Lecture Nineteen: Plato and Determination


                  Today I want to talk about another figure that Deleuze takes up in his analysis of the history of philosophy: Plato. Plato occupies an ambivalent position in Deleuze’s philosophy, and he claims that ‘the Heraclitean world still growls in Platonism.’ (DR 71) In this respect, the claim that one must ‘overturn’ [renverser] Platonism does not involve a complete repudiation of it. Rather, ‘that this overturning should conserve many Platonic characteristics is not only inevitable but desirable.’ (DR 71) We will turn to Deleuze’s analysis of Plato itself in detail next week, but this week, I want to focus on Plato himself, and particularly on the method of division. The text I want to look at is the Sophist, which presents a dialogue not with Socrates himself, but rather with the stranger, or visitor. The dialogue revolves around the attempt by the stranger to define his notion of the sophist. Socrates begins the dialogue by questioning whether the visitor believes that ‘sophists, statesmen and philosophers make up one kind of thing or two.’ (217a) The visitor then offers a series of possible definitions of the sophist. While much of the dialogue is taken up by an analysis of the forms, and the way in which they relate to one another. This is because the visitor has to explain how the sophist can profess knowledge that seems to be the case, but is not – in other words, how can the sophists knowledge really be about nothing, given that nothing is not, and therefore cannot be a subject that one can relate to. While there is much that is interesting (and relevant) in this analysis, I want to focus instead on the method of division that Plato presents earlier in the dialogue, in order to compare his approach with that of Aristotle. My focus will be on tracing out how this method differs from that of Aristotle, despite the apparent similarity to definition in terms of species and genera. In particular, I want to pick up Deleuze’s claim that ‘Platonic dialectic is neither a dialectic of contradiction nor of contrariety, but a dialectic of rivalry, a dialectic of rivals and suitors.’ (LS 292) In this respect, Plato’s dialectic is seen by Deleuze as closer to the procedure of Nietzsche in the eternal return than to the method of definition found in Aristotle. To see why this is the case, I want to begin by looking at how the visitor in the Sophist goes about determining the nature of the sophist.

Determination and the Method of Division

                  The central theme of the Sophist is the effort by the Eleatic visitor to draw out what exactly a sophist is using the method of division. To provide an example of how this works, the visitor suggests that they use the example of defining an angler, as the fact that an angler is ‘recognizable to everybody’ means that the method itself will be more easily seen. Now, the method of division appears to be very similar to the Aristotelian method which we looked at last term. The visitor begins by noting that the angler is an expert, and dividing expertise into arts of acquisition and arts of production. Acquisition is in turn divided into two categories, taking possession of something, and acquisition by exchange, and taking possession in turn into combat and hunting. We carry on dividing the various groups, between animal hunting and the hunting of the inanimate, animals that swim and animals that live on land, swimmers with wings and swimmers without, and through the various ways in which fish can be hunted. The result of this examination is therefore an account of what an angler is, arrived at through a progressive division of a whole into parts.

                  There are some restrictions on the way in which we divide the whole into different parts. In the Phaedrus, Socrates states that we should ‘cut up each kind according to its species along its natural joints, and not try to splinter any part, as a bad butcher might do.’ In this respect, the divisions cannot simply be arbitrary. In the Statesman, the procedure of division goes wrong because the young Socrates has failed to cut up reality at its joints properly. Here, the visitor gives the following general account of how division should occur in order to avoid such errors:

It’s as if someone tried to divide the human race into two and made the cut in the way that most people here carve things up, taking the Greek race away as one, separate from all the rest, and to all the other races together, which are unlimited in number, which don’t mix with one another, and don’t share the same language—calling this collection by the single appellation ‘barbarian’. Because of this single appellation, they expect it to be a single family or class too. Another example would be if someone thought that he was dividing number into two real classes by cutting off the number ten-thousand from all the rest, separating it off as a single class, and in positing a single name for all the rest supposed here too that through getting the name this class too came into existence, a second single one apart from the other. But I imagine the division would be done better, more by real classes and more into two, if one cut number by means of even and odd, and the human race in its turn by means of male and female, and only split off Lydians or Phrygians or anyone else and ranged them against all the rest when one was at a loss as to how to split in such a way that each of the halves split off was simultaneously a real class and a part. (Statesman 262 d-e)

In this sense, we can see that the attempt to define something appears to operate much like the search for essence that Aristotle proposes, where we arrive at the true nature of something through taking what appears to be a genus, and dividing into two classes. By the repetition of this procedure, when applied to one of the species, we gradually ‘home in’ on the species we are attempting to define.

