Combining Philosophers

All the ideas for Hermarchus, Richard Sorabji and Michael Hallett

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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]

12. Knowledge Sources / E. Direct Knowledge / 4. Memory

23304

The ancient Memorists said virtually all types of thinking could be done simply by memory [Sorabji]

23303

Stoics say true memory needs reflection and assent, but animals only have perceptual recognition [Sorabji]

25. Social Practice / F. Life Issues / 6. Animal Rights

6005	Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley]