Immanuel Kant (1724-1804)

1. Immanuel Kant (1724-1804) Prolegomena to Any Future Metaphysics

2. First Part of the main Transcendental • How is pure mathematics possible?

3. Pure Mathematics • Apodictic • A priori • Necessary • Synthetic

4. Pure Intuition • Mathematics requires pure intuition not empirical intuition. • Hence it is a priori. • Its judgments are always intuitive where philosophy’s are discursive.

5. A priori Intuition • An a priori intuition must precede an object. • But an intuition of anything requires an object. • But how can the intuition of the object precede the object itself? • That is, before the object is presented to me.

6. A priori Intuition • If intuition were of things as they are in themselves, then intuitions could not be a priori. • Intuitions would have to be empirical. • So, a priori intuitions cannot be of things as they are in themselves.

7. A priori Intuitions • “Therefore, in one way only can my intuition anticipate the actuality of the object, and be a cognition a priori, namely: if my intuition contains nothing but the form of sensibility, antedating in my mind all the actual impressions through which I am affected by objects” (30).

8. Form of Sensibility • The form of sensibility is what makes perception possible. • It is only applicable to objects of perception. • These intuitions can not be concerned with anything that is not an object of the sense. (laying the ground work to limit metaphysics).

9. The Form of Sensuous Intuition • We can only know appearances – phenomena. • We can never know things in themselves - noumena

10. Pure Mathematic • The intuitions of pure mathematics which are at the foundation of all its cognition and judgments are SPACE AND TIME. • Geometry is based upon the pure intuition of space. • Arithmetic achieves its concept of number by the successive addition of units in time.

11. Problem Solved • How is pure mathematics possible? • Through the pure intuitions of Space and Time

12. Formal Conditions of Our Sensibility • Space and time are part of our cognitive equipment that help us perceive the world in some human order and schema. • They preclude us from knowing the world as it is in itself. • Objects of the world are merely phenomena. • The form of the phenomenon, that is pure intuition, can by all means be represented as proceeding from ourselves, that is, a priori.

13. MIND All perception are possible through the form of sensibility. Geometry Space Thing in itself or noumena Appearance or Phenomenon Time Arithmetic

14. External Objects and Geometry • “Hence transcendental deduction of the notions of space and time explains at the same time the possibility of pure mathematics. Without such a deduction and the assumption ‘that everything which can be given to our sense (to the external senses in space, to the internal one in time) is intuited by us as it appears to us, not as it is in itself,’ the truth of pure mathematics may be granted, but its existence could by no means be understood” (32).

15. External Objects and Geometry • External appearances must necessarily and most rigorously agree with the propositions of the geometer, which he gets from the subjective basis (space) of all external appearances. • The a priori conception of space is the same.

16. Remarks II • Idealism: There are only minds and ideas. • Kant is not a genuine idealist because he believes there are bodies.

17. Kant on Bodies • “I grant by all means that there are bodies without us, that is, things which, though quite unknown to us as to what they are in themselves, we yet know by the representations which their influence on our sensibility procures us. These representations we call ‘bodies,’ a term signifying merely the appearance of the thing which is unknown to us, but not therefore less actual” (36).

18. Kant and Locke • “so little can my thesis be named idealistic merely because I find that more, nay all the properties which constitute the intuition of a body belong merely to its appearance” (37).

19. Remark III: Objection • By admitting the ideality of space and of time the whole sensible world would be turned into mere sham.

20. Perception vs. Understanding • Perceptions are not mistaken. • The understanding can be mistaken if it takes mere appearances as the objects themselves.

21. Truth • Concerns the use of sensuous representations in the understanding, and not of their origin. • All truths related to geometry hold good of both space and the objects of the sense, whether space is considered a form of the sensibility or a property of things. • The former, however, allows Kant to explain how one knows these truths a priori.

22. Critical Idealism • Descartes’ empirical idealism • Berkeley’s mystical or visionary idealism. • Kant prefers the name “Critical Idealism” over “Transcendental Idealism”.