3 N ov 2 01 5 L . E . J . Brouwer ’ s ‘ Unreliability of the logical principles ’ . A new translation , with an introduction

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. keywords: Luitzen Egbertus Jan Brouwer, George Griss, intuitionism, Jules Molk, principle of the excluded middle 1 Rationale for this translation In his seminal paper ‘The unreliability of the logical principles’ (1908b), Brouwer draws for the first time the revisionistic consequences of the general view on logic that he had presented in his dissertation (Brouwer, 1907, pp. 125–132), by rejecting the principle of excluded middle. The paper appeared in Dutch; Brouwer’s first published remarks in more widely read languages on the unreliability of the principle SND (CNRS/Paris 4), 28 rue Serpente, 75006 Paris, France. [email protected] Philosophical Institute, Leiden University, P.O. Box 2315, 2300 RA Leiden, The Netherlands. [email protected]