4 - Kant’s Theory of Mathematics

Summary

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.