Combining Texts

All the ideas for 'The Sign of Four', 'Through the Looking Glass' and 'Introduction to Zermelo's 1930 paper'

expand these ideas     |    start again     |     specify just one area for these texts

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6 ideas

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]

7. Existence / A. Nature of Existence / 3. Being / e. Being and nothing

21982

I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L]

14. Science / C. Induction / 1. Induction

22200

If you eliminate the impossible, the truth will remain, even if it is weird [Conan Doyle]