Intuitionism and the liar paradox

TL;DR

This paper addresses the liar paradox within intuitionism, identifies a subtle error in the traditional understanding of informal proof, and proposes a correction that resolves classical semantic paradoxes.

Contribution

It introduces a correction to the concept of informal proof in intuitionism, providing a novel resolution to the liar paradox and related semantic paradoxes.

Findings

Identifies a subtle error in the traditional interpretation of informal proof.

Proposes a correction that blocks the liar paradox.

Provides a general resolution to classical semantic paradoxes.

Abstract

The concept of informal mathematical proof considered in intuitionism is apparently vulnerable to a version of the liar paradox. However, a careful reevaluation of this concept reveals a subtle error whose correction blocks the contradiction. This leads to a general resolution of the classical semantic paradoxes. This paper is an expanded version of parts of my earlier paper "Constructive truth and circularity" [arXiv:0905.1681].