04 October 2006

Virtual Ideas-- Problems and Multiplicities

In chapter 4 of Difference and Repetition, "Ideas of Synthesis and Difference", Deleuze introduces his account of the virtual as the sufficient reason for the actual. This account unfolds in terms of what Deleuze refers to as "Ideas", which should be treated as a synonym for "multiplicities". By "Idea" we should not here understand the Lockean conception of mental entities, serving as copies of objects in the world. Rather, despite his anti-Platonism, Deleuze's account of Ideas is far closer to Plato's account of Ideas-- via Kant --than the conception of Ideas as psychological entities. It will thus be necessary to both determine how Deleuze draws on Plato and Kant, and how he diverges from them.

1. A Brief Detour Through Plato's Theory of the Ideas (Forms)

The man of knowledge must be able not only to love his enemies
but hate his friends.
Very roughly, it can be argued that Plato advances his account of the Forms or Ideas to explain how something like truth is possible with respect to abstract properties. The key criteria for truth here is that of identity (A = A). The greater degree of identity and independence something possesses, the greater the degree of reality that thing has. Here, I take it, that Plato is drawing on an intuition where truths are eternal. For Plato, for instance, if there is justice then there is no point where justice ceases to be justice or becomes something other than justice. The difficulty is easy to discern. If I write something like the following:

1 1 1 1

I can ask how many numbers are there before me. The answer seems obvious and easy: There are 4 numbers. However, a moments reflection indicates that this clearly will not do. If our mathematics is to hold up, then it is necessary that the number 1 (or any other number for that matter) must necessarily have the same property in all circumstances: The property of being One. However, if one must always be one, then the above violates this rule insofar as each of the ones above are either the same as one another or different from one another. Clearly these numbers differ from one another insofar as minimally they are in different places, and, no doubt, we can find that they differ as to their qualities as well (perhaps there are slight variations from inscription to inscription). Moreover, each of these numbers differs from itself insofar as it came to be (with my inscription of it) and it will someday pass away. But if the number one is the inscription itself, then this would imply that the number one is not the number one, which would undermine our mathematics.

As a consequence, the best we can say is that the above are representations of the number one, and not the number one itself. Each and every one of these inscriptions refers to one and the same thing. The natural question that emerges at this point is what this object is that these inscriptions refer to. We are accustomed to saying that judgments refer to objects, yet it does not seem that the number one could refer to any object. My pen is one, my cup is one, my computer is one, etc. But all of these objects differ from one another and an object-- from this perspective --cannot simultaneously be itself and another. So if the number one is not a physical object like a cup or pen (as all of these are one but the one is always one), it would seem to follow that the one must be something else. Our common-sense ontology tells us that there are two categories of being: physical objects and minds. So if the one is not a physical object, then it must be a mental concept. However, it's clear that this conclusion is equally disasterous. For just as each inscription is different, so too is each mind. This would lead once again to the conclusion that the one is not the same as itself, and would add the added insult that there is a different mathematics for each mind that conceives mathematics.

Plato's conclusion thus seems to be that we must introduce a third ontological category: Namely the forms. These forms are strange creatures. They cannot be seen, but only comprehended as they are not physical objects. Moreover, they are necessary eternal as the one could not have come into being as it would then not be identical to itself, nor can the one pass out of being for the same reason (so too in the case of all the other forms). Further, the one can be in many different places at once as everything that is one necessarily refers to the one in some way (it must have the same referent), while nonetheless the one must remain the same as itself.

The Forms are thus models or originals, whereas all beings that exist in the world are copies of these originals. For each type of thing that there is, there will be a corresponding form or idea, and the truth of that thing will be a function of how closely it approaches the form of which it is a copy. That is, for Plato, truth isn't a property of judgments or thoughts, so much as it is a property of things themselves. According to Plato, every object in the world has its untruth as every object is contradictory (in the flux of time it gains and loses its properties, such that what is true of it at one time becomes false at another). However, while all objects are irrational and unthinkable by virtue of existing in a constant state of flux, nonetheless an object can be more or less true at any give point in time. Thus, for example, Johnny Depp is perhaps "more true" than me with respect to the quality of beauty, as he more closely approaches the form or idea of beauty than I do. It's important to note here that this "truthiness" is not a property of my judgment about Johnny Depp. Plato's entire account of the forms is designed to de-subjectify judgments about things such as justice, the good, beauty, etc., by separating them from the sentiments of the person making the judgment. If you and I disagree about the beauty of Johnny Depp, then this is not because "we each have our own valid opinion and taste", but because we're either both wrong or one or the other of us are wrong. We cannot both be right. For Plato there are thus grades of truth ranging from very low degrees of truth such as images (images are untrue in that they distort what they copy, are three places removed from the forms, and are highly dependent in their being, requiring a medium to be reflected in, an object to copy, and a source of light) all the way to absolute truth which consists of the forms themselves. For instance, in The Symposium, Plato argues that love is a necessary step towards philosophical knowledge as in love I recognize and desire the form of beauty, desiring the beautiful thing not for its utilitarian properties such as sex, labor, etc., but for its beauty (in pre-critical philosophies, indeed even in Kant, there's a great mystery about beauty as beauty doesn't seem to be for anything). However, I am nonetheless in a state of ignorance when I love, for I believe that it is the beautiful thing that I want, not the form of beauty itself. Why would I choose a copy rather than the original?

