Combining Texts

All the ideas for 'The Case for Closure', 'Knowledge and the Philosophy of Number' and 'Locke on Essences and Kinds'

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16 ideas

4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
23623 Predicativism says only predicated sets exist [Hossack]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
23624 The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
23625 Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
23628 The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
23627 'Before' and 'after' are not two relations, but one relation with two orders [Hossack]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity
23626 Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
23621 Numbers are properties, not sets (because numbers are magnitudes) [Hossack]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
23622 We can only mentally construct potential infinities, but maths needs actual infinities [Hossack]
9. Objects / D. Essence of Objects / 13. Nominal Essence
15642 If kinds depend only on what can be observed, many underlying essences might produce the same kind [Eagle]
15645 Nominal essence are the observable properties of things [Eagle]
15643 Nominal essence mistakenly gives equal weight to all underlying properties that produce appearances [Eagle]
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]
26. Natural Theory / B. Natural Kinds / 4. Source of Kinds
15641 Kinds are fixed by the essential properties of things - the properties that make it that kind of thing [Eagle]