Combining Texts

All the ideas for 'The Case for Closure', 'De formis' and 'Review of Tait 'Provenance of Pure Reason''

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8 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13418 The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C]
6. Mathematics / C. Sources of Mathematics / 8. Finitism
13419 If functions are transfinite objects, finitists can have no conception of them [Parsons,C]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
13417 If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C]
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]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / c. Primary qualities
16719 The primary qualities are mixed to cause secondary qualities [Burley]
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]