Paraconsistent logics?
\textit{G. Priest} [``The logic of paradox'', J. Philos. Logic 8, 219-241 (1979; Zbl 0402.03012)] presents a paraconsistent logic, that is, one which does not collapse into all statements being provable but in which nevertheless ``\(A\vee \neg A\)'' is logically true and ``\(A \wedge\neg A\)'' is logically false. But, argues Slater in the present paper, in this system for the formula \(X\) to be ``logically false'' all that is required is that \(V(X)\leq 0\), and that is consistent with \(V(X)\geq 0\), so ``logically false'' does not exclude ``true'', and hence the negation operator ``\(\neg\)'' does not produce contradictories, as Priest pretends, but merely subcontraries; for contradictories, by definition, cannot be both true. To accept such a definition of course excludes the very cases Priest wants to consider. We can adhere to the definition only by denying that truth and falsity have the further properties Priest and other paraconsistentists ascribe to them. The debate must thus return to whether those ascriptions are justified; otherwise this paper begs the question against paraconsistency.
scientific article; zbMATH DE number 795338