Combining Texts

All the ideas for 'Letters to Antoine Arnauld', 'Introduction to Zermelo's 1930 paper' and 'Go Figure: a Path through Fictionalism'

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7 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]

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism

21963

It is possible that an omnipotent God might make one and two fail to equal three [Descartes]

7. Existence / D. Theories of Reality / 7. Fictionalism

19494

Fictionalism allows that simulated beliefs may be tracking real facts [Yablo]

10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / b. Worlds as fictions

19493

Governing possible worlds theory is the fiction that if something is possible, it happens in a world [Yablo]