Combining Texts

All the ideas for 'fragments/reports', 'Introduction to Zermelo's 1930 paper' and 'works'

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7 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]

13. Knowledge Criteria / D. Scepticism / 1. Scepticism

3061	Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]

14. Science / B. Scientific Theories / 1. Scientific Theory

22363

You have only begun to do real science when you can express it in numbers [Kelvin]

27. Natural Reality / A. Classical Physics / 2. Thermodynamics / a. Energy

20644

Energy has progressed from a mere formula, to a principle pervading all nature [Kelvin]