Objects, Structures, and Logics: FilMat Studies in the Philosophy of Mathematics
- Length: 373 pages
- Edition: 1
- Language: English
- Publisher: Springer
- Publication Date: 2022-03-09
- ISBN-10: 3030847055
- ISBN-13: 9783030847050
- Sales Rank: #0 (See Top 100 Books)
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.
Cover Front Matter 1. Introduction Part I. Mathematical Objects 2. Aristotle’s Problem 3. Hofweber’s Nominalist Naturalism 4. Exploring Mathematical Objects from Custom-Tailored Mathematical Universes 5. Rescuing Implicit Definition from Abstractionism Part II. Structures and Structuralisms 6. Structural Relativity and Informal Rigour 7. Ontological Dependence and Grounding for a Weak Mathematical Structuralism 8. The Structuralist Mathematical Style: Bourbaki as a Case Study 9. Grothendieck Toposes as Unifying ‘Bridges’: A Mathematical Morphogenesis Part III. Logics and Proofs 10. Game of Grounds 11. Predicativity and Constructive Mathematics 12. Truth and the Philosophy of Mathematics 13. On Lakatos’s Decomposition of the Notion of Proof 14. A Categorical Reading of the Numerical Existence Property in Constructive Foundations
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