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.