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Epistemology versus ontolog...
This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice (ZFC). This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively pursued today is predicativistic constructivism based on Martin-Löf type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-Löf. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-Löf and Wittgensteinian or other accounts of meaning-as-use? What can proof-theoretical analyses tell us about the scope and limits of constructive and predicative mathematics?
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monografia Rebiun15388215 https://catalogo.rebiun.org/rebiun/record/Rebiun15388215 m o d cr cnu---unuuu 120720s2012 ne ob 011 0 eng d 9789400744356 electronic bk.) 9400744358 electronic bk.) 9789400744349 940074434X hardcover : acid-free paper) 9789400744349 hardcover : acid-free paper) CBUC 991025780829706706 GW5XE. eng. pn. GW5XE. EBLCP. E7B. COO. UKMGB. ZMC. WAU. OCLCQ. OCLCO. OCLCQ. MEAUC. REB. OCLCO. OCLCF. BEDGE. NLGGC. OCLCQ. ES-VaUB 510.1 23 Epistemology versus ontology Recurs electrònic] essays on the philosophy and foundations of mathematics in honour of Per Martin-Löf Peter Dybjer [and others], editors Dordrecht New York Springer 2012 Dordrecht New York Dordrecht New York Springer 1 recurs electrònic (xv, 385 pages) 1 recurs electrònic (xv, 385 pages) Logic, epistemology, and the unity of science v. 27 Includes bibliographical references and index Part 1.) PHILOSOPHY OF LOGIC AND MATHEMATICS -- Kant and Real Numbers Mark van Atten. -- Wittgenstein's Diagonal Argument: A Variation on Cantor and Turing Juliet Floyd. -- Truth and Proof in Intuitionism Dag Prawitz. -- Real and Ideal in Constructive Mathematics Giovanni Sambin. -- In the Shadow of Incompleteness: Hilbert and Gentzen Wilfried Sieg. -- Evolution and Logic Jan M. Smith. -- The "Middle Wittgenstein" and Modern Mathematics Sören Stenlund. -- Primitive Recursive Arithmetic and Its Role in the Foundations of Arithmetic: Historical and Philosophical Reflections: In Honor of Per Martin-Löf on the Occasion of His Retirement William W. Tait -- Part 2.) FOUNDATIONS -- Type Theory and Homotopy Steve Awodey. -- A Computational Interpretation of Forcing in Type Theory Thierry Coquand and Guilhem Jaber. -- Program Testing and the Meaning Explanations of Intuitionistic Type Theory Peter Dybjer. -- Normativity in Logic Jean-Yves Girard. -- Constructivist Versus Structuralist Foundations Erik Palmgren. -- Machine Translation and Type Theory Aarne Ranta. -- Constructive Zermelo-Fraenkel Set Theory, Power Set, and the Calculus of Constructions Michael Rathjen. -- Coalgebras as Types Determined by Their Elimination Rules Anton Setzer. -- Second Order Logic, Set Theory and Foundations of Mathematics Jouko Väänänen This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice (ZFC). This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively pursued today is predicativistic constructivism based on Martin-Löf type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-Löf. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-Löf and Wittgensteinian or other accounts of meaning-as-use? What can proof-theoretical analyses tell us about the scope and limits of constructive and predicative mathematics? Martin-Löf, Per 1942- Martin-Löf, Per. Mathematics Philosophy Mathematics Philosophy History Sciences sociales. eclas Sciences humaines. eclas Mathematics Philosophy. fast Philosophy (General) Genetic epistemology Ontology Logic, Symbolic and mathematical Philosophy Mathematical Logic and Foundations Epistemology History of Mathematical Sciences Llibres electrònics Dybjer, Peter Logic, epistemology and the unity of science v. 27 SpringerLink eBooks