Combining Texts

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

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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]

9. Objects / C. Structure of Objects / 6. Constitution of an Object

6019	If someone squashed a horse to make a dog, something new would now exist [Mnesarchus]

28. God / A. Divine Nature / 6. Divine Morality / b. Euthyphro question

1515	Pythagoreans believe it is absurd to seek for goodness anywhere except with the gods [Iamblichus]