[FOM] `The unreliability of the logical principles'

[Mark van Atten]

A preprint of the following paper is available upon request:

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

Mark van Atten and Göran Sundholm

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.


Best wishes,
Mark.