A Heideggerian Interlude

I know, I know.  I said no Heidegger.  But in re-reading that section (pg. 64-66) after all this discussion of Plato, I realized that it actually prompted a number of thoughts.  I now feel like commenting on this section can advance my understanding without having to go back and read Being and Time again.

Hiking up to Mailbox Peak yesterday I started reflecting on the overall purpose of this chapter -- to put difference first, before identity, and think about difference in itself, rather than difference as something between two identities.  If this sounds paradoxical, well ... we've just spent a long time discovering that it is, in fact.  Why else were so many pixels sacrificed in an effort to understand something as goofy sounding as the Being of Not-Being?  Which brought me to the thought that even difference is different.  Not all difference is the same.  It's not a homogenous field.  There are certain distinctive points or distinctive differences.  That is to say, there are singularities of difference.

Deleuze has already mentioned singularities a number of times in the book, mostly in the context in their distinction from the specific (in the Aristotelian sense).  Now though, we have a clearer image of the singularity, even though it hasn't really been announced as such.  Because Plato's Ideas are singularities.  A singularity is a special point that structures a whole space of different possible points.  Or is structured and defined by them.  At this point it seems to me that the causality could run either way.  For Plato, we usually think it runs from Idea as model to Instantiation as copy.  But we've seen in the Sophist that maybe the question was somewhat ambiguous even for him, and in any case, we've learned that Plato's Ideas always seem to be tied up with some mythical circle, so the question of precedence might not make any sense to begin with.  At any rate, let's just say that singularities and the possibility space they structure are co-defined.

Take a very simple singularity like a black hole.  That singularity is a point (okay, 4-D volume, technically) in a gravitation field.  The singularity and the field of differences it summarizes are really two sides of the same coin.  Take this structure as an analogy for the difference within difference.  The singular point is like a special difference, one that structures a whole space of possible differences, and hence turns them into a unity.  It's a funny type of unity, yes, where it's hard to say whether the definition should go top-down or bottom-up.  But this confusion happens every time we see a structure of circular causality; a hurricane is no less unified for being 'just' a pattern of moving molecules.  Pushing this phase space analogy further, you see how we might describe a singularity as both a point and not-a-point, something more than a point.  Because it adds a sort of dimension to the field that enables us to think of it as one thing.  In addition, in the case of the black hole, the singularity quite literally turns what happens at every point and every resulting trajectory in the space into different solutions to the same problem.  In other words, the singularity is a real and not real thing that, in conjunction with its associated field, has the unity of a problem.  This is exactly the scheme that Deleuze is attributing to Plato.  Of course, as we'll see next time, he wants to 'overturn' Platonism by starting with the 'opposite' of the Idea, the 'fake' copies at the end of the chain, rather than the 'real' Idea at the beginning of it.  But if the chain is actually a circle, then 'inverting' it can only mean going around the circle in the opposite direction.  The points will actually all be the same, though the sense we have as we pass them will be different.

Heidegger is portrayed here as applying this scheme of singularity as the difference of difference to the most general question, "what is Being"?  Ontological difference is the difference between beings and Being.  It's the difference within Being, that makes it also a non-Being that is not its negation but is its differencing.  Ontological difference is basically the difference between the singularity and the field, which we've seen are the same and not-the-same, the one as many and the many as one.  Difference implies unity implies difference implies ... The image of the fold makes better sense now because it's clear we're not talking about singularity and field as opposites, but as two sides of the same coin.

Merleau-Ponty, on the other hand, undoubtedly followed a more thoroughly Heideggerian inspiration in speaking of 'folds' and 'pleating' (by contrast with Sartrean 'holes' and 'lakes of non-being')

In fact, with the idea that difference is different within itself, the whole commentary on Heidegger comes together for me.  Difference in itself, at its most abstract level, is also singularity.  It encompasses unity as well.  Now we can follow the theses on Heidegger:

1. The not expresses not the negative but the difference between Being and being.

2. This difference is not 'between' in the ordinary sense of the word. It is the Fold, Zwiefalt. Being is truly the differenciator of difference - whence the ex-pression 'ontological difference'.

3. Ontological Difference corresponds to questioning. It is the being of questions, which become problems, marking out the determinant fields of existence.

4. Understood in this manner, difference is not an object of representation. As the element of metaphysics, representation subordinates difference to identity, if only in relating it to a third term as the centre of a compari- son between two supposedly different terms (Being and being). Heidegger recognises that this point of view of metaphysical representation is still present in The Essence ofReasons (see the French translation, p. 59, where the third term is found in the 'transcendence of being-there'). But metaphysics is unable to think difference in itself, or the importance of that which separates as much as of that which unites (the differenciator). There is no synthesis, mediation or reconciliation in difference, but rather a stubborn differenciation. This is the 'turning' beyond metaphysics: 'Being itself can open out in its truth the difference of Being and beings preserved in itself only when the difference explicitly takes place'.

This fourth point is particularly interesting, because it alerts us to the fact that it's easy to slide back into seeing this notion of difference in itself as the distinction between the identities we have in mind with "the many" and "the one".  This leads us right back where we started though, with a boring Hegelian circle that always produces the self-identical.  We have to see this most abstract difference within difference as an ongoing process by which difference differentiates itself.  Novelty and movement and more difference are built right into the scheme.  The Univocity (not unity) of Being is Deleuze's description of this process of circulation of ontological difference, the way possibility converts into actuality converts into possibility ... 

5. Difference cannot, therefore, be subordinated to the Identical or the Equal but must be thought as the Same, in the Same.  The same never coincides with the equal, not even in the empty indifferent oneness of what is merely identical. The equal or identical always moves toward the absence of difference, so that everything may be reduced to a common denominator. The same, by contrast, is the belonging together of what differs, through a gathering by way of the difference. We can only say 'the same' if we think difference.... The same banishes all zeal always to level what is different into the equal or identical. The same gathers what is distinct into an original being-at-one.  The equal, on the contrary, disperses them into the dull unity of mere uniformity.

Difference isn't homogenous.  It's differs.

Plato 6 -- Not-Being and Problems

As I suspected earlier, the tangent into the Sophist got out of hand.  But since we now know that Non-Being = Difference = Possibility, we are in a position to deliver the last part of the promised thesis and relate this type of being to questions and problems.  This is the last link in Deleuze's exposition of Plato, and takes us right up to the Heideggerean interlude that begins on pg. 64.

There's actually not much explicit connection between non-being and problems in the Sophist.  The closest relation would be the approach we saw to the definition of the philosopher as someone who understands how the Forms blend.

Stranger: Shall we not say that the division of things by classes and the avoidance of the belief that the same class is another, or another the same, belongs to the science of dialectic?
Theaetetus: Yes, we shall.
Stranger: Then he who is able to do this has a clear perception of one form or idea extending entirely through many individuals each of which lies apart, and of many forms differing from one another but included in one greater form, and again of one form evolved by the union of many wholes, and of many forms entirely apart and separate. This is the knowledge and ability to distinguish by classes how individual things can or cannot be associated with one another. 

I say this simply because it appears to be describing a pragmatic, case-by-case problem solving type of approach, in contrast to Aristotle or Hegel's scheme which always seem to give the same general answer to every particular question.   Here, the only general answer is, "well, it's a complicated mix".  Door Openers and Door Closers.

There is also the more implicit connection that the Sophist shares with almost every Platonic dialogue -- it is structured according to the problem, "what is X?".  What is the Sophist, the Statesman, the Lover, the Just City?  In fact, all of Plato's Ideas are approached as problems investigated by Socratic irony and dialectical method.  

Irony consists in treating things and beings as so many responses to hidden questions, so many cases for problems yet to be resolved. We recall that Plato defined the dialectic as proceeding by 'problems', by means of which one attains the pure grounding principle - that is, the principle which measures the problems as such and distributes the corresponding solutions.

