Ideas from 'Prolegomena to Any Future Metaphysic' by Immanuel Kant [1781], by Theme Structure

[found in 'Prolegomena to Any Future Metaphysic' by Kant,Immanuel (ed/tr Lucas,Peter G.) [Manchester UP 1971,0-7190-0492-6]].

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1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
Metaphysics is generating a priori knowledge by intuition and concepts, leading to the synthetic
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Mathematics cannot proceed just by the analysis of concepts
6. Mathematics / A. Nature of Mathematics / 3. Numbers / a. Numbers
Numbers are formed by addition of units in time
6. Mathematics / A. Nature of Mathematics / 3. Numbers / q. Arithmetic
7+5 = 12 is not analytic, because no analysis of 7+5 will reveal the concept of 12
6. Mathematics / A. Nature of Mathematics / 5. Geometry
Geometry is not analytic, because a line's being 'straight' is a quality
Geometry rests on our intuition of space
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
Mathematics can only start from an a priori intuition which is not empirical but pure
All necessary mathematical judgements are based on intuitions of space and time
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
Mathematics cannot be empirical because it is necessary, and that has to be a priori
9. Objects / B. Unity of Objects / 2. Substance / e. Substance critique
The substance, once the predicates are removed, remains unknown to us
11. Knowledge Aims / C. Knowing Reality / 3. Idealism
I admit there are bodies outside us
12. Knowledge Sources / A. A Priori Knowledge / 5. A Priori Synthetic
A priori synthetic knowledge is only of appearances, not of things in themselves
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
A priori intuitions can only concern the objects of our senses
12. Knowledge Sources / A. A Priori Knowledge / 10. A Priori as Subjective
A priori intuition of objects is only possible by containing the form of my sensibility
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / e. Primary/secondary critique
I count the primary features of things (as well as the secondary ones) as mere appearances
12. Knowledge Sources / B. Perception / 3. Representation
I can't intuit a present thing in itself, because the properties can't enter my representations
12. Knowledge Sources / D. Empiricism / 4. Pro-Empiricism
Appearance gives truth, as long as it is only used within experience
12. Knowledge Sources / E. Direct Knowledge / 1. Intuition
Intuition is a representation that depends on the presence of the object
18. Thought / D. Concepts / 5. Origin of Concepts / a. Origin of concepts
Some concepts can be made a priori, which are general thoughts of objects, like quantity or cause
19. Language / F. Analytic/Synthetic / 2. Analytic Propositions
Analytic judgement rests on contradiction, since the predicate cannot be denied of the subject
Analytic judgements say clearly what was in the concept of the subject
26. Natural Theory / B. Concepts of Nature / 3. Space / a. Space
Space must have three dimensions, because only three lines can meet at right angles
26. Natural Theory / B. Concepts of Nature / 5. Space-Time
If all empirical sensation of bodies is removed, space and time are still left