H. Slater famously argued that there are no paraconsistent logics, inasmuch as paraconsistent negation is not a proper negation. Such a vivid attack has been variously replied, including an appropriate reply by J.Y. Beziau, where the author resorted to the same conceptual framework as Slater’s argument: the theory of opposition. Slater argues that, in order to overcome the view that everything follows from an inconsistent set of premises, some paraconsistentists unjustifiably neglect a crucial property of logical negation: to ban contradictions. The point is to shed new light upon the concepts Slater used in his argument to depict paraconsistency.
The impact of logical pluralism on the development of modern science still is disputable but there are studies in progress allowing to make this issue more popular. It would be demonstrated that some new aspects of those studies are connected with the pluralistic approach to the well-known results in mathematical logic, speciﬁcally in the theory of algebraic systems.