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Meaning in Classical Mathematics: is it at Odds with Intuitionism?

Katz Karin Usadi
Katz Mikhail
Language of the article : English
DOI: 10.3406/intel.2011.1154
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We examine the classical/intuitionist divide, and how it reflects on modern theories of infinitesimals. When leading intuitionist Heyting announced that “the creation of non-standard analysis is a standard model of important mathematical research”, he was fully aware that he was breaking ranks with Brouwer. Was Errett Bishop faithful to either Kronecker or Brouwer? Through a comparative textual analysis of three of Bishop’s texts, we analyze the ideological and/or pedagogical nature of his objections to infinitesimals à la Robinson. Bishop’s famous “debasement” comment at the 1974 Boston workshop, published as part of his Crisis lecture, in reality was never uttered in front of an audience. We compare the realist and the anti-realist intuitionist narratives, and analyze the views of Dummett, Pourciau, Richman, Shapiro, and Tennant. Variational principles are important physical applications, currently lacking a constructive framework. We examine the case of the Hawking–Penrose singularity theorem, already analyzed by Hellman in thecontext of the Quine-Putnam indispensability thesis.

Pour citer cet article :

Katz Karin Usadi, Katz Mikhail (2011/2). Meaning in Classical Mathematics: is it at Odds with Intuitionism? In Guignard Jean-Baptiste (Eds), Cognitive Linguistics: A Critical Exploration, Intellectica, 56, (pp.223-304), DOI: 10.3406/intel.2011.1154.