26 Mar 2015

Somers-Hall, (1.2), Deleuze’s Difference and Repetition, ‘1.2 Aristotle’s Conception of Difference (30–3/38–42)’, summary


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Corry Shores
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[The following is summary. All boldface, underlining, and bracketed commentary are my own. Proofreading is incomplete, so please forgive my typos and other distracting mistakes. Somers-Hall is abbreviated SH, and Difference and Repetition as DR.]

[UPDATE: My lack of knowledge, cleverness, and time prevent me in some cases from being able to re-explain in my own way some ideas in Somers-Hall's text. We are fortunate that the author has taken the time to remedy these gaps in my summary. Please see his clarifications in the comments section.]



Henry Somers-Hall


Deleuze’s Difference and Repetition:
An Edinburgh Philosophical Guide


Part 1
A Guide to the Text

 

Chapter 1. Difference in Itself

1.2 Aristotle’s Conception of Difference (30–3/38–42)


Summary



Brief summary:

Aristotle’s conception of difference is bound up with his theory of classification. A genus is divided into species, which differ in kind. The division terminates in the individuals, which differ in number and only accidentally [rather than essentially like species do]. The genus-species distinction is relative, such that any genus can be a species to a higher genus, just as any species can be a genus to a lower species. The one exception is the species-individual relation, in which the species cannot again serve as genus, given that there are no species below it; instead there are only individuals. Difference in its truest sense is the difference in kind which distinguishes one species from another.



Summary


Deleuze’s critique of representation begins with Aristotle, whose philosophy in this account is thought to have presented “the first formulation of representation” (23). Aristotle conceived of difference in terms of opposition: “x differs from y if x is not y”. Deleuze says that this implies a certain concept of being.  Deleuze will instead formulate a univocal conception of being in terms of intensive difference. Later Deleuze will discuss two ways of understanding difference, either spatially or as intensity. If spatially, then being is understood as fragment. If intensively, then being is understood univocally. In the following, SH will go over Aristotle’s basic ontological concepts of genus, species, difference, and accident, drawing primarily from his commentator Porphyry. Afterward we will see why Aristotle’s thinking leads him to certain problems. (24)


[The following can be confusing for a number of reasons. For example, there is terminology used in a way that is unfamiliar to me, and also the terminology is slightly inconsistent, namely in the cases of the phrases: predicated in and predicated of. Perhaps their meanings are identical, but even if so, I am not exactly sure I know how to define them. Also, there are two definitions given for genus, but in subtle ways they do not seem to line up, since the second one adds concepts not found in the first one. Another problem is that we might be familiar with this pairing: subject – predicate. And we might also be familiar with this pairing: genus – species. But somehow we need to combine them such that a genus, species, or individual can be predicated of or in something else. How to clearly conceptualize this is not apparent to me yet. The conclusion we will arrive at is that we need a species in between genus and individual. Yet, the exact reasoning for this is also unclear to me. The basic reason seems to be that the definition necessitates it. However I am not sure why the definition is formulated exactly in this way and not in some other manner. So according to the definition, the genus is made of different things that differ in kind. Working just with this definition, perhaps the reasoning is like this. We think of a set of individuals. If they are included in the genus, then so far we only know what generically is common to all of them (what is essential to them all) but their distinctions are not thereby designated. So it is as if they are all the same. In order for there to be a real diversity such that there are numerous members for the group, the individuals need to have differences in kind, which would be like subgroupings, and thus be species intermediateing between genus and individual. What is not clear to me is why genus is defined in this way and rather not just defined as a group of members. Perhaps the idea is that in order for it to be a group, it needs different things and not just one thing. And in order to have different things, they cannot be many instances of the same thing (or different quantitative variations of the same thing), since these could collapse again into one thing (or into one thing having different degrees of itself). They need to be different in kind in order to be a real multiplicity, and thus perhaps there needs to be species groupings among the members. Please read and discern the correct meaning of this paragraph for yourself.]

