Sunday, January 13, 2019

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.  

Saturday, January 12, 2019

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.

Sunday, January 6, 2019

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.