Truth, Existence and Explanation [electronic resource] : FilMat 2016 Studies in the Philosophy of Mathematics /
Piazza, Mario.editor.
Pulcini, Gabriele.editor.
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 interna tional conference, held at the University of Chieti-Pescara, May 2016. .
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?.
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 interna tional conference, held at the University of Chieti-Pescara, May 2016. .
Mathematics-Philosophy.
Logic.
Genetic epistemology.
Computer science.
Philosophy of Mathematics.
Logic.
Epistemology.
Mathematical Logic and Formal Languages.