We sometimes ask jokingly, Which came first: the chicken or the egg? If the chicken were first, where would it have come from if not from an egg? If the egg were first, where would it have come from if not from a chicken? Several ancient Greek philosophers asked more seriously, Which came first: Unity or Being? If Unity existed first, then it had Being. But if Being existed first, then it was one thing and therefore had Unity.
In Plato’s Parmenides, a very young Socrates travels to hear such questions discussed by Zeno, famous for his paradoxes of motion. Zeno, for instance, said that an arrow never reaches its target. It must first cover half the distance to the target, and then it must cover half the remaining distance, and then again half the remaining distance. But distance can be divided indefinitely, halves of halves of halves on into infinity. The stages the arrow must travel, then, are inifinite in number, and a journey to infinity, by definition, never ends. Curiously, in Plato’s dialog, it is Zeno’s teacher, Parmenides,who does all the talking. And he doesn’t say anything about flying arrows, but he does lead Socrates through some similarly weird paradoxes.
At the beginning of the dialog, Socrates has heard that Parmenides and Zeno teach that all is one -- that plurality is an illusion -- and he asks to hear the rationale. Parmenides responds by telling Socrates that he should examine the consequences of both sides of any hypothesis. For instance, supposing that unity exists as pure unity: it is nothing other than singleness itself. Well, then, it can’t change into something else, since then it would not be unity; but it can’t stay the same, because it would then have similarity (to itself) in addition to having unity. With similar arguments, he shows that unity cannot be a part or a whole, cannot be in any place or time, and so cannot exist.
And now, to flip the coin, Parmenides traces the consequences of unity having mixed qualities. If unity has being, then there are two things: unity and being. But then each of these is a single existing thing, so each of the two in turn have two parts. This division of each part into two more goes on forever, like the path of Zeno’s arrow, so unity is actually infinite. Yet it is itself and no other, so it is finite. It is other than not-one, but not-one is other than it, so they are both alike in being-other, and therefore one is the same as not-one.
Well, after all those troubles, perhaps unity just doesn’t exist. But if we say unity doesn’t exist, then we still have said something about it and seem to know what it is we’re denying existence to, so unity must exist. If it doesn’t exist, it must exist. Get it? Next Parmenides examines “the others” (i.e., everything that isn’t unity) and finds the same ultimate contradiction: they must not exist, and so they must exist. His conclusion: “Let us affirm what seems to be the truth, that whether one is or is not, one and the others in relation to themselves and one another, all of them, in every way, are and are not, and appear to be and appear not to be.”
Every time Plato talks about the “Ideas” (or “Forms”), it seems to me he makes the same mistake, a mistake that leads him to problems like Parmenides’ paradoxical conclusion. Plato always talks as if the Idea of a quality has the quality it represents. The Platonic Form of Heat is hot, Whiteness is white, Unity is single, and so on. But it seems to me that an idea of a quality doesn’t necessarily have the quality. Greatness may be great, but then so is smallness; all ideas are great things. Unity may be single, but so is duality; duality is a single idea. Duality itself is not two things. It may be an idea of two things, but one thing and one thing do not make a duality unless there is a tertium quid, some combination that makes a duality of the two things.
As long as I’m talking way above my philosophical pay grade, I’ll go a bit further. The doctrines of the Trinity and of what Aquinas calls the simplicity of God seem to me to solve all the problems of the Greeks’ search for the First Thing. That God is simple doesn’t mean He doesn’t have various attributes; it means the attributes come in indivisible community. It’s not that God is fundamentally the Existent, the I Am, and then also happens to be good and all-knowing. It’s not that He is fundamentally One and then also happens to be eternal and good. Existence, Unity, Goodness, and Intelligence all come as a package, all have equal priority. And if Parmenides discovered that the existence of One necessarily brings about all the other numbers, it shouldn’t be hard to accept that the One God exists in three Persons.