Combining Philosophers

All the ideas for Eucleides, Michael Hallett and Elliott Sober

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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]

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]

19. Language / B. Reference / 1. Reference theories

1757	The Electra: she knows this man, but not that he is her brother [Eucleides, by Diog. Laertius]

22. Metaethics / C. The Good / 1. Goodness / b. Types of good

3028	The chief good is unity, sometimes seen as prudence, or God, or intellect [Eucleides]