Combining Texts

All the ideas for 'Mathematics without Numbers', 'Philosophia Epicurea' and 'Warrant and Proper Function'

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5 ideas

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
9. Objects / C. Structure of Objects / 2. Hylomorphism / b. Form as principle
Form is the principle that connects a thing's constitution (rather than being operative) [Hill,N]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
Maybe a reliable justification must come from a process working with its 'proper function' [Plantinga, by Pollock/Cruz]