Abstract

Hermann's Weyl Das Kontinuum has inspired several studies in logic and foundations of mathematics over the last century. The book provides a remarkable reconstruction of a large portion of classical mathematics on a predicative basis. However, diverging interpretations of the predicative system formulated by Weyl have been proposed in the literature. In the present work, I analyze an early formalization of Weyl's ideas proposed by [Casari, E. 1964. Questioni di Filosofia Della Matematica, Milano: Feltrinelli] and compare it with other, more well-known, accounts, such as those proposed respectively by Feferman and Avron. In this way, I fill a gap in the literature on Weyl's predicative mathematics by shedding light on an interpretation that has never been studied. Moreover, Casari's work is plausibly the first systematic reconstruction of Weyl's system. In particular, I highlight the different insights about predicativity that can be found in Weyl's work. Casari's reconstruction focuses on the logical and mathematical processes described by Weyl in the first part of his book. Through the analysis of this unexplored perspective, I shed light on fundamental aspects of Weyl's work and elucidate the alleged ambiguities it presents. In particular, in line with Avron's most recent reconstruction of Weyl's ideas, this analysis supports a stronger conception of predicativity than what is commonly attributed to Weyl in the literature. As a result, this work not only provides an analysis of a neglected interpretation of Das Kontinuum, but also contributes to elucidating Weyl's classical conception of predicativity.