Is Logic Demarcated by its Expressive Role?

Michael Dummett and Robert Brandom, though sharing a good deal in their approaches to language and to logic, also differ markedly in their respective views. Although that is not an observation that is likely to strain one’s capacity for philosophical insight, the differences are worth noting and understanding. Brandom distinguishes logic by means of its expressive role. Logic plays a role in enabling the expression of the inferential commitments of any practice as claimings. Or in Brandomese: since inferential practice is PP-necessary for any autonomous discursive practice, the role of logic is in articulating those practices which are necessarily involved in being able to say anything. Logical vocabulary is deployed by practices that are algorithmically elaborated from practices that are PV-necessary for deploying every autonomous vocabulary and suffices to specify those PV-necessary practices. In the earlier work the role of logic is linked with the project of making explicit, in the later work it is linked with the project of analytic pragmatism. In Making it Explicit logic enables the expression of inferential commitments as claimings and thus as subject to the business of asking for and giving reasons. It thus exposes those commitments to the glare of reflective rationality. In the later Between Saying and Doing the interest shifts to resolving what Brandom calls the logicist’s dilemma, namely, explaining logical vocabulary in a way that ensures it does not contribute any significant content to the analyses in which it is caught up—that it is semantically transparent—while also ensuring that it is analytically efficacious—it must make a distinctive contribution to the process of analysis. The resolution is that logical vocabulary adds nothing to the, that is, any, target vocabulary because the capacities involved in deploying it emerge by algorithmic elaboration from the capacities required to deploy any vocabulary. It is analytically efficacious because it fulfils an expressive function enabling one to talk about the analytic articulation of any vocabulary and this—the ability to articulate what follows from what—is an essential part of being able to find expressions in one vocabulary which express the same contents as expressions in another. Though there are interesting differences between the accounts the upshot is similar: in order to perform its expressive function logic is required to be semantically transparent; however logic still has a purpose because that expressive role feeds into the business of analysis or the business of reflecting on one’s inferential practice. Michael Dummett poses a different, though in some respects similar, dilemma. His focus is not so much logical vocabulary as logical inference. He notes that our attempts to justify deduction pull in two directions: in an effort to see deductive inference as valid we tend to think that, in some sense, whatever is required to recognise the conclusion as true is already accomplished in recognising the premises as true; conversely we are tempted to think that there must be some gap here else we will have no way to account for the epistemic usefulness of deduction. As in the Brandomian dilemma the tension arises from both wanting to see logic as, in a sense, vacuous and as having a purpose. But unlike Brandom’s way of dealing with the tension, which promises complete resolution, Dummett sees the tension as irresovable: we can only conclude that deductive inference forces us to admit a gap between the truth of a sentence and its capacity to be recognised as such (at least by direct—non-inferential means). So on Dummett’s view, the admission of deductive inference into a practice necessitates a conception of contents expressible in that practice which would not have been required but for deductive inference. Thus whereas Brandom sees logic as being semantically transparent Dummett thinks that deductive inference places a metaphysical demand on content. The demand is metaphysical since the reconception of content derives from the very nature of deductive inference and involves construing content in terms that tend to be favoured by realists, though it doesn’t demand a fully realist reconstrual of content. I want to spend some time here simply exploring logic in the framework provided by these two dilemmas.