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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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