Combining Texts

All the ideas for 'The Philosophy of Logic', 'Absolute Necessities' and 'Comments on a Certain Broadsheet'

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14 ideas

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
Very large sets should be studied in an 'if-then' spirit [Putnam]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
Indispensability strongly supports predicative sets, and somewhat supports impredicative sets [Putnam]
We must quantify over numbers for science; but that commits us to their existence [Putnam]
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]
12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities
What experience could prove 'If a=c and b=c then a=b'? [Descartes]
18. Thought / D. Concepts / 2. Origin of Concepts / c. Nativist concepts
Qualia must be innate, because physical motions do not contain them [Descartes]
The mind's innate ideas are part of its capacity for thought [Descartes]