L.E.J. Brouwer's `Unreliability of the logical principles'. A new translation, with an introduction

TL;DR

This paper provides a new English translation of Brouwer's 1908 critique of the Principle of the Excluded Middle, including historical context, philosophical analysis, and its influence on negationless mathematics.

Contribution

It offers the first comprehensive translation and analysis of Brouwer's early objections to classical logic, highlighting its historical significance and impact on mathematical philosophy.

Findings

Brouwer questioned the universal validity of the Principle of the Excluded Middle.

He argued against the possibility of absolutely undecidable propositions.

The paper discusses Brouwer's influence on negationless mathematics.

Abstract

We present a new English translation of L.E.J. Brouwer's paper `De onbetrouwbaarheid der logische principes' (The unreliability of the logical principles) of 1908, together with a philosophical and historical introduction. In this paper Brouwer for the first time objected to the idea that the Principle of the Excluded Middle is valid. We discuss the circumstances under which the manuscript was submitted and accepted, Brouwer's ideas on the principle of the excluded middle, its consistency and partial validity, and his argument against the possibility of absolutely undecidable propositions. We note that principled objections to the general excluded middle similar to Brouwer's had been advanced in print by Jules Molk two years before. Finally, we discuss the influence on George Griss' negationless mathematics.