Combining Texts

All the ideas for 'The Case for Closure', 'Proof that every set can be well-ordered' and 'Types and Ontology'

expand these ideas     |    start again     |     specify just one area for these texts

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6 ideas

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / e. Countable infinity

15897

Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine]

7. Existence / E. Categories / 1. Categories

13127

Categories can't overlap; they are either disjoint, or inclusive [Sommers, by Westerhoff]

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]