E-Book Overview
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?
E-Book Content
Epistemology versus Ontology
LOGIC, EPISTEMOLOGY, AND THE UNITY OF SCIENCE VOLUME 27
Editors Shahid Rahman, University of Lille III, France John Symons, University of Texas at El Paso, U.S.A. Managing Editor: Ali Abasnezhad, University of Lille III, France Editorial Board Jean Paul van Bendegem, Free University of Brussels, Belgium Johan van Benthem, University of Amsterdam, the Netherlands Jacques Dubucs, University of Paris I-Sorbonne, France Anne Fagot-Largeault, Collège de France, France Göran Sundholm, Universiteit Leiden, The Netherlands Bas van Fraassen, Princeton University, U.S.A. Dov Gabbay, King’s College London, U.K. Jaakko Hintikka, Boston University, U.S.A. Karel Lambert, University of California, Irvine, U.S.A. Graham Priest, University of Melbourne, Australia Gabriel Sandu, University of Helsinki, Finland Heinrich Wansing, Ruhr-University Bochum, Germany Timothy Williamson, Oxford University, U.K.
Logic, Epistemology, and the Unity of Science aims to reconsider the question of the unity of science in light of recent developments in logic. At present, no single logical, semantical or methodological framework dominates the philosophy of science. However, the editors of this series believe that formal techniques like, for example, independence friendly logic, dialogical logics, multimodal logics, game theoretic semantics and linear logics, have the potential to cast new light on basic issues in the discussion of the unity of science. This series provides a venue where philosophers and logicians can apply specific technical insights to fundamental philosophical problems. While the series is open to a wide variety of perspectives, including the study and analysis of argumentation and the critical discussion of the relationship between logic and the philosophy of science, the aim is to provide an integrated picture of the scientific enterprise in all its diversity.
For further volumes: http://www.springer.com/series/6936
Peter Dybjer • Sten Lindström • Erik Palmgren Göran Sundholm Editors
Epistemology versus Ontology Essays on the Philosophy and Foundations of Mathematics in Honour of Per Martin-Löf
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Editors Peter Dybjer Department of Computer Science and Engineering Chalmers University of Technology Göteborg Sweden Erik Palmgren Department of Mathematics Stockholm University Stockholm Sweden
Sten Lindström Department of Historical, Philosophical and Religious Studies Umeå University Umeå Sweden Göran Sundholm Philosophical Institute Leiden University Netherlands
ISBN 978-94-007-4434-9 ISBN 978-94-007-4435-6 (eBook) DOI 10.1007/978-94-007-4435-6 Springer Dordrecht Heidelberg New York London Library of Congress Control Number: 20