Porphyry defines the genus as ‘what is predicated in answer to “What is it?”, of several items which differ in species, for example, animal’ (Porphyry 2003: 4). This follows from Aristotle’s own definition: ‘what is predicated in the category of essence of a number of things exhibiting differences in kind’ (Aristotle 1984d: 102a). What does it mean to be predicated of items that differ in kind? If we take the case of Socrates, it should be clear that ‘animal’ can be predicated of him, to the extent that Socrates is a man (a rational animal). For Porphyry and Aristotle, however, there is no difference in kind between different men, but rather a difference in number. While it is the case that a given genus, such as animal, is predicated of an individual, such as Socrates, the genus cannot simply be directly used to define the individual. If it were used in this way, the genus would be the only function which was essential to each individual. This would mean that in essence each individual would be different only in number, whereas the definition of genus requires that it is predicated of what also differs in kind. We therefore need the intermediary category, which Aristotle and Porphyry call the species.
(24)


[The terms predicated of and predicated to would seem to mean: “is a predicate to”. So for example, animal can be predicated of Socrates, since it is a predicate to Socrates as in the formulation: Socrates is an animal. Now we move to the definition of species. The genus, we saw above, is what can be the predicate to a species, which would be groups of individuals that differ in kind to other species. So the genus animal can be predicated to various species, such that, ‘man is an animal’, ‘dog is an animal’, and so on.] Species we now see are what are predicated to things which differ in number. [So perhaps there is no difference in kind between Socrates and Plato. They is just difference in number. They are different instances of the same species man. So, “Socrates is a man” and “Plato is a man”.] Thus the individual can be predicated of both its genus and its species. [But we ask now, how would we define the grouping above “animal”? Perhaps it might be, “living creature”, including also plants and whatever else. It would seem that ‘genus’ and ‘species’ are relative terms, such that a genus can serve as a higher genus’ species.]

Porphyry writes that ‘the intermediate | items will be species of the items before them and genera of the items after them. Hence these stand in two relations, one to the items before them (in virtue of which they are said to be their species), and one to the items after them (in virtue of which they are said to be their genera)’ (Porphyry 2003: 6).
(SH 24-25)

[This also means that only the lowest species has individuals as its more basic members. We need to define species now in terms of its genus, and not just in terms of having members differing in kind, like we saw above. I am not exactly sure how this is done. Perhaps the new definition of species would be: ‘a species is the subgrouping of the genus, and this grouping is based on differences in kind.” But that does not add anything to the definition of genus, so I am not sure.]

A consequence of this is that we now need to define the species in terms of something other than the individual, since only the lowest species relates directly to things which differ only in number. Instead, we now define the species in terms of its genus. Thus we have a hierarchy, reaching from the highest genera to the individual, through which the individual is specified by a process of division from the genus through the various species, gaining determinations as it goes, since each genus will determine the essence of that below it.
(25)

[Next we look at ‘accidents’. SH says they do not define species, so it is not clear yet why we need to mention them. Perhaps they are what distinguish individuals, which differ in number, but not in essence. There are separable and inseparable accidents. This distinction is not very clear to me. Separable accidents are not defined, but they are exemplified, for example, Socrates can be sitting or not sitting. It is clear why this is accidental, since it is arbitrary and does not change Socrates himself. Inseparable ones are explained as being accidental traits that were they removed from the individual, that individual could still keeps his essence. The counter example is a trait that were it removed, the individual does lose its essence. All this is clear, except it is not clear why the second kind of accidents are called inseparable, since they can be separated without changing the individuals essence. Perhaps they are inseparable in the sense that they are inherent to the individual and physically inseparable, even though they are non-essential.]

The last category we need to consider are accidents, which do not define a species. These can either be separable (as in the case of Socrates, who can be sitting or not sitting), or not separable (for instance, ‘being black is an inseparable accident for ravens and Ethiopians’ [Porphyry 2003: 12]), in that an Ethiopian could lose his skin colour without ceasing to be an Ethiopian, whereas a man without reason (at least potentially) is no longer a man.
(25)


