Change search
ReferencesLink to record
Permanent link

Direct link
On the relation between Heyting's and Gentzen's approaches to meaning
Stockholm University, Faculty of Humanities, Department of Philosophy.
2016 (English)In: Advances in proof-theoretic semantics / [ed] Thomas Piecha, Peter Schroeder-Heister, Cham: Springer, 2016, 5-25 p.Chapter in book (Refereed)
Abstract [en]

Proof-theoretic semantics explains meaning in terms of proofs. Two different concepts of proof are in question here. One has its roots in Heyting’s explanation of a mathematical proposition as the expression of the intention of a construction, and the other in Gentzen’s ideas about how the rules of Natural Deduction are justified in terms of the meaning of sentences. These two approaches to meaning give rise to two different concepts of proof, which have been developed much further, but the relation between them, the topic of this paper, has not been much studied so far. The recursive definition of proof given by the so-called BHK-interpretation is here used as an explication of Heyting’s idea. Gentzen’s approach has been developed as ideas about what it is that makes a piece of reasoning valid. It has resulted in a notion of valid argument, of which there are different variants. The differences turn out to be crucial when comparing valid arguments and BHK-proofs. It will be seen that for one variant, the existence of a valid argument can be proved to be extensionally equivalent to the existence of a BHK-proof, while for other variants, attempts at similar proofs break down at different points.

Place, publisher, year, edition, pages
Cham: Springer, 2016. 5-25 p.
, Trends in logic, ISSN 1572-6126 ; 43
Keyword [en]
Proof, Valid argument, Meaning, Semantics, Heyting, Gentzen
National Category
Research subject
Theoretical Philosophy
URN: urn:nbn:se:su:diva-125726DOI: 10.1007/978-3-319-22686-6_2ISBN: 978-3-319-22685-9OAI: diva2:894914
Available from: 2016-01-17 Created: 2016-01-17 Last updated: 2016-05-13Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Prawitz, Dag
By organisation
Department of Philosophy

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 43 hits
ReferencesLink to record
Permanent link

Direct link