Pt1.Ch2.Sb6 Somers-Hall’s Hegel, Deleuze, and the Critique of Representation. ‘Symbolic Logic.’ summary

by Corry Shores
[Search Blog Here. Index-tags are found on the bottom of the left column.]

[Central Entry Directory]
[Deleuze Entry Directory]
[Henry Somers-Hall, Entry Directory]
[Hegel, Deleuze, and the Critique of Representation, Entry Directory]

[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 6: Symbolic Logic

 

Very Brief Summary:

Russell deals with a paradox similar to Aristotle’s problem of defining the highest category being. Russell notes that we cannot determine whether or not the class of all non-self-including classes is included in itself, because either way, the classification contradicts its definition. Russell’s solution is to say that one level of the hierarchy refers to its lower level and not to itself. This has many problems, for example, we cannot make universal statements or predications like ‘truth’ that range over all levels.

Brief Summary:

Aristotle’s problem of defining the highest category is related to Russell’s solution to the paradox of the class of all classes that do not include themselves. In Russell’s set theory, something is included in a class if it has the property shared by all things in that set. One property could be ‘being a set that does not include itself as a member’. But then it becomes impossible to determine whether the set of all non-self-inclusive sets belongs to itself as a member. For, if it did, then it includes itself as a member, which makes it ineligible to be included in the class of non-self-inclusive classes. If it did not belong in itself, then it fits the criteria to be in the class of non-self-inclusive sets, which contradicts its status of not belong in itself. Russell’s solution is to divide levels in the hierarchy of classification, such that the properties shared at one level do not apply to the things of the higher level. So no set has self-referential properties, like ‘belonging to itself’. This is similar to Aristotle’s rule that differentiae differ from genera. In both Aristotle’s and Russell’s systems, we cannot define a highest class, because all classes need a higher one in order to be defined. And in Russell’s system, we cannot make universal statements about all levels of things; for we can only refer to one level at a time.

Summary

 

Previously we saw Aquinas solution to Aristotle’s problem of defining the highest category, being. Aquinas uses the concept of analogous isomorphic relations. We cannot say what God is, but we can say that the relation between the highest category and its species is like the relation between some other genus and its species. They are proportional relations.

Now Somers-Hall examines a similar sort of problem and solution in Russell’s and Whitehead’s Principia Mathematica. Here we deal symbolic logic, which examines pure syntactical relations between entities. This “creates a sharp divide between the form of thought and its subject matter.” (57) The hope is that the formal analysis does not involve some particular metaphysical view.

It also allows the characterization of phenomena in an artificial language, formulated to allow precision in the expression of propositions and to allow a purely mechanical movement between propositions, allowing the rules of derivation to be formally specified. (57)

In formal logic there are symbols for both variables and constants, constants like &, ∨, and ¬.
One of formal logic’s most fundamental formalizations is the logic of classes.

The logic of classes deals with the relations between sets of things (in the loosest possible terms), such as the inclusion or exclusion of both individuals and classes of things within classes of things. (57)

According to this view, Aristotle’s hierarchy is a theory of classes that provides “rules whereby different individuals and species can count as being included in or excluded from genera, which in turn are either included or excluded under their aspect as species”. (57) Recall Aristotle’s system. What makes a species belong to a particular genera is that the genera is predicated of the species (man is an animal that thinks), and what makes a species be a certain species to its genus is that it has a specific, essential difference from the genus [taken in its pure generality] and from the other species in that genus (man is a thinking animal [man is not just an animal, so it is different from the genus, and man is not like the other animals, so it is different from the other species.]) The modern theory of classes defines membership in a class using two methods.

The two methods for defining membership in the modern theory of classes:

[1] by extension: giving a list of all the members in the class, and

[2] by intension: giving a particular property that may identify the members of the class. This provides the criterion for membership.

Although we may theoretically use the extensional method, it could perhaps take too much time. So practically speaking we define membership intensionally by means of their common property. So in more formal terms, something is a member of a given class if and only if it has the property shared by all members of that class. In terms of Aristotle’s classification, a member of a species is as well a member of that species’ genus.

