Combining Texts

All the ideas for 'reports', 'The Rationalists' and 'Logicism, Some Considerations (PhD)'

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8 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers

13412

Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf]

13413

We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers

13411

If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf]

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism

13415

An adequate account of a number must relate it to its series [Benacerraf]

9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance

4304	Descartes says there are two substance, Spinoza one, and Leibniz infinitely many [Cottingham]

10. Modality / A. Necessity / 8. Transcendental Necessity

3016	Even the gods cannot strive against necessity [Pittacus, by Diog. Laertius]

12. Knowledge Sources / C. Rationalism / 1. Rationalism

4303	The notion of substance lies at the heart of rationalist metaphysics [Cottingham]

26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity

4306	For rationalists, it is necessary that effects be deducible from their causes [Cottingham]