Day 7: Kant on Mathematics

•      Review Structure of CPR

•      Geometry

•      Arithmetic

•      Problems?

•      Read CPR 92-128; Pr 42-53 (sections 14-22)

Review Structure of CPR

•      (1) How is pure mathematics possible?

•      (2) How is pure science of nature possible?

•      (3) How is metaphysics, as a natural disposition, possible?

•      (4) How is metaphysics, as science, possible?

 Implications of Transcendental Aesthetic for above questions

Geometry

•      Pr 30-31: Mathematics is made up of geometry and arithmetic

•      CPR-B65:

    (1) Two straight lines cannot enclose a space, and within them alone, no figure is possible.

    (2) Given three straight lines, a figure [i.e. enclosed space] is possible.

Geometry

•      What is the relationship between the pure form of space and the synthetic a priori truths of geometry?

Arithmetic

•      What is the relationship between the pure form of time and the synthetic a priori truths of arithmetic?

Problems

•      Logicism and Kant’s theory of arithmetic

•      Non-Euclidean Geometry and Kant’s theory of geometry

•      Other concerns