Combining Texts

All the ideas for 'works', 'works' and 'What Numbers Are'

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5 ideas

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems

17813

Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers [White,NP]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure

17812

Finite cardinalities don't need numbers as objects; numerical quantifiers will do [White,NP]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals

18086

Weierstrass eliminated talk of infinitesimals [Weierstrass, by Kitcher]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits

18092

Weierstrass made limits central, but the existence of limits still needed to be proved [Weierstrass, by Bostock]

23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues

20239

Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche]