§4 - Problem of One and Many

Summary

A final problem that will occupy us in the pages to follow is the problem of the one and the many. In his final publication, Donald Davidson discussed a version of this problem as the problem of predication (see §16). The problem, in short, is how to account for the relation between a predicate, descriptor, or universal and the particular subjects that bear this predicate. This problem arises when we take up the Stranger's challenge in the Sophist (see Davidson 2005a, 80–1) and wonder how we can meaningfully make true and false statements, such as ‘Theaetetus sits’ or ‘Theaetetus flies’ (Sophist 260A-C), when, as in the case of false statements, there is no particular subject (Theaetetus) for whom the predicate (…is flying) applies. How can we meaningfully refer to or speak of that which does not exist? Davidson will chart the history of attempts to address this problem, beginning with Plato’s, and he ends by offering his own suggested solution (to be discussed in §16). Long before turning to Davidson, we will begin with Plato's account of the relationship between the concepts and categories through which we think about the world and the many particulars that are identified by way of these concepts and categories. What is this relationship? Do we again have another version of the problem of relations, this time the problem of the relation between the One category, universal, or form and the Many particulars that share in this One form? It is to these questions that we now turn.