A mathematical theory of truth and an application to the regress problem

摘要

In this paper a class of languages which are formal enough for mathematicalreasoning is introduced. First-order formal languages containing naturalnumbers and numerals belong to that class. Its languages are calledmathematically agreeable (shortly MA). Languages containing a given MA languageL, and being sublanguages of L augmended by a monadic predicate areconstructed. A mathematical theory of truth (shortly MTT) is formulated forsome of these languages. MTT makes them MA languages which posses their owntruth predicates. MTT is shown to conform well with the eight norms presentedfor theories of truth in 'What Theories of Truth Should be Like (but Cannotbe)', by Hannes Leitgeb. MTT is free from infinite regress, providing a properframework to study the regress problem. Main tools used in proofs areZermelo-Fraenkel (ZF) set theory and classical logic.