At first this reads as just general commentary on Plato's style.  In fact, I would say that the whole connection between Plato and problems stays fairly abstract at this point in D&R.  It is the first time Deleuze has mentioned 'problems', and he hasn't really given us a definition here.  All we really know at this point is that he sees problems as ontological and not merely epistemological.

Neither the problem nor the question is a subjective determination marking a moment of insufficiency in knowledge. Problematic structure is part of objects themselves, allowing them to be grasped as signs, just as the questioning or problematising instance is a part of knowledge allowing its positivity and its specificity to be grasped in the act of learning.

I'm sure we'll see the concept of a problem get fleshed out as we go, but all the work on Ideas and Not-Being has already put us in a position to read between the lines.  We saw that the Forms were mythical, other-worldly principles that nevertheless structured a whole chain of real differences between things.  The chain was ordered by degree of participation in the Idea -- level 0 for the original true Being of the Idea itself, level 1 for the 'best' instantiation or copy of it, ... , down to level N for something that is so unlike the original that it was a 'fake' version of it, one mixed up with everything else with no claim to the throne.  So we see already that the Forms are directly related to the notion of possibility.  They are inseparable from the different possible copies of themselves.  They relate those differences to one another and bind them all together.  One universal Idea is already inherently many possible different things arranged in a particular order.  Said more simply, the Forms structure a possibility space.  They aren't a given point in a pre-existing space, some point that happens to be different from our current point.  They lay out the structure of the whole space of possibilities.  They are the singularities in a differential field.

But wait.  We discovered in the Sophist that even those things at the 'end' of the chain, those Nth derivative 'fakes' and 'semblances' that blend together many Forms in an impure mixture, also have a type of Being, the type of Being we established as non-Being.  But this non-Being was not the same as the negative or the opposite of Being.  In fact, by the grand finale of the Sophist, we're confusing him with the Philosopher, and finding we can't rely on contradiction to separate the images and fakes from the real thing.  This is why they invented 'scare quotes'.  You know something weird is going on when Plato starts talking about "divine fakes":  

Theaetetus: Tell me again how each part is distinguished.
Stranger:We know that we and all the other animals, and fire, water, and their kindred elements, out of which natural objects are formed, are one and all the very offspring and creations of God, do we not?
Theaetetus: Yes.
Stranger: And corresponding to each and all of these there are images, not the things themselves, which are also made by superhuman skill.
Theaetetus: What are they?
Stranger:The appearances in dreams, and those that arise by day and are said to be spontaneous—a shadow when a dark object interrupts the firelight, or when twofold light, from the objects themselves and from outside, meets on smooth and bright surfaces and causes upon our senses an effect the reverse of our ordinary sight, thus producing an image.
Theaetetus: Yes, these are two works of divine creation, the thing itself and the corresponding image in each case.

The way everything is muddled together in non-Being at the limit of participation in an Idea mirrors the way everything is muddled together at the end of the Sophist.  But this chaos of the Being of non-Being is in fact the very problem we began with!  

... an indefinite representing multiplicity which must be eliminated in order to bring to light the Idea which constitutes a pure line of descent. The search for gold provides the model for this process of division.

The mixtures we find in the world present a real problem, not just for our knowledge, but in themselves -- how could they have been constructed from blending together many Forms?  Given this point that we see, what spaces interacted to make it possible?  In a sense, this is the essence of philosophy.  We're not asking the scientific question: "why is this world like it is?"   We're asking: "how is a world like this possible, and so what other worlds are possible?"

Being (what Plato calls the Idea) 'corresponds' to the essence of the problem or the question as such. It is as though there were an 'opening', a 'gap', an ontological 'fold' which relates being and the question to one another.  In this relation, being is difference itself. Being is also non-being, but non-being is not the being of the negative; rather, it is the being of the problematic, the being of problem and question. Difference is not the negative; on the contrary, non-being is Difference: heteron, not enantion. For this reason non-being should rather be written (non)-being or, better still, ?-being. In this sense, it turns out that the infinitive, the esse, designates less a proposition than the interrogation to which the proposition is supposed to respond. This (non)-being is the differential element in which affirmation, as multiple affirmation, finds the principle of its genesis.

 

Plato 5 -- Not-Being in the Sophist

The Sophist is structured as the long and winding hunt for the true definition of the title character.  After some preliminary discussion of the method of division that we've already looked at, we come to the heart of the problem -- the Sophist is someone who gives the appearance of possessing true wisdom, but who really has none.  In other words, the Sophist is an imitation of the philosopher.  This already gives the hunt for his true definition a strange character; we are looking for the true definition of someone who is a fake.   Which pretty quickly bring us to the question of what do we mean when we say that something is fake.  Or is real, for that matter.  Or, stated most generally, how do we know what IS and what IS NOT?

STRANGER: ... And now I should like you to tell me, whether the Sophist is not visibly a magician and imitator of true being; or are we still disposed to think that he may have a true knowledge of the various matters about which he disputes?
THEAETETUS: But how can he, Stranger? Is there any doubt, after what has been said, that he is to be located in one of the divisions of children's play?
STRANGER: Then we must place him in the class of magicians and mimics.
THEAETETUS: Certainly we must.
STRANGER: And now our business is not to let the animal out, for we have got him in a sort of dialectical net, and there is one thing which he decidedly will not escape.
THEAETETUS: What is that?
STRANGER: The inference that he is a juggler.
THEAETETUS: Precisely my own opinion of him.
STRANGER: Then, clearly, we ought as soon as possible to divide the image-making art, and go down into the net, and, if the Sophist does not run away from us, to seize him according to orders and deliver him over to reason, who is the lord of the hunt, and proclaim the capture of him; and if he creeps into the recesses of the imitative art, and secretes himself in one of them, to divide again and follow him up until in some sub-section of imitation he is caught. For our method of tackling each and all is one which neither he nor any other creature will ever escape in triumph.
THEAETETUS: Well said; and let us do as you propose.
STRANGER: Well, then, pursuing the same analytic method as before, I think that I can discern two divisions of the imitative art, but I am not as yet able to see in which of them the desired form is to be found.
THEAETETUS: Will you tell me first what are the two divisions of which you are speaking?
STRANGER: One is the art of likeness-making;—generally a likeness of anything is made by producing a copy which is executed according to the proportions of the original, similar in length and breadth and depth, each thing receiving also its appropriate colour.
THEAETETUS: Is not this always the aim of imitation?
STRANGER: Not always; in works either of sculpture or of painting, which are of any magnitude, there is a certain degree of deception; for artists were to give the true proportions of their fair works, the upper part, which is farther off, would appear to be out of proportion in comparison with the lower, which is nearer; and so they give up the truth in their images and make only the proportions which appear to be beautiful, disregarding the real ones.
THEAETETUS: Quite true.
STRANGER: And that which being other is also like, may we not fairly call a likeness or image?
THEAETETUS: Yes.
STRANGER: And may we not, as I did just now, call that part of the imitative art which is concerned with making such images the art of likeness-making?
THEAETETUS: Let that be the name.
STRANGER: And what shall we call those resemblances of the beautiful, which appear such owing to the unfavourable position of the spectator, whereas if a person had the power of getting a correct view of works of such magnitude, they would appear not even like that to which they profess to be like? May we not call these 'appearances,' since they appear only and are not really like?
THEAETETUS: Certainly.
STRANGER: There is a great deal of this kind of thing in painting, and in all imitation.
THEAETETUS: Of course.
STRANGER: And may we not fairly call the sort of art, which produces an appearance and not an image, phantastic art?
THEAETETUS: Most fairly.
STRANGER: These then are the two kinds of image-making—the art of making likenesses, and phantastic or the art of making appearances?
THEAETETUS: True.
STRANGER: I was doubtful before in which of them I should place the Sophist, nor am I even now able to see clearly; verily he is a wonderful and inscrutable creature. And now in the cleverest manner he has got into an impossible place.
THEAETETUS: Yes, he has.
STRANGER: Do you speak advisedly, or are you carried away at the moment by the habit of assenting into giving a hasty answer?
THEAETETUS: May I ask to what you are referring?
STRANGER: My dear friend, we are engaged in a very difficult speculation—there can be no doubt of that; for how a thing can appear and seem, and not be, or how a man can say a thing which is not true, has always been and still remains a very perplexing question. Can any one say or think that falsehood really exists, and avoid being caught in a contradiction? Indeed, Theaetetus, the task is a difficult one.
THEAETETUS: Why?
STRANGER: He who says that falsehood exists has the audacity to assert the being of not-being; for this is implied in the possibility of falsehood.

