Plato 4 -- Ideas and Negativity

In the context of this chapter, the overarching point I think Deleuze is trying to make is that Plato's scheme comes close to seeing difference as productive, affirmative, directly generative.  The Idea "makes" difference.  It founds and orders differentiation.  Difference isn't opposition or contradiction but division.  The goal isn't identification or classification according to an object's similarity to a set of pre-conceived forms.  The goal is to select and arrange real differences, and to conceive the Forms through this arrangement.  Admittedly, the goal for Plato is still to isolate one Idea that accounts for many differences (aka mediation), to the find the "true" Form that lets us judge the authenticity of each difference.  But instead of conceiving of these differences as various accidental particulars cast off one essential mold, each difference is now essential, and the Idea only relates one essential difference to the next in a chain of division.

This role of the ground appears in all clarity in the Platonic conception of participation. (And no doubt it is this foundation which provides division with the mediation it seems to lack and, at the same time, relates difference to the One, but in such a peculiar manner... ). To participate means to have part in, to have after, to have in second place. What possesses in first place is the ground itself. Justice alone is just, says Plato. As for those whom we call the just, they possess the quality of being just in second, third or fourth place ... or in simulacral fashion. That justice alone should be just is not a simple analytic proposition. It is the designation of the Idea as the ground which possesses in first place. The function of the ground is then to allow participation, to give in second place. Thus, that which participates more or less in varying degrees is necessarily a claimant. The claimant calls for a ground; the claim must be grounded (or denounced as groundless). Laying claim is not one phenomenon among others, but the nature of every phenomenon. The ground is a test which permits claimants to participate in greater or lesser degree in the object of the claim. In this sense the ground measures and makes the difference. We must therefore distinguish between Justice, which is the ground; the quality of justice, which is the object of the claim possessed by that which grounds; and the just, who are the claimants who participate unequally in the object.

The negative is relegated to a very ancillary role here.  Negation and opposition aren't baked into the Idea from the start, as we saw they were with the concept (as understood from Aristotle through Hegel).  The opposite of the Idea is just the thing at the far end of this chain of differentiation, so removed from the starting point that it is like a fake version of it, a mere simulacrum.  So while division might sound like a very black or white binary procedure, it actually, in and of itself, produces whole shades of grey.

... the aim of division was not the broad distinction among species but the establishment of a serial dialectic, of series or lines of descent in depth which mark the operations of a selective foundation or an elective participation (Zeus I, Zeus II, etc.).  It seems, then, that contradiction, far from signifying the founding test itself, represents instead the state of an ungrounded claim at the limit of participation. If the true claimant (the first grounded, the well grounded, the authentic) has rivals who are like parents, auxiliaries or servants, all participating in his claim in various capacities, he also has simulacra or counterfeits who would be exposed by the test. Such, according to Plato, is the 'sophist', the buffoon, centaur or satyr who lays claim to everything, and who, in laying such claims to everything, is never grounded but contradicts everything, including himself ...

The opposite of the true philosopher, the lover of wisdom, is the sophist, the one who claims he already possesses wisdom.  But the hierarchy of wisdom isn't structured by the opposition of these two poles.  Again, difference isn't selected according to its location along a predefined line stretching from A to ~A.  Instead, difference is directly produced and ordered by the series of instantiations of the Idea.  As they differentiate, the Forms create a space of their own, just like we saw in the introduction with embryogenesis.  Opposition is not the starting point, but just the end point of a chain, where the lineage breaks off and becomes something else, something which, judged from the standard of the starting point, is inauthentic.

Keeping in mind this changed role of the negative, we're finally ready to go back and discuss the weirdest part of the Sophist -- the discussion of the being of "not-Being".  This discussion immediately precedes the grand finale that Deleuze referred to as a sort of parody, which, as you will undoubtedly recall, was our jumping off point for this section.  I suspect this is likely to get longish, so let me give the executive summary up front. 

The problem is to understand the ontological status of the Ideas, a question which came up through their connection to myth.  What kind of Being should we attribute to these things?  On the one hand, we've seen that they are literally "out of this world" in a way similar to physical law or mathematical structure.  So they have a more ethereal existence than the type of beings we bump into everyday.  On the other hand, the whole reason we're talking about these things is because we think they have a real effect in the world and produce a whole chain of real differences.  In this sense, these Ideas are actually the most real thing we can think of, providing a foundation for everything we see.  How do we resolve this?  We don't.  The Forms are both Being and Not-Being at the same time.  They are the difference between Being and Not-Being.  But as we've seen, for Plato, the negative is not at the center of the schema, but only appears at the periphery.  So Deleuze will claim that when he talks about "Not-Being", he doesn't mean, "the opposite of Being" or some sort of contradiction.  Instead, he means for "Not-Being" to be something in itself, and to refer to a different type of being, namely, the type of being that problems have.  In sum, the being of Ideas is the being of problems.  This sounds ludicrously abstract to me, so we'll try to come at it piece by piece.  Stay tuned!