IMPLICIT COMMITMENT IN TRUTH THEORY AND IN MATHEMATICS

The restrictive results of Kurt Godel and Alfred Tarski are often interpreted as a final demonstration for the impossibility of expressing the semantic characteristics of a theory by syntactic means. At the same time, the seemingly unshakable results have undergone significant revisions in recent decades. For example, the desire to overcome the hierarchical approach to the truth definition gave rise to the rapidly developing direction of creating untyped truth theories, going back to Saul Kripke. The article offers an analysis for the possibility of expressing, by syntactic means, the semantic characteristics of a theory applied to the problem of implicit commitments arising from the adoption of a mathematical theory and the axiomatic truth theory. The very problem of identifying implicit commitments, both in the case of adopting a mathematical theory, and in the case of adopting the truth theory, is far from its final resolution. The article shows that the rationale for adopting the principle of reflection in the case of the truth theory and the application of an autonomous progression in the case of implicit commitments for a mathematical theory adopting shows that modem philosophical logic is able to offer logical-syntactic tools for explication of semantic concepts of truth and implicit commitment for adopting a mathematical theory. This is a serious argument both in favor of the deflationary concept of truth, which interprets the latter as an exclusively logical-mathematical concept, and in favor of the statement that the semantic content of formal-mathematical concepts can be explicated by syntactic means.