Combining Philosophers

All the ideas for Christian Wolff, Michael Hallett and W Kneale / M Kneale

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7 ideas

2. Reason / B. Laws of Thought / 2. Sufficient Reason
18241 Sufficient reason is implied by contradiction, of an insufficient possible which exists [Wolff, by Korsgaard]
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 / 4. Axioms for Sets / f. Axiom of Infinity V
10051 The axiom of infinity is not a truth of logic, and its adoption is an abandonment of logicism [Kneale,W and 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]
28. God / A. Divine Nature / 6. Divine Morality / b. Euthyphro question
18242 Confucius shows that ethics can rest on reason, rather than on revelation [Wolff, by Korsgaard]