Oliveri G., Ternullo C., Boscolo S. (Eds.) Objects, Structures, and Logics: FilMat Studies in the Philosophy of Mathematics

Springer, 2022. — 365 p. — (Boston Studies in the Philosophy and History of Science 339). — ISBN 13 9783030847050.Объекты, структуры и логика: исследования FilMat в области философии математикиThis 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.Mathematical Objects
Aristotle’s Problem
Hofweber’s Nominalist Naturalism
Exploring Mathematical Objects from Custom-Tailored Mathematical Universes
Rescuing Implicit Definition from Abstractionism
Structures and Structuralisms
Structural Relativity and Informal Rigour
Ontological Dependence and Grounding for a Weak Mathematical Structuralism
The Structuralist Mathematical Style: Bourbaki as a Case Study
Grothendieck Toposes as Unifying ‘Bridges: A Mathematical Morphogenesis
Logics and Proofs
Game of Grounds
Predicativity and Constructive Mathematics
Truth and the Philosophy of Mathematics
On Lakatos’s Decomposition of the Notion of Proof
A Categorical Reading of the Numerical Existence Property in Constructive Foundations