Abstract: The subject of this research is the concept of reduction in logics and methodology of science. On the one hand, reduction is understood as a relation between the term and its defining expression within the scientific theory; while on the other – it represents the relation between two theories. Since the extension of theory is possible through introduction to its vocabulary of new terms by means of nominal definitions, the reduction represents an inverse operation – removing the terms from the vocabulary of the theory. At the same time, the theory itself is defined in accordance with the theoretical-multiple approach as a class of sentences closed in relation to derivability. The scientific novelty consists in examination of semantic and epistemological aspects of the formal definition of reduction. Particularly, the explication of reduction relation between two theories leans in the concept of functional equivalence of the theories. It is established that the list of basic terms of the theory can be set only conventionally. All terms introduces by the means of nominal definitions turn out to be reducible. Therefore, a distinctive feature of theoretical terms is the possibility of its reduction.

Abstract: This article explores the problem of the reduction of normative statements to descriptive statements. The starting point for discourse became the philosophical thesis “is–ought problem” (known as Hume’s guillotine) that speaks of the logical incompatibility of the statements on facts statements on values and norms. There have been determined three approaches towards solution of the question on norms reduction: semantic-ontological, emotive, and naturalistic. Each of the approaches has its merits and demerits. The semantic-ontological approach allows structuring and substantiating any deontic system, but does not suggest the selection criterion between these systems. The emotive approach denies the presence of logical meaning in normative statements and rejects the possibility of their reduction to the descriptive statements. However, the merit of such approach consists in the precise designation of the criteria of validity and falsity of statements. The naturalistic approach attempts to substantiate the normative statements using factual evidence on the animal behavior and theory of evolution, but faces the philosophical objections against physicalism and behaviorism. The scientific novelty lies in comparison of the aforementioned approaches and determination of their principal merits and demerits.

Abstract: The subject of this research is the explanatory model of reduction, which was originally formulated by E. Nagel and further developed by C. Hempel, P. Oppenheim, J. Kemeny, K. Schaffner, W. Stegmuller and other philosophers of science. The article clarifies the definition of reduction and determines its two basic aspects – epistemological and ontological. If the ontological aspects suggests the reduction of the ideal characteristics and essences to material, then the epistemological aspect implies studying of logical relations between the terms and propositions of scientific theories. The pivotal thesis of the article consists in the statement that the majority of problems of reduction occurs due to the fusion of ontological and epistemological aspects. Therefore, such problems can be eliminated through philosophical analysis of the language of modern epistemology. Examination of epistemological reduction must be separated for the discussions around reductionism, because such discussions are the result of improper interpretation of the terms, and caused by bringing ontological problems into epistemology. The author critically reviews the epistemological status of binding laws, idea of emergence and value of the specifics of certain areas of scientific knowledge. The novelty of this work lies in clarification of the idea of reduction, comparative analysis of reduction and its explanation.

Abstract:  
The subject of this research is the problem of foundations of mathematics in works of the representatives of logical empiricism and Wittgenstein. It is demonstrated that their solutions were original and significantly differed from the logicistic solution. If logicism suggests accepting this problem as a fact and develops the technical means for its circumvention, the logical empiricism tries to eliminate it as a pseudo-problem (and Wittgenstein as a philosophical puzzle) that occurred as a result of the intricacy of the language. Analyzing the problem of impredicative definition of mathematical concepts, the non-positivists and Wittgenstein acted in their usual role of analytical philosophers who clarify the meaning of the propositions of science. Textological analysis of the works of B. Russell, F. Ramsey, R. Carnap, P. Kaufman and L. Wittgenstein illustrates that neo-positivists and Wittgenstein grounded the solution of the problem of foundations of mathematics on the attempt of rectification of mathematical concepts (such as multiplicity, function, and definition), as well as initiating of mathematical and natural scientific discourses. Their approach is a vivid example of the analytical philosophy of science, if the philosophy of science is viewed as systematic comprehension of a certain scientific problem. The scientific novelty lies in identification of the elements of constructivism and finitism in the philosophy of mathematics of the aforementioned representatives of analytical philosophy. The author draws an original comparison between the positions of logicism, neo-positivism and Wittgenstein regarding the question of logical admissibility of the impredicative formation of concepts. Because the criticism of neo-positivists and Wittgenstein was aimed against the inaccurate application of the concepts, it is valuable in itself as a model of thought, despite the fact that at the time it did not lead to the revolutionary changes in mathematics.