The Being Or the Not-Being of One
A discourse on the relations among being, not-being, whole, part, one, many, same, other, rest and motion. Of all twenty-four Plato’s dialogues included in the Western Canon, this is the most abstract and mind-boggling to me, partly due to my lack of training in abstract reasoning, and partly due to a lack of clear definition of each abstract term, the root cause of which is the ambiguity and unsuitability of the language itself in dealing with abstract concepts.
The Socratic Method
You should go a step further, and consider not only the consequences which flow from a given hypothesis, but also the consequences which flow from denying the hypothesis.
When you suppose anything to be or not to be, or to be in any way affected, you must look at the consequences in relation to the thing itself, and to any other things which you choose,–to each of them singly, to more than one, and to all; and so of other things, you must look at them in relation to themselves and to anything else which you suppose either to be or not to be, if you would train yourself perfectly and see the real truth.
The Mode of Participation in Ideas/Forms
Parmenides: I imagine that the way in which you are led to assume one idea of each kind is as follows:–You see a number of great objects, and when you look at them there seems to you to be one and the same idea (or nature) in them all; hence you conceive of greatness as one. And if you go on and allow your mind in like manner to embrace in one view the idea of greatness and of great things which are not the idea, and to compare them, will not another greatness arise, which will appear to be the source of all these?… and so each idea instead of being one will be infinitely multiplied.
Socrates: But may not the ideas, asked Socrates, be thoughts only, and have no proper existence except in our minds, Parmenides? For in that case each idea may still be one, and not experience this infinite multiplication.
Parmenides: Must [thought] not be of a single something, which the thought recognizes as attaching to all, being a single form or nature? And will not the something which is apprehended as one and the same in all, be an idea? Then, if you say that everything else participates in the ideas, must you not say either that everything is made up of thoughts, and that all things think; or that they are thoughts but have no thought?
Socrates: In my opinion, the ideas are, as it were, patterns fixed in nature, and other things are like them, and resemblances of them–what is meant by the participation of other things in the ideas, is really assimilation to them.
Parmenides: But if the individual is like the idea, must not the idea also be like the individual, in so far as the individual is a resemblance of the idea? That which is like, cannot be conceived of as other than the like of like. And when two things are alike, must they not partake of the same idea? And will not that of which the two partake, and which makes them alike, be the idea itself? Then the idea cannot be like the individual, or the individual like the idea; for if they are alike, some further idea of likeness will always be coming to light, and if that be like anything else, another; and new ideas will be always arising, if the idea resembles that which partakes of it?
The theory, then, that other things participate in the ideas by resemblance, has to be given up, and some other mode of participation devised.
If Being is Not One
If being is predicated of the one, if the one is, and one of being, if being is one; and if being and one are not the same; and since the one is, the whole, if it is one, must itself be, and have for its parts, one and being. Then that which is one is both a whole and has a part. Again, of the parts of the one, if it is–I mean being and one–does either fail to imply the other? is the one wanting to being, or being to the one? Thus, each of the parts also has in turn both one and being, and is at the least made up of two parts; and the same principle goes on for ever, and every part whatever has always these two parts; for being always involves one, and one being; so that one is always disappearing, and becoming two. And so the one, if it is, must be infinite in multiplicity.