Combining Philosophers

All the ideas for Saunders MacLane, Geoffrey Hellman and Nicolas Malebranche

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9 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC could contain a contradiction, and it can never prove its own consistency [MacLane]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralism is now common, studying relations, with no regard for what the objects might be [Hellman]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
Maybe mathematical objects only have structural roles, and no intrinsic nature [Hellman]
8. Modes of Existence / B. Properties / 8. Properties as Modes
Everything that exists is either a being, or some mode of a being [Malebranche]
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
In a true cause we see a necessary connection [Malebranche]
A true cause must involve a necessary connection between cause and effect [Malebranche]