Combining Philosophers

All the ideas for Thrasymachus, Michael Hallett and James Joule

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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]

27. Natural Reality / A. Classical Physics / 2. Thermodynamics / b. Heat

20645

Heat is a state of vibration, not a substance [Joule]

20972

Joule showed that energy converts to heat, and heat to energy [Joule, by Papineau]

28. God / C. Attitudes to God / 3. Deism

1558	Clearly the gods ignore human affairs, or they would have given us justice [Thrasymachus]