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Full Description
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.
Contents
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 CategoricalReading of the Numerical Existence Property in Constructive Foundations (Maschio, S.).
