Carnap’s Tolerance, Language Change and Logical Pluralism

In this paper, I distinguish different kinds of pluralism about logical consequence. In particular, I distinguish the pluralism about logic arising from Carnap’s Principle of Tolerance from a pluralism which maintains that there are different, equally “good” logical consequence relations on the one language. I will argue that this second form of pluralism does more justice to the contemporary state of logical theory and practice than does Carnap’s more moderate pluralism. 1 Pluralism about Logical Consequence With JC Beall, I have argued for and defended a very particular account of logical pluralism [5, 6]. We take it that the notion of logical consequence is irreducibly plural in its application. That is, we take it that there are at least two distinct relations of logical consequence — and not simply two distinct relations in intension, but two distinct relations in extension. We take it that there are arguments which are valid according to one logic, and invalid according to another, and that there is no further fact of the matter as to whether the argument is really valid. For the sake of this paper let me be quite specific. I will take two particular argument forms. First, the argument form I will call explosion: From A∧ ∼A to infer B. This argument form is valid classically, and invalid relevantly. Similarly, the argument form of disjunctive syllogism: From A∨ B and ∼A to infer B is valid classically, and invalid relevantly [8]. As a pluralist about logical consequence, I take it that there is no further fact of the matter as to whether explosion, or disjunctive syllogism are really valid. For me, that question makes no more sense than to ask if a function on the real line is really smooth, without ∗Thanks to Peter Simons for asking the question “Isn’t your pluralism just Carnap’s tolerance?” I hope that I have managed to explain why it isn’t. Many thanks to JC Beall for discussion on the topics raised in this paper. Although we have written extensively on pluralism together and I have benefited greatly from working with him, the paper expresses my opinions, not his. Thanks also to Martin Allen, Robert Anderson, Nuel Belnap, Daniel Nolan, Koji Tanaka, and audiences at the Center for Philosophy of Science at the University of Pittsburgh and the Philosophy Departments at the Universites of Toronto and Queensland for comments on this paper. This research has been supported by the Australian Research Council, through Large Grant No. A00000348, and by Koji Tanaka who relieved me of some of my teaching duties for Semester 2, 2000.