Continuity and Intuition in Eighteenth-Century Analysis and in Kant

Abstract

This chapter considers the status of geometrical and kinematic representations in the foundations of 18th century analysis and in Kant’s understanding of those foundations. It has two aims. First, relying on relatively recent reassessments of the history of analysis, it will attempt to bring forward a more accurate account of intuitive representation in 18 ^th century analysis and the relation between British and Continental mathematics. Second, it will give a better account of Kant’s place in that history. The result shows that although Kant did no better at navigating the labyrinth of the continuum than his contemporaries, he had a more interesting and reasonable account of the foundations of analysis than an easy reading of either Kant or that history provides. It also permits a more accurate and interesting account of how and when a conception of foundations of analysis without intuitive representations emerged, and how that paved the way for Bolzano and Cauchy.