Combining Philosophers

Ideas for Herodotus, Saunders MacLane and Ian Hacking

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4 ideas

4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL

13833

'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking]

13834

Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking]

13835

Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

18189

ZFC could contain a contradiction, and it can never prove its own consistency [MacLane]