Varieties of Analytic Pragmatism

In his Locke Lectures Brandom proposes to extend what he calls the project of analysis to encompass various relationships between meaning and use. As the traditional project of analysis sought to clarify various logical relations between vocabularies—Russell’s theory of descriptions, for instance, showing how sentences containing definite descriptions can be rewritten, ostensibly without any change in meaning, as sentences containing only propositional functions and standard logical locutions—so Brandom’s extended project seeks to clarify various pragmatically mediated semantic relations between vocabularies. A vocabulary V1 is, for example, a pragmatic metavocabulary for another vocabulary V2 just if V1 enables one to say what one must be able to do to count as saying the things V2 enables one to say. The point of the exercise in both cases is to achieve what Brandom thinks of as algebraic understanding, “the sort of . . . understanding characteristic of mature mathematized sciences” (pp. 212-3). Because the pragmatist critique of the traditional project of analysis was precisely to deny that such understanding is appropriate to the case of natural language, the very idea of an analytic pragmatism is called into question by that critique. What I want to try to do here is to clarify the prospects for Brandom’s project, or at least something in the vicinity of that project, through a comparison of it with what I will suggest we can think of as Kant’s analytic pragmatism as developed by Peirce. Much as Brandom situates himself relative to the standard project of analysis as it was challenged by the later Wittgenstein’s pragmatism, so Kant situates himself relative to the dogmatism of Descartes’ new algebra as challenged, so he thought, by Hume’s skeptical doubts. Because what is at issue in Kant’s case would seem to be precisely the sort of algebraic understanding that Brandom esteems as “the very best sort of understanding to have” (p. 214), it is worth briefly rehearsing both Descartes’ achievement in mathematics and the skeptical challenge it engendered before turning to the version of analytic pragmatism Kant developed in response to that challenge. Before Descartes the paradigm of mathematics was Euclidean demonstration, a practice in which the task is to find, that is, to construct, a diagram that provides a path from one’s starting point to some desired conclusion. Because in this form of mathematics one achieves results by reasoning through a diagram, seeing it now this way and now that in an ordered progression of steps, the diagram is itself the locus of proof in this form of mathematics. Having an adequate diagram just is having a proof in ancient mathematics. Descartes’ signal achievement was to show how to dispense with diagrams in mathematics, bringing thereby a radically new level and sort of clarity to the subject. By way of illustration, consider the following problem: we are given a square AD and line BN; the task is to prolong the side AC to E so that EF, laid off from E on EB, is equal to NB. Heraclides’ solution, as given in Pappus’s Collection and reproduced in Descartes’ Geometry, is this diagram: