Combining Texts

All the ideas for 'Symposium', 'On the Concept of Number' and 'Absolute Necessities'

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10 ideas

6. Mathematics / C. Sources of Mathematics / 7. Formalism
Hilbert said (to block paradoxes) that mathematical existence is entailed by consistency [Hilbert, by Potter]
10. Modality / A. Necessity / 2. Nature of Necessity
Absolute necessity might be achievable either logically or metaphysically [Hale]
10. Modality / A. Necessity / 3. Types of Necessity
Maybe not-p is logically possible, but p is metaphysically necessary, so the latter is not absolute [Hale]
'Relative' necessity is just a logical consequence of some statements ('strong' if they are all true) [Hale]
A strong necessity entails a weaker one, but not conversely; possibilities go the other way [Hale]
10. Modality / A. Necessity / 5. Metaphysical Necessity
Metaphysical necessity says there is no possibility of falsehood [Hale]
10. Modality / A. Necessity / 6. Logical Necessity
'Broadly' logical necessities are derived (in a structure) entirely from the concepts [Hale]
Logical necessities are true in virtue of the nature of all logical concepts [Hale]
10. Modality / C. Sources of Modality / 4. Necessity from Concepts
Conceptual necessities are made true by all concepts [Hale]
22. Metaethics / B. Value / 2. Values / h. Fine deeds
Niceratus learnt the whole of Homer by heart, as a guide to goodness [Xenophon]