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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?.
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.
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