What follows is a long discussion of whether we can even conceive or talk about something that is unreal in a metaphysical sense.  How would we refer to the non-existent?  Is it a thing?  Many things?  Is it a whole?  Does it have parts?  It seems like we can't find a consistent way to even deny its existence without thereby treating it as real in some sense.  And if we can't get clear about what we mean by the not-real, that is, by mere icon or phantasm (these are the Greek words for "likeness" and "semblance" in the passage above) we are going to have trouble accusing the Sophist of manufacturing them.

STRANGER: And if we say to him that he professes an art of making appearances, he will grapple with us and retort our argument upon ourselves; and when we call him an image-maker he will say, 'Pray what do you mean at all by an image?'—and I should like to know, Theaetetus, how we can possibly answer the younker's question?
THEAETETUS: We shall doubtless tell him of the images which are reflected in water or in mirrors; also of sculptures, pictures, and other duplicates.
STRANGER: I see, Theaetetus, that you have never made the acquaintance of the Sophist.
THEAETETUS: Why do you think so?
STRANGER: He will make believe to have his eyes shut, or to have none.
THEAETETUS: What do you mean?
STRANGER: When you tell him of something existing in a mirror, or in sculpture, and address him as though he had eyes, he will laugh you to scorn, and will pretend that he knows nothing of mirrors and streams, or of sight at all; he will say that he is asking about an idea.
THEAETETUS: What can he mean?
STRANGER: The common notion pervading all these objects, which you speak of as many, and yet call by the single name of image, as though it were the unity under which they were all included. How will you maintain your ground against him?
THEAETETUS: How, Stranger, can I describe an image except as something fashioned in the likeness of the true?
STRANGER: And do you mean this something to be some other true thing, or what do you mean?
THEAETETUS: Certainly not another true thing, but only a resemblance.
STRANGER: And you mean by true that which really is?
THEAETETUS: Yes.
STRANGER: And the not true is that which is the opposite of the true?
THEAETETUS: Exactly.
STRANGER: A resemblance, then, is not really real, if, as you say, not true?
THEAETETUS: Nay, but it is in a certain sense.
STRANGER: You mean to say, not in a true sense?
THEAETETUS: Yes; it is in reality only an image.
STRANGER: Then what we call an image is in reality really unreal.
THEAETETUS: In what a strange complication of being and not-being we are involved!
STRANGER: Strange! I should think so. See how, by his reciprocation of opposites, the many-headed Sophist has compelled us, quite against our will, to admit the existence of not-being.
THEAETETUS: Yes, indeed, I see.
STRANGER: The difficulty is how to define his art without falling into a contradiction.

(

Parenthetically, part of my thought in quoting this dialogue at such length is to hear the way Plato's hunt for this dangerous and wily Sophist lends more weight to Deleuze's seemingly whimsical characterizations of difference as "monstrous" and "cruel" and of the Greeks as trying to "tame" and "harmonize" it.

It is true that Platonism already represents the subordination of difference to the powers of the One, the Analogous, the Similar and even the Negative. It is like an animal in the process of being tamed, whose final resistant movements bear witness better than they would in a state of freedom to a nature soon to be lost: the Heraclitan world still growls in Platonism.

) 

But back to the main story.  We're having trouble defining the not-real, the mere likeness or semblance.  Coming out of the mouth of Plato, this difficulty should sound pretty weird.  I mean, isn't this the guy who famously thinks we should focus on the unchanging abstract Forms as distinct from mere unreal appearances?  Isn't it obvious that if the truly real consists of these stable principles, then everything else, everything we see kaleidoscopically swirling and changing around us, is un-real?  Sure enough, the Stranger spends some time refuting the notion that all real things are just physical objects.  At the end of this, he even produces a definition of the real.

STRANGER: My notion would be, that anything which possesses any sort of power to affect another, or to be affected by another, if only for a single moment, however trifling the cause and however slight the effect, has real existence; and I hold that the definition of being is simply power.

But then, using this expansive definition of the real -- which I emphasize here because I think the formula being = power is key to understanding both Deleuze and his whole philosophical lineage (Spinoza, Nietzsche, Bergson, Whitehead) -- the Stranger goes on to also prove that while reality can't be just physical stuff, it can't be just the Forms either.  The conclusion almost reads like Plato demolishing his own philosophy (or perhaps a misconception of his own philosophy?).

STRANGER: On these grounds, then, it seems that only one course is open to the philosopher who values knowledge and the rest above all else.  He must refuse to accept from the champions of either of the one or of the many forms the doctrine that all reality is changeless, and he must turn a deaf ear to the other party who represent reality as everywhere changing.  Like a child begging for 'both,' he must declare that reality or the sum of things is both at once -- all that is unchangeable and all that is in change.

Just at this point where we are well and truly confused, Plato cuts to the heart of the matter, and upends the very principle of identity and non-contradiction that makes us feel childish for saying 'both'.  He launches into a discussion of the Forms -- in this example some of the most abstract: existence, motion, rest, sameness, and difference -- which we always imagine as completely stable, independent, self-identical objects, and promptly proves that they can't work that way.  They have to be able to blend with one another in specific combination, the way some letters blend to make words, in order to construct reality.

Stranger: Now does everybody know which letters can join with which others? Or does he who is to join them properly have need of art?
Theaetetus: He has need of art.
Stranger: What art?
Theaetetus: The art of grammar.
Stranger: And is not the same true in connection with high and low sounds? Is not he who has the art to know the sounds which mingle and those which do not, musical, and he who does not know unmusical?
Theaetetus: Yes.
Stranger: And we shall find similar conditions, then, in all the other arts and processes which are devoid of art?
Theaetetus: Of course.
Stranger: Now since we have agreed that the classes or genera also commingle with one another, or do not commingle, in the same way, must not he possess some science and proceed by the processes of reason who is to show correctly which of the classes harmonize with which, and which reject one another, and also if he is to show whether there are some elements extending through all and holding them together so that they can mingle, and again, when they separate, whether there are other universal causes of separation?
Theaetetus: Certainly he needs science, and perhaps even the greatest of sciences.
Stranger: Then, Theaetetus, what name shall we give to this science? Or, by Zeus, have we unwittingly stumbled upon the science that belongs to free men and perhaps found the philosopher while we were looking for the sophist?
Theaetetus: What do you mean?
Stranger: Shall we not say that the division of things by classes and the avoidance of the belief that the same class is another, or another the same, belongs to the science of dialectic?
Theaetetus: Yes, we shall.
Stranger: Then he who is able to do this has a clear perception of one form or idea extending entirely through many individuals each of which lies apart, and of many forms differing from one another but included in one greater form, and again of one form evolved by the union of many wholes, and of many forms entirely apart and separate. This is the knowledge and ability to distinguish by classes how individual things can or cannot be associated with one another.
Theaetetus: Certainly it is.
Stranger: But you surely, I suppose, will not grant the art of dialectic to any but the man who pursues philosophy in purity and righteousness.
Theaetetus: How could it be granted to anyone else?
Stranger: Then it is in some region like this that we shall always, both now and hereafter, discover the philosopher, if we look for him; he also is hard to see clearly, but the difficulty is not the same in his case and that of the sophist.
Theaetetus: How do they differ?
Stranger: The sophist runs away into the darkness of not-being, feeling his way in it by practice, and is hard to discern on account of the darkness of the place. Don't you think so?
Theaetetus: It seems likely.
Stranger: But the philosopher, always devoting himself through reason to the idea of being, is also very difficult to see on account of the brilliant light of the place; for the eyes of the soul of the multitude are not strong enough to endure the sight of the divine.

