The Univocity of Being 1: Expressive Being

I've been working on this Univocity section (35-42) for a while now and a straightforward translation continues to elude me, so I think we'll just have to wade in at random and see how it goes.  The concept of Univocity is a tough one because of how abstract and metaphysical it sounds.  Beyond even that though, Univocity exhibits a particularly gnarly form of ontological feedback that makes it especially tough.  In other contexts, Deleuze will discuss this concept as the question of immanence (as opposed to transcendence) and describe it as "the very vertigo of philosophy".  To succinctly state the problem: the idea of immanence really bakes your noodle because if everything comes from within, then so does your theory that everything comes from within.  In other words, your thought about things is another thing; there's no way to represent the world without adding to it.  If that recursive structure sounds like it's going to be as navel-gazingly simple as thinking about thinking ad infinitum, try watching some video feedback.

Anyhow, so, I think the first thing to notice about the concept of Univocity, at least as presented in this context, is that it is not Equivocity.  It is explicitly opposed to construing the unity of Being as analogy, which was how Aristotle understood it in the last section.  

The unity of analogy rested on some capacity for third party judgement -- a subject who could judge that two concepts were linked by analogy even though they "really" had nothing to do with one another (in fact, had so little connection that at first we weren't even able to call them "different " but simply "other").  I think my understanding of this point would improve a lot if I read more Kant.  But let's pass over the idea of judgement for now, because anyways Deleuze is about to replace it with a different idea, that of the expressive proposition.  According to Deleuze an expressive proposition has three parts: 1) a thing or mode or designator that does some pointing, 2) something designated or pointed at by those pointers, which, in the reverse directions is expressing itself through the pointers, and 3) the sense or meaning that is expressed by the proposition as a whole.  It's not completely clear to me why Deleuze chooses to introduce propositions and expressions here, other than the connection to Spinoza, who we'll see also believed in Univocity and considered everything an expression of God.  Maybe it also has something to do with the way that this concept of expression forms a circle where the designators point at the designated while the designated expresses itself through the designators, which would seem to obviate the need for a third party judgement.  

Or maybe, to return to our starting point, the whole idea is just to set up the contrast with analogy.  With propositions, we get a model of how different things could designate something in common in the same way, as opposed to analogous but different ways.

What is important is that we can conceive of several formally distinct senses which none the less refer to being as if to a single designated entity, ontologically one. It is true that such a point of view is not sufficient to prevent us from considering these senses as analogues and this unity of being as an analogy. We must add that being, this common designated, in so far as it expresses itself, is said in turn in a single and same sense of all the numerically distinct designators and expressors. In the ontological proposition, not only is that which is designated ontologically the same for qualitatively distinct senses, but also the sense is ontologically the same for individuating modes, for numerically distinct designators or expressors: the ontological proposition involves a circulation of this kind (expression as a whole).

 There's something really odd going on in this quote.  We've become accustomed to thinking of Being as a sort of ontological substance.  So the idea that many designators point to the same substance probably isn't too surprising to us.  This would be another version of the idea that there is one underlying principle behind reality, one type of "stuff" from which it is built (whether you think this is mathematical forms or Absolute Spirit or electrons depends on what age you were born into).  Everything we see is really just a manifestation of this stuff, which is the only stuff that really, ontologically, IS.  Other stuff is just illusion and mere appearance, not real reality.  But in the quote above, we're told that "the sense is ontologically the same" for the appearances that indicated this underlying reality.  "Sense" doesn't seem like an ontological substance though.  It seems like the reality of "sense" would be in the process by which a designated expresses itself through designators that in turn designate it.  Sorry for the mouthful there, but I'm trying to draw the circle I mentioned before that I think he means by the circulation of "expression as a whole".  That a process can be said to be, that it could be an "ontological thing" (see how our everyday language is biased?), is already a pretty strange idea in a Western metaphysics that worships stasis and despises motion.  

But in fact this quote gets even weirder when you realize that this whole discussion started with the name of Duns Scotus.  Now, I don't know spit about medieval theology, but I have gathered that for Scotus, the major point of the univocity of Being was to counteract Aquinas' idea that we only know God through analogy.  When I say that my dog is good and that my neighbor is good I mean to use "good" in the same sense.  But, for Aquinas, when I then say that God is good, I don't mean that in the exact same sense that I meant with my dog or neighbor, I mean it in a merely analogous sense.  Scotus was explicitly denying this and claiming that if we're going to genuinely know God at all, the qualities we attribute to him have to be in the same sense as we attribute them to everything else.  

In effect, the essential in univocity is not that Being is said in a single and same sense, but that it is said, in a single and same sense, of all its individuating differences or intrinsic modalities. Being is the same for all these modalities, but these modalities are not the same. It is 'equal' for all, but they themselves are not equal. It is said of all in a single sense, but they themselves do not have the same sense.

If we translate this reference to Scotus to our current context, I think we end up with three distinct senses of "being" that the doctrine of Univocity is claiming are all the same.  First, there's the "Being of Being", as it were.  Surely Being is, right?  This is familiar ontological substance sense we employ when we say talk about the unity of what "really exists" (God, electrons, whatever).  Second, there's the "Being of beings".  Normally, we think that these mere appearances are just there to point at the underlying Being, and aren't "really real" durable substances in and of themselves.  Following Duns and Deleuze though, we're now claiming that beings are in the exact same sense that Being is.  I exist and my dog exists and god exists, and while we are all different, in so far as we exist, we all exist in the same way.  Appearance now becomes as real as reality.  Third, I think there's an implication here that the sense itself in which Being is said of everything is an ontological "thing" of its own -- as if there were also a "Being of sense", which could only be a sort of process of the circulation of expression where Being expresses itself through beings that designate it.  And of course, this final sense of Being is the same sense as the first two.  Or perhaps it's better to say that this final ontological sense is the most fundamental one that gives meaning to the first two, which would lead you to a formula like: Being is process, the process of the expression of Being.

