L.E.J. Brouwer's 'Unreliability of the Logical Principles': A New Translation, with an Introduction. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Van Atten, Mark; Sundholm, Göran
• Is Part Of: History and philosophy of logic. Volume 38:Issue 1(2017)
• Page Start: 24
• Page End: 47
• Publication Date: 2017-01-02
• Subjects: Logic -- Periodicals; 160.905
• DOI: 10.1080/01445340.2016.1210986
• Languages: English
• ISSNs: 0144-5340

Abstract

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.