Socrates: Those, Protarchus, are the common and acknowledged paradoxes about the one and many, which I may say that everybody has by this time agreed to dismiss as childish and obvious and detrimental to the true course of thought; and no more favour is shown to that other puzzle, in which a person proves the members and parts of anything to be divided, and then confessing that they are all one, says laughingly in disproof of his own words: Why, here is a miracle, the one is many and infinite, and the many are only one.
Protarchus: But what, Socrates, are those other marvels connected with this subject which, as you imply, have not yet become common and acknowledged?
Socrates: When, my boy, the one does not belong to the class of things that are born and perish, as in the instances which we were giving, for in those cases, and when unity is of this concrete nature, there is, as I was saying, a universal consent that no refutation is needed; but when the assertion is made that man is one, or ox is one, or beauty one, or the good one, then the interest which attaches to these and similar unities and the attempt which is made to divide them gives birth to a controversy.
Protarchus: Of what nature?
Socrates: In the first place, as to whether these unities have a real existence; and then how each individual unity, being always the same, and incapable either of generation or of destruction, but retaining a permanent individuality, can be conceived either as dispersed and multiplied in the infinity of the world of generation, or as still entire and yet divided from itself, which latter would seem to be the greatest impossibility of all, for how can one and the same thing be at the same time in one and in many things? These, Protarchus, are the real difficulties, and this is the one and many to which they relate; they are the source of great perplexity if ill decided, and the right determination of them is very helpful.
Protarchus: Then, Socrates, let us begin by clearing up these questions.
Socrates: That is what I should wish.
Protarchus: And I am sure that all my other friends will be glad to hear them discussed; Philebus, fortunately for us, is not disposed to move, and we had better not stir him up with questions.
Socrates: Good; and where shall we begin this great and multifarious battle, in which such various points are at issue? Shall we begin thus?
Protarchus: How?
Socrates: We say that the one and many become identified by thought, and that now, as in time past, they run about together, in and out of every word which is uttered, and that this union of them will never cease, and is not now beginning, but is, as I believe, an everlasting quality of thought itself, which never grows old. Any young man, when he first tastes these subtleties, is delighted, and fancies that he has found a treasure of wisdom; in the first enthusiasm of his joy he leaves no stone, or rather no thought unturned, now rolling up the many into the one, and kneading them together, now unfolding and dividing them; he puzzles himself first and above all, and then he proceeds to puzzle his neighbours, whether they are older or younger, or of his own age—that makes no difference; neither father nor mother does he spare; no human being who has ears is safe from him, hardly even his dog, and a barbarian would have no chance of escaping him, if an interpreter could only be found.
Protarchus: Considering, Socrates, how many we are, and that all of us are young men, is there not a danger that we and Philebus may all set upon you, if you abuse us? We understand what you mean; but is there no charm by which we may dispel all this confusion, no more excellent way of arriving at the truth? If there is, we hope that you will guide us into that way, and we will do our best to follow, for the enquiry in which we are engaged, Socrates, is not unimportant.
Socrates: The reverse of unimportant, my boys, as Philebus calls you, and there neither is nor ever will be a better than my own favourite way, which has nevertheless already often deserted me and left me helpless in the hour of need.
Protarchus: Tell us what that is.
Socrates: One which may be easily pointed out, but is by no means easy of application; it is the parent of all the discoveries in the arts.
Protarchus: Tell us what it is.
Socrates: A gift of heaven, which, as I conceive, the gods tossed among men by the hands of a new Prometheus, and therewith a blaze of light; and the ancients, who were our betters and nearer the gods than we are, handed down the tradition, that whatever things are said to be are composed of one and many, and have the finite and infinite implanted in them: seeing, then, that such is the order of the world, we too ought in every enquiry to begin by laying down one idea of that which is the subject of enquiry; this unity we shall find in everything. Having found it, we may next proceed to look for two, if there be two, or, if not, then for three or some other number, subdividing each of these units, until at last the unity with which we began is seen not only to be one and many and infinite, but also a definite number; the infinite must not be suffered to approach the many until the entire number of the species intermediate between unity and infinity has been discovered—then, and not till then, we may rest from division, and without further troubling ourselves about the endless individuals may allow them to drop into infinity. This, as I was saying, is the way of considering and learning and teaching one another, which the gods have handed down to us. But the wise men of our time are either too quick or too slow in conceiving plurality in unity. Having no method, they make their one and many anyhow, and from unity pass at once to infinity; the intermediate steps never occur to them. And this, I repeat, is what makes the difference between the mere art of disputation and true dialectic.
Protarchus: I think that I partly understand you Socrates, but I should like to have a clearer notion of what you are saying.
Socrates: I may illustrate my meaning by the letters of the alphabet, Protarchus, which you were made to learn as a child.
Protarchus: How do they afford an illustration?
Socrates: The sound which passes through the lips whether of an individual or of all men is one and yet infinite.
Protarchus: Very true.
Socrates: And yet not by knowing either that sound is one or that sound is infinite are we perfect in the art of speech, but the knowledge of the number and nature of sounds is what makes a man a grammarian.
Protarchus: Very true.
Socrates: And the knowledge which makes a man a musician is of the same kind.