A theory of truth for a class of mathematical languages and an application

Abstract

In this paprer a class of so called mathematically acceptable (shortly MA) languages is introduced First-order formal languages containing natural numbers and numerals belong to that class. MA languages which are contained in a given fully interpreted MA language augmented by a monadic predicate are constructed. A mathematical theory of truth (shortly MTT) is formulated for some of these languages. MTT makes them fully interpreted MA languages which posses their own truth predicates, yielding consequences to philosophy of mathematics. MTT is shown to conform well with the eight norms presented for theories of truth in the paper 'What Theories of Truth Should be Like (but Cannot be)' by Hannes Leitgeb. MTT is also free from infinite regress, providing a proper framework to study the regress problem.

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References found in this work

The emperor’s new mind.Roger Penrose - 1989 - Oxford University Press.
Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Axiomatic Theories of Truth.Volker Halbach - 2010 - Cambridge, England: Cambridge University Press.
Human knowledge and the infinite regress of reasons.Peter D. Klein - 1999 - Philosophical Perspectives 13:297-325.

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