Combining Philosophers

Ideas for B Hale / C Wright, Immanuel Kant and Anaxagoras

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12 ideas

6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
12421 Kant's intuitions struggle to judge relevance, impossibility and exactness [Kitcher on Kant]
16910 Mathematics can only start from an a priori intuition which is not empirical but pure [Kant]
16917 All necessary mathematical judgements are based on intuitions of space and time [Kant]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
17617 Maths is a priori, but without its relation to empirical objects it is meaningless [Kant]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
16928 Mathematics cannot be empirical because it is necessary, and that has to be a priori [Kant]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
8788 Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology [Hale/Wright]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
10622 The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright]
8783 Logicism might also be revived with a quantificational approach, or an abstraction-free approach [Hale/Wright]
12225 Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment [Hale/Wright]
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]
12224 Are neo-Fregeans 'maximalists' - that everything which can exist does exist? [Hale/Wright]