Combining Texts

All the ideas for 'The Case for Closure', 'The Source of Necessity' and 'Whitehead and the Rise of Modern Logic'

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11 ideas

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
13639 Quine says higher-order items are intensional, and lack a clearly defined identity relation [Quine, by Shapiro]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
21557 Russell confused use and mention, and reduced classes to properties, not to language [Quine, by Lackey]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
12432 Explanation of necessity must rest on something necessary or something contingent [Hale]
12434 Why is this necessary, and what is necessity in general; why is this necessary truth true, and why necessary? [Hale]
12435 The explanation of a necessity can be by a truth (which may only happen to be a necessary truth) [Hale]
10. Modality / C. Sources of Modality / 3. Necessity by Convention
12433 If necessity rests on linguistic conventions, those are contingent, so there is no necessity [Hale]
10. Modality / C. Sources of Modality / 4. Necessity from Concepts
12436 Concept-identities explain how we know necessities, not why they are necessary [Hale]
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]