Combining Texts

All the ideas for 'Necessary Existents', 'Properties' and 'Introduction to Zermelo's 1930 paper'

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9 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 / B. Properties / 2. Need for Properties

18430

We accept properties because of type/tokens, reference, and quantification [Edwards]

8. Modes of Existence / B. Properties / 10. Properties as Predicates

18432

Quineans say that predication is primitive and inexplicable [Edwards]

8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism

18437

Resemblance nominalism requires a second entity to explain 'the rose is crimson' [Edwards]

9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts

18434

That a whole is prior to its parts ('priority monism') is a view gaining in support [Edwards]

19. Language / D. Propositions / 3. Concrete Propositions

19216

Propositions (such as 'that dog is barking') only exist if their items exist [Williamson]