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Single Idea 10163
[filed under theme 4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
]
Full Idea
At the age of 19 Saul Kripke published a completeness proof of propositional modal logic.
Gist of Idea
Propositional modal logic has been proved to be complete
Source
report of Saul A. Kripke (A Completeness Theorem in Modal Logic [1959]) by Feferman / Feferman - Alfred Tarski: life and logic Int V
Book Ref
Feferman,S/Feferman,A.B.: 'Alfred Tarski: life and logic' [CUP 2008], p.286
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
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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Quantified modal logic collapses if essence is withdrawn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
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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]
|