Philosophy Lexicon of Arguments

Multi-valued logic: a logic that assumes more than the two classical truth values true and false. There are trivalent logics with possibility or indeterminacy as a third value. For tetravalent logics there are e.g. ¼ or ¾ as additional values that introduce a gradation in the rating. In the case of infinite-valued logics, the truth values can be interpreted as probability values.
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II 144
Three-valued logic/Kleene/Field: Def correct/Kleene: an assertion is correct only if it has the highest of the three truth values. Field: Problem: not all of Tarski’s biconditionals remain correct. Even E.g. "If A, then A" is not generally assertible. Therefore, the Kleene logic is weak. - "If A then A" is not generally assertible -> Restall: "n-fold jump" ... + ...
II 145
Material conditional/Three-valued logic/Kleene/Field: the materal conditional is a conditional that has one of the two highest truth values. - So the Curry paradox is impossible: "If this statement is true, then p".

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie II
H. Field
Truth and the Absence of Fact Oxford New York 2001

H. Field
Science without numbers Princeton New Jersey 1980

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Ed. Martin Schulz, access date 2017-05-23