Combining Texts

All the ideas for 'fragments/reports', 'Knowledge and the Philosophy of Number' and 'Absolute Necessities'

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18 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]
10. Modality / A. Necessity / 2. Nature of Necessity
15086 Absolute necessity might be achievable either logically or metaphysically [Hale]
10. Modality / A. Necessity / 3. Types of Necessity
8261 Maybe not-p is logically possible, but p is metaphysically necessary, so the latter is not absolute [Hale]
15080 'Relative' necessity is just a logical consequence of some statements ('strong' if they are all true) [Hale]
15081 A strong necessity entails a weaker one, but not conversely; possibilities go the other way [Hale]
10. Modality / A. Necessity / 5. Metaphysical Necessity
15082 Metaphysical necessity says there is no possibility of falsehood [Hale]
10. Modality / A. Necessity / 6. Logical Necessity
15085 'Broadly' logical necessities are derived (in a structure) entirely from the concepts [Hale]
15088 Logical necessities are true in virtue of the nature of all logical concepts [Hale]
10. Modality / C. Sources of Modality / 4. Necessity from Concepts
15087 Conceptual necessities are made true by all concepts [Hale]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]