This chapter explains in detail how Resemblance Nominalism answers the Many over One, what Resemblance Nominalism's theoretical apparatus is, and how it can meet several objections. In a nutshell, Resemblance Nominalism's answer to the Many over One issue is that a particular can have many properties by resembling different particulars (e.g., it is F by resembling the F-particulars, G by resembling the G-particulars, and so on). The chapter also explains how this idea can be extended to account for how a particular can be related in different ways, as when a is bigger than b and to the right of b. The issue of the identification of properties with classes is also discussed. Several features of the notion of resemblance are discussed, such as its objectivity, its primitiveness, the notion of degrees of resemblance, the adicity of resemblance, and the transtemporality of resemblance. The chapter also discusses the formal properties of resemblance: its reflexivity, symmetry, and non-transitivity. It is shown how these formal properties of resemblance, as well as the formal properties of exact resemblance, can be derived from more basic axioms of Resemblance Nominalism. The chapter also includes an explanation of how Resemblance Nominalism can accept facts or states of affairs, and discusses several objections to Resemblance Nominalism.
Keywords: Armstrong, axioms of resemblance, adicity of resemblance, classes, degrees of resemblance, facts, paraphrase, properties, states of affairs, transtemporality of resemblance