Abstract

In the course of. his philosophic career, Charles Peirce made repeated attempts to construct mathematical definitions of the commonsense or experimental notion of 'continuity'. In what I will label his Final Definition of Continuity, however, Peirce abandoned the attempt to achieve mathe­matical definition and assigned the analysis of continuity to an otherwise unnamed extra-mathematical science. In this paper, I identify the Final Definition, attempt to define its terms, and suggest that it belongs to Peirce's emergent semiotics of vagueness. I argue, further, that it marks the transformation of Peirce's synechism. Before the time of his Final Definition, Peirce adopted a theory of continuity as a foundational principle of metaphysics and assumed this principle might be formalized in a mathe­matics of continuity. After the Final Definition, Peirce abandoned his foundationalism in favor of what he called a critical common-sensism. This is the claim that philosophy (and with it, logic) derives its norms from the observation of actual cognitive practices and that continuity is a distinguishing mark of actual as opposed to merely possible or imagined practices.