A discussion presented in this paper concerns the relationship between the rival views on fundamental problem of apodictic knowledge justification. The ideas reviewed here mostly date back to I. Kant and D. Hilbert. The processes of idealization and abstraction are analized in order to explain a phenomenon of spreading of the idealized and abstract objects throughout the scientific theories and their role in theories’ construction and development.
Keywords: APODICTIC KNOWLEDGE, SCIENTIFIC THEORY, IDEALIZATION, ABSTRACTION, CONCEPT
After a short introduction, in the second section, I consider E. Voishvillo’s approach to formal explication of dispositional predicates. The third section is a brief presentation of relevantly interpreted enthymematic implication. In the forth section I make an attempt to draw all-in-one and present a formalization of (enthymematic) reasoning with (dispositional) public announcements.
Keywords: DISPOSITIONAL PREDICATE, ENTHYMEMATIC IMPLICATION, PUBLIC ANNOUNCEMENT LOGIC
The paper contains the analysis of the Theory of Concept in its modern version worked out by E.K. Voishvillo. Its advances in the study of concept as a form of thought are observed. At the same time some points for further research are marked out.
Keywords: CONCEPT, EXTENSION, INTENSION, GENUS, PREDICATE, THEORY, ENTAILMENT, LOGICAL FORM, FORMALIZED LANGUAGE
In the article the object-theoretical logical theory of Ernst Mally is investigated. Considered its non-formal grounds, describes the features of theory, and explores the question of its compliance with the classical propositional logic. For realization of the proposed interpretation of non-trivial implication the intensional logic of object is constructed. The overall conclusion is that the logical theory of the object is Mally submitted the version of the formal semantics.
Keywords: OBJECT THEORY, FORMAL SEMANTICS, ERNST MALLY, INTENSIONAL LOGIC
Constructivist concepts not assuming that we know programs for each effective method (intuitionism et al) are analyzed here.
Keywords: INTUITIONISM, CONSTRUCTIVISM, REALIZABILITY, COMPUTABILITY, APPLICATION OF CONSTRUCTIVISM
The work is carried out in the line with a study of connections between classical logic, on one hand, and non-classical logics, on the other hand. In the paper an effectively computable mapping is constructed that embeds classical propositional logic into any paralogic, which includes logic Par from  and has the same language with Par.
Keywords: CLASSICAL PROPOSITIONAL LOGIC, PARACONSISTENT LOGIC, PARACOMPLETE LOGIC, EMBEDDING MAP
This article deals with the content of J. Buridan’s notion appellatio rationis. J. Buridan’s views are juxtaposed with those of Е.К. Voishvillo upon the differences between the intensional and extensional use of linguistic expressions. Here is presented the author’s original approach towards the interpretation of J. Buridan’s conception of intensional contexts, their specific character.
Keywords: APPELLATIO RATIONIS, INTENSIONAL AND EXTENSIONAL USE OF LINGUISTIC EXPRESSIONS, INTENSIONAL CONTEXTS
A concept of local factor-semantics is introduced while constructing matrices K and K', isomorphic to the standard rational-valued matrix for infinite-valued logic of Lukasiewicz.
Keywords: LOGICS OF LUKASIEWICZ, FACTOR-SEMANTICS, LOGICAL MATRICES, ISOMORPHISM, LOCAL FACTOR-SEMANTICS
The article sets out a generalization of logical to the level of operating signs.
Keywords: PROTOLOGIC, SEMIOTICS, THEORY OF SIGNS, FOUNDATIONS OF LOGIC, COMBINATORY LOGIC, LAMBDA-CALCULUS
Leibniz called the first article "New method maximums and minimums". Instead of considering the realisation of the method for maximums and minimums, it should have been considered from symbolic side as the Universal characteristic. The extremums as symbols of universal language covers all infinity of the certain subjects sense of which it is. Creation of a block matrix (by means of the left tensor square) allowed to reveal macrolevel and circular arrangement of charts. And in philosophy of a science there is no other way to follow the Nature except to follow to genetics. The logic reduction of a non-classical multi-valuedness to classical binarity of the designated and anti-designated values forms overlaps from right to left and from left to right, forming a hysteresis loop arranging the circular order. The complementarity of levels generates fractality of the main table structure.
Keywords: CHARACTERISTIC, EXTREMUMS, DESIGNATED, ANTI-DESIGNATED VALUES, FRACTALITY, LOGIC REDUCTION
In this paper we present the automated proof search technique in natural deduction paracomplete logic. Here, for some statements we do not have evidence to conclude if they are true or false, as it happens in the classical framework. As a consequence, for example, formulae of the type p ∨ ¬p, are not valid. In this paper we formulate the natural deduction system for paracomplete logic PComp, explain its main concepts, define proof searching techniques and the searching algorithm providing examples proofs.
Keywords: PARACONSISTENT LOGIC, NATURAL DEDUCTION, PROOF SEARCH
In this paper the class of three-valued matrices with classical consequence relations is defined.
Keywords: CLASSICAL PROPOSITIONAL LOGIC, THREE-VALUED LOGICS, CONSEQUENCE RELATION
I apply Kooi and Tamminga’s (2012) idea of correspondence analysis for many-valued logics to strong three-valued logic (K3). First, I characterize each possible single entry in the truth-table of a unary or a binary truth-functional operator that could be added to K3 by a basic inference scheme. Second, I define a class of natural deduction systems on the basis of these characterizing basic inference schemes and a natural deduction system for K3. Third, I show that each of the resulting natural deduction systems is sound and complete with respect to its particular semantics. Among other things, I thus obtain a new proof system for Lukasiewicz’s three-valued logic.
Keywords: THREE-VALUED LOGIC, CORRESPONDENCE ANALYSIS, PROOF THEORY, NATURAL DEDUCTION SYSTEMS
VOISHVILLO Evgenij Kazimirovich — D.Sc., Soviet and Russian Philosopher and Logician, Honoured Professor of Lomonosov Moscow State University, Lomonosov Prize I degree Winner.
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