One and Many

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.

If, now, being and unity are the same and are one thing in the sense that they are implied in one another as principle and cause are, not in the sense that they are explained by the same definition (though it makes no difference even if we suppose them to be like that-in fact this would even strengthen our case); for ‘one man’ and ‘man’ are the same thing, and so are ‘existent man’ and ‘man’, and the doubling of the words in ‘one man and one existent man’ does not express anything different (it is clear that the two things are not separated either in coming to be or in ceasing to be); and similarly ‘one existent man’ adds nothing to ‘existent man’, and that it is obvious that the addition in these cases means the same thing, and unity is nothing apart from being; and if, further, the substance of each thing is one in no merely accidental way, and similarly is from its very nature something that is:-all this being so, there must be exactly as many species of being as of unity. And to investigate the essence of these is the work of a science which is generically one-I mean, for instance, the discussion of the same and the similar and the other concepts of this sort; and nearly all contraries may be referred to this origin; let us take them as having been investigated in the ‘Selection of Contraries’.

"One" is opposed to "many," but in various ways. The "one" which is the principle of number is opposed to "multitude" which is number, as the measure is to the thing measured. For "one" implies the idea of a primary measure; and number is "multitude" measured by "one," as is clear from Metaph. x. But the "one" which convertible with "being" is opposed to "multitude" by way of privation; as the undivided is to the thing divided.