Stuffed Cabbage in the Old New School Cafeteria

The purpose of this lecture is to celebrate the memory of Aron Gurwitsch by examining and enlarging the domain of phenomenological clarification of some elements of what Gurwitsch called the logic of reality. Chief among those elements are the nature of the taken-for-grantedness of our existential belief, the difference between presentive and non-presentive indices of reality and the ground for the self-illumination of the world of working.     

Gestalt psychology in the soviet union

Summary The influence of the Berlin school of Gestalt psychology on Soviet psychology in the period before the reactological debate (1931) is analyzed. A review of the channels of communication (congresses personal visits, translations, review papers) shows that Soviet psychologists were well informed about Gestalt psychology, and that the members of L.S. Vygotskij's circle were the main promotors of Gestalt ideas in the Soviet Union. Gestalt psychology was welcomed as a potential ally in the construction of a Marxist psychology first outlined by K.N. Kornilov. The initial enthusiasm for Gestalt psychology was stimulated by the system concept as developed by Wolfgang Köhler, and A.R. Luria made an attempt to demonstrate the compatibility between Köhler's theory and some general methodological implications of dialectical materialism. Later on, the focus of interest shifted to Köhler's investigations of intelligent behavior in apes, which formed part of the empirical base of the historico-cultural theory of mental development. The impact of Gestalt ideas served an important function in the struggle against mechanistic theories of behavior which were at that time predominant in Soviet psychology.Thanks are due to Josef Broek and Sonia Argyle, who have kindly agreed to polish my English. The remaining teutonisms are not their fault. All translations from Russian or German sources were done by the author. Please address offprint requests to Eckart Scheerer, Universität Oldenburg, FB 1 - Psychologie, Birkenweg 3, 2900 Oldenburg, Federal Republic of Germany     

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.     

Confirmation holism and semantic holism

Fodor and Lepore, in their recent book Holism, maintain that if an inference from semantic anatomism to semantic holism is allowed, certain fairly deleterious consequences follow. In Section 1 Fodor and Lepore's terminology is construed and amended where necessary with the result that the aforementioned deleterious consequences are neither so apparent nor straightforward as they had suggested. In Section 2 their Argument A is considered in some detail. In Section 3 their argument attributed to Quine is examined at length and a shorter and more perspicacious argument suggested which avoids their charge that the Quinean argument is guilty of an equivocation on the word statement.     

Superintuitionistic Companions of Classical Modal Logics

This paper investigates partitions of lattices of modal logics based on superintuitionistic logics which are defined by forming, for each superintuitionistic logic L and classical modal logic , the set L[] of L-companions of . Here L[] consists of those modal logics whose non-modal fragments coincide with L and which axiomatize if the law of excluded middle p V p is added. Questions addressed are, for instance, whether there exist logics with the disjunction property in L[], whether L[] contains a smallest element, and whether L[] contains lower covers of . Positive solutions as concerns the last question show that there are (uncountably many) superclean modal logics based on intuitionistic logic in the sense of Vakarelov [28]. Thus a number of problems stated in [28] are solved. As a technical tool the paper develops the splitting technique for lattices of modal logics based on superintuitionistic logics and ap plies duality theory from [34].     

Third Men: The Logic of the Sophisms at Arist. SE 22, 178b36–170a10

This article aims at elucidating the logic of Arist. SE 22, 178b36–179a10 and, in particular, of the sophism labelled "Third Man" discussed in it. I suggest that neither the sophistic Walking Man argument, proposed by ancient commentators, nor the Aristotelian Third Man of the , suggested by modern interpreters, can be identified with the fallacious argument Aristotle presents and solves in the passage. I propose an alternative reconstruction of the Third Man sophism and argue that an explanation of the lines regarding the identity of Coriscus and Coriscus the musician (178b39–179a3) is indispensable for its correct understanding, since they hint at another sophism in some important aspects analogous. Finally, I show that two contradictions concerning spotted by scholars in the passage are only apparent and can be dissolved once the assumption that the anti-Platonic Third Man argument is at stake here is discarded, and once the passage is read in the light of its agonistic context.     

