Combining Philosophers

All the ideas for Brand Blanshard, Michael Hallett and Nicholas Bourbaki

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7 ideas

2. Reason / A. Nature of Reason / 6. Coherence
2764 Full coherence might involve consistency and mutual entailment of all propositions [Blanshard, by Dancy,J]
3. Truth / D. Coherence Truth / 1. Coherence Truth
19080 Coherence tests for truth without implying correspondence, so truth is not correspondence [Blanshard, by Young,JO]
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]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
10190 From the axiomatic point of view, mathematics is a storehouse of abstract structures [Bourbaki]