Tarski's Undefinability Theorem and first-order arithmetic

TL;DR

This paper critically analyzes the application of Tarski's Undefinability Theorem to first-order arithmetic, revealing that existing proofs assume the conclusion, thus challenging the standard interpretation of the theorem.

Contribution

It provides a detailed critique showing that proofs claiming to establish the non-definability of arithmetic truth actually assume this result as a premise.

Findings

Existing proofs assume the conclusion, not just derive it.

The standard interpretation of Tarski's theorem in arithmetic is questioned.

The paper clarifies logical assumptions underlying the proofs.

Abstract

This paper examines the application of Tarski's Undefinability Theorem to first-order arithmetic. The generally accepted view is that for this case the Theorem establishes that arithmetic truth is not arithmetic. A careful examination of these proofs shows however that they fail on the grounds that the result that is to be established is assumed as a premise.