To me though this is all getting a bit too academic.  I don't really love the term Being in the first place.  If you want to talk about God, talk about God.  Being seems a thin veneer.  And either way, they are both so abstract that it's hard to be sure you're actually saying anything and not just tossing word salad.  I think I learned something here, but the final formula seems a bit like something a geriatric Heidegger would be saying to his golf buddy.

Analogy

If Being can't be genus, are we now stuck with an infinity of possible concepts (genera) that can form the starting points for a specific description of reality?  This seems like a mess.  In fact, it seems like precisely the mess that specific difference was meant to solve at a lower level.  There, we found a small set of principal differences, organized by their opposition, that were meant to guarantee we could produce a description of anything and everything within the genus.  Here, we've got the same problem one level up.  We don't know how many genera we will need, we don't know how they're organized (not by contraries though) and we don't know if we're able to cover every aspect of Being with whatever concepts we can think up.  

This is where analogy rides in to save the day.  Being isn't officially a genus, but it is like a genus.  The general concepts that divide it aren't related to one another as opposites nor related as parts to a whole, but they are organized by analogy.  This is actually a pretty nifty solution to our earlier problems.  Sure, Being is equivocal and there are an infinity of thinkable concepts that might divide it.  But if they are all analogous to one another this makes perfect sense and restores the order that seemed lost.  Of course we can find as many analogies for a something as we would like to produce.  But this myriad doesn't lead us into confusion, because they are all really just abstract transformations of some underlying thing.  True, it's hard to say exactly what this root thing is; what is the "most analogous analogy" for something?  But still, we have a sense of simpler and more direct analogies and more distant and labored ones.  And most importantly, we can be sure that all the analogies reflect the same underlying unity, each in their own way.  Now it doesn't matter how many genera we need to "cover" Being, nor do we need to worry that parts of its will escape coverage, or that our concepts will get disorganized.  Every concept speaks of Being in an analogous way.  Analogy is actually a wonderful way to tame infinity.  

This concept of Being is not collective, like a genus in relation to its species, but only distributive and hierarchical: it has no content in itself, only a content in ,proportion to the formally different terms of which it is predicated. These terms (categories) need not have an equal relation to being: it is enough that each has an internal relation to being. The two characteristics of the concept of being - having no more than a distributive common sense and having a hierarchical primary sense - show clearly that being does not have, in relation to the categories, the role of a genus in relation to univocal species. They also show that the equivocity of being is quite particular: it is a matter of analogy.

I'm not completely sure why Deleuze brings up judgement in this context.  Perhaps the idea is that whereas specific difference divided the unity of a concept into real units, generic difference is really a conceptual division of Being into concepts that differ categorically (generically, as opposed to specifically).  And a conceptual division needs a subject to perform it and to verify that two things that aren't "really" related are in fact two different analogies for the same thing?  At any rate, it's clear that when we call two things analogous we are employing some idea of conceptual identity and unity -- analogous things are identical under some transformation.

Analogy is itself the analogue of identity within judgement ...

 

That is why we cannot expect that generic or categorial difference, any more than specific difference, will deliver us a proper concept of difference. Whereas specific difference is content to inscribe difference in the identity of the indeterminate concept in general, generic (distributive and hierarchical) difference is content in turn to inscribe difference in the quasi-identity of the most general determinable concepts

Now we can see why this whole section was presented as an investigation of the Large and the Small.  There are two levels at work here, but they both take a concept of identity as their way of corralling all possible differences.  What's more, the two levels, though distinct, work together.  We trust that the Small differences will give us the real units of the world because they are based off the Large differences that are all analogous approaches to the same unity.  

In effect, difference allows the passage from similar neighboring species to the identity of a genus which subsumes them - that is, the extraction or cutting out of generic identities from the flux of a continuous perceptible series. At the other pole, it allows the passage from respectively identical genera to the relations of analogy which obtain between them in the intelligible.

 

Difference has been completely tamed by identity.  It can now be classified as a Large or a Small difference, and the combination of those two will deliver all possible differences.  Deleuze's final example of how this works is the way we classify even embryological differentiations as Large or Small, based on whether we find a relationship of resemblance or analogy between the outcomes.    

Even neo-evolutionism will rediscover these two related aspects of the categories of the Large and the Small, when it distinguishes the large precocious embryological differenciations from the small, tardy, adult, species or intraspecies differenciations.

I think he's referring to those comparative embryological drawings here and the way we think of only small late differentiations accounting for, say, more hair or longer arms on a chimp than a human, but large early differentiations accounting for whether we find fins, or their analogous counterpart, arms.  

Aristotle

I'm not going to lie; this Aristotle section (pp. 30-35) took me forever.  At first I resisted going back to the sources cited in the footnotes because ... well because Aristotle always seemed so obscure in the short bits I remember from school, and because there's always the danger of getting off track and letting the overall trail go cold when you're trying to pin down a passage.  Was it really necessary to understand the Aristotelian references to get the main point of this section?  The main point seemed to be that Aristotle conceived of difference as the specific difference that divided up the general identity of a genus (or concept -- these are going to be be synonyms in this section) into different species.  It's almost too bad we don't have words like "species-ific" and "genus-al" to show this link as clearly as possible.  Since we're reading the chapter on "difference in itself" and we've already discussed the strange notion of starting metaphysics from difference rather than identity, is there really much more to say here? 

