Plato’s Full Nelson

In an a previous post I referred to the problem of “Plato’s Full Nelson” as one of the reasons Badiou strives to avoid providing any concept of difference in the formulation of his ontology. Plato’s Full Nelson can be read as one of the earliest versions of the correlationist argument. We find a particularly nice formulation of this argument in the context of a discussion of Plato’s theory of recollection and the immortality of the soul in the Phaedo.

And when the recollection is derived from like things, then there is sure to be another question, which is, whether the likeness of that which is recollected is in any way defective or not.

Very true, he said.
And shall we proceed a step further, and affirm that there is such a thing as equality, not of wood with wood, or of stone with stone, but that, over and above this, there is equality in the abstract? Shall we affirm this?

Affirm, yes, and swear to it, replied Simmias, with all the confidence in life.

And do we know the nature of this abstract essence?
To be sure, he said.
And whence did we obtain this knowledge? Did we not see equalities of material things, such as pieces of wood and stones, and gather from them the idea of an equality which is different from them?-you will admit that? Or look at the matter again in this way: Do not the same pieces of wood or stone appear at one time equal, and at another time unequal?

read on!

That is certain.
But are real equals ever unequal? or is the idea of equality ever inequality?

That surely was never yet known, Socrates.
Then these (so-called) equals are not the same with the idea of equality?

I should say, clearly not, Socrates.
And yet from these equals, although differing from the idea of equality, you conceived and attained that idea?

Very true, he said.
Which might be like, or might be unlike them?
Yes.
But that makes no difference; whenever from seeing one thing you conceived another, whether like or unlike, there must surely have been an act of recollection?

Very true.
But what would you say of equal portions of wood and stone, or other material equals? and what is the impression produced by them? Are they equals in the same sense as absolute equality? or do they fall short of this in a measure?

Yes, he said, in a very great measure, too.
And must we not allow that when I or anyone look at any object, and perceive that the object aims at being some other thing, but falls short of, and cannot attain to it-he who makes this observation must have had previous knowledge of that to which, as he says, the other, although similar, was inferior?

Certainly.
And has not this been our case in the matter of equals and of absolute equality?

Precisely.
Then we must have known absolute equality previously to the time when we first saw the material equals, and reflected that all these apparent equals aim at this absolute equality, but fall short of it?

That is true.
And we recognize also that this absolute equality has only been known, and can only be known, through the medium of sight or touch, or of some other sense. And this I would affirm of all such conceptions.

Yes, Socrates, as far as the argument is concerned, one of them is the same as the other.

And from the senses, then, is derived the knowledge that all sensible things aim at an idea of equality of which they fall short-is not that true?

Yes.
Then before we began to see or hear or perceive in any way, we must have had a knowledge of absolute equality, or we could not have referred to that the equals which are derived from the senses-for to that they all aspire, and of that they fall short?

That, Socrates, is certainly to be inferred from the previous statements.

And did we not see and hear and acquire our other senses as soon as we were born?

Certainly.
Then we must have acquired the knowledge of the ideal equal at some time previous to this?

Plato distinguishes between equal things and equality itself. Equality-itself would always be absolutely equal, containing no difference within itself. By contrast, equal-things would always contain differences of one sort or another. A good example of this would be optical illusions where two lines of exactly the same length nonetheless appear to be of different lengths. Moreover, light constantly plays off of objects in different ways as we look at them, presenting differences. Finally, we see things as the same that nonetheless differ as in the case of recognizing a blue and yellow coffee cup as both being coffee cups. This difference within equal-things is true not only of comparative differences between objects, but also of one and the same object in time. We say of an object that it is the same object, despite the fact that it changes in a variety of ways.

Plato’s argument thus runs as follows. Equal-things always differ in some respect or capacity. Because equal-things always differ, we cannot arrive at a concept of equality-itself from equal-things. Therefore, our concept of equality-itself does not arise after our experience of equal-things, but must precede our experience of equal-things, for how could we recognize equal-things as equal-things– all of which differ both from themselves and others like them –if we did not first know equality-itself. Consequently, our concept of equality itself is prior to any of our dealings with the world.

This would be a serious, though somewhat arid and technical, problem for any differential ontology. If differential ontology must begin with a concept of difference, and if a concept is a means of ident-ifying something, we are then led into a performative contradiction in which identity is prior to difference as a condition of difference. This would be one variant of Plato’s Full Nelson (present in the Sophist). The other would consist in demonstrating the priority of the concept over our encounters with the world as a necessary condition for any relation to the world, i.e., the correlationist move.

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