Three Schools of Paraconsistency

A logic is said to be paraconsistent if it does not allow everything to follow from contradictory premises. There are several approaches to paraconsistency. This paper is concerned with several philosophical positions on paraconsistency. In particular, it concerns three ‘schools’ of paraconsistency: Australian, Belgian and Brazilian. The Belgian and Brazilian schools have raised some objections to the dialetheism of the Australian school. I argue that the Australian school of paraconsistency need not be closed down on the basis of the Belgian and Brazilian schools’ objections. In the appendix of the paper, I also argue that the Brazilian school’s view of logic is not coherent. But though logic has come a long way very recently, it has a longer way to go, both in whom it involves and what it investigates. There are, for instance, virtually no black researchers, and exceedingly few women are engaged; and for all the proclaimed rationality of modern humans and their institutions, logic touches comparatively little human practice. Differently, there remain many notions of considerable logical import, some of historical significance, of which we lack decent accounts or, sometimes, a clear appreciation. To the satisfactory elucidation of these, sociative logics can make essential contributions. Sylvan (1989) p. 133.