Maybe not.  Maybe that's "good enough for government work", as my dad used to say.  I was unsatisfied leaving it there though, because it left certain passages  passages completely obscure to me.  Like, what does this stuff mean?

Difference carries with itself the genus and all the intermediary differences. The determination of species links difference with difference across the successive levels of division, like a transport of difference, a diaphora (difference) of diaphora, until a final difference, that of the infima species (lowest species), condenses in the chosen direction the entirety of the essence and its continued quality, gathers them under an intuitive concept and grounds them along with the term to be defined, thereby becoming itself something unique and indivisible [atomon, adiaphoron, eidos]. In this manner, therefore, the determination of species ensures coherence and continuity in the comprehension of the concept.

Or this:

Remember the reason why Being itself is not a genus: it is, Aristotle says, because differences are (the genus must therefore be able to attribute itself to its differences in themselves: as if animal was said at one time of the human species, but at another of the difference 'rational' in constituting another species ...). It is therefore an argument borrowed from the nature of specific difference which allows him to conclude that generic differences are of another nature.

Or this: 

However, it is precisely the nature of the specific differences (the fact that they are) which grounds that impossibility, preventing generic differences from being related to being as if to a common genus (if being were a genus, its differences would be assimilable to specific differences, but then one could no longer say that they 'are', since a genus is not in itself attributed to its differences). In this sense, the univocity of species in a common genus refers back to the equivocity of being in the various genera: the one reflects the other.

So I went to the footnotes.

Since the whole Metaphysics is available online, I'm going to quote the passages that pointed me in the right direction.  This first one helps to understand what Aristotle means by contrariety.  Contraries are almost more than mere opposites because they divided up a genus in a complete and essential way.  I almost imagine these contraries as the sort of standard unit basis vectors that can decompose any other.

Since things which differ may differ from one another more or less, there is also a greatest difference, and this I call contrariety. That contrariety is the greatest difference is made clear by induction. For things which differ in genus have no way to one another, but are too far distant and are not comparable; and for things that differ in species the extremes from which generation takes place are the contraries, and the distance between extremes-and therefore that between the contraries-is the greatest. 

But surely that which is greatest in each class is complete. For that is greatest which cannot be exceeded, and that is complete beyond which nothing can be found. For the complete difference marks the end of a series (just as the other things which are called complete are so called because they have attained an end), and beyond the end there is nothing; for in everything it is the extreme and includes all else, and therefore there is nothing beyond the end, and the complete needs nothing further. From this, then, it is clear that contrariety is complete difference;

This came across relatively clearly in what Deleuze was saying -- species are a special and essential difference that divides up genus in "the best" way.  Carving Nature at its joints, as the saying goes.  What didn't come across so clearly was the way that contraries are then used to form further divisions of the genus into "intermediaries".  This actually appears in Part 7 of Book X, which isn't cited in the footnotes.

Since contraries admit of an intermediate and in some cases have it, intermediates must be composed of the contraries. For (1) all intermediates are in the same genus as the things between which they stand. For we call those things intermediates, into which that which changes must change first; e.g. if we were to pass from the highest string to the lowest by the smallest intervals, we should come sooner to the intermediate notes, and in colours if we were to pass from white to black, we should come sooner to crimson and grey than to black; and similarly in all other cases

 If intermediates are in the same genus, as has been shown, and stand between contraries, they must be composed of these contraries. For either there will be a genus including the contraries or there will be none. 

But, again, the species which differ contrariwise are the more truly contrary species. And the other.species, i.e. the intermediates, must be composed of their genus and their differentiae. (E.g. all colors which are between white and black must be said to be composed of the genus, i.e. color, and certain differentiae. But these differentiae will not be the primary contraries; otherwise every color would be either white or black. They are different, then, from the primary contraries; and therefore they will be between the primary contraries; the primary differentiae are 'piercing' and 'compressing'.) 

Therefore also all the inferior classes, both the contraries and their intermediates, will be compounded out of the primary contraries. Clearly, then, intermediates are (1) all in the same genus and (2) intermediate between contraries, and (3) all compounded out of the contraries. 

So here you can start to see why I used the basis vectors as an analogy.  Equally, we could have talked about the primary colors.  The idea seems to be that contraries are these special primary differences that can then be used to compose any other differences further down the line.  When you think about it, this kinda changes the taxonomic tree image that I initially thought Deleuze was referring to in commenting on "successive levels".  It's not that the primary contraries are then subdivided into even smaller differences.  It's more that they can be recombined to produce other differences contained within the genus, precisely because they are the primary differences.  

The final piece I found important in Book X was the bit in Part 8 about how contraries are "indivisible":

This, then, is what it is to be 'other in species'-to have a contrariety, being in the same genus and being indivisible (and those things are the same in species which have no contrariety, being indivisible); we say 'being indivisible', for in the process of division contrarieties arise in the intermediate stages before we come to the indivisibles.

To sum up, it seems like Aristotle thinks of the difference that creates a species as being the primary natural building blocks or indivisible units that perfectly tile the world with no gaps and nothing left out.  Specific difference is the proper breakdown of reality into component parts.

But, wait, then, what is the role of a genus!?  Because on Aristotle's account it seems at first like a species isn't really even a thing in itself, but just a difference which perfectly and completely divides up the more fundamental identity of the genus.  So wouldn't the genus really be the more fundamental "unit" of reality then?  If this question sounds confusing when I ask it, imagine how much more confused it sounds coming out of Aristotle's mouth:

Apart from the great difficulty of stating the case truly with regard to these matters, it is very hard to say, with regard to the first principles, whether it is the genera that should be taken as elements and principles, or rather the primary constituents of a thing; e.g. it is the primary parts of which articulate sounds consist that are thought to be elements and principles of articulate sound, not the common genus-articulate sound; and we give the name of 'elements' to those geometrical propositions, the proofs of which are implied in the proofs of the others, either of all or of most.

