A self-contained theory of truth

TL;DR

This paper introduces a new formal system based on a restrictive language that can internally define its own truth predicate, challenging established limitations like Tarski's theorem and offering fresh foundational perspectives.

Contribution

It constructs a self-contained formal system capable of internal truth definition, providing an alternative to predicate logic-based systems and addressing classical logical paradoxes.

Findings

Demonstrates a formal system that can define its own truth predicate.

Challenges Tarski's undefinability theorem within a restricted language.

Offers new insights into foundational issues in logic and mathematics.

Abstract

Tarski's undefinability theorem states that a formal system based on conventional predicate logic (PL) cannot talk about its own truth predicate. PL is, however, not the only formal language imaginable. In this paper, it will be shown that it is possible to construct a formal system, based not on PL but a more restrictive formal language, which is self-contained in the sense that within this system, we can both talk about and even define the system's own truth predicate. This hints at new ways of understanding Russell's, G\"odel's, and Tarski's discoveries, and new ways of tackling the vicious circles that give rise to these problems. This new system presents an interesting alternative foundational mathematical framework.