Topoi 38 (3):591-603 (2019)

Luca Tranchini
Universität Tübingen
In the present paper, the Fregean conception of proof-theoretic semantics that I developed elsewhere will be revised so as to better reflect the different roles played by open and closed derivations. I will argue that such a conception can deliver a semantic analysis of languages containing paradoxical expressions provided some of its basic tenets are liberalized. In particular, the notion of function underlying the Brouwer–Heyting–Kolmogorov explanation of implication should be understood as admitting functions to be partial. As argued in previous work, the correctness of an inference rule should not be defined in terms of transmission of provability, but rather should be grounded on weaker principles, which I show that are motivated by consideration about the content of the inversion principle. In the conclusion, I briefly address the issue of compositionality, arguing that the violation of compositionality induced by paradoxes are no worse than others that are regarded, at least by Dummett, as wholly unproblematic.
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DOI 10.1007/s11245-018-9552-6
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References found in this work BETA

Natural Deduction: A Proof-Theoretical Study.Dag Prawitz - 1965 - Stockholm, Sweden: Dover Publications.
Frege.Michael Dummett - 1975 - Teorema: International Journal of Philosophy 5 (2):149-188.
Dummett on Frege. [REVIEW]Leslie Stevenson - 1974 - Philosophical Quarterly 24 (97):349-359.

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Citations of this work BETA

A Note on Paradoxical Propositions From an Inferential Point of View.Ivo Pezlar - 2021 - In Martin Blicha & Igor Sedlár (eds.), The Logica Yearbook 2020. College Publications. pp. 183-199.

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