Peirce’s Topical Continuum: A “Thicker” Theory

Although Peirce frequently insisted that continuity was a core component of his philosophical thought, his conception of it evolved considerably during his lifetime, culminating in a theory grounded primarily in topical geometry. Two manuscripts, one of which has never before been published, reveal that his formulation of this approach was both earlier and more thorough than most scholars seem to have realized. Combining these and other relevant texts with the better-known passages highlights a key ontological distinction: a collection is bottom-up, such that the parts are real and the whole is an ens rationis, while a continuum is top-down, such that the whole is real and the parts are entia rationis. Accordingly, five properties are jointly necessary and sufficient for Peirce’s topical continuum: rationality, divisibility, homogeneity, contiguity, and inexhaustibility.