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Axiomathes

pp 1–14 | Cite as

Rota on Mathematical Identity: Crossing Roads with Husserl and Frege

  • Demetra ChristopoulouEmail author
Original Paper

Abstract

In this paper I address G. C. Rota’s account of mathematical identity and I attempt to relate it with aspects of Frege as well as Husserl’s views on the issue. After a brief presentation of Rota’s distinction among mathematical facts and mathematical proofs, I highlight the phenomenological background of Rota’s claim that mathematical objects retain their identity through different kinds of axiomatization. In particular, I deal with Rota’s interpretation of the ontological status of mathematical objects in terms of ideality. Then I detect certain similarities among Rota’s views and Frege’s account of the constitution of arithmetical identity on the grounds of 1–1 correspondence. I point out an epistemic as well as an ontological aspect of this issue. In the sequel, I attempt to deal with the problem of “mixed identities” in mathematics stated by Benacerraf (1965) by taking in account Rota’s use of the phenomenological notion “Fundierung”.

Keywords

Identity Axiomatization Proof Phenomenology Ideality Object 

Notes

References

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversity of AthensAthensGreece

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