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Ideas for 'What is Logic?st1=Ian Hacking', 'The Principles of Chemistry' and 'What is Cantor's Continuum Problem?'

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5 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

8679	We perceive the objects of set theory, just as we perceive with our senses [Gödel]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L

9942	Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam]