Abstract

Timothy Williamson has offered a proof that any object that exists exists necessarily. Williamson’s conclusion depended crucially—as the Ontological Argument also depended—on the supposition that “exists” stands for a property of objects. According to Frege and Russell, ordinary grammar misleads us here. What we need in order to understand existence is not a first-level notion such as eat or growl but the second-level notion of the instantiation of first-level concepts. Among first-level concepts are individual concepts. Deploying these, the chapter shows how proper names can be fitted within the Russell/Frege account. It also offers a treatment of the problems presented by true sentences such as “Vulcan does not exist” or “Nausicaa does not exist”. These problems are best solved by deploying Frege’s idea that empty names depend for their sense upon the as if, and by reformulating in an entirely natural way the logical principles of existential generalization and universal instantiation.

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