Related Individuals in Plato’s Theory of Forms
Plato’s Theory of Forms is designed to offer the metaphysics of predication by showing what it is for an object to be qualified in any way. An object is f by partaking in the Form of F-ness:
Is there or is there not an absolute justice? Assuredly there is. And an absolute beauty and absolute good? Of course. (Phaedo 65d4-8)
They agreed that each of the abstract qualities exists and that other things which participate in these get their names from them. (Phaedo 102a10-b)
The individuals get their names from them, but also they become like the Form in which they partake:
... if there is anything beautiful besides Beauty itself, it is beautiful for no other reason
than that it shares in that Beauty____nothing else makes it beautiful other than the
presence of, or the sharing in, or however you may describe its relationship to that Beauty we mentioned, for I will not insist on the precise nature of the relationship, but that all things are made beautiful by Beauty. (Phaedo 100c4-d8)
Forms are transcendent entities, which, notoriously, makes partaking in them a theoretically challenging problem for the theory. But this will not be our concern here. It is a different aspect of the Forms that is of direct interest in our present inquiry, namely, what it is that a Form can offer to an individual that partakes in it, however the partaking is achieved.
Forms are of a single kind, monoeidic. This means that when an individual partakes of a Form F, all that the Form can do for that individual is to qualify it as an f. Plato is explicit in stating that Forms are monoeidic, each standing for a single kind:
Can the Equal itself, the Beautiful itself, each thing in itself, the real, ever be affected by any change whatever? Or does each of them that really is, being uniform [monoeides] by itself, remain the same and never in any way tolerate any change whatever? (Phaedo 78d3-7)
This does not mean that a Form has no further properties. It means that there is a single property that a Form stands for, which is the only property it can endow to its partakers.
The same is true when plural-subjects partake together in a Form; the partaking endows the subjects with a single instance, of a single attribute—the one the Form stands for—which belongs jointly to these subjects together. Thus, an individual or individuals partaking in a Form will be qualified with the kind that Form is, namely the single property that constitutes the Form, for example, Justice, Beauty, Goodness, Heat, Smallness, etc. Joint ownership of an instance of a property is like joint ownership of a book—there is only one book but more than one owner of it.
There are two problems that arise for a theory of related individuals based on the ontology of the Theory of Forms. The first is that qualifying a partaker does not relate the partaker to anything; and the second is that each Form can qualify its partaker(s) with a single qualification, while asymmetric relations qualify their relata with different qualifications.
I find the monoeidic (uni-form) character of the Forms to be the determining factor for whatever treatment of asymmetrically related objects can be given in Plato’s ontology. This is so because the monoeidic nature of the Forms prevents the Forms from standing for asymmetric relations. Asymmetric relations qualify their relata with different qualifications. For instance, the asymmetric teacher- student relation takes individuals as relata, and qualifies one with the role of the teacher and the other with the role of their student. There can be no Form in Plato’s Theory of Forms which could do the same for the particulars that partook in the Form. There can be a Form of Teacher, or a Form of Student; but no individuals that partook in either Form could be thereby qualified with the roles of teacher to student. Furthermore, although some individuals could be qualified as students by partaking in the Form of Student, and others as teachers by partaking in the Form of Teacher, they would not be thereby related to each other as teachers to their students.
Generally, partaking in Forms qualifies but does not relate partakers; and the monoeidic character of Forms results in there being no Form in Plato’s theory which would qualify its partakers with different qualifications. This, then, gives rise to the question of how Plato could explain the ontology of related individuals, and even more challenging, the ontology of asymmetrically related individuals in the Theory of Forms, if he has only qualifying (non-relational) monoeidic Forms at his disposal.
I will argue that Plato does address the question of the ontology of symmetrically and asymmetrically related individuals, and that he resolves this problem, not by introducing sui generis relational Forms, but uniquely, via plural- predication in monadic Forms and in forms of Opposites. Plato designs a special version of plural-partaking in Forms to address the problem of symmetrically and asymmetrically related objects. We shall first look at Plato’s description of asymmetrically related objects, because both ontological problems of asymmetry and of relatedness arise with respect to them.
Plato discusses the ontology of asymmetric relations in his dialogue the Phaedo. He offers examples of comparative relatives. He considers individuals that differ between them by being bigger or smaller than one another:
... it is through Largeness that large things are large and larger things are larger, and... smaller things are made small by Smallness. (Phaedo 100e5-6)
According to the Theory of Forms, if an individual is qualified as large, it is so qualified on account of its partaking in the Form of Largeness, and correspondingly with small individuals partaking in the Form of Smallness. This is in line with the monoeidic character of the Forms. (We assume that an individual that is larger than another is, by that token, also large, at least in that context.)
