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Ideal Objects for Set Theory

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Abstract

In this paper, we argue for an instrumental form of existence, inspired by Hilbert’s method of ideal elements. As a case study, we consider the existence of contradictory objects in models of non-classical set theories. Based on this discussion, we argue for a very liberal notion of existence in mathematics.

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Acknowledgments

We thank the many useful suggestions and corrections of two anonymous referees, who helped to improve and to correct many aspects of our work. We also thank the Journal of Philosophical Logic for the careful and professional editorial work. The first author acknowledges support from the FAPESP grant. n. 2017/23853-0. The second author wants to acknowledge FAPESP for providing him a Visiting Researcher grant (n. 2016/25891-3) to spend one year at the Philosophy Department of the University of Campinas. The third author acknowledges support from FAPESP, Jovem Pesquisador grant (n. 2016/25891- 3), and from CNPq grant (n. 301108/2019-6).

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Authors and Affiliations

  1. Department of Philosophy, University of Campinas (UNICAMP), Barão Geraldo, São Paulo, Brazil

    Santiago Jockwich & Giorgio Venturi

  2. St. Xavier’s College, 30 Mother Teresa Sarani, Kolkata, 700016, India

    Sourav Tarafder

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  1. Santiago Jockwich
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  2. Sourav Tarafder
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  3. Giorgio Venturi
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Correspondence to Giorgio Venturi.

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Jockwich, S., Tarafder, S. & Venturi, G. Ideal Objects for Set Theory. J Philos Logic 51, 583–602 (2022). https://doi.org/10.1007/s10992-021-09642-4

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