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The number of logical values. (English) Zbl 1469.03010

Başkent, Can (ed.) et al., Graham Priest on dialetheism and paraconsistency. Cham: Springer. Outst. Contrib. Log. 18, 21-37 (2019).
Summary: We argue that formal logical systems are four-valued, these four values being determined by the four deductive outcomes: A without \(\sim\mathrm{A}\), \(\sim\mathrm{A}\) without A, neither A nor \(\sim\mathrm{A}\), and both A and \(\sim\mathrm{A}\). We further argue that such systems ought to be three-valued, as any contradiction, A and \(\sim\mathrm{A}\), should be removed by reconceptualisation of the concepts captured by the system. We follow by considering suitable conditions for the removal of the third value, neither A nor \(\sim\mathrm{A}\), yielding a classically valued system. We then consider what values are appropriate for the meta-theory, arguing that it should be three-valued, but reducible to the two classical values upon the decidability of the object system.
For the entire collection see [Zbl 1432.03005].

MSC:

03A05 Philosophical and critical aspects of logic and foundations
03B50 Many-valued logic
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