325b7-10) and so too is one particular standard of worth, the standard of the best polis. Consequently, the question of the status of these three justifications, whether they are purely hypothetical or not, is a question about the minor premiss or premisses of each.In the case of the democratic premiss Aristotle's answer is straightforward: it is sometimes but not always true (Pol. III.11.1281bl5-21). Hence the justification of democracy is not purely hypothetical. Nor is the justification of absolute kingship. The man who is like a god among men (Pol. III.13.1284a10-11) would be a man of heroic virtue (see VII.14.1332bl6-27); and such a man, Aristotle says, is rare (ávo) (not nonexistent) (E.N. VII.1.1145a27-28).The minor premisses of the aristocratic argument describe a situation where all of the free men in a given polis have sufficient wealth for the exercise of the moral and intellectual virtues and where all of the older free men of the polis are men of practical wisdom. In the Politics Aristotle makes only the modest claim that such a situation is possible: It is not possible for the best constitution to come into being without appropriate equipment [that is, the appropriate quality and quantity of territory and of citizens and noncitizens]. Hence one must presuppose many things as one would wish them to be, though none of them must be impossible (Pol. VII.4.1325b37-38; see also II.6.1265al7-18). But Aristotle appears to subscribe to the principle that every possibility is realized at some moment of time (Top. 11.11.115bl7-18, Met. .4.1047b3-6, N.2.1088b23-25). This principle together with the claim that the situation described is possible entails that the situation sometimes occurs. Thus even Aristotle's justification of true aristocracy is not purely hypothetical.The final question is Aristotle's way of avoiding Protagorean relativism without embracing Platonic absolutism. The relativist, along with everyone else (E.N. V.3.1131a13-14, Pol. III.12.1282bl8), can accept the principle of distributive justice: Q(x)/Q(y) = V(T(x))/V(T(y)) And he can concede that particular instances of this principle, particular conceptions of justice, accurately describe the modes of distributing political authority that appear just to particular polises and to particular philosophers. What he denies is that there is any basis for ranking these various conceptions of justice or for singling one out as the best (Plato, Theaet. 172A-B). Aristotle, following in Plato's track (Laws X.888D7-890D8), maintains against the relativist that nature provides such a basis. But he departs from Plato in his conception of nature. For Plato the just by nature (ó o}) (Rep. VI.501B2) is the Form of justice, an incorporeal entity (Phdo. 65D4-5, Soph. 246B8) that exists beyond time and space (Tim. 37C6-38C3, 51E6-52B2), whereas for Aristotle the sensible world is the realm of nature (Met. A.1.1069a30-b2). Thus in appealing to nature Aristotle does not appeal to a transcendent standard. Nor does he appeal to his main criterion of the natural, namely, happening always or for the most part. Aristotle's theory of justice is anchored to nature by means of the polis described in Politics VII and VIII, and he regards this polis as natural because it fosters the true end of human life and because its social and political structure reflects the natural hierarchy of human beings and the natural stages of life. Thus the nature that Aristotle's theory of justice is ultimately founded on is human nature.     

Pair discrimination for a continuum of synthetic voiced stops with and without first and third formants

Phoneme labeling and discrimination experiments were conducted with a continuum of voiced stops produced by a Terminal Analog Speech Synthesizer. The stops ranged from |b| to |d|. Only second formant (F₂) transitions changed from one sound to another. (A formant is energy concentrated in a narrow frequency range.) In the labeling experiment conducted to locate the phoneme boundary, subjects identified the individual stimuli as |b| and |d|. In discrimination, difference and identity pairs were presented, with alternative responses of same and different. This allows separate consideration of discrimination (different/Different) and recognition (same/Identity) hits, and also analysis of the data in accordance with the theory of signal detectibility. The sounds were discriminated with and without F ₁ and F ₃ which contained no discriminatory information, but are responsible for perceived similarity to speech. With F ₁ F ₃ , sensitivity (d) was highest at the |b-d| boundary, but without F ₁ F ₃ this was not true. Spectral analysis of the sounds both with and without F ₁ F ₃ revealed a phonemic energy discontinuity for the 1/3 octave around the F ₂ steady-state frequency (1250 Hz). It therefore seems probable that subjects listened to frequencies which contained phonemic information when F ₁ F ₃ were included, but not when they were omitted. In spite of the high sensitivity at the |b-d| boundary, recognition hits (same /Identity) were lowest the boundary had to sound less like a difference to be called different than a pair away from the boundary.Indications, then, are quite strong that auditory-frequency selection helps the perception of speech, and it is clear that a strategy of criterion lowering helps it.     

