Combining Texts

All the ideas for 'fragments/reports', 'The Theory of Transfinite Numbers' and 'Remarks on the definition and nature of mathematics'

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8 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory

9616	A set is a collection into a whole of distinct objects of our intuition or thought [Cantor]

5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic

17807

To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities

15896

Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine]

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism

17806

It is untenable that mathematics is general physical truths, because it needs infinity [Curry]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

17808

Saying mathematics is logic is merely replacing one undefined term by another [Curry]

7. Existence / A. Nature of Existence / 3. Being / d. Non-being

18933

Not-Being obviously doesn't exist, and the five modes of Being are all impossible [Gorgias, by Diog. Laertius]

19. Language / F. Communication / 1. Rhetoric

5864	Destroy seriousness with laughter, and laughter with seriousness [Gorgias]

9866	Gorgias says rhetoric is the best of arts, because it enslaves without using force [Gorgias, by Plato]