Abstract

In his recent book Peirce and the Threat of Nominalism, Paul Forster presented how Peirce understood the nominalist scruple to individualise concepts for collections at the cost of denying properties of true continua. In that process Peirce showed some vibrant problems, as for example, the classic one of universals. Nonetheless that work is still incomplete; as long as that should be adequately related with what Peirce called his ‘scholastic realism’. Continuity is started by the theory of multitude and frees his analysis from any constraints of the nominalist theories of reality as integrated by incognizable things-in-themselves. His theory of multitude, instead, can be derived with mathematics: By drawing in the work of the ways of abstraction in diagrammatic reasoning made by Sun Jo Shin and in continuum theories by Cathy Legg I will show the device of diagrammatic reasoning as a plausible pragmatic tool to represent those continua and make sense of his scholastic realism. The analysis of continuity is a perfect example of how the method of diagrammatic reasoning helps unblock the road of philosophical inquiry and also helps to clarify other problems as, for example, the applicability of Mathematics. General concepts define continua, and, while the properties of true continua are not reducible to properties of the individuals they comprise, they are still intelligible and necessary to ground any science of inquiry.