Combining Texts

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

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8 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]
8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals
9103 A universal is not a real feature of objects, but only a thought-object in the mind [William of Ockham]
18. Thought / E. Abstraction / 2. Abstracta by Selection
9104 A universal is the result of abstraction, which is only a kind of mental picturing [William of Ockham]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]