Combining Texts

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

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7 ideas

3. Truth / H. Deflationary Truth / 1. Redundant Truth
"It is true that x" means no more than x [Ramsey]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
The first-order ZF axiomatisation is highly non-categorical [Hallett,M]
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
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
The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M]
19. Language / A. Nature of Meaning / 7. Meaning Holism / c. Meaning by Role
Sentence meaning is given by the actions to which it would lead [Ramsey]
19. Language / D. Propositions / 3. Concrete Propositions
Propositions (such as 'that dog is barking') only exist if their items exist [Williamson]