Semantical games and transcendental arguments

pp. 33-46

in: Jaakko Hintikka, The game of language, Berlin, Springer, 1983

Abstract

Kant had the right idea in his theory of mathematics, but he was misled by an antiquated philosophical dogma.¹ Following his general transcendental point of view, he maintained that our ways of reasoning about existence (especially inferences from the existence or nonexistence of an individual to the existence or nonexistence of a different individual) must be grounded in the human activities through which we come to know the existence of individuals. This is a deep and intriguing idea, and Kant's identification of the types of reasoning in question as mathematical rather than logical marks only a difference in terminology between Kant and contemporary philosophers of logic. What Kant was dealing with is unmistakably such logical reasoning as is now codified in the modern logic of quantification theory — not anything we would any longer consider distinctively mathematical reasoning.