 In the years immediately prior to the Peirce lectures, Royce’s metaphysical views had been sharply criticized on the grounds that his concept of the Absolute had made individuals unreal, subsumed by the whole (Howison in Royce 1897, 98–9). Royce countered the criticism, by arguing that the Absolute was a system that was composed of real individuals (2000, 297, 314–5). Royce, however, was unable to provide a compelling formal argument for the possibility of a system in which the parts of a whole could also be distinct, a view rejected with a well-known argument of F. H. Bradley (Royce 1959, 477–485). Peirce’s 1898 lecture included a case for his then-current conception of continuity (he proposed several) in which the unified whole was a logical consequence of a universe of discrete individuals (Moore 2007), that is, where “we have now reached a multitude so vast that the individuals of such a collection melt into one another and lose their distinct identities” (Peirce 1898 [1992, 159]). In making his case, Peirce called on resources from Boole, Cantor, Dedekind and Kempe among others. By 1900, Royce offered his own version of continuity, the concept of an infinite, self-representative system. Published as a lengthy “supplementary essay” to The World and Individual, First Series, and framed as an answer to Bradley, Royce aimed to provide a proof that a single infinite system could contain multitudes of distinct individuals.