Ivo Pezlar
Czech Academy of Sciences, Institute of Philosophy
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.
Keywords Deduction  Frege  Gentzen  indirect proofs  Tichý  TIL  two-dimensional inference
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Indiscernibility of Identicals.Pavel Tichý - 1986 - Studia Logica 45 (3):251 - 273.
On Inference.P. Tichy & J. Tichy - 1999 - In Timothy Childers (ed.), The Logica Yearbook 1998. Filosofia. pp. 73--85.

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