I would like to make seven points based on this foray into Plato:

First, there is a problem at the heart of Plato's theory of the forms: What is the precise relationship between the forms and copies? Plato argues that the relationship between forms and objects is one of participation. But the relation of participation is murky at best. There seems to be a gap or abyss between the forms and their copies, leading us to wonder why there should be copies or objects at all. Musn't the forms already differ from themselves so that there might be copies at all? (This sort of consideration will motivate the neoplatonists with their theories of emanation).

Second, what do the individuals that instantiate the forms contribute to being? Take Plato's account of love in The Symposium. Socrates suggests that Alcibiades is in error in his love of Socrates, as who he truly loves is Agathon. Agathon here, of course, is a pun, playing on both the man Agathon who is present at the drinking party and agathon as the "good". Yet is this truly the case? Is there not something the individual itself contributes? Or is the individual simply a fall from which we must redeem ourselve by reuniting with the forms?

Third, occasionally Plato will make reference to "simulacra". Roughly, we can distinguish between virtuous and non-virtuous images. Virtuous images, while having a low degree of truth, are nonetheless "virtuous" in that they copies of their originals (the reflection of a tree is a copy of a tree and the tree is a copy of the form of "treeness"). Yet there are also images that are not copies of anything. This suggests the possibility of a form of difference that doesn't trace back ultimately to the forms as models, indicating that Plato's ontology is not exhaustive.

Fourth, the forms are an ontological category, not a metaphysical category. Truth here isn't a question of knowledge, but of being. Beings are more or less true, not my knowledge of being (though that too). Here, I suggest, Deleuze draws heavily on Plato in his account of sense.

Fifth, speaking anachronistically, the forms are the "sufficient reason" for beings. If I ask what makes a being what it is, say Martin Luther Kings activism, the Platonic answer is that it is just. That is, it's the form that makes it what it is. Similarly, Deleuzian Ideas, multiplicities, or problems will function as the sufficient reason for actualized individuals.

Sixth, Plato argues that the world of objects is irrational and unthinkable because it is perpetually changing. Here, I think, we encounter one of Deleuze's most forceful arguments. If Deleuze is so fascinated with differential calculus, then this is because calculus allows us to think beings undergoing perpetual change. That is, Deleuze's account of the virtual is, in part, designed to demonstrate just how individuals are thinkable.

Finally, seventh, not all the difficulties that have emerged as a result of insisting on the primacy of identity. As a result of the axioms of identity (A = A), the law of non-contradiction (~(A & ~A) and the law of the excluded middle (A v ~A), we find ourselves confronted with irresolvable paradoxes and difficulties. Here I have the utmost admiration for Plato, as he took these principles seriously, ignoring all common sense or what is "obvious", and allowed himself to revamp all of ontology on the basis of what is implied in these principles. That is, Plato is audacious... Far more audacious than many of his postmodern critics. Yet as a result, we seem to find ourselves trapped within irresolvable antinomies. How might these antinomies be resolved?

2. A Brief Foray into Kant's Regulative Ideas

To be continued...


Anonymous Anonymous said...

As far as the example of 'numbers' is concerned, aren't there two very different things going on? The written symbol is a 'numeral', not a number properly speaking. So all the accidents that befall its inscription are wholly irrelevant to 'number' as such. It is also possible to see 'number', in the sense of 'arithmetic', as an 'a priori' - even in its Dennett-like materialist sense of being a product of 'design space', which he also associates with Plato.

I am simply an unashamed lurker, so excuse me if the question is out of place, but have you changed your mind about how devastating Hallward's critique of Deleuze is?

October 05, 2006 7:50 AM  
Anonymous Sinthome said...

Your point is exactly what I was trying to get at with number. We have to distinguish between number as such and what number counts, and must also distinguish between number as such and representations of number. The question then emerges as to what the ontological status of number is. I am not, of course, endorsing Plato's answer, only unfolding the line of reasoning (as I understand it) that led him to these conclusions.

As for Hallward's critique of Deleuze, yes I've seen the error of my ways. Both Hallward and Badiou ignore the question of individuation, which is what motivates his account of the virtual. Nonetheless, I still believe Hallward's book to be one of the better secondaries on Deleuze, and find that there's a lot of worthwhile analysis in it. I just disagree with the conclusions he draws.

October 05, 2006 8:07 AM  
Anonymous Anonymous said...

That's what happens when you read a carefully-written piece with too much haste: you make an elementary mistake.

I plan to try and tackle Simondon in a little while, but only after Metzinger's 'Being No One'.

Thank you for taking the time to reply.

October 05, 2006 11:33 PM  

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