At first, this seems to clear things up.  We get a definite image of the philosopher, who, as the hero of the story, must be the one contemplating true reality.  The philosopher as described here isn't in the businesses of identifying what unique Form is the true and correct one to associate with a given bit of the world.  Instead, he's tasked with reverse engineering the art by which nature combines Forms.  If we think of the forms as blending and interbreeding like organisms, we might think of the philosopher as performing a sort of genetic analysis of the world.  He establishes the complicated evolutionary history of something by exposing its DNA.  But this image of the philosopher means we have to give up the idea that only the Forms are real, as well as the idea that everything can be identified as either one Form or another.  We expect that many things can share one Form in the way that many copies share one model.  Only the model is understood as real.  But we didn't imagine that one thing could participate in many Forms, because this makes something other than the individual Forms real as well (namely, their particular combination in a given thing).  Understood this way, the theory of Ideas gives up the very principle of one-to-one correspondence and non-contradiction that is fundamental to something like Aristotle's taxonomic scheme.  

As we consider things more deeply though, we discover something really strange is going on.  Surprisingly, the search for the unreal Sophist has led us instead to the real philosopher.  This is no coincidence, and indicates how fine a line divides the two.  In addition, along the way, we've had to give up the very idea that the real and the unreal are opposites, and even forgo something as basic as the principle of non-contradiction.  Which means that our confusion is deeper than ever, because we are clearly no longer going to be able to describe the sophist as the opposite of the philosopher.  We've removed the very category that would let us oppose hero to villain.  This turns out to be only the beginning of our problems though, because the Stranger will go on to prove, in a way that sounds suspiciously like a bit of sophistry, that real existence actually must include "that which is not".   Not-being, the not-Forms, have a real existence in themselves.  Except that this "not" is no longer tied to opposition or contradiction (which has lost its binding force) but is now understood as pure difference. 

Stranger: In relation to motion, then, not-being is. That is inevitable. And this extends to all the classes; for in all of them the nature of other so operates as to make each one other than being, and therefore not-being. So we may, from this point of view, rightly say of all of them alike that they are not; and again, since they partake of being, that they are and have being.
Theaetetus: Yes, I suppose so.
Stranger: And so, in relation to each of the classes, being is many, and not-being is infinite in number.
Theaetetus: So it seems.
Stranger: Then being itself must also be said to be different than all other things.
Theaetetus: Yes, it must.
Stranger: And we conclude that existence likewise 'is not' in as many respects as there are other things, for, not being those other, while it is its single self, it is not all that indefinite number of other things.
Theaetetus: That is not far from the truth.
Stranger: Then we must not be disturbed by this either, since by their nature the classes have participation in one another. But if anyone refuses to accept our present results, let him reckon with our previous arguments and then proceed to reckon with the next step.
Theaetetus: That is very fair.
Stranger: Then here is a point to consider.
Theaetetus: What is it?
Stranger: When we say not-being, we speak, I think, not of something that is the opposite of being, but only of something different.
Theaetetus: What do you mean?
Stranger: For instance, when we speak of a thing as not great, do we seem to you to mean by the expression what is small any more than what is of middle size?
Theaetetus: No, of course not.
Stranger: Then when we are told that the negative signifies the opposite, we shall not admit it; we shall admit only that the particle "not" indicates something different from the words to which it is prefixed, or rather from the things denoted by the words that follow the negative.

With these argument the Stranger finally shoots down what we might interpret as Parmenides statement of the principle of non-contradiction, "For never shall this prevail, that things that are not are."  In fact, things that are not are different from things that are.  They are not one thing, but that doesn't mean necessarily that they are something else.  Difference has a type of Being that is not captured by any single form.  That type of Being is Not-Being.  Not-Being is everywhere, and connects us to an indefinite multiplicity of related Forms.  

STRANGER: Whereas we have not merely shown that things that are not, are, but we have brought to light the real character of 'not-being'.  We have shown that the nature of the different has existence and is parceled out over the whole field of existent things with reference to one another, and of every part of it that is set in contrast to 'that which is' we have dared to say that precisely that is really 'that which is not'.

As you may already be thinking after this long chain of reasoning, just following along with the Sophist leaves us in danger of remaining in the same highly abstract territory we started in.  So let me venture an ancient Greek to Plain English translation.  The core issue here is the being of possibility.  This is actually one way to understand the main contribution of Deleuze's philosophy -- the possible is real.  It is real because, as defined above, it has power, it has the capacity to affect and to be affected. 

But what kind of reality can possibility have?  Obviously not the same kind of reality as the actual.  But is it just not-actual?  In other words is there just "a" possibility, defined by exactly the same type of reality as "an" actuality, except with the caveat that it is not here or not now?  This would mean that there's only one type of existence, but sometimes it would have a positive sign and sometimes a negative sign.  Here, the possible, the different, is denied any true reality of its own and limited in advance to just duplicating the Titanic with some the deck chairs rearranged.  This is State thinking at its finest.  The power of possibility is tamed by actual power..  This type of thought turns out to be surprisingly well illustrated by the famous quote I remembered from W.V.O. Quine about the possible bald man in the doorway.  Here is the part I remembered, where Quine tries to make the very idea of possibility seem absurd:

Take, for instance, the possible fat man in that doorway; and, again, the possible bald man in that doorway. Are they the same possible man, or two possible men? How do we decide? How many possible men are there in that doorway? 

I had never actually read the whole essay this came from though.  And still haven't.  Though given that it even starts off with an obvious reference to the Sophist, I guess I need to now.  But check out the whole paragraph I found when I went looking for the exact wording:

Wyman's overpopulated universe is in many ways unlovely. It offends the aesthetic sense of us who have a taste for desert landscapes, but this is not the worst of it. Wyman's slum of possibles is a breeding ground for disorderly elements. Take, for instance, the possible fat man in that doorway; and, again, the possible bald man in that doorway. Are they the same possible man, or two possible men? How do we decide? How many possible men are there in that doorway? Are there more possible thin ones than fat ones? How many of them are alike? Or would their being alike make them one? Are no two possible things alike? Is this the same as saying that it is impossible for two things to be alike? Or, finally, is the concept of identity simply inapplicable to unactualized possibles? But what sense can be found in talking of entities which cannot meaningfully be said to be identical with themselves and distinct from one another? These elements are well-nigh incorrigible. By a Fregean therapy of individual concepts, some effort might be made at rehabilitation; but I feel we'd do better simply to clear Wyman's slum and be done with it.

What a splendid illustration of the connection between politics and metaphysics!  Quine is the sort of guy who wants the slum of possibility cleared before it breeds "disorderly elements".  He thinks maybe we can "rehabilitate" some of these folks who are different, who don't obey the laws of self-identity and perfect individual separation.  But wouldn't it be easier to just gas them all?  This is who we're up against.  The bureaucrats of pure reason who want to make actuality great again.

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! 

Plato 3 -- Platonic Myth

Last week we discovered that the Platonic Forms that found a line of descent through division are a myth.  Not "myth" figuratively, as in they don't really exists, but literally, as in Plato puts a myth where the definition of the Form ought to be.  Deleuze cites a couple of examples from Plato: the mythical shepherd-God is the true Statesman taking care of humanity, who defines what it means to be a Statesman; the true lover of the Phaedrus is the one who best remembers the mythical world of Forms we all contemplated before our birth.  To these we might add the famous founding "myth of the metals" that justifies the structure of the Republic.  In all these cases, the Ideas that are meant to ground our understanding of this world are explicitly taken out of it by conceiving them as myths.  

