Combining Texts
Ideas for
'The Evolution of Logic', 'Critique of Pure Reason' and 'reports'
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10 ideas
6. Mathematics / A. Nature of Mathematics / 2. Geometry
8739
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Geometry studies the Euclidean space that dictates how we perceive things [Kant, by Shapiro]
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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 / e. Ordinal numbers
13459
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The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD]
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13491
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The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD]
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13463
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There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD]
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13492
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Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
13446
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19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
13509
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We can establish truths about infinite numbers by means of induction [Hart,WD]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / c. Potential infinite
9632
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Kant only accepts potential infinity, not actual infinity [Kant, by Brown,JR]
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