Abstract

One of the central and most distinctive theses of Kant’s philosophy of mathematics is that mathematical knowledge is synthetic. In this context, synthetic judgments are defined in opposition to analytic ones, whose predicate concept is “contained in” the subject. Kant’s thesis has often been attacked as indefensible, but just as frequently critics have complained that the thesis itself, and even the analytic/synthetic distinction on which it rests, are simply unintelligible. Thus, even prior to questions of its correctness, the Kantian doctrine has been rejected as unclear, based on general skepticism that there is a real distinction of “containment”—or indeed any tolerably clear distinction at all—between analytic and synthetic judgments.