Game Logic and its Applications II

This paper provides a Genzten style formulation of the game logic framework GLm (0 m ), and proves the cut-elimination theorem for GLm. As its application, we prove the term existence theorem for GL used in Part I.     

Die Entwicklung der Diskussion um die formale Logik in der Sowjetunion

Ohne ZusammenfassungDie Literatur zur Logik in der Sowjetunion ist sehr bescheiden. Nebst einigen Kapiteln in grösseren Werken sind es folgende Schriften: Bochénski, I. M., Soviet Logic,SST, 1, 29–38. — Dahm, H., Renaissance der formalen Logik,Ost-Probleme, 1957,8, 254–267. — Philipov, A.,Logic and Dialectic in the Soviet Union, New York 1952, XI+89 pp. — Winkelmann, A., Die Stellung der formalen Logik im Sowjet-system,Scholastik, 1956,1, 85–89.     

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.     

A reduction rule for Peirce formula

A reduction rule is introduced as a transformation of proof figures in implicational classical logic. Proof figures are represented as typed terms in a -calculus with a new constant P ⁽⁽⁾⁾. It is shown that all terms with the same type are equivalent with respect to -reduction augmented by this P-reduction rule. Hence all the proofs of the same implicational formula are equivalent. It is also shown that strong normalization fails for P-reduction. Weak normalization is shown for P-reduction with another reduction rule which simplifies of (( ) ) into an atomic type.This work was partially supported by a Grant-in-Aid for General Scientific Research No. 05680276 of the Ministry of Education, Science and Culture, Japan and by Japan Society for the Promotion of Science. Hiroakira Ono     

A Note on Algebras of Substitutions

We will study the class RSA of -dimensional representable substitution algebras. RSA is a sub-reduct of the class of representable cylindric: algebras, and it was an open problem in Andréka [1] that whether RSA can be finitely axiomatized. We will show, that the answer is positive. More concretely, we will prove, that RSA is a finitely axiomatizable quasi-variety. The generated variety is also described. We note that RSA is the algebraic counterpart of a certain proportional multimodal logic and it is related to a natural fragment of first order logic, as well.     

Rethinking the Fallacy of Hasty Generalization

This paper makes a case for a refined look at the so- called fallacy of hasty generalization by arguing that this expression is an umbrella term for two fallacies already distinguished by Aristotle. One is the fallacy of generalizing in an inappropriate way from a particular instance to a universal generalization containing a for all x quantification. The other is the secundum quid (in a certain respect) fallacy of moving to a conclusion that is supposed to be a universal generalization containing a for all x quantification while overlooking qualifications that have to be added to the more limited kind of generalization expressed in the premise. It is shown that these two fallacies relate to two different kinds of generalization.The classification of fallacious generalizations is based on a new theory of generalization that distinguishes three kinds of generalizations – the universal generalization of the for all x type, used in classical deductive logic, the inductive generalization, based on probability, and the presumptive generalization, which is defeasible, and allows for exceptions to a general rule. The resulting classification goes beyond a logic-oriented analysis by taking into account how a respondent may oppose a potentially fallacious generalizing move by falsifying it. Using a dialectical interpretation of premise-conclusion complexes, the paper outline a richer concept of generalizing argument moves embedded in a communicational reconstruction of the strategic uses of such moves in which two parties take part in an orderly dialectical exchange of viewpoints.     

An Exploration of Johnson's Sense of ‘Argument’

This essay attempts to give definitions and identity conditions for the two predominant senses of Argument currently in use, the one involving reasons for a conclusion and the other denoting an expressed disagreement with ensuing verbal behaviour by two parties. I see Johnson's new concept of Argument, as developed in his book Manifest Rationality, as a hybrid of the two common senses of Argument, and, accordingly, I try to define and give the identity conditions of Johnson-arguments. Finally, I disagree with Johnson on the nature of the definition he thinks he has proposed, and I conclude with observations suggesting that his logical perspective has dialectical and rhetorical components.     

A modification of kendall's tau for measuring association in contingency tables

A coefficient of association is described for a contingency table containing data classified into two sets of ordered categories. Within each of the two sets the number of categories or the number of cases in each category need not be the same.=+1 for perfect positive association and has an expectation of 0 for chance association. In many cases also has –1 as a lower limit. The limitations of Kendall's _a and _b and Stuart's _c are discussed, as is the identity of these coefficients to' under certain conditions. Computational procedure for is given.     