At first glance this seems like a strange way of explaining things.  Though, as I pointed out last time by comparing the Ideas to Nozick's "Invisible Hand Explanations", it may be the only non question-begging type of explanation. In fact, the modern mind shouldn't find the idea strange at all, since it's just the core idea of science (as I portrayed it a while back in the debate between Socrates and Scientist).  We are completely accustomed to the concept that the world is "just" physical stuff, but that it perfectly obeys laws which are not physical stuff; we call that idea "physics" now.  Notice that physicists don't think that they are inventing these laws.  They see themselves as discovering them.  In other words, the laws have an independent reality, and are not just concepts existing in a mind that help connect that mind to the world.  When we think of the Plato's Forms, we should be thinking of something with an ontological status similar to the laws of gravitation.  Whatever that status is; I'm drawing an analogy here which for the moment only succeeds in replacing one mystery with another.  

But let's not get into the thorny metaphysical question of how exactly physical law is connected to the physical world.  Let's focus on (what Deleuze says about) how Plato's mythical Ideas are connected to the ordinary world.  You may not be entirely surprised, after our discussion of circles and centers, to discover that the connection involves a type of circulation.

The structure of this myth in Plato is clear: it is a circle, with two dynamic functions - namely, turning and returning, distributing and allocation: the allocation of lots is carried out by the turning wheel of an eternally recurring metempsychosis.

 

... myth establishes the model of a partial circulation in which appears a suitable ground on which to base the difference, on which to measure the roles or claims. In the Phaedrus, this ground appears as the Ideas, such as these are contemplated by the souls which circulate above the celestial vault. In The Statesman, it appears in the form of the shepherd-God who presides over the circular movement of the universe. The ground may be either the centre or the motor of the circle. It is constituted by the myth as the principle of a test or selection which imparts meaning to the method of division by fixing the degrees of an elective participation. Thus, in accordance with the oldest tradition, the circular myth is indeed the story-repetition of a foundation. Division demands such a foundation as the ground capable of making the difference. Conversely, the foundation demands division as the state of difference in that which must be grounded.

The Ideas have a very particular necessary relationship to their instantiations arrayed along a chain of divisions. It almost seems best to say that Ideas differentiate into those instances.  The whole point here is that the various instances are grouped together under the lineage of an Idea not by their similarity, but precisely by their difference.  This set of differences is created and ordered by the Idea.  Conversely, the Idea, being something out of this world, only manifests itself through those differences.  The Idea circulates through, or is elaborated via, the chain of descent that it founds.  

This explains part of the confusion we had before about whether the "true angler" is at the beginning or end of the chain.  Do we work down?  Acquiring-hunting-water-fishing-striking-barbs-upwards.  Or does the chain go back up? From the true angler, through spear-fishers, net-fishers, land hunters, etc ... In fact, the Idea is at the beginning and the end both, simultaneously distributing all the points and gathering them in an order.  This is like the origin myth of a city, told and re-told to continually explain the character of the place and lay out a genealogy.  Since the starting point of the chain is actually a myth, the whole structure becomes a circle instead of a line.  We depart from the myth and we return to it, again and again, each time renewing and extending the lineage we are part of.  

If this sounds like a description of the 4th of July, well, then, at least we're getting in the spirit at the right time of year!

Plato 2 -- The Theory of Forms and The Method of Division

So, what are the Platonic Forms, and how do we go about finding them?  Deleuze starts off this section by focusing on the latter question.  He contrasts Plato's method for uncovering the foundations of our world (division) with Aristotle's method (generalization of specific differences).  

Division is not the inverse of a 'generalisation'; it is not a determination of species. It is in no way a method of determining species, but one of selection. It is not a question of dividing a determinate genus into definite species, but of dividing a confused species into pure lines of descent, or of selecting a pure line from material which is not.

Aristotle, you may recall, was essentially trying to come up with a finite scheme for classifying and identifying everything.  It consisted of dividing a genus into species.  Crucially, the species that divide the pre-conceived unity of a genus will cover it perfectly because they form primary contrary pairs -- like black and white, or with and without wings.  This means that Aristotle's concept of specific difference actually relies on what the things have in common in general.  Identity as well as negation (you are either in species A or species ~A) are the foundation of the scheme for understanding what differentiates one thing from another.  

Plato's attempt to organize and understand the world through the method of division works completely differently.  Here's a taste of the method from the Sophist (though perhaps this is a parody of it?)

STRANGER: ... Meanwhile you and I will begin together and enquire into the nature of the Sophist, first of the three: I should like you to make out what he is and bring him to light in a discussion; for at present we are only agreed about the name, but of the thing to which we both apply the name possibly you have one notion and I another; whereas we ought always to come to an understanding about the thing itself in terms of a definition, and not merely about the name minus the definition. Now the tribe of Sophists which we are investigating is not easily caught or defined; and the world has long ago agreed, that if great subjects are to be adequately treated, they must be studied in the lesser and easier instances of them before we proceed to the greatest of all. And as I know that the tribe of Sophists is troublesome and hard to be caught, I should recommend that we practice beforehand the method which is to be applied to him on some simple and smaller thing, unless you can suggest a better way.
THEAETETUS: Indeed I cannot.
STRANGER: Then suppose that we work out some lesser example which will be a pattern of the greater?
THEAETETUS: Good.
STRANGER: What is there which is well known and not great, and is yet as susceptible of definition as any larger thing? Shall I say an angler? He is familiar to all of us, and not a very interesting or important person.
THEAETETUS: He is not.
STRANGER: Yet I suspect that he will furnish us with the sort of definition and line of enquiry which we want.
THEAETETUS: Very good.
STRANGER: Let us begin by asking whether he is a man having art or not having art, but some other power.
THEAETETUS: He is clearly a man of art.
STRANGER: And of arts there are two kinds?
THEAETETUS: What are they?
STRANGER: There is agriculture, and the tending of mortal creatures, and the art of constructing or moulding vessels, and there is the art of imitation—all these may be appropriately called by a single name.
THEAETETUS: What do you mean? And what is the name?
STRANGER: He who brings into existence something that did not exist before is said to be a producer, and that which is brought into existence is said to be produced.
THEAETETUS: True.
STRANGER: And all the arts which were just now mentioned are characterized by this power of producing?
THEAETETUS: They are.
STRANGER: Then let us sum them up under the name of productive or creative art.
THEAETETUS: Very good.
STRANGER: Next follows the whole class of learning and cognition; then comes trade, fighting, hunting. And since none of these produces anything, but is only engaged in conquering by word or deed, or in preventing others from conquering, things which exist and have been already produced—in each and all of these branches there appears to be an art which may be called acquisitive.
THEAETETUS: Yes, that is the proper name.
STRANGER: Seeing, then, that all arts are either acquisitive or creative, in which class shall we place the art of the angler?
THEAETETUS: Clearly in the acquisitive class.
STRANGER: And the acquisitive may be subdivided into two parts: there is exchange, which is voluntary and is effected by gifts, hire, purchase; and the other part of acquisitive, which takes by force of word or deed, may be termed conquest?
THEAETETUS: That is implied in what has been said.
STRANGER: And may not conquest be again subdivided?
THEAETETUS: How?
STRANGER: Open force may be called fighting, and secret force may have the general name of hunting?
THEAETETUS: Yes.
STRANGER: And there is no reason why the art of hunting should not be further divided.
THEAETETUS: How would you make the division?
STRANGER: Into the hunting of living and of lifeless prey.
THEAETETUS: Yes, if both kinds exist.
STRANGER: Of course they exist; but the hunting after lifeless things having no special name, except some sorts of diving, and other small matters, may be omitted; the hunting after living things may be called animal hunting.
THEAETETUS: Yes.
STRANGER: And animal hunting may be truly said to have two divisions, land-animal hunting, which has many kinds and names, and water-animal hunting, or the hunting after animals who swim?
THEAETETUS: True.
STRANGER: And of swimming animals, one class lives on the wing and the other in the water?
THEAETETUS: Certainly.
STRANGER: Fowling is the general term under which the hunting of all birds is included.
THEAETETUS: True.
STRANGER: The hunting of animals who live in the water has the general name of fishing.
THEAETETUS: Yes.
STRANGER: And this sort of hunting may be further divided also into two principal kinds?
THEAETETUS: What are they?
STRANGER: There is one kind which takes them in nets, another which takes them by a blow.
THEAETETUS: What do you mean, and how do you distinguish them?
STRANGER: As to the first kind—all that surrounds and encloses anything to prevent egress, may be rightly called an enclosure.
THEAETETUS: Very true.
STRANGER: For which reason twig baskets, casting-nets, nooses, creels, and the like may all be termed 'enclosures'?
THEAETETUS: True.
STRANGER: And therefore this first kind of capture may be called by us capture with enclosures, or something of that sort?
THEAETETUS: Yes.
STRANGER: The other kind, which is practised by a blow with hooks and three-pronged spears, when summed up under one name, may be called striking, unless you, Theaetetus, can find some better name?
THEAETETUS: Never mind the name—what you suggest will do very well.
STRANGER: There is one mode of striking, which is done at night, and by the light of a fire, and is by the hunters themselves called firing, or spearing by firelight.
THEAETETUS: True.
STRANGER: And the fishing by day is called by the general name of barbing, because the spears, too, are barbed at the point.
THEAETETUS: Yes, that is the term.
STRANGER: Of this barb-fishing, that which strikes the fish who is below from above is called spearing, because this is the way in which the three-pronged spears are mostly used.
THEAETETUS: Yes, it is often called so.
STRANGER: Then now there is only one kind remaining.
THEAETETUS: What is that?
STRANGER: When a hook is used, and the fish is not struck in any chance part of his body, as he is with the spear, but only about the head and mouth, and is then drawn out from below upwards with reeds and rods:—What is the right name of that mode of fishing, Theaetetus?
THEAETETUS: I suspect that we have now discovered the object of our search.
STRANGER: Then now you and I have come to an understanding not only about the name of the angler's art, but about the definition of the thing itself. One half of all art was acquisitive—half of the acquisitive art was conquest or taking by force, half of this was hunting, and half of hunting was hunting animals, half of this was hunting water animals—of this again, the under half was fishing, half of fishing was striking; a part of striking was fishing with a barb, and one half of this again, being the kind which strikes with a hook and draws the fish from below upwards, is the art which we have been seeking, and which from the nature of the operation is denoted angling or drawing up (aspalieutike, anaspasthai).
THEAETETUS: The result has been quite satisfactorily brought out.
STRANGER: And now, following this pattern, let us endeavour to find out what a Sophist is.

