Combining Texts

All the ideas for 'Philosophical Essay on Probability', 'Syntactic Structure' and 'Introduction to Zermelo's 1930 paper'

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8 ideas

2. Reason / F. Fallacies / 8. Category Mistake / c. Category mistake as semantic
18009 Chomsky established the view that category mistakes are well-formed but meaningless [Chomsky, by Magidor]
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]
13. Knowledge Criteria / C. External Justification / 7. Testimony
7458 The reliability of witnesses depends on whether they benefit from their observations [Laplace, by Hacking]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
3441 If a supreme intellect knew all atoms and movements, it could know all of the past and the future [Laplace]
19. Language / C. Assigning Meanings / 1. Syntax
18007 Syntax is independent of semantics; sentences can be well formed but meaningless [Chomsky, by Magidor]