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!
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