Kant on geometry and spatial intuition

Geometry, Construction, and Intuition in Kant and His Successors

Flexible intuitions of Euclidean geometry in an Amazonian indigene group.

Kant argued that Euclidean geometry is synthesized on the basis of an a priori intuition of space. This proposal inspired much behavioral research probing whether spatial navigation in humans and animals conforms to the predictions of Euclidean geometry. However, Euclidean geometry also includes concepts that transcend the perceptible, such as objects that are infinitely small or infinitely lar...

Frege's Contribution to Philosophy of Language

Gottlob Frege’s contributions to philosophy of language are so numerous and so fundamental that it is difficult to imagine the field without them. That this should be so was not, however, Frege’s original intent. Frege was trained as a mathematician, and most of his non-foundational mathematical work lay at the intersection of geometry and complex analysis. That makes it at least somewhat surpr...

A crisis of intuition as viewed by Felix Klein and Hans Hahn and its resolution by fractal geometry

at the start, to have constant regard to the applications, and to refer to the refinements only gradually as the student becomes able to understand them. This is, of course, nothing but a universal pedagogical principle to be observed in all mathematical instruction.... I am led to these remarks by the consciousness of growing danger in Germany of a separation between abstract mathematical scie...

“ The Unity of Time ’ s Measure ”

According to Kant, the understanding generates concepts in virtue of its own capacity to judge (A69/B94), but knowledge requires the application of concepts to what is given by the sensible faculty. His Transcendental Deduction is intended to show that the Categories, concepts that express the unity required for objective judgment, apply to all objects given in sensible intuition. In the Critiq...