When we turn to the case of the definition of the sophist, however, the situation is not so straightforward. The visitor begins by noting that both the sophist and the angler are hunters, although rather than hunting fish, the sophist hunts men, and rather than hunting by force, the sophist hunts by ‘legal oratory, political oratory and conversation,’ that is, by persuasion. The sophist therefore turns out to be ‘the hunting of rich, prominent young men’ in private for money. This definition, however, turns out not to be a complete account of the sophist, and so the visitor offers another. It is also ‘the expertise of the part of acquisition, exchange, selling, wholesaling, and soul-wholesaling, dealing with words and learning that have to do with virtue.’ (Sophist 224b) The sophist is therefore a merchant of knowledge. He can also be defined as a cleanser of the spirit:

So let it be the cleansing part of the expertise of discriminating things; and let it be marked off as the part of that which concerns souls; and within that if s teaching; and within teaching it’s education. And let’s say that within education, according to the way the discussion has turned now, the refutation of the empty belief in one’s own wisdom is nothing other than our noble sophistry. (Sophist 231b)

This presents us with a problem, as it appears as if none of the definitions provided has been truly adequate to capturing the nature of the sophist. In this sense, it fails as an Aristotelian account of the definition of the individual. When we looked at Aristotle’s account, we saw that definition proceeded along one particular branch of the tree, and so each species had one definition. We cannot determine the essence of the sophist by tracing one line from the genus to the species, however. In fact, we cannot even say that sophisty is one kind of science. The visitor classifies it under the arts of production and the arts of acquisition at different points during his attempt to tie it down. Now, we can begin to explain this fact by noting that sophistry ‘isn’t a trivial sort of expertise, but quite a diverse one’ (223c), and as such it differs from cases such as angling that can be specified by the progressive determination of a single genus. What Plato is offering, therefore, is a more complex form of determination that that which is provided by Aristotle.

The ‘Quilt’ Interpretation of Division

                  Moravcsik, in his Plato and Platonism, provides a reading of this form of determination where he characterises it, in opposition to Aristotle’s ‘tree’ interpretation of division, as a ‘quilt’ interpretation of division. We can begin by noting that even the basic division of art into productive and acquisitive arts is not the only way in which art can be divided. In the Statesman, for instance, Plato divides art as follows:

Visitor: Well then: isn’t it the case that arithmetic and some other sorts of expertise that are akin to it don’t involve any practical actions, but simply provide knowledge?

Young Socrates: That’s so.

Visitor: Whereas for their part the sorts of expertise involved in carpentry and manufacture as a whole have their knowledge as it were naturally bound up with practical actions, and use it to complete those material objects they cause to come into being from not having been before? (Statesman 258d-e)

Art or expertise can therefore also be divided by whether it is purely theoretical, or also contains a practical component. The Sophist provides six different attempts at the definition of the sophist, each of which traces a different path through possible divisions. In his discussion of Plato’s account of division, Aristotle sees this as a fundamental problem, in that Plato has not given the proper difference in these kinds of cases:

Is man an animal or animate? If he assumed animal, he has not deduced it. Again every animal is either terrestrial or aquatic: he assumed terrestrial. And that man is the whole – a terrestrial animal – is not necessary from what he has said, but he assumes this too…For what prevents all this from being true of man yet not making clear what a man is or what it is to be a man? (Posterior Analytics 18-28)

So for Aristotle, the fact that there is more than one possible path to the sophist – that the sophist shows up on more than one branch of the tree, implies that Plato has failed to capture what is essential about the sophist. While the sophist may indeed be in fact a hunter of rich, prominent young men, this is not what he necessarily is in essence.

                  While such a criticism would be appropriate if Plato were dividing according to an arborescent model, such as Aristotle’s, we should note that instead that there is something more like a geometrical model at play in Plato’s approach. What we have is something more like the genus, art, as a space that can be demarcated in a variety of manners which can overlap with one another, rather than the model of man as a collection of individuals that are separated off from others by process of selection. In this way, the addition of alternative potential modes of division does not invalidate the original as not providing the essential determination of the sophist, but allows us to grasp the multifaceted nature of the art of sophistry. Each different definition further cuts down the space in the genus that the sophist occupies, and we thus arrive at a picture of him through the addition of a number of ‘brush strokes’ that together make up a definition. In a sense, what we are presented with here, to use the characteristics found in Deleuze and Guattari’s later thinking, is something like a rhizomatic model of thought – that is, a thought not defined by hierarchy, and a central line, but rather by a kind of flat multiplicity.

