LEADER 05493nam 22006855 450 001 9910483702403321 005 20200919234748.0 010 $a3-319-10434-9 024 7 $a10.1007/978-3-319-10434-8 035 $a(CKB)3710000000306109 035 $a(EBL)1967972 035 $a(SSID)ssj0001386499 035 $a(PQKBManifestationID)11809742 035 $a(PQKBTitleCode)TC0001386499 035 $a(PQKBWorkID)11374143 035 $a(PQKB)10188629 035 $a(DE-He213)978-3-319-10434-8 035 $a(MiAaPQ)EBC1967972 035 $a(PPN)183095529 035 $a(EXLCZ)993710000000306109 100 $a20141128d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFrom Logic to Practice $eItalian Studies in the Philosophy of Mathematics /$fedited by Gabriele Lolli, Marco Panza, Giorgio Venturi 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (345 p.) 225 1 $aBoston Studies in the Philosophy and History of Science,$x0068-0346 ;$v308 300 $aDescription based upon print version of record. 311 $a3-319-10433-0 320 $aIncludes bibliographical references. 327 $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. 330 $aThis book brings together young researchers from a variety of fields within mathematics, philosophy and logic. It discusses questions that arise in their work, as well as themes and reactions that appear to be similar in different contexts. The book shows that a fairly intensive activity in the philosophy of mathematics is underway, due on the one hand to the disillusionment with respect to traditional answers, on the other to exciting new features of present day mathematics. The book explains how the problem of applicability once again plays a central role in the development of mathematics. It examines how new languages different from the logical ones (mostly figural), are recognized as valid and experimented with and how unifying concepts (structure, category, set) are in competition for those who look at this form of unification. It further shows that traditional philosophies, such as constructivism, while still lively, are no longer only philosophies, but guidelines for research. Finally, the book demonstrates that the search for and validation of new axioms is analyzed with a blend of mathematical historical, philosophical, psychological considerations. 410 0$aBoston Studies in the Philosophy and History of Science,$x0068-0346 ;$v308 606 $aEpistemology 606 $aMathematical logic 606 $aPhilosophy and science 606 $aEpistemology$3https://scigraph.springernature.com/ontologies/product-market-codes/E13000 606 $aMathematical Logic and Foundations$3https://scigraph.springernature.com/ontologies/product-market-codes/M24005 606 $aPhilosophy of Science$3https://scigraph.springernature.com/ontologies/product-market-codes/E34000 615 0$aEpistemology. 615 0$aMathematical logic. 615 0$aPhilosophy and science. 615 14$aEpistemology. 615 24$aMathematical Logic and Foundations. 615 24$aPhilosophy of Science. 676 $a510.1 702 $aLolli$b Gabriele$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aPanza$b Marco$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aVenturi$b Giorgio$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483702403321 996 $aFrom Logic to Practice$92855373 997 $aUNINA