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4. Formal Logic / D. Modal Logic ML / 1. Modal Logic

[general ideas about the nature of modal logic]

18 ideas
Modal Square 1: □P and ◊P are 'contraries' of □P and ◊P [Fitting/Mendelsohn on Aristotle]
Modal Square 2: □P and ◊P are 'subcontraries' of □P and ◊P [Fitting/Mendelsohn on Aristotle]
Modal Square 3: □P and ◊P are 'contradictories' of □P and ◊P [Fitting/Mendelsohn on Aristotle]
Modal Square 4: □P and ◊P are 'contradictories' of □P and ◊P [Fitting/Mendelsohn on Aristotle]
Modal Square 5: □P and ◊P are 'subalternatives' of □P and ◊P [Fitting/Mendelsohn on Aristotle]
Modal Square 6: □P and ◊P are 'subalternatives' of □P and ◊P [Fitting/Mendelsohn on Aristotle]
Quantified modal logic collapses if essence is withdrawn [Quine]
Maybe we can quantify modally if the objects are intensional, but it seems unlikely [Quine]
It was realised that possible worlds covered all modal logics, if they had a structure [Dummett]
Propositional modal logic has been proved to be complete [Feferman/Feferman on Kripke]
Possible worlds allowed the application of set-theoretic models to modal logic [Kripke]
Kripke's modal semantics presupposes certain facts about possible worlds [Zalta]
The interest of quantified modal logic is its metaphysical necessity and essentialism [Soames]
Modal operators are usually treated as quantifiers [Shapiro]
Modal logic gives an account of metalogical possibility, not metaphysical possibility [Burgess/Rosen]
Quine says quantified modal logic creates nonsense, bad ontology, and false essentialism [Melia]
First-order predicate calculus is extensional logic, but quantified modal logic is intensional (hence dubious) [Melia]
Simple Quantified Modal Logc doesn't work, because the Converse Barcan is a theorem [Merricks]