To judge from these arguments, then, the principles of things would not be the genera; but if we know each thing by its definition, and the genera are the principles or starting-points of definitions, the genera must also be the principles of definable things. And if to get the knowledge of the species according to which things are named is to get the knowledge of things, the genera are at least starting-points of the species. And some also of those who say unity or being, or the great and the small, are elements of things, seem to treat them as genera. 

But, again, it is not possible to describe the principles in both ways. For the formula of the essence is one; but definition by genera will be different from that which states the constituent parts of a thing. 

Besides this, even if the genera are in the highest degree principles, should one regard the first of the genera as principles, or those which are predicated directly of the individuals? This also admits of dispute. For if the universals are always more of the nature of principles, evidently the uppermost of the genera are the principles; for these are predicated of all things. There will, then, be as many principles of things as there are primary genera, so that both being and unity will be principles and substances; for these are most of all predicated of all existing things. But it is not possible that either unity or being should be a single genus of things; for the differentiae of any genus must each of them both have being and be one, but it is not possible for the genus taken apart from its species (any more than for the species of the genus) to be predicated of its proper differentiae; so that if unity or being is a genus, no differentia will either have being or be one.  But if unity and being are not genera, neither will they be principles, if the genera are the principles. Again, the intermediate kinds, in whose nature the differentiae are included, will on this theory be genera, down to the indivisible species; but as it is, some are thought to be genera and others are not thought to be so. Besides this, the differentiae are principles even more than the genera; and if these also are principles, there comes to be practically an infinite number of principles, especially if we suppose the highest genus to be a principle. But again, if unity is more of the nature of a principle, and the indivisible is one, and everything indivisible is so either in quantity or in species, and that which is so in species is the prior, and genera are divisible into species (for man is not the genus of individual men), that which is predicated directly of the individuals will have more unity.

It goes on some more, but you get the idea (or don't, as the case may be).  He's not real sure what the first elements or principles are, and he seems to have backed himself into a corner with regards to whether it should be the individual examples of a species, the species itself, the genus, or something like "being" or "unity", of which individual genera would just be specific examples.  It's this confusion that Deleuze is elaborating on when he discusses why Being cannot be a genus, and if it isn't a genus, what sort of thing it would be.  Understanding this point about how Being is not a genus adds an extra layer of complexity to the commentary on Aristotle, but I think it's going to come in handy for the next section (sneak preview: the univocity of Being).  So bear with me.  

Broadly, the goal is to find the principle axes, so to speak, of reality.  We want to divide up the mess of reality into understandable parts or principles of some sort that help us classify and name it.  Aristotle has decided that species seems to do this perfectly for things in the same genus.  Further, you don't have to subdivide specific differences any further to get to the essence of real individual things.  That's because species are based on the way contraries create a sort of orthogonal unit system for reality that allows you to then construct more "intermediate" species based on mixing these.  Finally, we get down to the correct combination of "principal species" that defines the type or form of whatever we're talking about (the infima species).  And then of course there can be many distinct copies of this form, and they can have all sorts of variations, but that's not really essential, that's just a simple difference in the material used to fill up the essential form or mold, as you can see from what I promise is our last Aristotle quote:

One might raise the question, why woman does not differ from man in species, when female and male are contrary and their difference is a contrariety; and why a female and a male animal are not different in species, though this difference belongs to animal in virtue of its own nature, and not as paleness or darkness does; both 'female' and 'male' belong to it qua animal. This question is almost the same as the other, why one contrariety makes things different in species and another does not, e.g. 'with feet' and 'with wings' do, but paleness and darkness do not. Perhaps it is because the former are modifications peculiar to the genus, and the latter are less so. And since one element is definition and one is matter, contrarieties which are in the definition make a difference in species, but those which are in the thing taken as including its matter do not make one. And so paleness in a man, or darkness, does not make one, nor is there a difference in species between the pale man and the dark man, not even if each of them be denoted by one word. For man is here being considered on his material side, and matter does not create a difference; for it does not make individual men species of man, though the flesh and the bones of which this man and that man consist are other. The concrete thing is other, but not other in species, because in the definition there is no contrariety. 

The correct and essential name for something takes the form: genus>primary species>intermediate species (mix of primaries).  The specification of a particular individual takes over from that point, but it is not essential.

The problem comes when you realize that every true name starts with a genus -- and that's potentially a lot of names.  We're not just talking about the natural genera of birds and dogs here.  Pretty much any abstract concept we can think of -- like unity or being -- would qualify as a genus which we could seemingly subdivide into different species of unity or being.  It seems that if genera is the top level of our scheme for naming essences, we're going to have a near infinity of names.  This defeats the whole goal of ordering and organizing reality the same way that Funes el memorioso defeats the whole purpose of memory.  The end result would be a conceptual world that's just as much of a mess as the real one, a map that's as big as the territory.

At first, the solution to this problem seems completely obvious.  Just add a level above the genera.  Start with a higher level principle of which each genus would be just one specific example.  Any essence would be of the form: genus of genera>genus>primary species>intermediary species.  Being seems like an obvious candidate for the top level, because surely everything is, right?  So just call Being a genus, and presto, problem solved, a nice taxonomic tree.  

