Combining Texts

All the ideas for 'Paradoxes: Form and Predication', 'Why there isn't a ready-made world' 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 / G. Quantification / 6. Plural Quantification
14235 Saying 'they can become a set' is a tautology, because reference to 'they' implies a collection [Cargile]
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 / 2. Realism
17644 Metaphysical realism is committed to there being one ultimate true theory [Putnam]
7. Existence / D. Theories of Reality / 4. Anti-realism
17648 It is an illusion to think there could be one good scientific theory of reality [Putnam]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
17643 Shape is essential relative to 'statue', but not essential relative to 'clay' [Putnam]
12. Knowledge Sources / B. Perception / 4. Sense Data / b. Nature of sense-data
17642 The old view that sense data are independent of mind is quite dotty [Putnam]
26. Natural Theory / C. Causation / 8. Particular Causation / d. Selecting the cause
17645 An alien might think oxygen was the main cause of a forest fire [Putnam]