Combining Texts

All the ideas for 'fragments/reports', 'Introduction to Zermelo's 1930 paper' and 'Reference and Essence: seven appendices'

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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]

7. Existence / D. Theories of Reality / 10. Vagueness / g. Degrees of vagueness

14742

It can't be indeterminate whether x and y are identical; if x,y is indeterminate, then it isn't x,x [Salmon,N]

19. Language / B. Reference / 3. Direct Reference / a. Direct reference

18885

Kripke and Putnam made false claims that direct reference implies essentialism [Salmon,N]

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]