Abstract
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.
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This paper is quite different from the one presented at the conference on General Proof Theory (to be found, somewhat modified, in the proceedings published on line; [23]), but there are some overlaps; in particular, both contain a presentation of a new notion of valid inference.
Special Issue: General Proof Theory.
Edited by Thomas Piecha and Peter Schroeder-Heister.
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Prawitz, D. The Fundamental Problem of General Proof Theory. Stud Logica 107, 11–29 (2019). https://doi.org/10.1007/s11225-018-9785-9
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DOI: https://doi.org/10.1007/s11225-018-9785-9