Combining Texts

All the ideas for 'Content Preservation', 'The Philosophy of Logic' and 'Reals by Abstraction'

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5 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers

10632

The real numbers may be introduced by abstraction as ratios of quantities [Hale, by Hale/Wright]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity

18200

Very large sets should be studied in an 'if-then' spirit [Putnam]

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics

18199

Indispensability strongly supports predicative sets, and somewhat supports impredicative sets [Putnam]

8857	We must quantify over numbers for science; but that commits us to their existence [Putnam]

13. Knowledge Criteria / C. External Justification / 1. External Justification

9382	Subjects may be unaware of their epistemic 'entitlements', unlike their 'justifications' [Burge]