This post is, in a way, against logical pluralism. But the form of monism about the consequence relation I want to put forward is unlike existing, or at least the most visible, contenders. It is inspired by Colin R. Caret and Ole Hjortland's first chapter to the new volume Foundations of Logical Consequence. (The chapter has just appeared on Academia.edu.)
Some philosophers, such as Prawitz and Dummett above, have argued that there is one correct logic —in their case, intuitionistic logic. More frequently, philosophers have taken classical logic to be the one true logic (e.g.Quine 1986; Burgess 1982; Williamson 1984). Others strive for an inclusive position on which there are several equally good candidates for the extension of the consequence relation, a view now known as logical pluralism.
This framework, however, is not entirely unproblematic, since it appears that if the diﬀerence in logic only arisesas a result of a diﬀerence in language, then disagreements about logic (andabout logical consequence) are merely verbal disputes. Quine’s (1986) meaning-variance argument makes heavy weather of the fact that non-classical logicians only seemingly disagree with the classical logician. In reality, Quine claims, they only ‘change the subject’.
What I want to suggest is that we go along with Quine's point here (at least in the cases of logical systems whose formulae we can make sense of - a requirement, by the way, in need of investigation) and draw the to my mind natural consequence that these alternative logical systems each give partial specifications of the consequence relation. Perhaps very partial, compared to the space of possible propositions and their inferential properties, if not to the much smaller space of possible propositions we humans employ.
On this view, there is in a sense one true logic, but to specify it we would need to conjoin (some of, perhaps many of) the logics we have, and probably add very much more we haven't dreamt of.
This seems like a natural view to me, which almost jumps out of the Caret-Hjortland chapter. If anyone knows of any antecedents to this sort of view I'd be very interested to hear about them. Objections are very welcome too.