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A Mathematical Theory of Truth with Application to the Regress Problem

Hannes Leitgeb formulated eight norms for theories of truth in his paper [12]: ‘What Theories of Truth Should be Like (but Cannot be)’. We shall show in the present paper that a theory of truth can be formulated for suitably constructed metalanguages of the first-order language L = {∈} of set theory which conforms with those norms, added by the norm: Metalanguages for which mathematical theories of truth are formulated should be free from contradictions. In proofs only ZF set theory, concepts definable in L and classical two-valued logic are used. Similar theory of truth can be formulated also for each consistent theory of every countable first–order formal language. The presented theory is free from infinite regress, whence it provides a proper framework to study the regress problem. MSC: 00A30, 03A05, 03B10, 03C62, 03E04, 03F50, 06A07, 47H04, 47H10