SH now asks what the role of difference is in this hierarchical schema. For Aristotle, only things sharing something in common can also differ, for otherwise the difference would be so great as to disallow any basis for them to stand in relation to one another. [The commonality seems to be a shared genus at some higher level]. SH then asks “If differences between things of different genera are too broad, how can we formulate a narrower conception of difference?” [But it is not yet clear to me yet how some genera are similar enough to have an evident difference and others do not, and I also do not understand what is meant by a narrower conception of difference and how it would solve this problem.] SH explains that [in the face of this problem] there are three forms of difference, namely, common difference, proper difference, and the most proper difference. Yet Porphyry only considers the most proper difference to be real difference. Common difference is not real difference, because it is the difference between accidents, meaning that that the difference is between “non-essential predicates, and is not effective in determining a real difference between entities” (SH 25). Proper differences are in fact real differences because they are inseparable properties of things [above we looked at inseparable accidents, like the black of the Ethiopian. It is not clear how that notion fits here into proper differences. Perhaps they are the same, and here proper differences distinguish individuals but perhaps like inseparable accidents they do not distinguish species.] (25) Then we have the most proper difference, which is specific difference. It “is what allows species to be defined in Porphyry’s tree by dividing the genus” (25d). [It is not clear to me what the ‘proper’ means here and why more proper brings the difference to the difference between species. Accidental traits it seems distinguish individuals. Proper differences do too. And somehow, the more proper, the less distinguishing of individuals and the more of species.] [So now we are somehow no longer thinking of proper difference as distinguishing individuals but instead as dividing genera into species. Recall also that difference between genera can be so great such that the genera are too other to one another that they cannot be properly distinguished. (There was no example for this, so it is difficult to conceptualize. Perhaps this would happen if the genera are at least two steps removed. So consider these two classifications: 1) Socrates – Man – Animal – Living Thing. 2) The largest cut diamond – Gem – Stone – Non-Living Thing. Perhaps Gem and Man are too other, since we cannot say, Both Man and Gem are X, except Man is has these distinguishing traits and Gems have these other distinguishing traits. For, the next most common genus is ‘thing’, but to make the comparison, we would say, a man is a thing, that is also a living thing, that is also an animal, while a Gem is a thing, which is also, … etc. So specific difference, which would also for some reason be equated with conceptually significant difference, is in between the otherness of genetic difference and the ultimate specificity of individual difference. Perhaps also to see just individual difference is to be aware of metamorphoses, on account of very specific changes which cannot be reduced to a single common thing happening over those changes. I am not sure, so please judge for yourself the meaning of these sentences.]

The most proper difference, however, is specific difference. Specific difference is what allows species to be defined in Porphyry’s tree by dividing the genus. So, if we take the genus, animal, we are able to determine the species, man, by dividing animals into two kinds: rational and non-rational animals. Difference is the criterion by which | we divide the genus into two species. Conceptually significant difference therefore occupies a middle point between the extremes of otherness and accidental difference: ‘Specific difference refers only to an entirely relative maximum, a point of accommodation for the Greek eye – in particular for the Greek eye which sees the mean, and has lost the sense of Dionysian transports and metamorphoses’ (DR 32/40).
(25-26)


Porphyry then, by means of these divisions based on essential differences, “provides an account of the determination of objects that allows us to characterise all of their essential determinations through a process of division. We begin with a property which belongs to everything, for instance, substance, and by a repeated process of division of things into contrary classes, we eventually arrive at a complete determination of the subject” (SH 26). [SH then quotes Porphyry who speaks of the form-matter distinction in this context. It seems to add concepts that we will not need later, so I will just replicate the text without commenting on it.]

He puts this point as follows [quoting Porphyry up to the citation]:

For in the case of objects which are constituted of matter and form or which have a constitution at least analogous to matter and form, just as a statue is constituted of bronze as matter and figure as form, so too the common and special man is constituted of the genus analogously to matter and of the difference as shape, and these – rational mortal animal – taken as a whole are the man, just as they are the statue. (Porphyry 2003: 11)

Of course, Porphyry is not implying that what we have here is a temporal constitution (we don’t find in the world beings that are only determined as animals, for instance). Rather, his point is that the series of genera and species provide an account of the logical order of determinations of a particular object.
(SH 26)

 



Citations from:

Somers-Hall, Henry. Deleuze’s Difference and Repetition. An Edinburgh Philosophical Guide. Edinburgh: Edinburgh University, 2013.


Or if otherwise noted:

Aristotle (1984d), ‘Topics’, trans. W. A. Pickard-Cambridge, in Jonathan Barnes (ed.), The Complete Works of Aristotle, Princeton: Princeton University Press, 167–277.




