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Issue #17 -- October 2006. Pp. 7-16

About Properties of L-Inconsistent Theories

Copyright © by Vyacheslav Moiseyev and SORITES

Vyacheslav Moiseyev

EDITOR'S NOTE

It seems to us that one of the interesting ideas here is the idea of some connection between CLD and concept of limit. For example, Nicholas from Cusa tried to express idea of God in the image of a straight line which is limit for the infinite sequence of tangent circumferences. Our paper is an attempt to extend this trend and to formulate a version of CLD, where dialectical contradictions (antinomies) can be expressed as limits of ifinite sequences of formulas in a formal language. Main new idea is here in the technique of work with the limiting sequences of *formulas*, not terms. This idea is fully correlated with the method of extension of rational numbers by irrational ones in mathematical analysis. As is well known, every irrational number can be represented by a limiting sequence of rational numbers. Then we can represent rational numbers itselves as a particular case of limiting sequences, i.e., as stationary sequences. Thus we are passing to a new type of objects and we can define operations with these objects generalizing of operations on rational numbers. The same approach is demonstrated below but in the logical sphere.

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In our opinion, by the similar way another philosophical and religious antinomies may be interpreted in suitable L-inconsistent theories. Taking into account the analogy between method of construction of mathematical continuum and method of L-inconsistent theories formation, one may conclude that numerous antinomies, constantly have been reproduced in the history of human thinking, are examples of «logical irrationalities». These are antinomies of all the limiting concepts of philosophy, for example, «World», «Being», «Consciousness», «Will», «Freedom», «Personality», etc. And just as there exists common method of mathematical irrationalities expression, there could be a common method of logical irrationalities representation. Author hopes that ideas of this paper could to help us to come nearer to this method.

Vyacheslav Moiseyev

Moscow Medical Stomatological University

<vimo [at] list.ru>

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