Combining Texts

All the ideas for 'Precis of 'Limits of Abstraction'', 'Mathematics without Numbers' and 'Metaphysical Foundations of Mathematics'

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8 ideas

2. Reason / D. Definition / 2. Aims of Definition
10528 Definitions concern how we should speak, not how things are [Fine,K]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
10529 If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
10530 Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
8698 Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
9557 Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
10263 Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10527 An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]
27. Natural Reality / D. Time / 2. Passage of Time / g. Time's arrow
22908 When one element contains the grounds of the other, the first one is prior in time [Leibniz]