Combining Texts

All the ideas for 'The Case for Closure', 'Frege on Apriority' and 'The Philosophy of Logic'

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8 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry

9159	You can't simply convert geometry into algebra, as some spatial content is lost [Burge]

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]

11. Knowledge Aims / B. Certain Knowledge / 2. Common Sense Certainty

19553

Commitment to 'I have a hand' only makes sense in a context where it has been doubted [Hawthorne]

13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / c. Knowledge closure

19551

How can we know the heavyweight implications of normal knowledge? Must we distort 'knowledge'? [Hawthorne]

19552

We wouldn't know the logical implications of our knowledge if small risks added up to big risks [Hawthorne]

19554

Denying closure is denying we know P when we know P and Q, which is absurd in simple cases [Hawthorne]