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Tichý’s Two-Dimensional Conception of Inference

Organon F, 2013, vol. 20, Supplementary Issue 2, pp. 54-65.
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In this paper we revisit Pavel Tichý’s novel distinction between one-dimensional and two-dimensional conception of inference, which he presented in his book Foundations of Frege’s Logic (1988), and later in On Inference (1999), which was prepared from his manuscript by his co-author Jindra Tichý. We shall focus our inquiry not only on the motivation behind the introduction of this non-classical concept of inference, but also on further inspection of selected Tichý’s arguments, which we see as the most compelling or simply most effective in providing support for his two-dimensional account of inference. Main attention will be given to exposing the failure of one-dimensional theory of inference in its explanation of indirect (reductio ad absurdum) proofs. Lastly, we discuss shortly the link between two-dimensional inference and deduction apparatus of Tichý’s Transparent Intensional Logic.

Kľúčové slová

Deduction, Frege, Gentzen, indirect proofs, Tichý, TIL, two-dimensional inference

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