From Logic to Practice Italian Studies in the Philosophy of Mathematics - Lolli, Gabriele; Panza, Marco; Venturi, Giorgio (Cham : Springer International Publishing, 2015)
PART I: THE HISTORICAL DIMENSION OF MATHEMATICS -- Chapter 1: A Geometrical Constructive Approach to Infinitesimal Analysis: Epistemological Potential and Boundaries of Tractional Motion; Pietro Milici -- Chapter 2: Plane and Solid Geometry: A Note on Purity of Methods; Paolo Mancosu and Andrew Arana -- Chapter 3: Formalization and Intuition in Husserl's Raumbuch; Edoardo Caracciolo -- PART II: LOOKING AT MATHEMATICS THROUGH LOGIC -- Chapter 4: Frege's Grundgesetze and a Reassessment of Predicativity; Francesca Boccuni -- Chapter 5: A Deflationary Account of the Truth of the Gödel Sentence G; Mario Piazza and Gabriele Pulcini -- Chapter 6: Rule-following and the Limits of Formalization: Wittgenstein's Considerations Through the Lens of Logic; Paolo Pistone -- Chapter 7: Paradox and Inconsistency: Revising Tennant's Distinction Through Schroeder-Heister's Assumption Rules; Luca Tranchini -- Chapter 8: Costructability and Geometry; Alberto Naibo -- Chapter 9: A Cut-like Inference in a Framework of Explicit Composition for Various Calculi of Natural Deduction; Michael Arndt and Laura Tesconi -- Chapter 10: On the Distinction Between Sets and Classes: A Categorical Perspective; Samuele Maschio -- PART III: PHILOSOPHY AND MATHEMATICS -- Chapter 11: Structure and Applicability; Michele Ginammi -- Chapter 12: Defending Maddy's Mathematical Naturalism from Roland's Criticism: The Role of Mathematical Depth; Marina Imocrante -- Chapter 13: On the Indispensable Premises of the Indispensability Argument; Marco Panza and Andrea Sereni -- Chapter 14: Naturalness in Mathematics: On the Statical-dynamical Opposition; Luca San Mauro and Giorgio Venturi -- Chapter 15: An Inquiry Into the Practice of Proving in Low-dimensional Topology; Silvia de Toffoli and Valeria Giardino.
Keywords: Philosophy; Epistemology; Philosophy and science; Mathematical logic