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000724631 08204 $$a510.1$$223
000724631 24500 $$aFrom logic to practice$$h[electronic resource] :$$bItalian studies in the philosophy of mathematics /$$cGabriele Lolli, Marco Panza, Giorgio Venturi, editors.
000724631 264_1 $$aCham :$$bSpringer,$$c[2015]
000724631 264_4 $$c©2015
000724631 300__ $$a1 online resource.
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000724631 337__ $$acomputer$$bc$$2rdamedia
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000724631 4901_ $$aBoston studies in the philosophy and history of science ;$$v308
000724631 504__ $$aIncludes bibliographical references.
000724631 5050_ $$aPART 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.
000724631 506__ $$aAccess limited to authorized users.
000724631 520__ $$aThis 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.
000724631 650_0 $$aMathematics$$xPhilosophy.
000724631 650_0 $$aLogic.
000724631 650_0 $$aMathematics$$xHistory.
000724631 7001_ $$aLolli, Gabriele,$$d1942-$$eeditor.
000724631 7001_ $$aPanza, Marco,$$eeditor.
000724631 7001_ $$aVenturi, Giorgio,$$eeditor.
000724631 77608 $$iPrint version:$$z3319104330$$z9783319104331
000724631 830_0 $$aBoston studies in the philosophy and history of science ;$$vv. 308.
000724631 852__ $$bebk
000724631 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-10434-8$$zOnline Access$$91397441.1
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