Paraconsistent Logics!

March 1997

“Paraconsistent Logics!,” Bulletin of the Section of Logic of the Polish Academy of Sciences 26 (1997) 156–163.

I respond to an interesting argument of Hartley Slater to the effect that there is no such thing as paraconsistent logic. Slater argues that since paraconsistent logics involve interpreting a sentence and its negation as both true at points in a model structure, it is not really negation that is being modelled, since negation is meant to be a contradictory forming operator. I sketch how different paraconsistentists can respond to his argument, and I then defend my own response, that although contradictions are indeed never true (and cannot be true) it does not follow that a semantics ought not evaluate them as true in certain models.

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