The Aim of Plato’s Method of Division

                  Given that Plato is not providing something like a biological taxonomy – the kind of thing we found in Aristotle, the question naturally arises, what is it that Plato is attempting to do in the Sophist? Deleuze claims that Platonic division in no way proposes to determine the species of a genus … rather, it proposes to do so, but superficially, and even ironically, the better to hide under this mask its true secret.’ (DR 72) The answer starts to become clearer when we note the fact that a sophist is a thinker who resembles a philosopher, without actually being one. Similarly, in the Statesman, the Eleatic visitor there defines a statesmanship as ‘knowledge of the collective rearing of human beings.’ (Statesman, 267d) Once we have this definition, we are still faced with a difficulty, however, as it appears that there are a large number of people who fulfil this description: ‘merchants, farmers, millers and bakers’ (Statesman, 267e). Even with a given definition, we have not answered the question at the root of the dialogue. As Deleuze puts it, ‘difference is not between species, between two determinations of a genus, but entirely on one side, within the chosen line of descent.’ (DR 72) What Plato is trying to do, according to Deleuze, is not to define a particular class of individuals, but rather to do something different – to trace the genealogy of the subject in question – to distinguish between the sophist and the philosopher in terms of their origin. The visitor makes this project explicit in the Statesman, where he describes the project of determining statesmanship in the following way:

Visitor: Yes, but there is something else remaining that is still more difficult than this, by reason of its being both more akin to the kingly class, and closer to it, and harder to understand; and we seem to me to be in a situation similar to that of those who refine gold.

Young Socrates: How so?

Visitor: I imagine that these craftsmen also begin by separating out earth, and stones, and many different things; and after these, there remain commingled with the gold those things that are akin to it, precious things and only removable with the use of fire: copper, silver, and sometimes adamant, the removal of which through repeated smelting and testing leaves the ‘unalloyed’ gold that people talk about there for us to see, itself alone by itself.

Young Socrates: Yes, they certainly do say these things happen in this way.

Visitor: Well, it seems that in the same way we have now separated off those things that are different from the expert knowledge of statesmanship, and those that are alien and hostile to it, and that there remain those that are precious and related to it. (Statesman 303d-304a)

How, do we therefore distinguish the statesman from the merchants, farmers, millers and bakers, or Socrates from the sophist? Well, in many dialogues, though ironically, not in the sophist, we have the introduction of a myth. In the Statesman, the visitor introduces the fable of two cosmic eras, that of Cronos, and the present age of Zeus. Each of these gods allows ordered existence to carry on in the world by ensuring that the universe continues to revolve around its circle. By incorporating a myth into the structure of our enquiry, we are able to resolve the question of which of the various contenders is in actual fact the statesman. That is, myth provides an archetype by which to properly separate the pure gold of the statesman from the mixed elements of the other figures. How does it do this? Well, these gods’ governance of the universe provides us with a model by which to assess which of the claimants is the true statesman. When we looked at the notion of time in joint, we saw that Plato argues that the world of appearances is derivative, or secondary to, an atemporal rational structure. The demiurge in that myth created the universe as a ‘moving image of eternity’. Now, the statesman and the true philosophers are both going to be figures who relate to the true ground of the world, the atemporal realm of ideas or forms, rather than the realm of appearances. Obviously, however, a statesman or a philosopher cannot actually be a god, just as they cannot be atemporal, but they can still resemble one. Here, therefore, we find the Platonic view that the world of appearances contains just shadows or copies of real things. Those copies that resemble real things has more reality than those which do not. An important point to note, however, is that there are two ways in which something can be a copy of, or resemble, something else. The visitor sets these two ways out in the Sophist:

Visitor: One type of imitation I see is the art of likeness-making. That’s the one we have whenever someone produces an imitation by keeping to the proportions of length, breadth, and depth of his model, and also by keeping to the appropriate colours of its parts.

Theaetetus: But don’t all imitators try to do that?

