Somers-Hall, (1.3), Deleuze’s Difference and Repetition, ‘1.3 Aristotle’s Conception of Being (32–5/41–4)’, summary

by 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.]

Summary of

Henry Somers-Hall

Deleuze’s Difference and Repetition:
An Edinburgh Philosophical Guide

Part 1
A Guide to the Text

 

Chapter 1. Difference in Itself

1.3 Aristotle’s Conception of Being (32–5/41–4)

Very brief summary:

Aristotle’s system of genus-species classification and definition runs into a problem when we reach the highest category, being or unity. Normally, each genus is understood  as serving as a species to a higher genus. But ‘being’ or ‘unity’ can have no higher genus. Aristotle’s solution is to say that rather than having a higher genus, there is a focal concept to which the genera refer; and to still have difference so to make being conceptualizable in a determinate and specifiable way, he says that there are multiple senses of being which refer to this focal concept. This compromises the coherence of his system, since the genus-species structure does not operate consistently throughout, despite the structure holding throughout. At the highest level, equivocity in the senses of being is required to terminate the ascension of levels in a way that makes ‘being’ sensible, while all the species, many of which also serve as genera, require univocity in order for their meanings to be specific and defining.

Brief summary:

Aristotle’s system of categorization and definition involves designating the essential differences between species within a genus. Thus we might have these definitions and classifications: ‘man (species) is an animal (genus) that reasons (species difference),’ while ‘fish (species) is an animal (genus)  that lives under water (species difference)’. A grave problem this presents to the system is that it undermines its own foundations. All the elements that are classified in the system presuppose a concept of unity or being. As well, the notion of difference which is required to distinguish the parts is also something that has being, and thus it too requires a concept of being for it to be a sensible part of the system. However, being cannot be given a clear conceptualization, since there is no higher genus under which it can be distinguished from other species of its general type. Aristotle’s solution is that there is no one highest genus but rather there are many senses of being that all refer to the same focal concept of being, which is not to be understood as a higher genus. It is like paronymous  meanings, that is, meanings which are related by morphology, like grammarian and grammar. Nonetheless, this solution compromises the coherence of the system, since genus, especially the highest one that encompasses all others, functions by means of a different rule than the species do. Species require univocity in order to be specific and determinate. But genera require equivocity in order to be multiple yet ultimately terminal.

Summary

[We saw previously that for Aristotle, there are three basic elements in classification. We need first to recognize that something is distinguished from something else on the basis of its classification. To define something, and thereby establish what makes it different from something else, we first designate its higher grouping, the genus, and then what makes it specifically different from other members of that group. Here we are dealing just with species and genus. So {species} man is {genus} an animal {specifying difference} that reasons, unlike other species of animals, which do not reason. The lowest division would be the individuals, each of which differ from one another by means of accidental features. However, groups of individuals may share the same essence, and as a group would form the species for a genus.] Now SH will look at some problems with Aristotle’s (and his commentator Porphyry’s) system. Deleuze thinks that there are two main classes of problems with this model, the problems of the Large and the problems of the Small. The Large problems concern difficulties with conceptualizing the highest genus, and the Small problems “relate to the unity of empirical objects” (26). According to Deleuze, Aristotle’s model falls short when it needs to deal with these extreme ends of the hierarchy. [I am not sure how the next sentence follows from the prior. It seems that the structure of a generic layer encompassing from above specific items is imposed in our experience, if we assume that we experience directly an undifferentiated flux of sense data that is processed according to conceptual unities.]

Thus, Aristotle’s model relies on the ‘extraction or cutting out of generic identities from the flux of a continuous perceptible series’ (DR 34/43). This involves a problematic notion of resemblance between changing perceptions and an unchanging essence.
(SH 26)

[Recall the discussion previously about the undifferentiated. We said that: Deleuze gives two examples of indifference: 1) The undifferentiated abyss into which everything dissolves, and 2) The white nothingness on which are scattered unconnected determinations (SH 21-22). In the first case, a lack of difference makes everything seem indistinguishable and seemingly be identical. In the second case, the lack of difference prevents things from forming determinate relations with one another.] SH now recalls the previously discussed distinction between the dark abyss of indifference (where things are too murky for anything to be differentiated) and the white surface (where nothing can enter into relation with anything else [but I am not sure why. Keeping with the metaphor, perhaps we are blinded by the light. But what that metaphor refers to is not evident to me.]) SH claims that this polarity is like the two kinds of problems in Aristotle’s system of classification.