Unfortunately, Aristotle has closed off this possibility to us because of the way he defined specific difference to begin with.  That last bit is the important point that took me a long time to understand.  Specific differences divide up genera in a complete way that covers everything that can fall under the unity of the genus.  The non-overlap of the parts and the unity of the whole they divide make them predetermined, as it were, to fit perfectly together.  To find any species in the genus, you just need to mix the primary contraries.  These are the real indivisible building blocks from which essences are constructed; ie. not from further sub-divisions of the primaries into smaller units.  This scheme is what's lurking behind the assertion that "differences are" -- that is, are real individual units (of essence, in this case).  This is what Delezue is calling "the univocity of species in a common genus".  All the things that fall under the genus "speak" its name in the same way, as combinations of the primary oppositions that are its essential differences.  They are differences within a unity, parts within a whole, locations in a predefined and pre-limited space.

When you try to make Being into a genus, you run afoul of this scheme.  If Being were a genus, then the original genera would be like species.  But if they're like species, they have to be essential differences that form indivisible units that completely cover a presumed whole.  This creates two problems.  First, we already know the genera are divisible.  In fact, Aristotle has made them perfectly divisible like a garlic head and its cloves.  And divisible things can't be the building blocks of reality.  This is exactly what the quote on the confusion over principles uncovered.  Divisible things "are not" real units.  Second, genera do not form contrary differences.  They are too far apart to do that.  As Deleuze puts it, they are not contrary, but simply Other.  Or as Aristotle said, "... things which differ in genus have no way to one another, but are too far distant and are not comparable".  So the genera are not going to be the natural units that perfectly cover Being the way that species did for a genus.  

This is the exactly point where Deleuze sees an alternative direction that Aristotle's confusion over first principles might have taken.

It is therefore an argument borrowed from the nature of specific difference which allows him to conclude that generic differences are of another nature. It is as though there were two 'Logoi', differing in nature but intermingled with one another: the logos of Species, the logos of what we think and say, which rests upon the condition of the identity or univocity of concepts in general taken as genera; and the logos of Genera, the logos of what is thought and said through us, which is free of that condition and operates both in the equivocity of Being and in the diversity of the most general concepts. When we speak the univocal, is it not still the equivocal which speaks within us?

Aristotle's scheme seems to lead towards an equivocal understanding of Being.  Every genus, every general concept, we use to divide up the world gives voice to Being in a different way.  Maybe there are an infinity of ways and we only know about some of them?  Each of our concepts, then, would form generic unities that could be divided into specific parts, but there would seem to be no guarantee that we would cover every being, all of Being, with these descriptions.  

As Deleuze goes on to observe, Aristotle doesn't take this route, and instead converts Being into a pseudo-genus of sorts.  But the punchline will have to wait till the next post on analogy.

Difference In Itself

From me, the most important point Deleuze is trying to make in the early part of Chapter 1 is that we usually think of difference between two forms and not difference in itself. That is, we usually start with identity instead of starting with difference. If we want to develop a concept of difference in itself then, we will have to back up to a world "before" forms and their relations. There would seem to be two approaches to a formless world – nothingness and everything; chaos and the void.

Indifference has two aspects: the undifferenciated abyss, the black nothing- ness, the indeterminate animal in which everything is dissolved - but also the white nothingness, the once more calm surface upon which float un- connected determinations like scattered members: a head without a neck, an arm without a shoulder, eyes without brows.

It's tempting to think that difference is somehow between these two poles of indifference.  But either pole still seems to be conceived in terms of forms – either absence of any forms or presence of all the forms -- so it's not clear that whatever is between these will help us.

Could we try to think of difference in itself by dispensing altogether with forms and considering the moment of differencing or distinguishing, when difference is created between a thing and a not-thing?  This is like the moment of the creation of a form, the moment where it distinguishes itself as such, that is, as a thing distinct from a non-thing?

However, instead of something distinguished from something else, imagine something which distinguishes itself - and yet that from which it distinguishes itself does not distinguish itself from it. Lightning, for example, distinguishes itself from the black sky but must also trail it behind, as though it were distinguishing itself from that which does not distinguish itself from it. It is as if the ground rose to the surface, without ceasing to be ground.

The lightning strike is the first of three images to appear in this short section at the beginning of Chapter 1 (pp 28-30) that repeat throughout all of Deleuze's work. The other two are very much related – the abstract line, and the body-without-organs (here only implicitly through the mention of Artaud). I think the first two are basically synonyms for one another and refer to the formation of a form (as opposed to a pre-existing form that then happens to appear). And the body-without-organs is another name for the ground, though in reading Deleuze we should hear "ground" as in "background" of a painting, the contrast to "figure", and not "foundation" or "root" or "first principle", which is often what it means for other philosophers.

The key idea behind the abstract line or the lightning strike is the one-sided distinction of something from an infinite and amorphous ground. The ground is not the lack of things or a collection of possible things; it would be better to call it a "not-thing". Somehow this not-thing rises to the surface and takes on a life of its own, without itself becoming a thing. I think this is why Deleuze ends up calling it "monstrous". Think of the "shadowy forms" we see in the movies that seem to consist of nothing but varying density of shadows. There is no bright contour line that demarcates the form as a thing unto itself, no place where we can clearly separate figure from ground or inside from outside. And yet the form is there nevertheless, even though the line which draws it is "abstract", even if it is constructed of nothing more than lighter and darker ground just like in a chiaroscuro.  The ground can rise up anywhere, it seems, and create something out of nothing.

