This book contains more than 15 essays that explore issues in truth, existence, and explanation. It features cutting-edge research in the philosophy of mathematics and logic.
Renowned philosophers, mathematicians, and younger scholars provide an insightful contribution to the lively debate in this interdisciplinary field of inquiry. The essays look at realism vs. anti-realism as well as inflationary vs. deflationary theories of truth. The contributors also consider mathematical fictionalism, structuralism, the nature and role of axioms, constructive existence, and generality. In addition, coverage also looks at the explanatory role of mathematics and the philosophical relevance of mathematical explanation.
The book will appeal to a broad mathematical and philosophical audience. It contains work from FilMat, the Italian Network for the Philosophy of Mathematics. These papers collected here were also presented at their second international conference, held at the University of Chieti-Pescara, May 2016.
Mario Piazza is Full Professor of Logic and Philosophy of Mathematics at the Scuola Normale Superiore of Pisa. Previously, he has been Full Professor at University of Chieti-Pescara. He studied philosophy at the University of Rome and received his Ph.D. in Philosophy of Science from the University of Genoa in 1995. He was a post doc researcher in the Department of Mathematics at the University of Warsaw (1995-96), in the Utrecht Institute of Linguistics (OTS) (1997-98), in the Département d'Informatique at École Normale Supérieure of Paris (2000). His main results and interests are in proof-theory and its applications, computation theory, philosophy of logic and mathematics, epistemology.
Gabriele Pulcini is a postdoctoral researcher at the Department of Mathematics of the New University of Lisbon. He worked as postdoctoral fellow in many academic institutions, including the Department of Computer Science at the École Normale Supérieure of Paris and the Centre for Logic, Epistemology and History of Science (State University of Campinas, Brazil). He obtained his PhD at the University of Rome 3 and the University of Aix-Marseille 2, jointly. His fields of research and interest range from the proof theory of classical and non-classical logics to the philosophy of logic, as well as the philosophy of mathematics. He is author of many research papers appeared in the most important journals in the field such as the Annals of Pure and Applied Logic and the Journal of Logic and Computation. Since 2012, he is member of the Italian Network for the Philosophy of Mathematics.
Part I: Truth and expressiveness.- Chapter 1. Some Remarks on True Undecidable Sentences.- Chapter 2. Penrose's New Argument and Paradox.- Chapter 3. On expressive power over arithmetic.- Chapter 4. Intensionality in Mathematics.- Chapter 5. Deflationary truth is a logical notion.- Chapter 6. Making sense of Deflationism from a formal perspective: Conservativity and Relative Interpretability.- Part II: Structures, existence, and explanation.- Chapter 7. Structure and Structures.- Chapter 8. Towards a Better Understanding of Mathematical Understanding.- Chapter 9. The explanatory power of a new proof: Henkin's completeness proof.- Chapter 10. Can proofs by mathematical induction be explanatory?.- Chapter 11. Ontological Commitment and the Import of Mathematics.- Chapter 12. Applicability Problems Generalized.- Chapter 13. Church-Turing Thesis, in Practice.- Chapter 14. Existence vs Conceivability in Aristotle: Are Straight Lines Infinitely Extendible?.