Combining Philosophers
Ideas for Anaxarchus, Barbara Vetter and Ian Hacking
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6 ideas
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL
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'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking]
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Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking]
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Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking]
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4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / c. System D
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Deontic modalities are 'ought-to-be', for sentences, and 'ought-to-do' for predicates [Vetter]
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4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
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S5 is undesirable, as it prevents necessities from having contingent grounds [Vetter]
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4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
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The Barcan formula endorses either merely possible things, or makes the unactualised impossible [Vetter]
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