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About Properties of L-Inconsistent Theories

Domenii publicaţii > Stiinte umaniste + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: V.Moiseyev

Editorial: SORITES, ISSN 1135-1349, 17, p.7-16, 2006.


In the paper a new type of the formal theory, «L-inconsistent theory», is constructed and some properties of such theories are investigated. First a theory T* is defined as a set of limiting sequences of formulas from a theory T with a language L. A limiting sequence {An}∞n=1 of the formulas from T is said to be a theorem of the theory T* if there exists an m≥0 such that for any n≥m the formula An of the language L is a theorem of the theory T. T is embeded into T*. Then, a theorem of T* is called an L-contradiction if the limit of this theorem equals B∧¬B, where B is a formula of the language L. Finally, the theory T* is said to be an L-inconsistent theory if there exists an L-contradiction in T*. It is proved that the theory T* is consistent, complete, etc., iff the theory T is consistent, complete, etc. However, T* contains more theorems and inferences than T. L-inconsistent theory T* can be presented as a new approach to the Philosophical Logic, dealing with an extension of Method of Limits to thinking. Namely some philosophical antinomies, for example Kantian ones, could be presented as L-contradictions in an L-inconsistent theory

Cuvinte cheie: philosophical logic, antinomy, limit