Objects, structures, and logics : FilMat studies in the philosophy of mathematics / Gianluigi Oliveri, Claudio Ternullo, Stefano Boscolo, editors.
Oliveri, Gianluigi.; Ternullo, Claudio.; Boscolo, Stefano, 1986-
2022
QA8.4
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Title Objects, structures, and logics : FilMat studies in the philosophy of mathematics / Gianluigi Oliveri, Claudio Ternullo, Stefano Boscolo, editors.
ISBN 9783030847067 (electronic bk.)
3030847063 (electronic bk.)
3030847055
9783030847050
DOI https://doi.org/10.1007/978-3-030-84706-7
Publication Details Cham : Springer, 2022.
Language English
Description 1 online resource (365 pages)
Item Number 10.1007/978-3-030-84706-7 doi
Call Number QA8.4
Dewey Decimal Classification 510.1
Summary This edited collection casts light on central issues within contemporary philosophy of mathematics such as the realism/anti-realism dispute; the relationship between logic and metaphysics; and the question of whether mathematics is a science of objects or structures. The discussions offered in the papers involve an in-depth investigation of, among other things, the notions of mathematical truth, proof, and grounding; and, often, a special emphasis is placed on considerations relating to mathematical practice. A distinguishing feature of the book is the multicultural nature of the community that has produced it. Philosophers, logicians, and mathematicians have all contributed high-quality articles which will prove valuable to researchers and students alike.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed March 17, 2022).
Added Author Oliveri, Gianluigi.
Ternullo, Claudio.
Boscolo, Stefano, 1986-
Series Boston studies in the philosophy and history of science ; v. 339.
Available in Other Form Objects, Structures, and Logics.
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1. Introduction
Part 1. Mathematical Objects
2. Aristotle's Problem (Zanetti, L)
3. Hofweber's Nominalist Naturalism (Snyder, E., Samuels, R., Shapiro, S)
4. Exploring Mathematical Objects from Custom-Tailored Mathematical Universes (Blechschmidt, I.)
5. Rescuing Implicit Definition from Abstractionism (Waxman, D.)
Part 2. Structures and Structuralisms
6. Structural Relativity and Informal Rigour (Barton, N.)
7. Ontological Dependence and Grounding for a Weak Mathematical Structuralism (Bianchi, S.)
8. The Structuralist Mathematical Style: Bourbaki as a Case Study (Marquis, J.-P.)
9. Grothendieck Toposes as Unifying Bridges: a Mathematical Morphogenesis (Caramello, O.)
Part 3. Logics and Proofs
10. Game of Grounds (Catta, D., Piccolomini D'Aragona, A.)
11. Predicativity and Constructive Mathematics (Crosilla, L.)
12. Truth and the Philosophy of Mathematics (Cantini, A.)
13. On Lakatos's Decomposition of the Notion of Proof (Moriconi, E.)
14. A Categorical Reading of the Numerical Existence Property in Constructive Foundations (Maschio, S.).

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