Intellect and imagination in geometrical cognition in Descartes's Regulae ad directionem ingenii

Abstract

The aim of the paper is to determine the exact sense in which geometrical analysis is to count as a model of certain, evident and true cognition according to Descartesʼs Regulæ ad directionem ingenii. This requires an examination of the respective functions of the two cognitive powers of intellect and imagination in such a paradigmatically conceived geometrical cognition, with a special emphasis on Descartesʼs theories of abstraction and on his ontological distinctions.

Keywords

• geometry
• intellect
• imagination
• mathematical cognition
• philosophy of mathematics
• Descartes