Combining Texts

All the ideas for 'Letters to Edward Stillingfleet', 'Absolute Necessities' and 'Paradoxes of the Infinite'

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12 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
An aggregate in which order does not matter I call a 'set' [Bolzano]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
A truly infinite quantity does not need to be a variable [Bolzano]
9. Objects / D. Essence of Objects / 3. Individual Essences
Every individual thing which exists has an essence, which is its internal constitution [Locke]
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]
A strong necessity entails a weaker one, but not conversely; possibilities go the other way [Hale]
'Relative' necessity is just a logical consequence of some statements ('strong' if they are all true) [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]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
If it is knowledge, it is certain; if it isn't certain, it isn't knowledge [Locke]