Combining Texts

All the ideas for 'The Case for Closure', 'New Foundations for Mathematical Logic' and 'talk'

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7 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

9879	NF has no models, but just blocks the comprehension axiom, to avoid contradictions [Quine, by Dummett]

5. Theory of Logic / A. Overview of Logic / 3. Value of Logic

10152

Set theory and logic are fairy tales, but still worth studying [Tarski]

8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism

10151

I am a deeply convinced nominalist [Tarski]

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]