We're going to see this metaphor again and again because Deleuze sees thought itself as a sort of lightning strike.  A thought is there at the moment some determinate form rises out of the background of non-thought.   Basically, thought is a difference or modification of non-thought:

Nor is it certain that it is only the sleep of reason which gives rise to monsters: it is also the vigil, the insomnia of thought, since thought is that moment in which determination makes itself one, by virtue of maintaining a unilateral and precise relation to the indeterminate. Thought 'makes' difference, but difference is monstrous.

But we're probably getting ahead of ourselves on that one and will have to come back to the question of "what is a thought". For the moment, let's try to understand why, if the ground becomes monstrous, the difference is cruel.  This is related to Artaud's idea of the cruelty of the "judgement of God".   "They're trying to cut my body up into organs".   Difference in itself is cruelty because it is carving a figure out of the ground.   It is introducing distinctions into something that has no interest in them, something that "wants" to be whole.  

When you will have made him a body without organs, then you will have delivered him from all his automatic reactions and restored him to his true freedom.
Then you will teach him again to dance wrong side out as in the frenzy of dance halls and this wrong side out will be his real place.

So difference in itself, caught on the wing, so to speak, in the act of differing, is cruel and monstrous, wild and unpredictable. A lightning strike, an abstract line. I always feel like I've understood Deleuze when I've managed to read him completely literally.

This kind of difference is too wild for us though. We seem to feel the need to tame it, to domesticate it. We try to relate this unilateral determination to other determinations, or to a ground that we re-conceive as undetermined rather than indeterminate. Notice the change in prefix. We convert that infinite and amorphous ground into a whole set of possible things in waiting, from which determination will actually select just one. Later on, Deleuze will call this confusing the possible with the virtual. Here he talks about it as an "organic representation" of difference, giving it a fixed form that can be compared to other forms, making it a piece in a whole to which it belongs, the one reflecting the other.  This is what an organism is – some parts working together to form a whole, a whole keeping each of its parts in the proper place. The basic move is to construct the pre-determined, pre-formed possibility space of the whole, and then see difference as the specification of one or another of the forms contained within that space. This specification process determines the limits of difference, which now will have to fit between the Largest and Smallest possible allowed values.

At this point the expression 'make the difference' changes its meaning. It now refers to a selective test which must determine which differences may be inscribed within the concept in general, and how. Such a test, such a selection, seems to be effectively realized by the Large and the Small. For the Large and the Small are not naturally said of the One, but first and foremost of difference.

It bears repeating that this taming of difference depends crucially on converting the not-thing of the ground into a thing conceived as a whole. It morphs from something infinite and amorphous, to which the idea of identity doesn't even apply (is the ground even identical to itself?) into a thing or set of possible things that simply has yet to be determined.   This latter is a closed set with determinate boundaries, which should clearly be identical to itself.   This is what Deleuze is going to call, always pejoratively, the concept.  

Signs and Learning

How do we learn to swim?  This example that pops up on several occasions throughout Deleuze's work, and here on page 23.  

The movement of the swimmer does not resemble that of the wave, in particular, the movements of the swimming instructor which we reproduce on the sand bear no relation to the movements of the wave, which we learn to deal with only by grasping the former in practice as signs. That is why it is so difficult to say how someone learns: there is an innate or acquired practical familiarity with signs, which means that there is something amorous - but also something fatal - about all education. We learn nothing from those who say: 'Do as I do'. Our only teachers are those who tell us to 'do with me', and are able to emit signs to be developed in heterogeneity rather than propose gestures for us to reproduce.

I think he chooses the example of swimming in particular to illustrate the general failure of the idea of imitation to account for learning.  Someone shows you the movements are involved in the crawl stroke.  You mime them on the beach.  It's actually a very simple pattern.  You imitate the instructor till everything looks exactly the same.  Then you get in the water and try to reproduce those movements and you sink like a stone.  You can't learn to swim by imitating the motions of someone who knows how to swim.  If you could, there wouldn't be any process of learning to swim at all; someone would tell you or show you how to do it, and you'd just do it.  

What you're actually doing when you learn to swim is learning to fit the pattern of your motions together with the patterns of how the water moves.  You're not copying an external model like the swim instructor.  That is just providing you with a set of signs that will hopefully enable you to grasp how you can interact successfully with the water.  A good teacher is not just someone who knows how to do something well, and so provides a good model, but someone who knows how to explain it in a way that triggers your ability to fit your motions together with the world.  If they are transmitting some sort of information to you, it is at best in the manner that a seed transmits information to the next generation of tree -- not like a copy, but like a recipe.

I think it's easy to acknowledge this distinction in the case of learning a new physical skill like swimming or playing tennis.  But what about areas where we seem to be able to just learn that as opposed to learning how?  Aren't there plenty of situations where we learn the right answer more or less instantaneously just by someone telling us what it is?  We do seem to learn information or facts this way, and certainly a lot of our schooling seems to revolve around force feeding people these facts.  I think these situations may actually be the exception that proves the rule though.  Inevitably the new information we acquire so quickly by copying it is actually just a small new modification within a very large framework that took us a long time to build up, just like acquiring physical skills.  

You might call this sort of thing "propositional learning".  Where you learn, say, the definition of something, or what formula to use to calculate the internal rate of return on an investment, or even what Plato said about the concept of repetition.  We tend to think of a lot of "higher" learning as propositional learning, perhaps because it's only this type of learning that can end with a right or a wrong answer.  You either correctly copy the instructor, or you don't.  

