Combining Texts
Ideas for
'works', 'Critique of Pure Reason' and 'Explanatory Coherence'
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11 ideas
6. Mathematics / A. Nature of Mathematics / 2. Geometry
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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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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 / 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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6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
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3343
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Euclid's could be the only viable geometry, if rejection of the parallel line postulate doesn't lead to a contradiction [Benardete,JA on Kant]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
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8737
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Kant suggested that arithmetic has no axioms [Kant, by Shapiro]
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5557
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Axioms ought to be synthetic a priori propositions [Kant]
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6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
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12421
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Kant's intuitions struggle to judge relevance, impossibility and exactness [Kitcher on Kant]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
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17617
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Maths is a priori, but without its relation to empirical objects it is meaningless [Kant]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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12458
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Kant taught that mathematics is independent of logic, and cannot be grounded in it [Kant, by Hilbert]
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2795
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If 7+5=12 is analytic, then an infinity of other ways to reach 12 have to be analytic [Kant, by Dancy,J]
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