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Valuations, combinatorial vs ‘realizable’

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This is request for references on an issue in very elementary logic! To set the scene, suppose we take the atoms of a formal language for propositional logic to be interpreted. Yes, yes, I know that different authors take different official lines about how to treat their ‘P’s and ‘Q’s — hence the ‘suppose’! We are considering the approach where a formal language is indeed taken to be a language, with meaningful wffs, so inferences in the language really are genuine inferences, etc. Perhaps then the glossary for a particular PL language reads P: Water is H2O, Q: Jill is married, R: Jill is single. So now consider, then, writing down a truth-table for a wff built from these atoms, as it might be ‘(P ∧ (Q ∨ R))’. We of course standardly consider all combinatorially possible assignments of values to the three propositional atoms, giving us an eight-line table. But we might now remark that (according to most) there is no possible world at which ‘P’ is false. And (according to. . .

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News source: Logic Matters

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