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Objects, structures, and logicsFilMat studies in the philosophy of mathematics /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Objects, structures, and logicsedited by Gianluigi Oliveri, Claudio Ternullo, Stefano Boscolo.
Reminder of title:	FilMat studies in the philosophy of mathematics /
other author:	Oliveri, Gianluigi.
Published:	Cham :Springer International Publishing :2022.
Description:	x, 363 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	MathematicsPhilosophy.
Online resource:	https://doi.org/10.1007/978-3-030-84706-7
ISBN:	9783030847067$q(electronic bk.)

Objects, structures, and logicsFilMat studies in the philosophy of mathematics /
Objects, structures, and logicsFilMat studies in the philosophy of mathematics /[electronic resource] :edited by Gianluigi Oliveri, Claudio Ternullo, Stefano Boscolo. - Cham :Springer International Publishing :2022. - x, 363 p. :ill., digital ;24 cm. - Boston studies in the philosophy and history of science,v. 3392214-7942 ;. - Boston studies in the philosophy and history of science ;v.295..

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. Structelativity 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.)

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.

ISBN: 9783030847067$q(electronic bk.)

Standard No.: 10.1007/978-3-030-84706-7doiSubjects--Topical Terms:

187658
Mathematics
--Philosophy.

LC Class. No.: QA8.4 / .O35 2022

Dewey Class. No.: 510.1

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505 0 $a 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. Structelativity 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.)
520 $a 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.
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