engleski

In what sense is Kantian principle of contradiction non-classical?

On the ground of Kant's reformulation of the principle of contradiction, a non-classical logic KC and its extension KC+ are constructed. In KC and KC+, \neg (\phi \wedge \neg\phi), \phi \rightarrow (\neg\phi \rightarrow \psi), and \phi \vee \neg \phi are not valid due to specific changes in the meaning of connectives and quantifiers, although there is the explosion of derivable consequences from {;\phi, \neg\phi}; (the deduction theorem lacking). KC and KC+ are interpreted as fragments of an S5-based first-order modal logic M. The quantification in M is combined with a ``subject abstraction'' device, which excepts predicate letters from the scope of modal operators. Derivability is defined by an appropriate labelled tableau system rules. Informally, KC is mainly ontologically motivated (in contrast, for example, to Jaskowski's discussive logic), relativizing state of affairs with respect to conditions such as time.

Kant; paracompleteness; paraconsistency; principle of contradiction; square of oppositions; subject abstraction; labelled tableau

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