Clearly, this method involves a much longer series of differentiations that simple genus and species.  And despite the conclusion that each division is "half" of the the preceding one, it's not at all clear that productive/acquisitive or capturing-with-a-net/striking-a-blow divide up a totality without missing anything (the way A and ~A divide up a closed space of possibility).  Instead of identifying some form, the goal of this method does appear to be to trace some line of descent, a genealogy almost.  When the Stranger asks "who is the true angler, or what is the true definition of angling?" he isn't so much trying to identify the angler according to a type, but to differentiate him from all kinds of other superficially similar characters.  In fact, we almost get the sense from this example that this differentiating could go on indefinitely towards more and more precise definitions.  This wouldn't be at all what you are looking for if you were trying to identify something by matching it to an essential genus.species type, because in that case you want to make sure that there are only a fairly limited number of types.  Deleuze points out that Platonic division parses things much finer than Aristotle's categories, and thus brings us much closer to the level of the particular individual.  Aristotle was content to create a high level classification of essential types or generic individuals.  These operate like formal molds that you can pour inert matter into to manufacture another particular thing, though one that is "essentially" just another copy of widget #4568/b9734.   Aristotle's types or molds or concepts are what Deleuze is what talking about when he continually refers to the way Aristotle creates a representative scheme that "mediates" difference.  These concepts stand in between the one universal of Being and many particular individual beings (the whole point of mediation is to represent the many as one).  

... the dialectic of difference has its own method - division - but this operates without mediation, without middle term or reason; it acts in the immediate and is inspired by the Ideas rather than by the requirements of a concept in general.

Plato's method is instead headed down to (or up to, depending on your point of view) the "true angler", of which there will clearly be just one singular example.  The goal is to decide who best qualifies for this title.

The meaning and the goal of the method of division is selection among rivals, the testing of claimants - not antiphasis but antisbetesis (we can see this clearly in Plato's two principal examples of division: in The Statesman, where the statesman is defined as the one who knows 'the pastoral care of men', but many introduce themselves by saying 'I am the true shepherd of men', including merchants, farmers, bakers, as well as athletes and the entire medical profession; and in the Phaedrus, where it is a question of defining the good madness and the true lover, but many claimants cry: 'I am love, I am the lover'). There is no question here of species, except ironically. There is nothing in common with the concerns of Aristotle: it is a question not of identifying but of authenticating. The one problem which recurs throughout Plato's philosophy is the problem of measuring rivals and selecting claimants.

You might even say there's a geometric distinction here, with Aristotle constructing a shallow horizontal scheme, and Plato preferring a deep vertical one.

Plato's method of division doesn't go infinitely deep though.  At some point the line of descent reaches a ground and comes to an end.  This is where the Forms (or, equivalently, Ideas) come in.  Something has to found or ground (see the translator's preface for the relation between these) the lineage of the angler.  Clearly, this is meant to be the one true angler, the ur-angler.  But in a weird twist I've never given much thought to, Plato seem to explicitly acknowledge that this elusive foundation is actually a myth.  

Our question is not yet that of knowing whether the selective difference is indeed between the true and false claimants, as Plato says it is, but rather of knowing how Plato establishes the difference thanks to the method of division. To the reader's great surprise, he does so by introducing a 'myth'.

 

In effect, once the question of the claimants is reached, The Statesman invokes the image of an ancient God who ruled the world and men: strictly speaking, only this God deserves the name of shepherd-King of mankind. None of the claimants is his equal, but there is a certain 'care' of the human community which devolves to the statesman par excellence, since he is closest to the model of the archaic shepherd-God. The claimants find themselves in a sense measured according to an order of elective participation, and among the statesman's rivals we can distinguish (according to the ontological measure afforded by the myth) parents, servants, auxiliaries and, finally, charlatans and counterfeits.

The Form or Idea that founds a pure line of descent is literally out of this world.  It may structure the whole chain from its position at one end, but it isn't really even attached to the series of divisions that lead towards (or away) from it.  For me, this really changes my understanding of what a Form is.  I remember snickering sophomoric critiques of Plato's "Form of a Table" -- along the lines of, "Do you mean the Form of a dining table or a coffee table? Or what about a small table I'm now using as a bench?  Is that the Form of a bench then?  Don't we need a distinct Form for every single thing we see, and isn't that a reductio ad absurdum of the whole idea?"  But of course, I didn't understand anything as a sophomore.  The Forms aren't "like" the things in the world.  They are principles that stand apart from the world, and don't resemble its contents.  There's not a Form for each thing in the world, that corresponds to it; rather, the Forms make the things in the world.  They are meant to be the unchanging principles of its creation and founding, so they can't be of the same order as the stuff they found.  This is exactly the problem with Aristotle's essential genera and species.  These are concepts that just duplicate the world we see around us in idealized form.  The molds look just like the finished product, though each particular casting is slightly different in some inessential way.  Essential difference only happens between the molds, and even then, they are only different because they together compose a higher unity.  Apparently my sophomore self was criticizing Aristotle, not Plato (probably also poorly at that).  

