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Ideas for 'Philosophy of Mathematics', 'Critique of Pure Reason' and 'Primitive Thisness and Primitive Identity'

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12 ideas

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10200 We distinguish realism 'in ontology' (for objects), and 'in truth-value' (for being either true or false) [Shapiro]
10210 If mathematical objects are accepted, then a number of standard principles will follow [Shapiro]
10215 Platonists claim we can state the essence of a number without reference to the others [Shapiro]
10233 Platonism must accept that the Peano Axioms could all be false [Shapiro]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
12421 Kant's intuitions struggle to judge relevance, impossibility and exactness [Kitcher on Kant]
10244 Intuition is an outright hindrance to five-dimensional geometry [Shapiro]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
10280 A stone is a position in some pattern, and can be viewed as an object, or as a location [Shapiro]
17617 Maths is a priori, but without its relation to empirical objects it is meaningless [Kant]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
12458 Kant taught that mathematics is independent of logic, and cannot be grounded in it [Kant, by Hilbert]
2795 If 7+5=12 is analytic, then an infinity of other ways to reach 12 have to be analytic [Kant, by Dancy,J]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
10254 Can the ideal constructor also destroy objects? [Shapiro]
10255 Presumably nothing can block a possible dynamic operation? [Shapiro]