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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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7 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
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16918
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Mathematics cannot proceed just by the analysis of concepts [Kant]
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6. Mathematics / A. Nature of Mathematics / 2. Geometry
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16930
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Geometry is not analytic, because a line's being 'straight' is a quality [Kant]
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16919
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Geometry rests on our intuition of space [Kant]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
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16920
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Numbers are formed by addition of units in time [Kant]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
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13487
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In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
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16146
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Two can't be a self-contained unit, because it would need to be one to do that [Democritus, by Aristotle]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
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16929
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7+5 = 12 is not analytic, because no analysis of 7+5 will reveal the concept of 12 [Kant]
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