Why Brouwer was right in suggesting that Hilbert's Law of the Excluded Middle needed qualification

2006/03/26 by Bhupinder Singh Anand, Anand, Bhupinder Singh
Computer Science · Mathematics · Psychology · #03B10 #Computability, Logic, AI Algorithms #FOS: Mathematics #General Mathematics (math.GM) #History and Theory of Mathematics #Philosophy and Theoretical Science #math.GM #msc:03B10

paper · pdf · doi:10.48550/arxiv.math/0603604

10 pages; an HTML version is available at http://alixcomsi.com/Why_Brouwer_was_right.htm

arxiv created 2006/03/26 · openalex publication_date 2006/03/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We reproduce Hilbert's axiomatic formalisation of Number Theory, and argue that his enunciation of the Law of the Excluded Middle is inconsistent with a Turing-verifiable model of the axioms under the standard interpretation.

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