We present a formalization of first-order predicate calculus with equality which, unlike traditional systems with axiom schemata or substitution rules, is finitely axiomatized in the sense that each step in a formal proof admits only finitely many choices. This formalization is primarily based on the inference rule of condensed detachment of Meredith. The usual primitive notions of free variable and proper substitution are absent, making it easy to verify proofs in a machine-oriented application. Completeness results are presented. The example of (...) Zermelo-Fraenkel set theory is shown to be finitely axiomatized under the formalization. The relationship with resolution-based theorem provers is briefly discussed. A closely related axiomatization of traditional predicate calculus is shown to be complete in a strong metamathematical sense. (shrink)

We show that in quantum logic of closed subspaces of Hilbert space one cannot substitute quantum operations for classical (standard Hilbert space) ones and treat them as primitive operations. We consider two possible ways of such a substitution and arrive at operation algebras that are not lattices what proves the claim. We devise algorithms and programs which write down any two-variable expression in an orthomodular lattice by means of classical and quantum operations in an identical form. Our results show that (...) lattice structure and classical operations uniquely determine quantum logic underlying Hilbert space. As a consequence of our result, recent proposals for a deduction theorem with quantum operations in an orthomodular lattice as well as a, substitution of quantum operations for the usual standard Hilbert space ones in quantum logic prove to be misleading. Quantum computer quantum logic is also discussed. (shrink)

The set of 60 real rays in four dimensions derived from the vertices of a 600-cell is shown to possess numerous subsets of rays and bases that provide basis-critical parity proofs of the Bell-Kochen-Specker (BKS) theorem (a basis-critical proof is one that fails if even a single basis is deleted from it). The proofs vary considerably in size, with the smallest having 26 rays and 13 bases and the largest 60 rays and 41 bases. There are at least 90 basic (...) types of proofs, with each coming in a number of geometrically distinct varieties. The replicas of all the proofs under the symmetries of the 600-cell yield a total of almost a hundred million parity proofs of the BKS theorem. The proofs are all very transparent and take no more than simple counting to verify. A few of the proofs are exhibited, both in tabular form as well as in the form of MMP hypergraphs that assist in their visualization. A survey of the proofs is given, simple procedures for generating some of them are described and their applications are discussed. It is shown that all four-dimensional parity proofs of the BKS theorem can be turned into experimental disproofs of noncontextuality. (shrink)

The monograph shows that in the last 50 years theoretical linguistics remains a compendium of mutually contradicting doctrines on multiple levels: the level of general theories of language, the level of its main constituents (the lexicon, syntax, and the lexical-syntactic interface that connects them), and the lower levels of specific linguistic problems (such as lexical polysemy, grammatical meanings, etc.). The contradictions of contemporary linguistic theories are indicative of a deep crisis. Evolutionary-synthetic theory of language is aimed at overcoming this crisis. (...) It implements a multidisciplinary approach that describes the language a) in evolutionary and ontogenetic development and b) in close interaction with other human subsystems: the mental representation of the world, human activity and social interaction. Language is defined as a dual system developing in ontogeny: 'universal sensory sublanguage + ethnically specific functional sublanguage' where the sensory sublanguage is used to describe the 'visible' world (accessible to the senses), and the functional sublanguage is employed to describe the conceivable world ('comprehended by human mind'). Within the framework of the approach presented, many problems are solved: 1) the cognitive (non-verbal) language for representing language meanings; 2) diversity and unity of languages (using the structure alternative to Chomsky's Universal Grammar); 3) the main (original) function of the language; 4) the cognitive language of thought (its basis is the lexical and grammatical meanings of the sensory sublanguage); 5) dual (functionally prototypical) structure of human categories; 6) mechanisms in the early acquisition of lexical and grammatical meanings; 7) the meaning (assignment) of the syntactic structure of a sentence, etc. The book deals with a wide range of issues related to human cognition, glottogenesis and anthropogenesis, universal cognitive structures for the representation of objects, actions and situations, so it will be of interest not only to linguists, but also to psychologists, anthropologists, sociologists, philosophers. (shrink)

Originally published in 1949. Understanding the questions is the major problem when beginning philosophy. This book does not attempt to provide the answers, but defines the questions and shows by example how they should be tackled. Subjects treated include the nature of the objects of thought and judgment; truth and error in belief; perception and knowledge of the material world; the status and function of memory.

The paper examines a single, apparently simple argument for the existence of incompatibilities between the virtues as traits of character. This argument appeals not to empirical truths about human psychology or human nature but to the possibility of conflict between the exercise of different virtues in action. There are, for example, situations in which we can exercise the virtue of truthfulness only at the expense of not exercising the virtue of tact, as when we are asked a question to which (...) the straightforward answer will pain our questioner. The person who in these situations would give a straightforward answer possesses the virtue of truthfulness to a higher degree than the person who would respond more evasively, whereas the latter person possesses the virtue of tact to a higher degree than the former. But since the two responses are mutually exclusive, it follows that the degree to which we possess the virtue of truthfulness must, at least in some measure, correlate inversely with the degree to which we possess the virtue of tact. And similarly for many other pairs of virtues. My paper focusses on the two cardinal assumptions of this argument, viz., (i) that sometimes the exercise of one virtue can conflict with the exercise of another, and (ii) that the degree to which a person possesses a virtue correlates directly with the extent of its exercise, and defends both assumptions against a variety of objections which allege that, in different ways, they are insensitive to the complexity of the virtues. (shrink)

A new criterion is introduced for judging the suitability of various fuzzy logics for practical uncertain reasoning in a probabilistic world and the relationship of this criterion to several established criteria, and its consequences for truth functional belief, are investigated.