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Umeå University, Faculty of Arts, Department of historical, philosophical and religious studies.
2012 (English)In: Epistemology versus Ontology: Essays on the Philosophy and Foundations of Mathematics in Honour of Per Martin-Löf / [ed] Dybjer, P.; Lindström, S.; Palmgren, E.; Sundholm, G., Dordrecht: Springer, 2012, vii-xiv p.Chapter in book (Refereed)
Abstract [en]

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?

Place, publisher, year, edition, pages
Dordrecht: Springer, 2012. vii-xiv p.
, Logic, Epistemology, and the Unity of Science, 27
Keyword [en]
Constructive Type Theory - Dummett - Gentzen - Intuitionism - Martin-Löf - Martin-Löf's type theory - Mathematical structuralism - Meaning-as-use - Prawitz - Proof Theory - Wittgenstein - axiom of choice (ZFC) - category theoretic foundations - predicativistic contructivism - set theory
National Category
Philosophy, Ethics and Religion Philosophy Algebra and Logic
Research subject
Theoretical Philosophy; Mathematical Logic
URN: urn:nbn:se:umu:diva-60039DOI: 10.1007/978-94-007-4435-6ISBN: 978-94-007-4434-9ISBN: 978-94-007-4435-6OAI: diva2:557793
Available from: 2012-09-29 Created: 2012-09-29 Last updated: 2013-06-13Bibliographically approved

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Lindström, Sten
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ReferencesLink to record
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