18 Dec 2012

Pt1.Ch2.Sb3 Somers-Hall’s Hegel, Deleuze, and the Critique of Representation. ‘The Genus and Equivocity in Aristotle.’ summary

Corry Shores
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[Note: All boldface and underlining is my own. It is intended for skimming purposes. Bracketed comments are also my own explanations or interpretations.]

Henry Somers-Hall


Hegel, Deleuze, and the Critique of Representation.

Dialectics of Negation and Difference


Part 1: The Problem of Representation

Chapter 2: Difference and Identity

Subdivision 3: The Genus and Equivocity in Aristotle


Very Brief Summary:

The structure of Aristotle's hierarchical system of divisions is seemingly grounded on difference. However, because a single genus lies at the top, Aristotle ultimately must unify all divisions with a self-identical meaning, even though it is multi-faceted in its actualizations.

Brief Summary:

Aristotle uses a concept of difference in his hierarchical categorization. An essential specific difference distinguishes species from one another and from their genus. The highest genus would not be a part of yet a higher genus. So nothing is predicated of the highest genus, being [we cannot say that being is an x that blah-blah-blah like how we say man is an animal that thinks]. But the predication of species (subdivisions of genera) is the method of defining things. So the highest, genus, being or unity, has no basis for determining its meaning. Yet, things exhibit their being in many different ways [for example, qualitatively (characterizing the nature of the thing, curved, straight, white, grammatical, for example), quantitatively (continuous or discreet, for example), and so forth.] These are not higher categories, rather they are different actualizations of the same focal meaning of being. This means that the senses of being are unified while diversely applied. The unity is not found in being’s definition, because we cannot define being. So Aristotle must somehow provide an empirical account of both the unity and the diversity of application of the senses of being. And the focal meaning also cannot act like a self-referential category. However, because all beings actualize one focal meaning, difference does not seem to lie at the basis of Aristotle’s system of classification, so it is not a good model for Deleuze’s notion of difference. Another problem is explaining the way individuals differ from themselves temporally.



Previously we examined Aristotle’s “special difference” as a possible model for the genetic difference found in Deleuze’s transcendental field. There is a difference that makes a species different from other species in its genus and from the genus itself (taken in its homogenous generality). This special difference tells us what is essential to the species. Because it is essential, it does not result from the division of the genus. So in a way, the specific differences are productive of the species’ differentiations. There were some problems with using this as the model for Deleuze’s difference. Aristotle’s specific difference does not explain the differences between individuals, because these differences can be accidental traits, but specific differences are essential traits.

Now Somers-Hall (SH) elaborates on the problems with Aristotle’s notion of difference with respect to genera. He quotes Aristotle’s formulation of the problem of the relation between genera and differentiae:

"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 have both being and be one, but it is not possible for the genus to be predicated of the differentiae taken apart from the species (any more than for the species of the genus to be predicated of the proper differentiae of the genus); so that if unity or being is a genus, no differentia will either be one or have being" (MP, 998b). [SH quoting, 49]


This is a condensed presentation of Aristotle’s argument, so SH will explicate it (he cites Bochenski History of Formal Logic for more on this argument, footnote 13). A genus is

"what is predicated in the [category of essence] of a number of things exhibiting differences in kind." [Aristotle Topics]

In order for something to be a genus, it must possess differentiae [attributes that distinguish a species of thing from other species of the same genus]. The differences must be different from the genus, because the “ ‘genera are prior to the differences under themselves’ (ISA, 51).” (49) The highest genus would be predicated of all genera. But then, if this were so, the highest genus would be predicated of itself, which is not possible given that in the definition of a genus, it must not be predicated of itself. (49)

The highest genus, therefore, that of being or one, becomes contradictory. If we are to maintain the stability of the system, this highest genus must therefore be left undefined. 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. Aristotle lists ten in total. This means that the terms in the hierarchy are now to be characterized in two divergent ways. In the intermediate terms, difference will descend from the identity of the genus, whereas for the highest genus, difference itself will reign, as it does not itself partake in a higher identity. As Deleuze puts it, "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, 32-33) . [49]

The problem is that this makes metaphysics stand above the particular sciences. Aristotle says three things regarding metaphysics that together seem to be in contradiction.

