Stairway to Heaven: The Abstract Method and Levels of Abstraction in Mathematics

Marquis, Jean‐Pierre

doi:10.1007/s00283-016-9672-z

Cited by 4 publications

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“…However, for more on Bourbaki's set theory, see for instance [31]. 9 I have looked at this method in more details in the following two papers: [28], [29]. 10 It has to be pointed out that when Bourbaki writes and decides to systematically develop this standpoint, he finds resistance among contemporary mathematicians who believed that the axiomatic method was unable to produce any genuinely new concepts and results.…”

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confidence: 99%

Forms of Structuralism: Bourbaki and the Philosophers

Marquis

2020

Structures Mères: Semantics, Mathematics, and Cognitive Science

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In this paper, we argue that, contrary to the view held by most philosophers of mathematics, Bourbaki's technical conception of mathematical structuralism is relevant to philosophy of mathematics. In fact, we believe that Bourbaki has captured the core of any mathematical structuralism. * The author gratefully acknowledge the financial support of the SSHRC of Canada while this work was done. This paper is part of a larger project on Bourbaki and structuralism which would not have seen the day without Michael Makkai's influence and generosity. I want to thank him for the numerous discussions we had on the subject. I also want to thank Alberto Perruzzi and Silvano Zipoli for inviting me to present this work at the conference on Bourbaki, mother structures and category theory.

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