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Ideas for 'works (fragments)', 'Prolegomena to Any Future Metaphysic' and 'Investigations in the Foundations of Set Theory I'

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13 ideas

6. Mathematics / A. Nature of Mathematics / 1. Mathematics
16918 Mathematics cannot proceed just by the analysis of concepts [Kant]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
16930 Geometry is not analytic, because a line's being 'straight' is a quality [Kant]
16919 Geometry rests on our intuition of space [Kant]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
16920 Numbers are formed by addition of units in time [Kant]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
13487 In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
16146 Two can't be a self-contained unit, because it would need to be one to do that [Democritus, by Aristotle]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
16929 7+5 = 12 is not analytic, because no analysis of 7+5 will reveal the concept of 12 [Kant]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
18178 For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
13027 Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
9627 Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
16910 Mathematics can only start from an a priori intuition which is not empirical but pure [Kant]
16917 All necessary mathematical judgements are based on intuitions of space and time [Kant]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
16928 Mathematics cannot be empirical because it is necessary, and that has to be a priori [Kant]