Validity of inferences and validity of demonstrations

Abstract

The lecture spells out the difference between the validity of inference (‐figure)s and validity applied to demonstrations (‘proof acts’). The latter notion is not an ordinary characterizing one; in Brentano's terminology it is a modifying one. A demonstration lacking validity is not a real demonstration, just as a false friend is no true friend. Throughout, the treatment makes crucial use of an epistemological perspective that is cast in the first person. Furthermore, the difference between (logical) consequence among propositions and the validity of inference from judgement to judgement is explained. Particular attention is paid to alleged issues of circularity in the definition of the validity of inference, and to the ‘explosion’ validity of inference from contradictory premisses. Drawing upon a version of the dialogical framework of Per Martin‐Löf, namely, ‘When I say Therefore, I give others my permission to assert the conclusion’, while stressing also the importance of the first person perspective, both difficulties can be neutralized.