Combining Philosophers
Ideas for Lynch,MP/Glasgow,JM, Immanuel Kant and Michael Jubien
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10 ideas
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
9963
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If we all intuited mathematical objects, platonism would be agreed [Jubien]
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9962
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How can pure abstract entities give models to serve as interpretations? [Jubien]
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9964
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Since mathematical objects are essentially relational, they can't be picked out on their own [Jubien]
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6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
12421
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Kant's intuitions struggle to judge relevance, impossibility and exactness [Kitcher on Kant]
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16910
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Mathematics can only start from an a priori intuition which is not empirical but pure [Kant]
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16917
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All necessary mathematical judgements are based on intuitions of space and time [Kant]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
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 / 4. Mathematical Empiricism / c. Against mathematical empiricism
16928
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Mathematics cannot be empirical because it is necessary, and that has to be a priori [Kant]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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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