[A] Metaphysics is a science that investigates being as being, and it investigates the attributes that belong to being in virtue of its nature.

[B] There is a single sort of perception for each class of things, thus there is a particular science for each class of things. For example, grammar investigates all articulate sounds. So, investigating the science of being qua being requires just one science.


[C] "There are many senses in which a thing can be said to 'be."' (MP, 1003b)

Recall Aristotle’s designations homonymous, synonymous, and paronymous.

Homonymy [equivocity]: things are homonymous when they have a name in common but the definition differs. For example a man and a picture of an animal can both be called an animal [in our conversations about the man or the image in the picture], but we would need a different definition for each one [since they are not both animals in the same sense, as one is a pictoral representation of an animal]

Synonymy [univocity]: things are synonymous when both their name and their definition is the same. Consider for example how both man and ox are animals. [Insofar as we define both strictly as animal, both their name and definition would be the same.]

Paronymy [derivativity]: things are paronymous when they derive their name from a common source but their endings differ. For example, grammarian and grammar, brave and bravery. (45)

[Because there are many senses that a thing can be said to be, that means there are many senses to the term being. So] being is not synonymous [(univocal); its senses are not synonymous. There are different senses of being not because each sense of being calls for a different definition; it is not that the names are the same but the definitions differ, so] being is not homonymous [(equivocal)]. It must therefore be paronymous [(derivative), which means that the different senses of being are more like words derived from a common word, that is, words with a common stem but different endings.]

So, for example, in the case of the words health and healthily, although they differ in their meanings, these meanings are clearly related one to another by some kind of central meaning, which is common to both terms, albeit actualized in different ways. This central term is what Aristotle calls a focal meaning. We can say therefore that whereas for synonymy, the term and its focal meaning coincide, and for homonymy, there is no focal meaning for the different terms, paronymy provides a situation where there is a focal meaning, but one that does not coincide directly with any of the terms. Thus, Aristotle will claim that what is really at issue in the definition of a science is not the identity of the sense through which the class is spoken, but rather the identity of the focal meaning that underlies the differing senses. (50c.d)

So being would have a self-identical meaning, even though it actualizes in different ways, hence it seems impossible here that difference would become “an essential moment of the system in its own right”. (51a)

[We previously noted the problem of the possible self-referentiality of the highest genera, being. It would be predicated of all genera, itself included, but this contradicts the definition of genus, which says it cannot be predicated of itself. So the highest genus seemingly cannot be defined. Thus there seems to not be a solid ground for the entire hierarchical system of classification. Thus] Aristotle’s paronynymity of being seems to solve the problem of grounding his system. However, there are serious problems with determining focal meaning. Deleuze’s analysis raises doubts to whether a concept of an ontology of difference is possible. Aristotle must demonstrate that the concept of being, or unity, is itself a unified concept. (51) Aristotle thinks that there must be a central meaning of being, so he needs an empirical account to explain its different applications the multitude of different domains, all while these different meanings remain semantically related; “the empirical account must explain how these various divergent meanings of being come to be both separated from the central meaning and remain semantically related.” (51) Also, to avoid the problem of self-reference, the focal meaning cannot be like a highest genus, “Being must therefore remain outside of the world as described by the hierarchy and merely be referred to indirectly through the categories, as opposed to the categories themselves, of which we can speak.” (51) But if being is paronymous, then all its senses must somehow be related to a root one running through all of them. [Later we discuss this problem in terms of Aquinas’s concept of analogy and Russell and Whitehead’s Principia Mathematica.] Recall also one of the sorts of difference found in individuals. Such a difference might differentiate a thing from itself; for example, the difference between Socrates the man and Socrates the boy. In a similar way, because of their common focal meaning, the categories must somehow remain the same while differing from another. SH later returns to the question of transition in Hegel at the end of this chapter. (52)


Somers-Hall, Henry (2012) Hegel, Deleuze, and the Critique of Representation. Dialectics of Negation and Difference. Albany: SUNY.

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