Combining Philosophers

All the ideas for Rescher,N/Oppenheim,P, Gregory Vlastos and Michael Hallett

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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]

9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts

12887

A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim]

25. Social Practice / D. Justice / 3. Punishment / b. Retribution for crime

1658	In early Greece the word for punishment was also the word for vengeance [Vlastos]