We can relate these difficulties to the two forms of indifference which are to be avoided. As we have seen, these are ‘the black nothingness, | the indeterminate animal in which everything is dissolved – but also the white nothingness, the once more calm surface upon which float unconnected determinations like scattered members’ (DR 28/36). While Deleuze’s characterisation of these problems may seem obscure, they relate to two key issues with Aristotle’s theory. First, how do we determine the nature of the highest genus in the Aristotelian hierarchy (black nothingness), and second, how do we explain the constitution as well as the determination of the subject (the problem of white nothingness)?
(26-27)

Aristotle himself was aware of the problem of the highest genus. [SH then quotes Aristotle, but its meaning is not immediately clear to me. One reason is that it introduces a concept we have not dealt with yet at least under this name: differentiae. Let us for the moment guess that a differentia is a species difference. Still, interpreting this passage is difficult. We said before that predicated of seems to mean “is a predicate to”. Aristotle will write: “it is not possible for the genus to be predicated of the differentiae taken apart from its species”. We think of the highest genus, ‘being’ or ‘unity’. It would help to know what comes next. Let us guess that the two most basic kinds of things are real (physical) things and unreal (abstract) things. Let us also guess that the differentiae are ‘real vs unreal’. Were that to be so, we could make the following substitutions into the definition: “it is not possible for the genus ‘being’ to be the predicate for the differentiae ‘real & unreal’ were these differentiae taken apart from the genus being’s species, ‘real things’ and ‘unreal things’. It is still not clear how a difference can itself be predicated, so let us assume that we are speaking of predication to the different species. Still I cannot grasp the meaning. Aristotle’s conclusion will be that were unity or being the genus (thus the highest genus), then no differentiae will be unified or have being. I wonder if this is because were unity or being the highest genus, then we cannot formulate a concept for unity or being. This is because, in order to define it, we need to differentiate it from some other species belonging to a common genus, which in this case does not exist, as none are higher. Then maybe the reasoning continues like this. Since we cannot define unity, that means we have no basis to say that the differentiated species groupings have unity either. Please read the Aristotle quotation for your own interpretation.]

It is not possible that either unity or being should be a 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 to be predicated of the differentiae taken apart from its species (any more than for the species of the genus to be predicated of the proper differentiae of the genus); so that if either unity or being is a genus, no differentiae will either be one or have being. (Aristotle 1984b: 998b)
(SH 27)

We return now to the idea that a genus is what is the predicate to the shared essence of things (species) that otherwise differ in kind, such that for the genus animal, we might predicate it to such various species in this manner: ‘man is an animal’, ‘dog is an animal’, ‘elephant is an animal’ and so on. [Or as Aristotle puts it, perhaps meaning something slightly different: “a genus is ‘what is predicated in the category of essence of a number of things exhibiting differences in kind’ (Aristotle 1984d: 102a)” (SH).] We thus can define what it means to be an X by designating its genus and what differentiates it (its differentiae) from all other species in that genus. [The next part is a little confusing for me. The conclusion will be that a difference cannot be of the same type of that which it differentiates, with the problem of infinite regress being the reason why. To illustrate, SH has us consider the example of living bodies. We are to first consider the possibility that “the difference between living bodies was itself a living body”. It is not clear to me yet how to conceptualize or imagine this possibility. If a difference is understood as a sort of relation, how would it be understood as well as a living body? Also, the conclusion is hard for me to arrive at. In the prior section we distinguished types of differences, namely, common difference and proper difference. Is not the difference between them a difference itself? And thus, is not the difference of the same kind as that which it differentiates? Perhaps the issue is that it is neither a common nor a proper difference. But recall that a common difference is accidental but proper differences are essential. Would not the difference between common difference and proper difference itself be a proper difference, if indeed they are two species of difference? If we were defining our terms, perhaps there would be a problem here. What is an essential difference? It is what makes a difference not accidental. What makes a difference not accidental? It is not accidental if it belongs to a category, namely ‘essential difference’, which itself is defined in terms of its essential difference to accidental difference. Please read the following to find a better interpretation.]

a genus, along with the differentiae, determines what it is to be an X. It should be clear that a difference cannot be the same type of thing as that which it differentiates. We can show this by taking as an example the case of living bodies. If the difference between living bodies was itself a living body, then we would be caught in an infinite regress, as in order for this living body to function as a difference, we would need to differentiate it from other living bodies. Thus, we would require a further difference, which would in turn need to be differentiated and so on to infinity. What thus differentiates living bodies, the difference sensible/non-sensible, must itself not be a living body.
(SH 27)

[If we take this point that a difference cannot be of the same type of that which it differentiates, we will conclude that] “what differentiates beings into different species cannot itself be a type of being. Therefore, if being is a genus, then difference itself cannot be a being” (SH). [However, since we know that differences do have being, that means being cannot itself be a genus.] “As Deleuze puts it, ‘Being itself is not a genus . . . because differences are’ (DR 32/41)” (SH 27). [The next point seems to be that there can be no highest genus if there be any differentiation in the system. It seems that instead somehow there are multiple highest genera, since no higher one can be conceived.]