Porphyry (2003), Introduction, trans. Jonathan Barnes, Oxford: Clarendon Press.

 

6 comments:

  1. There’s lots of terminology in this section, much of it setting up debates later in DR. For instance, accidents aren’t terribly important here, but they become so later – Deleuze for instance will say that the virtual is something like an essence, but conceived of in terms of accidents (i.e., it captures the totality of the behaviour of a system, rather than simply extracting some moments as being the fundamental aspects of something, and seeing the rest as ‘noise’). I’ve included a chunk of one of the lectures that formed the basis for my guidebook at the end of these comments.

    Predicated of/to – I’m afraid that this is simply a typo, and should read as predicated of throughout. It simply means that we can attribute property in question to x. so when animal is predicated of Socrates, we simply mean that Socrates has the property, animal.

    Much of this discussion is terminological. The key points are that a species is defined by a genus and a difference. So, for instance, the species, human being, is defined by a genus, animal, plus the difference, rational. Here, what defines a genus and a species is essentially their relative positions (a genus is something divided, and a species is a genus plus a difference). This means that we can form a hierarchy of terms. The genus, animal, is itself a species of the genus, body, plus the difference animate.

    On accidents:

    *[All this is clear, except it is not clear why the second kind of accidents are called inseparable, since they can be separated without changing the individuals essence. Perhaps they are inseparable in the sense that they are inherent to the individual and physically inseparable, even though they are non-essential.]

    – yes, I take this to be Porphyry’s point. A white crow would still be a crow, but crows just happen to be materially constituted as black – don’t try to artificially whiten a crow! But we can separate the accident of sitting from Socrates simply by making him stand up.

    *SH now asks what the role of difference is in this hierarchical schema. For Aristotle, only things sharing something in common can also differ, for otherwise the difference would be so great as to disallow any basis for them to stand in relation to one another. [The commonality seems to be a shared genus at some higher level]. SH then asks “If differences between things of different genera are too broad, how can we formulate a narrower conception of difference?” [But it is not yet clear to me yet how some genera are similar enough to have an evident difference and others do not, and I also do not understand what is meant by a narrower conception of difference and how it would solve this problem.]

    To see why difference relies on a prior identity, and why it operates in terms of opposition, we need to bear in mind that Aristotle’s aim is to develop a taxonomy that covers everything. This means that we need to make sure that if we proceed methodically, we cannot mis-define an object. In effect, Aristotle’s taxonomy is a complex game of ‘animal, mineral vegetable’. We begin with the most general notion possible, for instance, substance. We know that Socrates is a substance, but this is too vague a definition, so divide this class of things into two further classes, for example, material and immaterial substances. These have to be opposites, as if they weren’t we would risk there being a third type of substance not included in our hierarchy. We know (according to the law of excluded middle) that everything is P or –P (material or not-material). Difference cannot be less than opposition, therefore. Similarly, for Aristotle, difference occurs within a prior identity (the genus). This supplies the field of possibilities that the difference divides in two. Difference is therefore WITHIN a genus, rather than between genera. Loosely, differences between genera subvert the hierarchical process of determination by jumping between levels.