Russell therefore originally put forward the intuitive axiom that given a class of things with a property F, x will be a member of this class if and only if it has the property F. On this basis, we are therefore able to formalize aspects of the hierarchy of Aristotle. Thus all mammals are animals is rendered as ∀x(x∈a → x∈b) . Literally, this means that for any arbitrary object (x), if that object is a member of the class of mammals (a), then it is a member of the class of animals (b). We could further define the set of men as a subset of mammals and in this way allow the mechanical derivation of the animality of man from his status as a mammal. This process could be repeated to give a complete set-theoretic representation of Aristotle's arborescent hierarchy. (57)

[Recall Aristotle’s problem of the equivocity of the highest category, being. All other things falling under it are beings. So they have the same name as being. However, as they are species of being, they must have a different definition. And also recall, being itself cannot be defined, because definition requires differentiation from a genus, but there is no higher genus than being.] We may formulate in set theory Aristotle’s problem of the equivocity of being: is it possible to specify the class of all class (the class to which all classes belong)? In Aristotle’s system, differentiae must differ from genera, so the highest category ‘being’ cannot be included as a member of itself. In Russell’s system, however, there can be the self-referentiality of saying that if something is a class, then it is a member of the class of all classes (thus classifying the class of all classes within itself).

In the case of Russell's system, however, at first glance it is possible to specify a class that is a member of itself, as, given the class of things that have the property of being classes, x will be a member of this class only if it is a class. The class of all classes meets this definition and is therefore a member of itself. (57)

Let’s first note one of Russell’s earlier paradoxes, the paradox of the barber. There is a barber who only shaves men who do not shave themselves. But then, who shaves the barber? If he shaves himself, then he is not in the class of men who do not shave themselves, and thus he should not be shaving himself in the first place. But if he does not shave himself, then he is in the class of men who do not shave themselves, and thus should be shaving himself. “In this case, therefore, the barber is both in a state and not in that same state simultaneously, which, within a representational system, will lead to the collapse of all states within that system.” (58) The solution in this paradox is simple. We merely say that there can be no such barber.
But in class theory, we can have empty sets, like ‘descendents of the last Tsar of Russia’. We need not affirm that there are any members in the set. [So we can say there is the class of barbers who always shave those who don’t shave themselves, and then also say that there are no members in this class.] So we can say there is a class whose members are classes that are not members of themselves. If that class itself is a member, then it is not included in itself, which means it could not have been a member to begin with. But if that class is not a member, then it is a class that is not included in itself, which should have made it a member in the first place. [Now, because our thinking is fundamentally based on such classification principles, we can say that] the paradox is an inherent part of the structure of our thinking.

One of the fundamental principles of the theory of classes is that a class can be defined intensionally by any clearly defined property that belongs to all members. Such a definition of class carries with it no existential statements, so we could define the class of, for example, the descendents of the last Tsar of Russia, without having to affirm that this class contains any members. It could instead simply be an empty class. Given this, we can specify the following class: "Let w be the class of all those classes which are not members of themselves." If we take a class, x, and say of it that it is a (member of) w, then this is equivalent of stating that "x is not an x" (as we might say that the class of all chairs is not itself a chair) . If we give x the value of w, however, then the statement "w is a w" becomes equivalent to the statement "w is not a w." This is because if w is a member of itself (w is a w), then according to the definition of what it is to be a w, w is not a member of itself. On the other hand, if it is not a member of itself, then it meets the definition for membership of itself. It is therefore the case that w both is and is not a w. Clearly this particular case parallels the result of the barber's paradox, but whereas in that case, the paradox relied on the subject matter being discussed, the barber, this second paradox instead is derived from the fundamental rules of the logical system itself. The paradox is therefore implicit in the very structure of thought. (58)

So we see that this problem mirrors Aristotle’s problem. Later we will examine Russell's solution, “Whatever contains an apparent variable must not be a possible value of that variable”. (58) But already we can see how it is similar to Aristotle’s stipulation. “This principle is analogous to Aristotle's requirement that the differentiae must differ from the genus under | consideration, which also prevented genera from referring to themselves”. (58-59) For Russell, the individual is absolutely simple, and then there is a hierarchy building up from it. So in this hierarchy, we classify something as belonging to higher class. The class on the higher level is on an ordered different from the lower level, so it is meaningless to have a class that includes itself. At best, we can have a class of all other lower-order classes that do not contain themselves.

