umu.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Epistemology versus Ontology: Essays on the Philosophy and Foundations of Mathematics in Honour of Per Martin-Löf
Umeå University, Faculty of Arts, Department of historical, philosophical and religious studies.
2012 (English)Collection (editor) (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. , 412 p.
Series
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
Humanities Natural Sciences
Research subject
Mathematical Logic; Theoretical Philosophy
Identifiers
URN: urn:nbn:se:umu:diva-57490DOI: 10.1007/978-94-007-4435-6ISBN: 978-94-007-4434-9 (print)ISBN: 978-94-007-4435-6 (print)OAI: oai:DiVA.org:umu-57490DiVA: diva2:542571
Available from: 2012-08-02 Created: 2012-08-02 Last updated: 2013-01-03Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full texthttp://www.springer.com/philosophy/logic+and+philosophy+of+language/book/978-94-007-4434-9

Search in DiVA

By author/editor
Lindström, Sten
By organisation
Department of historical, philosophical and religious studies
HumanitiesNatural Sciences

Search outside of DiVA

GoogleGoogle Scholar

doi
isbn
urn-nbn

Altmetric score

doi
isbn
urn-nbn
Total: 169 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf