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Single Idea 9728

[filed under theme 4. Formal Logic / D. Modal Logic ML / 1. Modal Logic ]

Full Idea

Modal Square of Opposition 1: 'It is necessary that P' and 'It is not possible that not P' are the contraries (not both true) of 'It is necessary that not P' and 'It is not possible that P'.

Gist of Idea

Modal Square 1: □P and ¬◊¬P are 'contraries' of □¬P and ¬◊P

Source

report of Aristotle (On Interpretation [c.330 BCE], Ch.12a) by M Fitting/R Mendelsohn - First-Order Modal Logic 1.4

Book Ref

Fitting,M/Mendelsohn,R: 'First-Order Modal Logic' [Synthese 1998], p.7

The 18 ideas with the same theme [general ideas about the nature of modal logic]:

9728 Modal Square 1: □P and ¬◊¬P are 'contraries' of □¬P and ¬◊P [Aristotle, by Fitting/Mendelsohn]
9729 Modal Square 2: ¬□¬P and ◊P are 'subcontraries' of ¬□P and ◊¬P [Aristotle, by Fitting/Mendelsohn]
9730 Modal Square 3: □P and ¬◊¬P are 'contradictories' of ¬□P and ◊¬P [Aristotle, by Fitting/Mendelsohn]
9731 Modal Square 4: □¬P and ¬◊P are 'contradictories' of ¬□¬P and ◊P [Aristotle, by Fitting/Mendelsohn]
9732 Modal Square 5: □P and ¬◊¬P are 'subalternatives' of ¬□¬P and ◊P [Aristotle, by Fitting/Mendelsohn]
9733 Modal Square 6: □¬P and ¬◊P are 'subalternatives' of ¬□P and ◊¬P [Aristotle, by Fitting/Mendelsohn]
5745 Quine says quantified modal logic creates nonsense, bad ontology, and false essentialism [Melia on Quine]
13591 Quantified modal logic collapses if essence is withdrawn [Quine]
10928 Maybe we can quantify modally if the objects are intensional, but it seems unlikely [Quine]
16951 It was realised that possible worlds covered all modal logics, if they had a structure [Dummett]
10163 Propositional modal logic has been proved to be complete [Kripke, by Feferman/Feferman]
10559 Kripke's modal semantics presupposes certain facts about possible worlds [Kripke, by Zalta]
16985 Possible worlds allowed the application of set-theoretic models to modal logic [Kripke]
15163 The interest of quantified modal logic is its metaphysical necessity and essentialism [Soames]
10206 Modal operators are usually treated as quantifiers [Shapiro]
9924 Modal logic gives an account of metalogical possibility, not metaphysical possibility [Burgess/Rosen]
5744 First-order predicate calculus is extensional logic, but quantified modal logic is intensional (hence dubious) [Melia]
19209 Simple Quantified Modal Logc doesn't work, because the Converse Barcan is a theorem [Merricks]