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  2. Species and Genera
    The key question is therefore, how does something become determined, or, how does form emerge. This is a central question for representation itself, as representation relies on the recognition of an isomorphism between the subject’s representation and the object in order to allow thinking to adequately relate to the world. Porphyry provides an account of the five terms which together allow us to form a representation of an object. These are genera, species, difference, property and accident.
    To go through the terms quickly, the genus is ‘what is predicated in answer to “What is it?”, of several items which differ in species, for example, animal.” (ISA, 4) Genus therefore is determinative of the essence of something, as is made clear by Aristotle himself: ‘what is predicated in the category of essence of a number of things exhibiting differences in kind.’ (Aristotle, Topics, 102a) I want to return to this connection between the question ‘what is it’ and the nature of essence when I discuss when we get to the notion of accident. What does it mean to be predicated of items that differ in kind? If we take the case of Socrates, it should be clear that ‘animal’ can be predicated of him, to the extent that Socrates is a man (a rational animal). For Porphyry and Aristotle, however, there is no difference in kind between different men, but rather a difference in degree (one man is just more or less rational than another). . While it is the case that for a given genus, say, animal, it is predicated of an individual, for instance Socrates, since it is clear that Socrates is an animal, the reference to a difference in kind in Aristotle’s definition means that there must be an intermediary between the genus (animal) and the individual (Socrates). This is because if the genus were related directly to the individual, the genus would be the only function which was essential to each individual. This would mean that in essence each individual would be different only in number, whereas the definition of genus requires that what it is predicated of also differs in kind. The necessity of this requirement will become clear shortly, but for now it is enough to recognise that between the genus and the individual is an intermediary category. This category is the species. In the simplest case, we can define the species as ‘that which is predicated, in answer to “What is it?”, of many things which differ in number’ (ISA 5). This case would be the one reached so far, where we have one genus, one group of individuals, and one level of species (a genus cannot simply have one species as in this case we could not meet the definition of a genus as applying to a number of things differing in kind). In this case, we can see that a given genus can be predicated of a species, and of an individual can be predicated both the species and the genus. Thus, of Socrates, we can say that he is both animal (according to his genus) and man (according to his species).
    So Socrates now has two determinations: we can define him according to his genus on the one hand, and his species on the other. In fact, we might want to make a more fine grained definition by adding in more terms. As Porphyry writes, “the species intermediate between the extremes they call subordinate genera and species, and they regard each of them as a species and a genus, since each is comprehended in relation to the highest genus and the lowest species” (ISA, 38). A corollary of this is that we now need to define the species in terms of something other than the individual, as only the lowest species relates directly to a field of numerical identity. The species will now therefore become defined in terms of the genus above it. Thus we now have a hierarchy, reaching from the highest genera to the individual, through which the individual is specified by a process of division from the genus through the various species, gaining determinations as it goes, since each genus will determine the essence of that below it:

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  3. Taken from: http://faculty.washington.edu/smcohen/433/PorphyryTree.html
    This leads to the so-called Tree of Porphyry (above), where we have a hierarchy of genera. Here, body is the species of substance, but the genus of living things.

    Accidents and Properties
    Before talking about difference, I just want to note briefly the other two parts of the Porphyrian system. First, properties. These define a species, but do not determine its essence (such as, for instance, laughter, which Prophyry takes to be a trait which only man exhibits, but which is not definitive of him). Second, accidents, which do not define a species. These can either be separable (as in the case of Socrates, who can be sitting or not sitting), or not separable (for instance, ‘being black is an inseparable accident for ravens and Ethiopians’ [ISA 12]), in that an Ethiopian could lose his skin colour without ceasing to be an Ethiopian, whereas a man without reason (at least potentially) is no longer a man. The fact that accidents cannot be a part of essence can be seen if we return to the original meaning of the Greek for essence, ti ēn einai, which can be translated as ‘the what it was to be that thing’. What is important to recognise about this definition of essence is that it provides a self-identical underpinning for the thing whose essence we are searching for. Through this self-identity, the underlying essence allows the same individual to be re-identified, even though the individual in question may have altered in his passage through time. Thus essence provides a tool for the selection of properties which are properly definitive of an individual, as opposed to those which are merely accidental to the individual. The fact that Socrates may be sitting is not constitutive of the essence of Socrates himself, although it does represent a state that he is in. If inessential states such as this were taken to be definitive, the identity of Socrates himself would break down through the collapse of all continuity. Whilst Socrates is becoming, the development of a fixed definition of his essence is problematic, as there is no way to differentiate accident and essence. It is only, however, once Socrates has ceased to be that the fixity we require for a determination of essence comes into being. Thus essence, as the “what it was to be a thing” is essentially retrospective. This means that the becoming of Socrates is related entirely to an atemporal state of being.

