Combining Texts

All the ideas for 'Mathematics and Indispensibility', 'Actualism and Thisness' and 'Introduction to Zermelo's 1930 paper'

expand these ideas     |    start again     |     specify just one area for these texts

---

6 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]

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 / 11. Ontological Commitment / e. Ontological commitment problems

9558	All scientific tests will verify mathematics, so it is a background, not something being tested [Sober]

9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity

16463

Adams says actual things have haecceities, but not things that only might exist [Adams,RM, by Stalnaker]