From Tarski to G\"odel. Or, how to derive the Second Incompleteness Theorem from the Undefinability of Truth without Self-reference

TL;DR

This paper presents a general proof of the Second Incompleteness Theorem that avoids self-reference, deriving it from Tarski's Undefinability of Truth, thus offering a new perspective on foundational logic.

Contribution

It introduces a novel self-reference-free proof of the Second Incompleteness Theorem based on Tarski's theorem, expanding understanding of logical incompleteness.

Findings

Proof of the Second Incompleteness Theorem without self-reference

Connection established between Tarski's theorem and incompleteness

Provides a new foundational perspective on logical theorems

Abstract

In this paper, we provide a fairly general self-reference-free proof of the Second Incompleteness Theorem from Tarski's Theorem of the Undefinability of Truth.