Proceeding, Plato examines the relativity of asymmetrically related objects. He begins with the following problem:
When you say that Simmias is larger than Socrates and smaller than Phaedo, do you not say that there is in Simmias largeness and smallness? (Phaedo 102b ff.)
This raises for Plato the problem of how something large can be small, since they are antithetical qualifications. The solution he finds is to identify (for the first time in the history of metaphysics) the contingency and so non-intrinsicness of some of the properties that qualify an individual:
... do you agree that the words of the statement ‘Simmias is larger than Socrates’ do not express the truth of the matter? It is not, surely, the nature of Simmias to be larger than Socrates because he is Simmias but because of the largeness he happens to have? Nor is he larger than Socrates because Socrates is Socrates, but because Socrates has smallness compared with [pros] the largeness of the other?
Nor is he [Simmias] smaller than Phaedo because Phaedo is Phaedo, but because Phaedo has largeness compared with the smallness of Simmias?
—That is so. (Phaedo 102b8-c9).
What this explanation introduces is a distinction between what it is to be a particular individual, say Simmias, and the qualifications Simmias may happen to have which are not aspects of being that individual, of his nature. It is not in the nature of Simmias to be larger than Socrates, but this is only a contingent feature of Simmias. Plato introduces the following criterion for distinguishing between contingent and non-contingent qualifications: ‘I admit and endure smallness and still remain the same person and am this small man’. (Phaedo 102e2-5). This criterion licenses the counterfactual test for the distinction between an individual’s nature and its contingent properties—for instance, if I was qualified as large, I would be the same person I am. Plato does not offer further explanation in the text for us to be able to tell whether he believes that the largeness of Simmias is not an aspect of the nature of Simmias (of being a person), or whether he believes that largeness is not an aspect of his identity (of being Simmias)— there are indications in Plato’s language for both. These metaphysical distinctions can be studied in the more precise treatment of the conceptions of ‘essential nature’ and of ‘individual’ in Aristotle’s system.
Plato detects and addresses the relativity of contingent asymmetric qualifications, which is due to the circumstantial conditions of the related individuals:
Then Simmias is called small and large, being between the two [Phaedo and Socrates], presenting his smallness to be overcome by the largeness of one [Phaedo], and his largeness to overcome the shortness of the other [Socrates].
(Phaedo 102c10-d2, my emphasis)
Having established that largeness and smallness are not in the nature of each of the compared individuals, Plato turns to the context in which these qualifications emerge. Each individual is qualified as large or small, not in itself, but only in comparison to another individual. Thus, Simmias is larger than Socrates and smaller than Phaedo because it so happens. Simmias has largeness, not in himself, as Simmias, but in comparison to Socrates’ smallness, and has smallness in comparison to Phaedo’s largeness.
Plato even becomes graphic in his description of the contingency and relativity of the comparison in this context:
One of two things must take place: either the largeness in us flees, or withdraws when its
opposite, smallness, advances toward it, or it is destroyed by the opposites’ approach____either
it goes away or is destroyed when that happens. (Phaedo 102d-103a, my emphasis)
What is significant for our own purposes in this description is that the partaking in Largeness or Smallness is temporary and contextual. Simmias’ largeness surpasses the smallness of Socrates, while his smallness is surpassed by the largeness of Phaedo. What Plato is emphasizing is that the presence of largeness or smallness in an individual is circumstantial, and dictated not by the individual’s nature, but by the context. The contextuality of the relative qualifications is expressed in Plato’s theory, not in a relation between Opposite Forms, but in the joint-partaking by the two individuals (which is developed in what follows).
-  This also introduces the comparison of the sizes of the individuals. But Plato does not generalizethis into a metaphysics of quantity, in the way that Aristotle will, as he is focusing on Forms ofOpposites. Forms of Quantities, such as so much weight, or such and such a height would raiseproblems of their own in the theory of Forms, which Plato does not seem willing to introduce. Anindication of this is that he immediately says, after the quoted sentence: “And he [Socrates] laughedand said, ‘I seem to be speaking like a legal document, but it really is very much as I say’.” The claimof legal fastidiousness is only to indicate that he was already being overly meticulous in hisontological description. Nevertheless, it may be that quantitative qualifications are unavoidable ina complete account of the theory. More generally, Plato does not develop a theory of what occasionsor grounds partaking in Forms.