Remarks on Recursive Definitions of Truth

Abstract

For the sake of simplicity, we adopt the same logical frame as Tarski's in his Wahrheitsbegriff (Wb). There, Tarski is mainly interested in the possibility of explicitely defining truth for an object-language, he does not pay much attention to recursive definitions of truth. We say why. However, recursive definitions have advantages of their own. In particular, we prove the positive theorem: if L is of finite order ≥ 4, then a recursive definition is possible for L in a metalanguage of the same order as L. We indicate how this result could be used for a solution of a generalized version of Frege's paradox.

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Philippe De Rouilhan
Centre National de la Recherche Scientifique

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