Visitor: Not the ones who sculpt or draw very large works. If they reproduced the true proportions of their beautiful subjects, you see, the upper parts would appear smaller than they should, and the lower parts would appear larger, because we see the upper parts from further away and the lower parts from closer. (Sophist, 235d-236a)

Something can therefore resemble the way something is (in which case it is an icon), or just in the way in which sculptors may employ tricks of perspective, it can resemble the way something appears (in which case it is a phantasm). The true statesman resembles the Idea or form of the statesman in the first of these senses, as the form itself cannot be given in appearance, as it is not spatiotemporal. The pretender only resembles the appearance of the form, not the form itself. The problem, therefore, is to distinguish the candidates who bear a true likeness from those which merely appear to. We can now also see why there is no myth in the Sophist. The sophist resembles the forms in the second sense: that is, he presents the appearance of knowledge, which is a resemblance to the philosopher. The philosopher, on the contrary, presents a resemblance to the forms themselves, in that he has knowledge. As the sophist relates himself to appearances, and not to the forms, there is no lineage in him to trace back to the forms, as there is with the statesman. The sophist, rather, is determined by a lesser reality. In this sense, there can be no myth of the sophist, because there is no eternal form that he resembles. Most of the dialogue itself attempts to make this notion of existing but not being a copy of the forms coherent.

                  It is this distinction between different forms of resemblance that Deleuze takes to be the essential feature of Platonism, and is a key distinction for Deleuze’s own early philosophy:

In Chapter I, we suggested that Plato’s thought turned upon a particularly important distinction: that between the original and the image, the model and the copy. The model is supposed to enjoy an originary superior identity (the Idea alone is nothing other than what it is: only Courage is courageous, Piety pious), whereas the copy is judged in terms of a derived internal resemblance… More profoundly, however, the true Platonic distinction lies elsewhere: it is of another nature, not between the original and the image but between two kinds of images [idoles], of which copies [icones] are only the first kind, the other being simulacra [phantasmes]. The model-copy distinction is there only in order to found and apply the copy-simulacra distinction, since the copies are selected, justified and saved in the name of the identity of the model and owing to their internal resemblance to this ideal model. The function of the notion of the model is not to oppose the world of images in its entirety but to select the good images, the icons which resemble from within, and eliminate the bad images or simulacra. (DR 154-5)


                  In what sense, therefore, can Plato be seen as the instigation of representation, but also the point at which representation has not yet properly asserted itself (‘an animal in the process of being tamed’ [DR 71])? Well, when we look at Aristotle, we see that the notion of difference relies on a prior identity. This is what allows different species to be related without simply being ‘other’ to one another. Aristotelian taxonomy therefore presupposes the presence of identity as a ground for differences. Aristotle’s complaint against Plato is that Plato has not properly grounded the notion of division. This is the reason why the determinations he gives (‘man, the terrestrial animal’) are not, according to the Aristotelian account, essential determinations. As we saw, while it appears that Plato is providing a hierarchical taxonomy, in fact, his characterisations specify lines that cut up the world according to its joints. Deleuze makes the following comment on this situation:

The Idea is not yet the concept of an object which submits the world to the requirements of representation, but rather a brute presence which can be invoked in the world only in function of that which is not “representable” in things. (DR 71)

I take Deleuze to mean by this that essence is not yet determined by default according to a categorial scheme that presumes a central identity, but rather has to be given by something that falls outside of the dialectic, that is, by myth. Myth therefore plays an essential role in the Platonic method, and places Plato outside of representation.

                  In making myth central to his philosophical account, Plato resembles Nietzsche, with his myth of the evil demon which grounds the eternal return. We can draw further parallels. In both cases, we have a test of selection that attempts to determine the true grounds of entities. Or Nietzsche, this test was the Eternal Return, which sought to select those entities which were grounded in an ontology of becoming, whereas for Plato, this test selects those entities which can be grounded in the proper realm of being, the forms. In both cases, this test cannot be expressed propositionally, so the eternal return appears in two forms – on the one hand as the thought experiment of the evil demon, and on the other as the story of Zarathustra. For Plato, we instead have the turn to mythology as that which grounds the test of selection. The choice, which for Deleuze is still open in the work of Plato, is therefore whether we take the test as selecting icones, and thereby instituting representation, or as selecting perspective, and phantasma, thus opening up the possibility of a philosophy of difference.

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