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Ideas for
'Lectures 1930-32 (student notes)', 'Logicism, Some Considerations (PhD)' and 'Political Philosophy: all that matters'
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6 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
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13412
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Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf]
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13413
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We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
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13411
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If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
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18738
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We don't get 'nearer' to something by adding decimals to 1.1412... (root-2) [Wittgenstein]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
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18708
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Infinity is not a number, so doesn't say how many; it is the property of a law [Wittgenstein]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
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13415
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An adequate account of a number must relate it to its series [Benacerraf]
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