It is not simply the difference in being that would lack being, but as differences are inherited (man is a rational animal, but also a material substance), all differences would lack being. For this reason, the ultimate categories through which being is understood must be multiple, as they themselves are species in relation to the undefined genus.
(SH 27)

If there are multiple highest genera, this is a problem for Aristotle, who wanted a coherent metaphysical system, which, in order to be scientific, would need  unity at its basis [a science needs to be defined in terms of the objects it studies, but if they cannot be univocally determined, the science would perhaps be unable to designate its own objects of study. In this case, metaphysics as the study of beings would be unable to designate what beings are in the first place and thus be unable to properly begin its studies of them.] So we have different senses of being [different highest genera each for being but also each somehow different, in a way not yet specified]. Their senses cannot be identical [as then we would really just have one genus]. As we will see, it will be by using a grammatical metaphor, namely, the concept of paronymy, that we will understand how the senses differ while also are senses of the same thing.

If there was no governing principle to how the things in our world are grouped, then we would not be able to speak sensibly about them [since what we are talking about are not coherent concepts or coherent groups of things]. This is Aristotle’s motivation for differentiating the groupings in terms of what is essentially common to them. [Somehow on account of this], Aristotle begins his Categories with the following three terms: homonymy, synonymy and paronymy. If things are homonymous, then they share the same name but really they are different. For example, if we show a picture of an ox and we also show a live man himself, we would in both cases say, ‘this is an animal’ and ‘that is an animal’ even though what defines each is very different [one is a piece of paper while the other is a living, breathing creature]. [Now consider if we have a man and a real ox before us, and we say, “this is an animal” and “that is an animal”, both cases of ‘animal’ are synonymous, since the definition for ‘animal’ is the same in both cases and as well the names are the same.] “When things have a name in common and the definition of being which corresponds to the name is called the same, they are called synonymous. Thus, for example, both a man and an ox are animals” (Aristotle 1984a: 1a), (SH 28). [How the third case of paronymy fits into these distinctions is not so clear, but it would seem important given the role this concept plays in helping us understand how we can have multiple categories for being. We take the example of a grammarian getting his name from grammar. When words get their name from other words, they are paronymous. It is not stated this way, but to fit this concept in with the other definitions, it would seem that two things are paronymous if their definitions are not identical but their names are morphologically derivative. But this does not help me understand how the highest genera of being are paronymous. It would be nice if these different senses were each stated, described, and named.] “When things get their name from something, with a difference in ending, they are called paronymous. Thus, for example, the grammarian gets his name from grammar, the brave get theirs from bravery. (Aristotle 1984a: 1a)” (SH 28). SH says that what we gain from this is that “some attempts to define species may not capture what is essential to the species itself” (SH 28). In the case of the picture of an animal, we use the same name, which might lead us to believe they are of the same species, when in fact they are not. We need instead to look beyond the names and seek instances of synonymity. Now, the genera with the name ‘being’ cannot be synonymous, since then they would be identical. They also cannot be homonymous, since then they are really different and have no good reason for all being called being. So instead, for Aristotle being is a paronymous concept. [Explaining this will involve an analogy, so we begin first with a different concept, health. We think of all things that are healthy. Let us guess that we have nutrition, Olympian athletes, positive emotions, smooth clear skin, and such things. They do not all fall into the same categories. However, they all refer to health in one manner or another. Perhaps they produce health (nutrition, positive emotions) or perhaps they are signs of health (smooth clear skin, positive emotions), or perhaps they can receive health (Olympian athletes perhaps). We also will need to think of being this way too. Aristotle will refer specifically to being’s representation as the copula ‘is’. We use ‘is’ in several ways, so perhaps these are the different senses of being. I can think of ‘is’ used as an equating function, as in “that person is Roger”, or as a predicating, “that person is angry”. I am not sure what else. Also, I am not sure how these can be senses of being understood in terms of unity or as the highest category.]

Aristotle proposes that we consider being to be a paronymous concept. What would such a concept look like? Aristotle gives the following example [the following is quotation of Aristotle]:

Just as that which is healthy all has reference to health – either because it preserves health, or because it produces it, or because it is a sign of health, or because it is capable of receiving health – . . ., so too that which is is said in several ways, but all with reference to a single principle. (Aristotle 1984b: 1003a)
(SH 29)

Before moving back to the notion of being, we begin first with the idea that health is paronymous, and SH draws the following consequences from this.

