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The Fundamental Problem of General Proof Theory
Stockholm University, Faculty of Humanities, Department of Philosophy.
Number of Authors: 12019 (English)In: Studia Logica: An International Journal for Symbolic Logic, ISSN 0039-3215, E-ISSN 1572-8730, Vol. 107, no 1, p. 11-29Article in journal (Refereed) Published
Abstract [en]

I see the question what it is that makes an inference valid and thereby gives a proof its epistemic power as the most fundamental problem of general proof theory. It has been surprisingly neglected in logic and philosophy of mathematics with two exceptions: Gentzen's remarks about what justifies the rules of his system of natural deduction and proposals in the intuitionistic tradition about what a proof is. They are reviewed in the paper and I discuss to what extent they succeed in answering what a proof is. Gentzen's ideas are shown to give rise to a new notion of valid argument. At the end of the paper I summarize and briefly discuss an approach to the problem that I have proposed earlier.

Place, publisher, year, edition, pages
2019. Vol. 107, no 1, p. 11-29
Keywords [en]
Proof theory, Proof, Valid inference, Valid argument, Gentzen's naturaldeduction, Intuitionism
National Category
Mathematics Computer and Information Sciences Philosophy, Ethics and Religion
Identifiers
URN: urn:nbn:se:su:diva-166562DOI: 10.1007/s11225-018-9785-9ISI: 000458570100003OAI: oai:DiVA.org:su-166562DiVA, id: diva2:1293288
Available from: 2019-03-04 Created: 2019-03-04 Last updated: 2019-03-04Bibliographically approved

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