In fact, a lot of philosophy is taught as if it were a form of propositional learning.  Was Descartes "right" when he said that the pineal gland was the seat of the soul?  Was Kant "correct" when he said that we can never know a thing-in-itself?  Obviously, in philosophy the answer is up for debate in a way it usually is not in physics.  But the discipline is still mainly taught as if there were a right answer that we will somehow eventually come to.  So the other reason I think Deleuze invokes his swimming example early on in the book is to alert us to the fact that he does not see philosophy in this mold.  We are meant to "do it with him" and not just "do it as he does".  Perhaps this helps us appreciate his unique writing style a little more?  It's a lot easier to simply agree or disagree with Plain English than it is with French Philosophy, where you have to struggle over a sentence just to figure out what it might mean.  I don't think the goal is obscurity, so much as to try and unfold the complexity of the problem, instead of simply offering a ready made solution.

And we're back

Okay, enough about Stengers and the War Machine and the philosophy of science.  It's time to get back to Difference & Repetition.

Last episode on FPiPE we were using embryogenesis as our central metaphor to get a grip on what Deleuze has in mind when he talks about true repetition and its relationship to difference in the introduction.  I got a lot of mileage out of that analogy, and I generally find it useful to think of Deleuze modeling his philosophy after biology rather than after physics or mathematics.  But it's probably time to back up a step and and think a little more abstractly about the point we've arrived at and not get locked in to one metaphor.

The broad sweep of the Introduction seems to be:

1. How can true perfect repetition exist in an objective rule based world?  
2. If true repetition is an illusion, what's happening when we see something that looks like repetition?  It must be that we're seeing a general form or concept get repeated, with some of the particular details changed.  This general form would either be some objectively existing Platonic thing out there in the world, or some concept existing in our head.  Either way, the phenomenal world would be understood as never repeating.  Each moment of each thing is completely distinct and unique.  Our sense of true deja vu (as opposed to general) repetition would only arise when we see two things that are so close that they should share one concept, but somehow there are mysteriously two of them, like a left and a right hand.  These must be some sort of "degenerate" case (as the mathematicians like to say).
3. But wait, nature shows us all kinds of things like left and right hands that seem to be exact repetitions of the same concept.  This presents a major problem if we think that there should be a 1-to-1 correspondence between conceptual forms and things in the world.  The difference between left and right hands doesn't seem to map onto a conceptual difference.  And yet that difference also doesn't seem to fall into the form of a particular variation of a general form (like, say, longer or shorter fingers might).
4. So there seem to be some cases of true repetition that aren't general but that don't correspond to conceptual differences.  This is what real repetition is -- difference, but without a concept for it.
5. This kind of repetition can be explained by a repeated or ongoing process that has some difference within it that leads it to produce two forms as an end product. This is where embryogenesis came in.  The process, as an algorithm or recipe, can be repeated exactly, but the outcome can be slightly, or even radically, different every time.  The difference between the final forms isn't an external conceptual difference (as there is none in the case of symmetrical objects), but a difference internal to the process that creates the forms.  And the difference is also not a particular difference that falls within some general limits.  The difference between left and right can't be explained on the basis of how close they are to one another or to some general model.  The "level" at which the difference happens isn't the same level of the two distinct forms, it is somehow before or beneath them.

I've collected a few of the quotes that step 5 translates: 

We are right to speak of repetition when we find ourselves confronted by identical elements with exactly the same concept. However, we must distinguish between these discrete elements, these repeated objects, and a secret subject, the real subject of repetition, which repeats itself through them. Repetition must be understood in the pronominal; we must find the Self of repetition, the singularity within that which repeats.

It is true that we have strictly defined repetition as difference without concept. However, we would be wrong to reduce it to a difference which falls back into exteriority, because the concept embodies the form of the Same, without seeing that it can be internal to the Idea and possess in itself all the resources of signs, symbols and alterity which go beyond the concept as such.

The interior of repetition is always affected by an order of difference: it is only to the extent that something is linked to a repetition of an order other than its own that the repetition appears external and bare, and the thing itself subject to the categories of generality.

So, basically, there are two kinds of repetition -- repetition of process, and repetition of form.  These operate like subject and object.  

For the object, all the differences between instances lies outside the form, external to its completed individuality.  That's why when we think about two repeated objects, we find that the specifying their difference requires invoking some other level of explanation that doesn't have to do with the objects themselves.  We need ideas like "number", or "reflection" or "translation" or some other mathematical transformation that would apply equally to all objects.  The difference between objects isn't itself an object.  We have no concept or form for this repetition like we have for the objects, and when we reach for it, we immediately reach for descriptions that involves process and movement.  

The subject of repetition -- that is, the repeating process -- actually has an inside to it.  The difference that gives rise to the repeated forms is built into the process.  I think this is Deleuze's answer to the question, "what is a subject"?  The subject is a form of interiority.  It has a "what it is like from the inside" to it.  Only processes have an inside.  Finished forms do not.  Sure, we may take them apart and find other forms within them, but that's exactly when we start to say that the larger form is an illusion that "is really" reducible to smaller forms following laws which are also external to them.  

Now we find ourselves at a strange moment though.  It seems to me there's an ambiguity in the notion of a repeating process that I've already alluded to a couple of times.  Is it really right to say that the process repeats, in order to produce two forms?  In the case of embryogenesis it was more like the process bifurcated or differentiated based on some internal difference.  In other words, the different outputs were products of one ongoing process, albeit one that can spawn new subprocesses.  This is the paradox, as it were, of true repetition -- it's always yet again for the first time.   This brings us back to where we started with the introduction.  Repetition is an infinite series just like the repeated celebration of the 4th of July.  Because the event is historic we repeat it, and repeating it makes it historic.  Without the repetition, it is no longer a singular event, but just some stuff that happened a long time ago.  To understand the inner and subjective form of repetition, we have to understand the singular process that gives rise to the outward repetition of forms.  

