Combining Philosophers
Ideas for Lynch,MP/Glasgow,JM, Immanuel Kant and M.R. Ayers
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11 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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8739
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Geometry studies the Euclidean space that dictates how we perceive things [Kant, by Shapiro]
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16919
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Geometry rests on our intuition of space [Kant]
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8740
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Geometry would just be an idle game without its connection to our intuition [Kant]
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16899
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Geometrical truth comes from a general schema abstracted from a particular object [Kant, by Burge]
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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 / 4. Using Numbers / d. Counting via concepts
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17518
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Counting 'coin in this box' may have coin as the unit, with 'in this box' merely as the scope [Ayers]
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17516
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If counting needs a sortal, what of things which fall under two sortals? [Ayers]
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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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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / c. Potential infinite
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9632
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Kant only accepts potential infinity, not actual infinity [Kant, by Brown,JR]
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