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A Note on the Ontology of Mathematics

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Logic and Its Applications (ICLA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13963))

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Abstract

Provocation behind writing this paper has come from celebrated French philosopher Alain Badiou’s slogan “Mathematics is ontology” and subsequent reading of his book [2]. However, this is not a critique of the book or a response to his philosophy. Some philosophico-mathematical issues have been raised by the author of the book in order to clarify and establish the slogan. In this paper, responses to some such issues have been presented such as the issues of continuum, Continuum Hypothesis, constructible sets and Axiom of Foundation. Remarks on these issues are made, though in brief. Finally, it is remarked that in the present era ontology of mathematics has to be pluralistic and inconsistency-tolerant.

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Acknowledgement

I thank my student Mr. Sayantan Roy for extending technical help in writing this paper and making some important remarks.

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Authors and Affiliations

  1. School of Cognitive Science, Jadavpur University, Kolkata, 700032, India

    Mihir Kumar Chakraborty

  2. Indraprastha Institute of Information Technology, Delhi, Delhi, 110020, India

    Mihir Kumar Chakraborty

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  1. Mihir Kumar Chakraborty
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Correspondence to Mihir Kumar Chakraborty .

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Editors and Affiliations

  1. Indian Institute of Technology Kanpur, Kanpur, India

    Mohua Banerjee

  2. Indian Institute of Technology Goa, Ponda, India

    A. V. Sreejith

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Chakraborty, M.K. (2023). A Note on the Ontology of Mathematics. In: Banerjee, M., Sreejith, A.V. (eds) Logic and Its Applications. ICLA 2023. Lecture Notes in Computer Science, vol 13963. Springer, Cham. https://doi.org/10.1007/978-3-031-26689-8_1

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  • DOI: https://doi.org/10.1007/978-3-031-26689-8_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-26688-1

  • Online ISBN: 978-3-031-26689-8

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