1) Different things can be healthy. 2) In each case, we apply the definition for health in a different way. 3) All of these meanings of health, although different, refer to a focal meaning.

SH writes, “It is quite straightforward to relate this idea of paronymy to the concept of being” (29). Thus as noted in point 3 above, all the senses of being refer to the focal concept of being. SH then lists some concepts. [It would seem that these would each be different senses of being, and perhaps thus also each a different highest genus. But I am not sure.]

Rather than simply being a heap, the different categories of being are all related to a single concept. Things can therefore be said to be. For instance, properties, substance and differentia can all be said to exist, despite being different from one another.
(SH 29)

SH’s next point is that although the senses are different, they relate to one another [and not just independently to one focal meaning]. His third point is that all these notions refer to the central concept being [this is like his first point. The difference here seems to be that now he specifies that concept as ‘being’.] [The explanation that follows is not clear to me. It exemplifies how all the senses of being refer to the central concept of being. The example is that properties must be properties of some substance, thus the notion of property is secondary to a focal concept of substance. However, I am not sure if this is just an example unrelated to the focal concept of being or if ‘substance’ is to be understood as one of the senses of being.]

Third, these different notions of being will all relate to a central concept of being. If we look at the notions of substance and properties, for instance, it is clear that a property can only exist as a property of something. Therefore it is going to be logically secondary to a focal meaning, in this case the notion of substance to which properties are attributed.
(29)

SH notes that paronymy is a concept that will return in our discussion of the Scholastic tradition. For now, however, we return to the original idea that the problem of the Large is also to be understood in terms of the black abyss of the undifferentiated. [The point here seems to be that we really seem not to have a way to differentiate things in Aristotle’s system, since the basic notion underlying all others, the notion of being, cannot itself be explicated. This means that even difference cannot be understood in this system. Thus furthermore nothing can be understood as different from anything else, at least not in any clear determinate way. In the quote SH uses, Deleuze uses a term that we have not yet discussed, so it might be a bit confusing. He uses here the term Logos. Perhaps we mean by this just ‘rational basis’. We then distinguish the logos of species and the logos of genera. As we noted, genera do not operate according to univocity, but rather in accordance with the equivocity of paronymous senses. Species, however, need to be clearer and more coherent, since they definitively divide the genera, and thus the logos of species is one of identity and the univocity of the genera that they divide. In other words, in this one system seemingly based merely on the logos of class inclusion, we really need two different and perhaps incompatible laws of operation, which compromises its coherence.]

To deal first with the question of black nothingness, we can see that even if we can now solve the logical problem of how the terms at the top of the hierarchy are related, we are still left with a question as to how we are able to define the concept of being. Being still cannot be defined without presupposing a yet higher concept. Being is therefore put outside of the world of species and genera. As Deleuze writes, ‘it is as though there were two “Logoi”, differing in nature, but intermingled with one another: the logos of species . . . which rests upon the condition of the identity or univocity of concepts in general taken as genera; and the logos of Genera . . . which is free of that condition and operates both in the equivocity of Being and in the diversity of the most general concepts’ (DR 32–3/41).
(SH 30a)

[The final point that SH makes seems to be a preparation for a later elaboration, and so here we may be unable to present it clearly. His point seems to be that Aristotle’s system is lacking in another way. It tells us what determines something as being what it is. But it does not tell us how that thing could have come about. We always ask in his system, what is it? (What genus belongs to its species’ essence?) For this, we presuppose the existence of the thing, and thus we do not probe into its genesis. This is somehow related to the undifferentiated white nothingness, but I am not sure how. Perhaps it will be explained later. It may have something to do with the fact that the genetic relations between things is not evident, like how the relations between things in the white nothingness are not given. But I do not understand how at the moment.]

Second, Deleuze argues that while Aristotle provides an account of the determination of objects, he cannot provide an account of the constitution of objects. As we saw, properties are understood as properties of something, and the same could be said of differences. When we ask the question, ‘what is it?’, we have already presupposed the existence of a logical subject to which predicates will be attributed by means of an answer. This rules out in advance any possible account of the genesis of the subject. It is for this reason that Deleuze introduces the indifference of white nothingness. He is going to argue that we need to think the faintly paradoxical notion ‘unconnected determinations’ if we are to think of the emergence of the subject itself.
(SH 30)

Citations from:

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

Or if otherwise noted:

Aristotle (1984a), ‘Categories’, trans. J. L. Ackrill, in Jonathan Barnes (ed.), The Complete Works of Aristotle, Princeton: Princeton University Press, 3–24.

Aristotle (1984b), ‘Metaphysics’, trans. W. D. Ross, in Jonathan Barnes (ed.), The Complete Works of Aristotle, Princeton: Princeton University Press, 1552–1728.

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