Mathematics, Intuition, and Language in the first Critique and the Tractatus

Proposition 6.233 from Wittgenstein’s Tractatus has been read as a rejection of the Kantian claim that mathematics relies on intuition. Contrary to previous contributions, I develop a reading of the Critique and the Tractatus that shows how the two had a similar understanding of what kind of account mathematics calls for. I do so by focusing on a fundamental structural similarity between the Tractarian notion of Satz (proposition) and the Kantian one of Erkenntnis (cognition). I argue that we can fruitfully read much of the fundamental terminology of the two works as the result of an analysis of these two notions in terms of form and matter; moreover, both terms are best understood by considering their paradigmatic employment: empirical cognition for Kant and the significant proposition for Wittgenstein. This analysis allows us to gain a better understanding of Kantian pure intuition and Tractarian logical form of propositional symbols, thus elucidating the domains in which the two authors think mathematics operates