Socrates has portrayed sensible objects as “partaking” of Forms, suggesting some kind of metaphorical connection between them, like taking a bite out of a Form. But what exactly does this mean? Parmenides asks him if an object that participates in a Form gets the whole of the Form or only a part of it. Probably the whole. But then how will there be anything left over for other objects to participate in? Socrates suggests it is like the case of a day, which many people experience at the same time. Parmenides counters with the image of a sail, which could cover many people at the same time, but only part of it would cover any one person. This would imply that each object would get only a part of the Form. Suppose then that we look at the Form of Largeness. If we divide that up among many individuals who participate in it, won’t each part of the Large be, paradoxically, a small part?
Now suppose that we consider a group of large things; they all will participate in Largeness itself, which embodies largeness. So now we can consider the group of large things together with Largeness, and ask, what makes them all large. They must, it seems, all participate in another Form of Largeness, say Largeness2 in contrast to Largeness1, which we have already met. Now we have a group of large objects plus Largeness1 and Largeness2. What makes them all large? Presumably, participating in Largeness3, and so on. It turns out, then, that the same reasoning that gives us one Form of Largeness gives us an infinite series of them.
At this point, Socrates suggests that the Form might be a thought or a concept rather than an entity. But, Parmenides objects, will it be a thought of nothing or of something? Surely of something, which brings us back to treating the Form as an entity independent of the thinker.
Well, probably each Form is a prototype or a pattern (paradeigma) which things in the world imitate or copy. But, Parmenides objects, if the copy is like the prototype, it must be because they share the same feature; and the only way for that to happen is for there to be another prototype common to both. And this brings us back to the case in which we need yet another prototype for all of the preceding instances, generating an infinites series.
This in turn brings us to what Parmenides calls the greatest difficulty of all. If the Forms are as Socrates says they are, they must be part of a network of relations that connect them only with other Forms, not with us. So Knowledge itself will be related to Truth itself, but not to anything in our world.
Furthermore, if the gods have the highest knowledge, then they will participate in Knowledge itself, but they will have no awareness of us, who are cut off from such cognition. Thus the knowledge of Forms will be a kind of divine knowledge, but it will not be accessible to us mortals.
Thus it appears that Plato’s Theory of Forms faces almost insuperable objections.[12]
[12] Plato Parmenides 130e-135a.