This paper discusses the place of the infinite in Kant’s philosophy, in particular as required for continuity in mathematics and physics. A fine-grained examination of the roles that the infinite and the infinitesimal play in Kant’s theory that illuminates the notion of construction in Kant’s philosophy of mathematics also uncovers challenges to certain prominent interpretations of Kant’s reliance on logic and intuition in mathematics.

Hintikka reprises and enhances some of his original themes, and argues that Kant’s notion of construction in intuition is codified in the modern predicate logic inference patterns of universal and existential instantiation. Hintikka traces back the device of construction to the Euclidean ekthesis, drawing a figure according to a definition. He shows that a geometrical construction allows one to deduce more about the definition than is made possible by the concept of deduction prevalent in Kant’s time. Hintikka couches this analysis in the context of his discussion of the logic of the mathematical method as an epistemic logic of seeking and finding, and thus displays a comprehensive picture of his own mature view.