Combining Texts

All the ideas for 'The Birth of Tragedy', 'Identity over Time' and 'Introduction to Zermelo's 1930 paper'

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8 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy

7848	Philosophy begins in the horror and absurdity of existence [Nietzsche, by Ansell Pearson]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

17833

The first-order ZF axiomatisation is highly non-categorical [Hallett,M]

17834

Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal [Hallett,M]

4. Formal Logic / F. Set Theory ST / 7. Natural Sets

17837

Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis

17836

The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M]

9. Objects / E. Objects over Time / 1. Objects over Time

16025

If things change they become different - but then no one thing undergoes the change! [Gallois]

9. Objects / E. Objects over Time / 4. Four-Dimensionalism

16026

4D: time is space-like; a thing is its history; past and future are real; or things extend in time [Gallois]

9. Objects / F. Identity among Objects / 6. Identity between Objects

16027

If two things are equal, each side involves a necessity, so the equality is necessary [Gallois]