Combining Texts

All the ideas for 'fragments/reports', 'The Theory of Logical Types' and 'Introduction to Zermelo's 1930 paper'

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10 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]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
21566 'Propositional functions' are ambiguous until the variable is given a value [Russell]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
21567 'All judgements made by Epimenedes are true' needs the judgements to be of the same type [Russell]
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]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
23457 Type theory cannot identify features across levels (because such predicates break the rules) [Morris,M on Russell]
21556 Classes are defined by propositional functions, and functions are typed, with an axiom of reducibility [Russell, by Lackey]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
21568 A one-variable function is only 'predicative' if it is one order above its arguments [Russell]
28. God / A. Divine Nature / 1. God
6011 There is a remote first god (the Good), and a second god who organises the material world [Numenius, by O'Meara]