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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Towards unified field theory: Quantitative differences and qualitative sameness

A survey is given of the concepts of interaction (force) and matter, i.e., of process and substance. The development of these concepts, first in antiquity, then in early modern times, and finally in the contemporary system of quantum field theory is described. After a summary of the basic phenomenological attributes (coupling strengths, symmetry quantities, charges), the common ground of concepts of quantum field theory for both interactions and matter entities is discussed. Then attention is focused on the gauge principle which has been developed to describe all interaction fields in the same way, and hopefully to unite them all into one unified field. While a similar unification of all fundamental types of matter fields (quarks and leptons) into one family may be possible (SU ₅), there still remains at this level a duality between interaction quanta (bosons with spin 1) and matter particles (fermions with spin 1/2). Whether this duality may be removed in some future supersymmetric theory is not discussed in this paper. Nor is Quantum Gravitation discussed, though the analogy of the gauge principle for the three fundamental non-gravitational interactions (hadronic, electromagnetic and weak) to Einstein's principle of equivalence for gravitation in spacetime is noted. However, the equivalence concept is applied not to spacetime but to the internal spaces for the matter (or charge) fields which are the sources between which the fundamental interactions operate. The gauge principle states that a change in the measures of the internal space charge of gauge or phases of the matter fields is equivalent to, and can be compensated by, suitably introduced interaction fields. From such an interaction field, the gauge potential field in the internal space, one may derive a gauge force field by exterior differentiation.Geometrically, the collection of all internal spaces, one over each point of spacetime, constitutes a fiber bundle. The gauge potential field represents a connection on the fiber bundle, and the gauge force field is the curvature (calculated by taking the exterior derivative of the connection and adding to it the exterior product of the connection with itself). Thus, just as gravitational force is interpreted as spacetime curvature, so the three other fundamental forces are interpretable as internal space curvature. The Standard Model which unites the three non-gravitational fields into an SU _c ³ ×SU ₂×U ₁ structure, and the grand unified model, SU ₅, are discussed briefly, and difficulties are noted. Finally it is suggested that a composite model, based on more subtle structure, may be needed to remove the present obscurities and difficulties that stand in the way of a unified theory.     

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.     

Syntactic criteria in prearticulatory editing: Evidence from laboratory-induced slips of the tongue

Earlier studies of laboratory-induced verbal slips have provided a partial model of prearticulatory editing in speech production—a cognitive process by which impending phoneme strings are evaluated for their linguistic and extralinguistic integrity prior to articulation. These studies have provided evidence of editing based upon phonotactic, lexical, and semantic criteria. The present study demonstrates the existence of syntactic editing criteria via laboratory-induced spoonerisms. Experiment I demonstrates that syntactically legitimate spoonerism errors (e.g., mice saw) are more frequent than syntactically anomalous spoonerism errors (e.g., mice sees), suggesting that prearticulatory phonological processing decisions are modified on the basis of syntactic criteria. Experiment II demonstrates that the criteria for syntactically legnitimate spoonerisms can be influenced by aspects of the syntactic context. Implications are discussed.     

Teach Your Students Well: The Seminary and a Hermeneutics of Suspicion

In Freud and Philosophy, Paul Ricoeur argues that religious believers must be willing to expose their faith to Freud's hermeneutics of suspicion. Believers will not, following the encounter, be the same people with the same faith, but, according to Ricoeur, the alternative of avoiding the encounter is not a viable option. However, a philosophy of total exposure to Freud, or anyone else issuing a challenge to religious faith, can be difficult for seminary faculty to apply, pedagogically. Indeed, seminaries are expected to graduate into ministry, not individuals experiencing a crisis of faith or meaning, but rather spiritually rock-solid men and women. The temptation, then, for seminary faculty is to go easy on their students, but this pedagogical strategy inevitably backfires. Seminarians who are sheltered from Ricoeur's challenge may be rock-solid at the persona or surface level of human personality, but this is not, necessarily, an indication that they are individuated or integrated people of faith.