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1 Introduction The paper will explore the formal validity of proof by contradiction in Kant’s logic. This will allow us to analyse the conditions under which apagogical proof, conceived as a hypothetical inference expressed by a modus tollens , can account for the logical truth of a
in Kant 31 Mark Siebel Kant on the Necessity of Necessity 66 Jessica Leech On the Formal Validity of Proof by Contradiction in Kant’s Logic 95 Davide Dalla Rosa Reconsidering Kant’s Rejection of Indirect Arguments in Transcendental Philosophy 115 Marcel Buß Transcendental Knowability and A Priori
-style natural deduction calculus [1], using a small number of basic proof rules. Definition 4 The basic proof rules are given by the rules of a) contradiction A not Acontradiction b) proof by contradiction not A implies contradictionA c) modus ponens A implies B AB d) instantiation for all x holds A(x)A(y) e
contradiction. A proof by contradiction is an indirect argument that starts by assuming ¬ T and then shows that this assumption implies a contradiction. In this way, the proof can establish that ¬ T is necessarily false. But the indirect transcendental arguments I described above do not establish that ¬ T