29 Dec 2012

Pt1.Ch2.Sb5 Somers-Hall’s Hegel, Deleuze, and the Critique of Representation. ‘Aquinas.’ 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 5: Aquinas


Very Brief Summary:

Aquinas deals with Aristotle’s problem of defining the highest category by saying we can know, by means of analogy, the way that its species relate to it, when we compare those relations to ones between other genera and species that are isomorphic with the relations to God [‘being’ or the highest category.]

Brief Summary:

Somers-Hall moves now from Aristotle to Aquinas on the problem of categorization. The intermediary step is Porphyry, who [1] shows that paronymity is a type of homonymity, because in homonymity there is the same name for several meanings, and in paronymy there are similar names for several meanings. So if the highest category, being, is not is not homonymous, it must be synonymous; and [2] [because of him] Aristotle’s terms are translated into Latin. For Aquinas, God [the highest category ‘being’] can be neither homonymous nor synonymous. Instead we must think in terms of analogy, in particular proportionality. We cannot know the predication of the highest category, but we can know how its species relate to it by comparing them with other relations between genus and species that are isomorphic with relations to God.



Previously we saw how Aristotle’s philosophy of essences in his system of hierarchical classifications falls short when trying to account for the differential basis of continuous alteration.

Somers-Hall now turns to Aquinas to see the development in Aristotle’s terminology and his form of analogy. (55) The intermediary stop is Porphyry's Isagoge, the commentary on Aristotle’s Categories. It was a central text for scholastic Middle Age philosophers. There are two effects of this adoption.

[1] Porphyry uncovers the relation between homonymy and paronymy. First 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)

[We consider all things to be beings, because everything falls under the highest genus, being or unity. So we call everything a being. If ‘being’ in every case had the same definition, then all beings are synonymous. If ‘being’ in each case had a different definition, then all beings are homonymous. And if all things are beings but with being having a different variation on a common focal meaning, then all beings are paronymous. Because in paronymy there are similar names for different meanings,] paronymy is a species of homonymy. So if being is not homonymous, it must be synonymous. 
[2] [(the second effect of the Middle Age’s adoption of Porphyry’s ISA)] Aristotle’s formal terms are translated into Latin. “It was Boethius who produced the earliest and most fundamental translation in the late fourth or early fifth century (ISA, 21), which led to the standard translations of aequivoce for 'homonymously,' and univoce for 'synonymously. ' From these two terms we derive the English terms equivocity and univocity.” (55)

Aquinas also takes up Aristotle’s problem of the highest genus [which he equates with God]. He says that God and all creatures cannot share the same univocal predication, and yet they cannot share the same equivocal predication [perhaps he is saying something like not all things can be identical with God nor can they be thought apart from him.]

Aquinas’ solution is the concept of analogy, thought in terms of proportion and proportionality.

Analogy: Proportion:

There is proportion if something

a) is analogically predicated of two things when one of those things corresponds to another, and

b) corresponds to Aristotle’s categories of being [55-56]

In proportion, there is relation between two things.

Analogy: Proportionality:

There is proportionality when there is

a) a relation between two relations, and

b) (sometimes) a predication made according to the second kind of conformity. For example, ‘sight’ is predicated of bodily sight and intellectual sight, because just as sight is in the so, so intellect is in the mind.

What is important here is that we may specify the properties of relations between different categories and their species without knowing the nature of the terms that stand in these relations [we can say that sight in the eye is like intellect in the mind, without necessarily knowing a whole lot about what the intellect is, the mind is, sight is, and the eye is. We merely can say that we know a’s relation to b is like c’s relation to d].

Thus we can talk about the nature of God's wisdom without having to specify the nature of the being of God himself. In this way, scholastic logic allows the discussion of things that derive from different categories in the same terms. This is in effect the discovery of an isomorphism across the different senses of being. (56)

Somers-Hall ends by noting that “this is a clarification of the notion of analogy, and its reliance on the concept of an indeterminate identity, rather than a solution to the problem of the fracture of being itself” (56). We now turn to similar issues in Whitehead’s and Russel’s Principia Mathematica.


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

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