As I thought back and tried to remember these books, I realized that while Aristotle indeed talks a lot about actual plants and animals, Plato always has his head in the clouds.  The important Forms are the Good, the Just, the Beautiful, the Statesmen, the Lover, the Just City of the Republic.  But these are all completely abstract.  Just for kicks I tried to figure out where the whole "Form of the table" thing came from.  Did Plato even use that as an example anywhere?  Turns out he did, in Book X of The Republic:

Well then, shall we begin the enquiry in our usual manner: Whenever a number of individuals have a common name, we assume them to have also a corresponding idea or form. Do you understand me?

I do.
Let us take any common instance; there are beds and tables in the world --plenty of them, are there not?

Yes.
But there are only two ideas or forms of them --one the idea of a bed, the other of a table.

True.
And the maker of either of them makes a bed or he makes a table for our use, in accordance with the idea --that is our way of speaking in this and similar instances --but no artificer makes the ideas themselves: how could he?

Impossible.
And there is another artist, --I should like to know what you would say of him.

Who is he?
One who is the maker of all the works of all other workmen.
What an extraordinary man!
Wait a little, and there will be more reason for your saying so. For this is he who is able to make not only vessels of every kind, but plants and animals, himself and all other things --the earth and heaven, and the things which are in heaven or under the earth; he makes the gods also.

He must be a wizard and no mistake.
Oh! you are incredulous, are you? Do you mean that there is no such maker or creator, or that in one sense there might be a maker of all these things but in another not? Do you see that there is a way in which you could make them all yourself?

What way?
An easy way enough; or rather, there are many ways in which the feat might be quickly and easily accomplished, none quicker than that of turning a mirror round and round --you would soon enough make the sun and the heavens, and the earth and yourself, and other animals and plants, and all the, other things of which we were just now speaking, in the mirror.

Yes, he said; but they would be appearances only.
Very good, I said, you are coming to the point now. And the painter too is, as I conceive, just such another --a creator of appearances, is he not?

Of course.
But then I suppose you will say that what he creates is untrue. And yet there is a sense in which the painter also creates a bed?

Yes, he said, but not a real bed.
And what of the maker of the bed? Were you not saying that he too makes, not the idea which, according to our view, is the essence of the bed, but only a particular bed?

Yes, I did.
Then if he does not make that which exists he cannot make true existence, but only some semblance of existence; and if any one were to say that the work of the maker of the bed, or of any other workman, has real existence, he could hardly be supposed to be speaking the truth.

At any rate, he replied, philosophers would say that he was not speaking the truth.

No wonder, then, that his work too is an indistinct expression of truth.

No wonder.
Suppose now that by the light of the examples just offered we enquire who this imitator is?

If you please.
Well then, here are three beds: one existing in nature, which is made by God, as I think that we may say --for no one else can be the maker?

No.
There is another which is the work of the carpenter?
Yes.
And the work of the painter is a third?
Yes.
Beds, then, are of three kinds, and there are three artists who superintend them: God, the maker of the bed, and the painter?

Yes, there are three of them.
God, whether from choice or from necessity, made one bed in nature and one only; two or more such ideal beds neither ever have been nor ever will be made by God.

Why is that?
Because even if He had made but two, a third would still appear behind them which both of them would have for their idea, and that would be the ideal bed and the two others.

Very true, he said.
God knew this, and He desired to be the real maker of a real bed, not a particular maker of a particular bed, and therefore He created a bed which is essentially and by nature one only.

So we believe.
Shall we, then, speak of Him as the natural author or maker of the bed?

Yes, he replied; inasmuch as by the natural process of creation He is the author of this and of all other things.

And what shall we say of the carpenter --is not he also the maker of the bed?

Yes.
But would you call the painter a creator and maker?
Certainly not.
Yet if he is not the maker, what is he in relation to the bed?
I think, he said, that we may fairly designate him as the imitator of that which the others make.

Good, I said; then you call him who is third in the descent from nature an imitator? 

It's pretty clear that Plato chose to use the table and the bed as a simple pedagogical device, and not because he thinks tables and beds actually have Forms.  The point of this passage is clearly the chain of division between the various tables -- the form of the table, the particular table, and the imitation of the table.  Reducing the scheme to three divisions conveys its essence.  I don't think we're meant to imagine a free floating "ideal table" blueprint in God's head though.  What else could this be than another image of the tables we know?   The Form of the table here is some principle that is clearly put out of this world and into the heavens.  However we think of this Form as existing (and we'll come to this in a while) it is not the same type of being as the particular tables or the images of tables.  In short, the Idea of a table is not going to look like a table.  It founds the chain of possible tables, but is not really part of the chain.  

I think this is a deep and important point, both for reconsidering Plato and for understanding Deleuze, so I'm going to dedicate our next episode to "Platonic Myth".  For now, I just want to make a connection between the way Ideas are different in kind from things (without their simply existing in the the representative mind of Aristotle) and Robert Nozick's concept of "Invisible-Hand Explanations".  Ideas turn out to function precisely as invisible-hand explanations of the world as Nozick defined these in Anarchy, State, and Utopia.

Within a barter system, there is great inconvenience and cost to searching for someone who has what you want and wants what you have, even at a marketplace, which, we should note, needn't become a marketplace by every- one's expressly agreeing to deal there. People will exchange their goods for something they know to be more generally wanted than what they have. For it will be more likely that they can exchange this for what they want. For the same reasons others will be more willing to take in exchange this more generally desired thing. Thus persons will converge in exchanges on the more marketable goods, being willing to exchange their goods for them; the more willing, the more they know others who are also willing to do so,
in a mutually reinforcing process.
...
There is a certain lovely quality to explanations of this sort. They show how some overall pattern or design, which one would have thought had to be produced by an individual's or group's successful attempt to realize the pattern, instead was produced and maintained by a process that in no way had the overall pattern or design "in mind." After Adam Smith, we shall call such explanations invisible-hand explanations. ("Every individual intends only his own gain, and he is in this, as in so many other cases, led by an invisible hand to promote an end which was no part of his intention.") The specially satisfying quality of invisible-hand explanations (a quality I hope is possessed by this book's account of the state) is partially explained by its connection with the notion of fundamental explanation adumbrated in Chapter 1. Fundamental explanations of a realm are explanations of the realm in other terms; they make no use of any of the notions of the realm. Only via such explanations can we explain and hence understand everything about a realm; the less our explanations use notions constituting what is to be explained, the more ( ceteris paribus) we understand. Consider now complicated patterns which one would have thought could arise only through intelligent design, only through some attempt to realize the pattern. One might attempt straight-forwardly to explain such patterns in terms of the desires, wants, beliefs, and so on, of individuals, directed toward realizing the pattern. But within such explanations will appear descriptions of the pattern, at least within quotation marks, as objects of belief and desire. The explanation itself will say that some individuals desire to bring about something with (some of) the pattern-features, that some individuals believe that the only (or the best, or the ...) way to bring about the realization of the pattern features is to ... , and so on. Invisible-hand explanations minimize the use of notions constituting the phenomena to be explained; in contrast to the straightforward explanations, they don't explain complicated
patterns by including the full-blown pattern-notions as objects of people's desires or beliefs. Invisible- hand explanations of phenomena thus yield greater understanding than do explanations of them as brought about by design as the object of people's intentions. It therefore is no surprise that they are more satisfying.

That's my emphasis up there.  Because I see that as the crucial question to answer.  How does the From of a table structure the pattern of actual tables or imitations of tables without having these patterns "in mind"?  Plato puts the Ideas in a different realm.  But this realm does no useful work for us if it's just a blurry eyed version of our everyday realm, just a copy of it with some of the details left undetermined.  This was exactly the problem with Aristotle's concepts.  Plato and Deleuze have something different in mind.  Cue Heidegger on "ontological difference", we're outta here!

 

Science Philosophy

Plato has been momentarily interrupted to bring you this special news bulletin from the future ...

