Relations as Plural Predications in Plato
Plato’s core metaphysical intuition is that transcendent properties—the Forms— are responsible for things being qualified in the way they are. These transcendent properties are universal in the sense that many individuals at a time ‘partake’ in each of the transcendent properties. Partaking in any one Form qualifies the partaking individual with the property that Form is; thus, an individual is courageous by partaking in the Form of Courage. The intuition is that the property of courageousness comes to qualify an individual in virtue of the individual partaking in the Form (however ‘partaking’ is interpreted ontologically). Since each Form stands for a single property (it is monoeidic), partaking in a Form qualifies the individual with that property.
An ontological theory needs to account for, not only qualified individuals, but also for related individuals. Related individuals have been a thorny issue for Plato’s Theory of Forms, because the theory does not prima facie seem to be designed to offer an ontology of related individuals, since, strikingly, it does not contain any relational Forms. Nevertheless, Plato was aware of the need for an explanation, and so did attempt to account for related individuals through his Theory of Forms. What I aim to show in the present paper is that, in fact, his account of related individuals is a unique and philosophically deeply insightful account, despite the fact that it has evaded recognition in the history of metaphysics.
Plato’s solution could not have been the introduction of relational Forms in his ontology. This is because partaking in a Form qualifies an individual only with the property the Form stands for. But asymmetric relations, such as the mother- daughter relation, involve the qualification of two (or more) individuals with
different properties each. There could be no Form partaking in which would qualify different individuals with different properties, for instance, no ‘maternal relational’ Form, such that if two individuals partook of it, one individual would be qualified as mother, and the other as offspring.
I will argue that Plato solves the problem of related individuals in his Theory of Forms by using his theory of plural-partaking in Forms, which he developed in one of his early dialogues, the Hippias Major. On his account of plural- predication, two or more individuals can partake in a Form as plural-subjects, and come to be jointly qualified by a single instance of the property of the Form; for instance, Michael and George, acting jointly, are courageous. Remarkably Plato was insightful enough to see and show in his theory that this does not make Michael courageous, or George courageous, but only both of them together courageous. Plato will exploit plural-partaking to explain how related objects acquire their relational qualifications, rather than introduce relations as additional entities between individuals. The related individuals share a monadic property instance in symmetric cases, or a pair of property instances in asymmetric cases. Neither the shared property nor the shared pair of properties are relational bridges between the plural-subjects, but a qualification of the subjects like any monadic qualification of an object. The subjects are conjoined in sharing this instance of a property, which is attained by the joint-partaking in the Form (dictated by the relativizing context, as in being equal to, or greater than, etc.). The joint partaking does not turn the subjects into one, but retains the plurality of the subjects. Rather than requiring the oneness of the subjects, plural-partaking furnishes the sharing of the instance of the property between the subjects, which perform jointly the metaphysical function of partaking. We shall first turn to Plato’s theory of plural subjects and plural-partaking in Forms, and then come to examine (symmetrically and asymmetrically) related individuals through pluralpartaking.