Combining Texts

All the ideas for 'On Multiplying Entities', 'talk' and 'Introduction to Zermelo's 1930 paper'

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9 ideas

2. Reason / B. Laws of Thought / 6. Ockham's Razor

8207	The quest for simplicity drove scientists to posit new entities, such as molecules in gases [Quine]

8208	In arithmetic, ratios, negatives, irrationals and imaginaries were created in order to generalise [Quine]

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]

7. Existence / B. Change in Existence / 4. Events / c. Reduction of events

8205	Explaining events just by bodies can't explain two events identical in space-time [Quine]

10. Modality / A. Necessity / 11. Denial of Necessity

8206	Necessity could be just generalisation over classes, or (maybe) quantifying over possibilia [Quine]

14. Science / C. Induction / 5. Paradoxes of Induction / b. Raven paradox

7006	Observing irrelevant items supports both 'all x are y' and 'all x are non-y', revealing its absurdity [Schofield,J]