I went to the Wing Luke Museum last night to hear Ted Chiang give a brief talk and participate in a panel discussion. He only spoke for about 15 minutes, and made two very simple, but very profound, points.

First, he pointed out that sci-fi is a fiction of possibilities.  It is a fiction of new and different worlds.  It tells a story of change, where the world at the end is not the same as the world at the beginning.  In other words it's a progressive fiction, regardless of whether it depicts the future as utopian or dystopian.  As a result, it only makes sense to people who have seen the industrial revolution.  If you go back more than 200 years or so, you discover that the rate of change of human society is so small relative to the human life span that the world essentially looks static.  Your children's jobs are going to be just like your parent's were.  This ratio only starts to change with the industrial revolution, and has only accelerated since then.  Once we've seen with our own eyes that the world can change, we can start to appreciate the possibilities of further change.  

He contrasted this with the storyline implicit in other types of fiction.  For example, consider Star Wars.  While nominally science fiction, this is really a retelling of the oldest fable.  An untested young hero gets a magic sword from a mysterious old wizard and has to go rescue a princess from a castle guarded by an evil mage.  Sound like a familiar space opera?  These stories basically follow a classic arc where the world is basically good, evil intrudes, a hero rises and defeats the evil, and the world is restored to its rightful good order.  Fiction like this is inherently conservative, regardless of whether it's overtly political message comes straight from Elizabeth Warren.  Fiction like this makes perfect sense when no one in society can remember it ever being any different.  

Second, he suggested that this distinction between science and other fictions is meant to be explicitly political.  In other words, in his view, science fiction is an inherently progressive genre.  It shows people how the world they live in could be different.  It tells us about futures we've been told are impossible.  In short, it questions the status quo.  It may reveal an optimistic or a pessimistic future, but either way it illustrates a tomorrow's world organized differently from today's.  So writing or reading science fiction is an inherently political act.  More generally, imagination is an inherently political act.  He summed up his position by citing Neo's speech at the end of the first Matrix movie:

I know you're out there. I can feel you now. I know that you're afraid. You're afraid of us. You're afraid of change. I don't know the future. I didn't come here to tell you how this is going to end. I came here to tell you how it's going to begin. I'm going to hang up this phone, and then I'm going to show these people what you don't want them to see. I'm going to show them a world without you, a world without rules and controls, without borders or boundaries, a world where anything is possible. Where we go from there, is a choice I leave to you.

Anyone who sees a different world is inevitably headed for a clash with the authorities in this one.   

As you might imagine, I enjoyed Ted's remarks, because I wrote them myself.  Maybe his version makes a better and more vivid story 🤔?  But this is exactly the point I was making in that post about the importance to Deleuze of having a philosophy built on affirmation rather than negation.  One side is focused on the limits and necessity of identity.  The other cares about the possibilities and contingencies offered by difference.  The latter is an inherently progressive philosophy, even if it focuses on metaphysics and never makes an explicit political statement.  This is the philosophy of the future.  It doesn't tell you how it has to be, it just hangs up the phone and starts imagining it.

In considering this deep distinction between progressive and conservative thinking, I've encountered what I see as a corollary to the thesis.  One of the most refreshing aspects of Ted Chiang's work is his optimism.  Now, I wouldn't say that the guy is Herr Doktor Pangloss exactly; he's plenty capable of bringing up ways that technology can go wrong.  Generally though, he has an optimistic view of the new possibilities technology affords us, and his thoughtful characters find a way to end with a better world than the one they started with.  I claimed earlier though that science fiction was a progressive genre regardless of whether it envisioned a utopia or a dystopia.  Which seems to imply that you could equally well be a pessimistic progressive.  Surely which side you prefer is to some degree just a matter of taste.  But perhaps being deeply drawn to the progressive aspect of sci-fi (enough to talk about it in a lecture at least) actually fits very naturally with an affirmative view of the future.  After all, the dystopias we read generally posit a world of either totalitarian control or chaotic free for all.  You can have A Brave New World, or you can have Mad Max.  Both are certainly different from our current world, and in this sense are progressive visions.  But in both cases, "progress" seems to lead to a dead end.  Totalitarianism and chaos both return us to the same static society that prevailed before the industrial revolution.  Once we descend into these dystopias we are stuck.  We can't imagine any more change coming after that.  I suppose a perfect utopia like Plato's Republic would work the same way (and now that I think about it, the fact that it wouldn't in reality is the driving idea behind another amusing piece of sci-fi) which is perhaps why these can seem as creepy as the dystopias.  So while being a pessimistic progressive may make logical sense, it's a very limited, one step, procedure.  

If you are an optimistic progressive, however, you can imagine a different world that then continues to change.  Your imagination opens up new possibilities that open up new possible imaginings.  This type of multiple affirmation is at the core of Deleuze's thinking.  It means selecting the difference that makes even more difference ad infinitum.  This is what he's describing with a theory of difference "in itself", that is, referring only to more difference "in the state of permanent revolution which characterizes the eternal return".  

Plato 1 -- Preamble

The last section of this first chapter (pg. 59-69) is an extended reflection on Plato's theory of forms. 

There's also a brief interlude that deals with Heidegger that I'll probably skip over just because it has been way too long since I read Being and Time, and it's not one of those books you can pick up and quickly skim to remember the gist.  I imagine that this Heidegger section is here mainly to forestall a quick response of, "Hey, Heidegger already did that!" to Deleuze's thesis: "The task of modern philosophy has been defined: to overturn Platonism".  Certainly Heidegger often claimed to be "overcoming metaphysics".  Deleuze's summary of his philosophy here acknowledges that they share an aim, as well as some particular points of correspondence, but then questions whether Heidegger fully succeeded in reaching the goal.  At some point soon, it might be time to go back to Heidegger.  My interest was recently renewed when I read Graham Hartman's Object-Oriented Ontology, which was heavily influenced by Heidegger.  I'm still a bit reluctant though since I read about half of The Question Concerning Technology a few years back and found it mildly interesting but hugely portentous. 

I can't say I remember Plato any better than Heidegger really, but him at least one can relatively quickly re-read.  Deleuze discusses three of the dialogues -- Phaedrus, Sophist, and Statesmen.  The first is a perennial college classic, but I had never read the others.  So I picked up the Sophist and gave it a cursory once over.  And that shit is weird man.  I guess I hadn't read any of these "late" dialogues because I had always heard that they were "dogmatic", and also were hardly genuine dialogs with opposing points of view at all.  In retrospect, I understand why folks say the latter, because the main character of Socrates only gets about one line, and because very little would be lost if Plato dropped the pretense of multiple speaking characters.  The Sophist is basically just a monologue by an "Eleatic stranger".  Eleatic as in dude-from-Elea, home of Parmenides and Zeno.  To call it "dogmatic" though seems to me a major mistake.  In fact, as Deleuze points out here, it's almost the exact opposite of dogmatic.   The main thrust of the Sophist seems to completely undermine our usual conception of Plato's whole theory of forms.  It almost reads like an illustration of what goes wrong if you are overly dogmatic in your application of "Platonism".

Was it not inevitable that Plato should push irony to that point - to parody?  Was it not inevitable that Plato should be the first to overturn Platonism, or at least to show the direction such an overturning should take? We are reminded of the grand finale of the Sophist: difference is displaced, division turns back against itself and begins to function in reverse, and, as a result of being applied to simulacra themselves (dreams, shadows, reflections, paintings), shows the impossibility of distinguishing them from originals or from models. The Eleatic Stranger gives a definition of the sophist such that he can no longer be distinguished from Socrates himself: the ironic imitator who proceeds by brief arguments (questions and problems).

So I think one way to understand the whole final section of the chapter is to build up to understanding this quote.  To do this though, we have to go back to the beginning and ask what problem the dogma of the theory of forms was meant to solve to begin with.  This post is already getting long, so I'll do it in installments.

Next time on FPiPE -- The Theory of Forms and The Method of Division.  Stay tuned!