From logic to practice [electronic resource] : Italian studies in the philosophy of mathematics / Gabriele Lolli, Marco Panza, Giorgio Venturi, editors.
Lolli, Gabriele, 1942- editor.; Panza, Marco, editor.; Venturi, Giorgio, editor.
2015
QA8.4 .F76 2015eb
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Title From logic to practice [electronic resource] : Italian studies in the philosophy of mathematics / Gabriele Lolli, Marco Panza, Giorgio Venturi, editors.
ISBN 9783319104348 electronic book
3319104349 electronic book
9783319104331
3319104330
DOI https://doi.org/10.1007/978-3-319-10434-8
Published Cham : Springer, [2015]
Copyright ©2015
Language English
Description 1 online resource.
Item Number 10.1007/978-3-319-10434-8 doi
Call Number QA8.4 .F76 2015eb
Dewey Decimal Classification 510.1
Summary This book brings together young researchers from a variety of fields within mathematics, philosophy and logic. It discusses questions that arise in their work, as well as themes and reactions that appear to be similar in different contexts. The book shows that a fairly intensive activity in the philosophy of mathematics is underway, due on the one hand to the disillusionment with respect to traditional answers, on the other to exciting new features of present day mathematics. The book explains how the problem of applicability once again plays a central role in the development of mathematics. It examines how new languages different from the logical ones (mostly figural), are recognized as valid and experimented with and how unifying concepts (structure, category, set) are in competition for those who look at this form of unification. It further shows that traditional philosophies, such as constructivism, while still lively, are no longer only philosophies, but guidelines for research. Finally, the book demonstrates that the search for and validation of new axioms is analyzed with a blend of mathematical historical, philosophical, psychological considerations.
Bibliography, etc. Note Includes bibliographical references.
Access Note Access limited to authorized users.
Added Author Lolli, Gabriele, 1942- editor.
Panza, Marco, editor.
Venturi, Giorgio, editor.
Series Boston studies in the philosophy and history of science ; v. 308.
Available in Other Form Print version: 9783319104331
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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.

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