Axiomatization of ‘Peircean’ branching-time logic

The branching-time logic called Peircean by Arthur Prior is considered and given an infinite axiomatization. The axiomatization uses only the standard deduction rules for tense logic.     

Gentzen-type formulation of the prepositional logic LQ

We give a Gentzen-type formulation GQ for the intermediate logic LQ and prove the cut-elimination theorem on it, where LQ is the propositional logic obtained from the intuitionistic propositional logic LI by adding the axioms of the form AV A.     

The relationship between perceived surface-lightness and perceived illumination

Summary An attempt was made to specify the relationship between perceived surface lightness and perceived illumination under the stimulus conditions where different combinations of albedo and illuminance gave 10 approximately equal-luminance levels of a test field (TF) on three different (black-, gray- and white-appearing) backgrounds. Two types of category judgments for TF-lightness and overall illumination were made on the total of 94 TFs by 5 Ss. The results indicated that under the condition where achromatic surface colors appear, the perceptual scission which produces two different perceptual dimensions (lightness and perceived illumination) from one sort of stimulation (luminance) was clearly observed. The relation between the two judgments was consistent with the lightness-illumination invariance hypothesis: As lightness judgments (A) changed from darker to lighter, illumination judgments (I) shifted form brighter to dimmer, the sum of A and I being kept nearly invariant for a given luminance of the TF; the psychological relationship between lightness and illumination, A+I, changed as a linear function of the photometric combination of albedo and illuminance, log A+log I. It was also found that the albedo of the background was an important factor determining the extent of perceptual scission between lightness and illumination.     

Philosophie der Arrieregarde

Bulgarian philosophical life is particularly poor and fruitless. As well as in all communist countries the development of Bulgarian Marxism-Leninism was marked by some very sharp controversies between dogmatics and revisionists. Bulgarian Orthodoxes are particularly militant and intolerant and on the contrary, revisionists are in reality very moderate and rather conservative. Therefore the deviations are insignificant and the degree of the destalinization is very small.     

On two arguments for the indeterminacy of personal identity

Both arguments are based on the breakdown of normal criteria of identity in certain science-fictional circumstances. In one case, normal criteria would support the identity of person A with each of two other persons, B and C; and it is argued that, in the imagined circumstances, A=B and A=C have no truth value. In the other, a series or spectrum of cases is tailored to a sorites argument. At one end of the spectrum, persons A and B are such that A=B is clearly true; at the other end, A and B are such that the identity is clearly false. In between, normal criteria of identity leave the truth or falsehood of A=B undecided, and it is argued that in these circumstances A=B has no truth value.These arguments are to be understood counterfactually. My claim is that, so understood, neither establishes its conclusion. The first involves a pair of counterfactual situations that are equally possible or tied. If A=B and A=C have no truth value, a counterfactual conditional with one of them as consequent and an antecedent that is true in circumstances in which either is true should have no truth value. Intuitively, however, any such counterfactual is false. The second argument can be seen to invite an analogous response. If this is right, however, there is an important disanalogy between this and the classical paradox of the heap. If the disanalogy is only apparent, the argument shows at most that the existence of persons can be indeterminate.     

Saving the Truth Schema from Paradox

The paper shows how we can add a truth predicate to arithmetic (or formalized syntactic theory), and keep the usual truth schema Tr(A)A (understood as the conjunction of Tr(A)A and ATr(A)). We also keep the full intersubstitutivity of Tr(A)) with A in all contexts, even inside of an . Keeping these things requires a weakening of classical logic; I suggest a logic based on the strong Kleene truth tables, but with as an additional connective, and where the effect of classical logic is preserved in the arithmetic or formal syntax itself. Section 1 is an introduction to the problem and some of the difficulties that must be faced, in particular as to the logic of the ; Section 2 gives a construction of an arithmetically standard model of a truth theory; Section 3 investigates the logical laws that result from this; and Section 4 provides some philosophical commentary.