Asymptotically Objective

So, I finished reading Stenger's book of essays about slowing science down.  I was thinking of writing some more about it when I looked back at the two earlier posts and realized that I would mostly be repeating myself.  There are some interesting details along the way, but taken together I've mostly covered her basic critique and suggestion.  Scientist should drop the philosophically dubious idea that they are producing objective, authoritative knowledge, and instead focus on the particularly interesting situation they really do create -- a human system that takes into account what matters for  other parts of the cosmos in reliably useful ways.  Science is a human system with human goals, but it cares deeply about what the rest of the world "thinks".  Which is to say that the world can prove scientists wrong, which is the only way one can learn from another entity.

It's a deceptively simple suggestion, and in the later essays you can really hear how it resonates with her thinking about Whitehead and James (who she thinks Whitehead was elaborating on).  To follow all of it would be a very long conversation about Whitehead's idea that everything (including, say, elementary particles) is actually a "society" defined by its own "values", by what "matters" for that society.  The main difference between societies for Whitehead is the way their values incorporate those of other societies by way of contrast.  Which is to say the way they incorporate the possible into the real.  Like I say though, without a much longer discussion, that's not going to sound convincing or even intelligible, so after putting several everyday words in scare quotes, I'm stopping here.

I did have one final thought though, inspired by a comment from Dr. CC that has been rolling around in my head for a while now.  Is science "asymptotically objective"?

This idea seems like a natural and appealing fallback in the face of something like Kuhn's thinking about the possibility of a paradigm shift.  Sure "we once thought" that gravity "was really" the point-to-point attraction of massive bodies, "but now we know" that it's really about curved space-time.  What we thought was "objectively true" has proven to be a complete abstraction that merely worked well to help us do what we wanted.  And we're conscious that our new abstraction is also going to someday fall victim to this same pattern.  Still, though, we know that with each revolution we are somehow getting closer to the one true real explanation.  The objective world at the end of the asymptote.

This is a strange image though.  Because how is a progression of what we now freely admit are abstractions created for human purposes supposed to be magically transmuted into an "objective description" at the end of the asymptote?  And how exactly can a description be objective anyhow?  It's certainly not just in someone's head, because many of us share it.  And it's certainly not just a collective delusion because it allows us to effectively do all kinds of things.  But at the same time a description of the object is clearly not the object itself, but only one aspect of it; the one that matters for our purposes.  Whitehead calls the problem the "fallacy of misplaced concreteness".  An electron is pretty clearly an idea, not a thing, so we must be pulling a fast one when we claim that the world is made up of electrons.  And no matter how much further or smaller we go in our abstractions, we're not going to ever magically hit the "objective" world with them because this same problem is going to apply.

What content would be left to the claim of asymptotic objectivity then? Isn't it really about creating ideas that allows us to do more and more with the world?  Explanations that allows us to do some new stuff on top of all the old stuff we used to be able to do?  Seems like a noble goal and a good candidate for the content behind what we'd like the claim to do.  If you believe A, you'll be able to do X and Y.  But believing B is better (slip the word "more objective" in here) because you can do X, Y, and Z.

Unfortunately, this claim doesn't seem to have anything to do with objectivity, though it does sound a lot like our idea of progress.  Once you drop the claim of objectivity though -- which seems at first may seem costless and merely semantic  -- you will also have to subtly modify your definition of progress.  Because now there's no such thing as "general progress".  There's only specific progress along a particular dimension you happen to value.  But not all of these dimensions point in the same direction and some may even be opposed (as in predictive accuracy and mathematical elegance in the standard model vs. string theory debates).  If you wanted to do Z, then believing B was definitely better.  But what if you wanted to do Q?  

This "progress" then begins to look a lot more like Brownian motion.  Or maybe an amoeba moving up a sucrose gradient at best.  It may have a direction, but there is no a priori reason to think that it's the right or unique one.  The metaphor of an asymptote only makes sense if there is some value to converge to.  If we start to see our direction as inevitably defined by our value space (so to speak), then it seems like we're wandering in a very, very large space indeed, and we're going to need to ask much more complex questions about how our values might overlap with other possible sets of values (say, alien or computer values).

A final thought occurs to me here.  One I don't completely understand  In some sense, Brownian motion does have a sort of asymptote that we call "equilibrium" -- the diffusion of something to occupy a volume at a uniform concentration.  Maybe I've inadvertently defined something exactly like general progress?  Perhaps, yes, science always has a particular direction at a particular time, but maybe somehow, on average over time, it expands in every direction to completely describe everything that could matter about the world?  This is a wildly ambitious hypothesis that makes the physicist's dreams of a final theory-of-everything look like a silly footnote.  Because were they to announce the current version of this theory tomorrow, it still wouldn't describe a fraction of the things that matter just to me -- like why Deleuze is so great or even whether it will rain April 3, 2056452.  But maybe, someday, there could be an ever bigger ToE that would explain those things?

Tough question.  I'm going to go with Stuart Kauffman on this one though, and posit that the universe is actually non-ergodic.

Consider next the number of proteins with 200 amino acids: 20 to the 200th power. Were the 10 to the 80th particles in the known universe doing nothing but making proteins length 200 on the Planck time scale, and the universe is some 10 to the 17th seconds old, it would require 10 to the 39th lifetimes of the universe to make all possible proteins length 200 just once. But this means that, above the level of atoms, the universe is on a unique trajectory. It is vastly non-ergodic. Then we will never make all complex molecules, organs, organisms, or social systems.

 And if life and matter is wandering through this non-ergodic universe, then so are our explanations of it.