A mathematically derived definitional/semantical theory of truth

TL;DR

This paper develops a rigorous, mathematically grounded theory of truth using set theory and recursion, creating a fully interpreted language with an embedded truth predicate that aligns with philosophical norms.

Contribution

It introduces a novel formal construction of a truth predicate within a fully interpreted language using advanced set-theoretic methods.

Findings

Constructs a new language with an embedded truth predicate

Ensures the interpretation aligns with sentence meanings

Satisfies philosophical norms for theories of truth

Abstract

Ordinary and transfinite recursion and induction and ZF set theory are used to construct from a fully interpreted object language and from an extra formula a new language. It is fully interpreted under a suitably defined interpretation. This interpretation is equivalent to the interpretation by meanings of sentences if the object language is so interpreted. The added formula provides a truth predicate for the constructed language. The so obtained theory of truth satisfies the norms presented in Hannes Leitgeb's paper 'What Theories of Truth Should be Like (but Cannot be)'.