L.E.J. Brouwer's ‘Unreliability of the Logical Principles’: A New Translation, with an Introduction

History and Philosophy of Logic 38 (1):24-47 (2017)

Abstract

We present a new English translation of L.E.J. Brouwer's paper ‘De onbetrouwbaarheid der logische principes’ 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.

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Author's Profile

Mark van Atten
Centre National de la Recherche Scientifique