1. According to Aristotle, the Platonists had an argument for the existence of Forms that he called the “One Over Many.” Plato himself never used this title, although he sometimes described a Form as being a “one over many.”

2. The idea behind the One Over Many is probably best exemplified in Plato’s dialogues in the principle enunciated at Rep. 596a:

   We customarily hypothesize a single form in connection with each collection of many things to which we apply the same name.

3. The idea is this:

   If there is a set of things all of which have the same “name,” then there is a Form for that set.

   By “name” here we should probably understand “general term” or “predicate” (to use the word that Aristotle invented for this kind of “name”) - that is, a term that can be applied in the same way to many different things that all have something in common, a term like ‘bed’ or ‘table’. Cf. the next speech in Rep. 596a-b:

   Then let’s now take any of the manys you like. For example, there are many beds and tables ... but there are only two forms of such furniture, one of the bed and one of the table.

4. What the principle tells us in this case is:

   For any set of things to which we apply the term ‘table’, there is a single Form.

   This is the Form of Table, or (perhaps) Tablehood, or (as Plato would say) The Table Itself.

5. Since the things to which we apply the term ‘table’ are obviously tables, we can reformulate this instance of the principle as follows:

   For any set of tables, there is a single Form.
   

6. But surely the principle must tell us more than this. It must tell us in what way the single Form is relevant to the set of tables (or whatever) it is Over. Here we get some help from Phaedo 100c-d, where we also see One-Over-Many reasoning at work:

   ... if there is anything beautiful besides Beauty itself, it is beautiful for no other reason that 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.

   So what the principle tells us can now be fleshed out a bit:

   For any set of tables, there is a single Form, and it is in virtue of some relationship to that Form that they are all made to be tables.

   That is, it is the Form of Table that makes something a table.

7. We are now in a position to see why Aristotle called this an argument for the Forms. The only thing we have seen so far that even looks like an argument would go like this:
   1. a, b, and c are all tables (i.e., things to which we apply the name “table”).
   2. Therefore, there is a Form (the Table Itself) that a, b, and c all share in; and it is by virtue of sharing in this Form that they are all tables.

   The argument moves from a premise asserting the existence of a plurality of things that have something in common to a conclusion that asserts the existence of something else. But what is this something else?

   • One might suggest: it is some feature that they all have in common. But this seems too weak; for it’s already asserted in the premise that they all have something in common: they are all tables.
   • Rather: the conclusion asserts the existence of some entity that explains the fact that they all have some feature in common.

   [Aristotle, in his Peri Ideôn, attributed to the Platonists a more elaborate version of this argument, but it is not found in any of Plato’s dialogues.]

8. Plato never made completely clear the nature of the relationship between the many things and the one Form that is “over” them. He tended to use the term “participation” or “sharing in” to describe this relation. The idea seems to be that it is by participating in a Form that a thing comes to be the kind of thing that it is - tables are tables because they participate in the Form Table; beautiful things are beautiful because they participate in the Form Beauty. That is: participation explains predication. A thing is F because it participates in the Form, F-ness.

9. But what more can be said about the nature of participation? There are some clues in the Phaedo. Recall 74-76: equal sticks and equal stones are said to be like the form of Equality, but to be deficient, to fall short. This suggests that participation involves, at least in part, deficient resemblance.

   
   This idea is supported by the Allegory of the Cave in Republic 514ff.

10. The view that emerges from these passages (Republic 514ff, 596aff; Phaedo 74-76, 100c-d) may be called the Resemblance Theory of Predication:
    • Forms are paradigms, perfect examples of the properties or common features of the things they are invoked to explain. These paradigms are accessible to the mind, and it is by comparison to them that we apply their “names” to objects of sense-perception. It is by resemblance to a Form that is (perfectly) F that a participant in that Form is said to be (imperfectly) F.

    • The semantic theory embedded in this: general terms are proper names of Forms. We can apply these terms to participants in the Forms by a kind of courtesy, provided that the participants measure up sufficiently closely to the paradigms.

11. Plato came to be critical of the resemblance theory of predication. The criticism emerges in his dialogue Parmenides, to which we now turn.

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Copyright © 2006, S. Marc Cohen