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  4. Difference
    So what is the role of difference in this hierarchy? Porphyry talks about three forms of difference: common difference, proper difference, and more proper difference, only the third of which would be considered to be real difference. Common difference is the difference between two accidents, or non-essential predicates, and is not effective in determining a real difference between two entities. This is because it is possible for the same individual to support contrary accidents (Socrates sitting and later, Socrates standing up, for instance). Proper differences deal with inseparable properties of things, and so do really serve to determine the difference between two things. The most proper difference, however, is specific difference. Specific difference is what allows species to be defined in Porphyry’s tree by dividing the genus. So, if we take the genus, animal, we are able to determine the species, man, by dividing animals into two kinds: rational and non-rational animals. In fact, the tree is formed by applying specific differences to the preceding genera until we reach the lowest possible species (we cannot reach the individual itself as they are infinitely numerous, and ‘[Plato] tells us to leave the infinities alone, for there will be no knowledge of them’ [ISA, 7]).
    So Prophyry provides an account of the determination of objects that allows us to characterise all of their essential determinations through a process of division. We begin with a property which belongs to everything, for instance, substance, and by a repeated process of division of things into contrary classes, we eventually arrive at a complete determination of the subject. This therefore is representation’s attempt to solve the problem of grounds which Deleuze highlights at the beginning of the chapter. The problem was that representation seemed incapable of giving an account of how something could become determined. It now appears that by the repeated addition of predicates, representation is able to account for this process.
    In fact, on page 39 of Difference and Repetition, Deleuze gives a whole series of characteristics which seem to show that it is difference which allows representation to escape from the undifferenciated abyss through determination. It appears to be an essential concept, in that it determines the essence of the species, by dividing the genus, it is both synthetic and productive, in that it is what produces species, and it explains the genesis of the species. In this sense, we can see specific difference as giving form to a previously unformed genus. In fact, Porphyry makes explicit this account of generation:
    For in the case of objects which are constituted of matter and form or which have a constitution at least analogous to matter and form, just as a statue is constituted of bronze as matter and figure as form, so too the common and special man is constituted of the genus analogously to matter and of the difference as shape, and these – rational mortal animal – taken as a whole are the man, just as they are the stature. (ISA 11)

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  5. Clearly, Deleuze does not consider this account to be satisfactory, however. The reason for this is that whilst difference appears to play a productive role in the Aristotelian account of determination, in fact it is always understood through (or mediated by) another concept, what he calls the four shackles of mediation. These ‘shackles’ are identity, opposition, analogy and resemblance. Difference clearly has to be understood in terms of opposition if Porphyry’s tree is to function, as each division of the genus has to be complete. If we are to provide an absolute determination of the object, it cannot be possible that it escapes from the hierarchy by existing as some third term between, for instance, rational and non-rational. Identity is essential because in order to determine that two things are different, they need to share a background of identity; otherwise, they are simply diverse, or, in Porphyry’s terms, ‘otherlike’. We can clarify this by noting that whereas the question which relates to genera is, ‘what is it?’, the question which relates to differences is, ‘what sort of such and such is it?’ (ISA 10), for instance, we ask, ‘what sort of animal is man?’. In this case, the question of difference makes clear that differences rely on the pre-existing genus in order to be posed. The difference between rational and non-rational only makes sense on the basis that the entities we are discussing share the trait, animality. Resemblance is required because we need some way of determining which particulars fall under which concept. As the properties they possess will be actualised in different ways, we subsume them under a species not on the basis of identity, but of resemblance with the difference.
    In spite of this, representation is clearly able to give an account of how an object is determined (namely by the attribution of predicates to it). It therefore does have an account of the determination of form. The last of the shackles of mediation that I want to look at, and will form the topic for next week, emerges in response to a more serious challenge. If difference determines, but only on the basis of a prior genus, then how do we define the highest and most general genus, being, itself? Either we posit an identity above it in the hierarchy, in which case we need to explain this higher identity, or else we seem to be in the position of having to declare this concept itself indeterminate. Aristotle, or more correctly, Aristotle’s successors, introduced the concept of analogy in order to try to solve this problem.

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  6. Conclusion
    The central topic of the opening of chapter one is therefore the genesis of form, and the failure of recognition to explain this genesis. As we saw, difference is a key concept both in the account of genesis provided by Deleuze and by Aristotle. While Aristotle (or Porphyry) has shown that form can be further determined by the attributions of differences to a genus, the key question for representation is whether the origin of form itself can be explained. This returns us to the problematic of the monstrous – we can explain how the given is determined (the centaur or griffin), but can we explain how the given itself, as abstract subject of predication, is given, from within representation?

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