Abstract
An inference is valid if it guarantees the transferability of knowledge from the premisses to the conclusion. If knowledge is here understood as demonstrative knowledge, and demonstration is explained as a chain of valid inferences, we are caught in an explanatory circle. In recent lectures, Per Martin-Löf has sought to avoid the circle by specifying the notion of knowledge appealed to in the explanation of the validity of inference as knowledge of a kind weaker than demonstrative knowledge. The resulting explanation is the main topic of this article.
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Notes
- 1.
It is possible to formulate dialogue rules also for assertions of the form \(\vdash a\Rightarrow c : A\), but it would complicate the presentation here to enter into those rules. Instead we take the more intuitive approach that the task \(a\Rightarrow c : A\) is solved by an act of calculation.
References
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Acknowledgements
I am grateful to Per Martin-Löf, Göran Sundholm, and Shahid Rahman for discussions on topics of relevance to this article, and to the same as well as to Bruno Bentzen, Will Stafford and an anonymous referee for comments on an earlier draft. While researching and writing the article, I was supported by a Lumina quaeruntur fellowship (LQ300092101) from the Czech Academy of Sciences.
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Klev, A. (2024). Martin-Löf on the Validity of Inference. In: Piccolomini d'Aragona, A. (eds) Perspectives on Deduction: Contemporary Studies in the Philosophy, History and Formal Theories of Deduction. Synthese Library, vol 481. Springer, Cham. https://doi.org/10.1007/978-3-031-51406-7_8
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