Sharing a property

The Socratic discussion in the Hippias Major, 300-303, is not a passing comment on plural reference; it is a theory of plural subjecthood. It has escaped attention because it is a small part of a larger complex argument on the topic of which pleasures are fine. Socrates’s theory is further concealed by the fact that it is presented as an antithesis between Hippias and himself, whereas in fact, Hippias’s position becomes part of Socrates’s theory. I begin by examining Hippias’s position, and subsequently Socrates’ criticism of it. I then turn to Socrates’s further proposal, and the development of a theory of plural subjects that incorporates elements of Hippias’s position, and Socrates’s own. At the end, I address the question of the ontology of plural subjects. I argue that the key to sharing a property between subjects is not in the way that the plural terms refer to these subjects, or in any decomposition of the commonly owned property instance into parts distributed to these subjects. Rather, I follow Socrates in finding the common ownership of a property instance central to plural subjecthood, and develop an account of how this metaphysical function can be performed by the plural subjects without threatening their distinctness and plurality.