Russell's own implementation of this principle is to propose a hierarchy of types, meaning that an apparent variable must be of a different type to its possible values, known as Russell's theory of types This works by constructing a hierarchy from the most basic individuals to the highest classes. The individual in Russell's system functions as the anchor for the whole and is considered to be absolutely simple. By means of this, Russell hopes to remove the possibility of any self-reflexivity at the base of the hierarchy. Taking absolutely simple, nonreflexive elements as our starting point means that, provided we are rigorous in our development of the system from these points, the problem of self-reflexivity may not arise. Designating these simple individuals using the subscript 1, as they form the base of the hierarchy, we can formulate simple propositions of the form, a₁ is F, or this individual has a specified property (F) . This proposition, as the highest type it contains is of the first order, we can call a first order proposition. We can then generalize this proposition into the form "All a₁’s are F." Here, a₁ is no longer taken as an individual, but instead as a variable ranging over all individuals. The statement "All a₁’s are F" will be a second-order proposition; it will be of a different type to the previous statement, a₁ is F. This process can be repeated indefinitely, thus generating a hierarchy of classes, each level of which is of a different type . As statements refer to the level below themselves, reflexivity is blocked. If we return to the issue of Russell's paradox, it is now clear how this difficulty has been solved. The class w now must be of a different level to the classes over which it ranges, so if its members are classes of type n, w will be itself a class of type n + 1. This means that the question of w's membership of itself becomes not even false, but meaningless, as it is impossible within the system to formulate the function w being applied to itself. Instead, w is a type n + 1 class, which refers only to type n classes that are not a member of themselves. Types thus parallel the function of the differentiae in Aristotle's system by creating a hierarchy of terms, and the problem that emerges is in turn similar. (59)

One problem regards the impossibility of univocity in the system: we cannot have a highest type, because every type requires a higher one, and also, there cannot be simple universal statements [because any statement must refer specifically to one level and not to the others], and furthermore, there cannot be central notions like truth as it would apply to all levels, for it cannot refer beyond a particular type. [Also, properties have levels too] so we would need to say ‘all n-th level properties of a’, because we cannot say ‘all properties of a’. If we wanted to speak of all properties of a, we would need really to be implying that we are making just as many statements as levels of properties. [But this means we are making use of the parallel in structure between one order to the next, so we are using analogy as with Aquinas’ solution. In both cases, there is an ambiguity: what makes one level higher to another is the same relation as some other level to another. But then in the end we would not be able to say something about a highest class, at best only the sort of relations to it.]

As "it will be possible, sometimes, to combine into a single verbal statement what are really a number of different statements, corresponding to different orders in the hierarchy," it becomes clear that what is being used to overcome the limitations of the symbolic system is once again a form of analogy, and in particular a form of isomorphy, as that which grounds the single verbal usage are the structural parallels between the various statements. Thus, the Principia Mathematica ultimately suffers from the same limitations as the scholastic system, systematic ambiguity being synonymous with analogy. (60)

[Recall how Aristotle’s theory of essence was unable to explain the nature of the transition from state-to-state involved in change. It can tell us about the state in one moment and the state in the next moment, but not the in between when the thing takes on two incompatible states at the same time.] For Russell, we cannot give an account of a flux of change. We can only speak of the different moments in a change, and consider time to be the differences in status between something at time 1 and that something at time 2. So like Aristotle, Russell does not give a satisfactory account of the change from state-to-state. For Zeno, we may infinitely divide time or space. His

view derives from his belief that a stretch of time merely involves a particular kind of infinity, namely, that between any two points of time, there is another point of time. This means that time appears as a continuum, while each moment is instead a fixed state. The stability of the system is therefore once again purchased at the cost of excising all traces of motion. The problem of the nature of change itself is still present, however, as is clear from Russell's definition: "Change is the difference, in respect to truth or falsehood, between a proposition concerning an entity and a time T and a proposition concerning the same entity and another time T', provided that the propositions differ only by the fact that T occurs in the one where T' occurs in the other." This definition suffers from the difficulty that although it gives us a criterion to show that a change has taken place, it in no way defines the nature of that change itself. The same explanatory gap that occurred through Aristotle's use of analogy again occurs here. (60)

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

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

by Corry Shores
[Search Blog Here. Index-tags are found on the bottom of the left column.]

[Central Entry Directory]
[Deleuze Entry Directory]
[Henry Somers-Hall, Entry Directory]
[Hegel, Deleuze, and the Critique of Representation, Entry Directory]

[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.

Summary

 

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.

Pt1.Ch2.Sb4 Somers-Hall’s Hegel, Deleuze, and the Critique of Representation. ‘Change and the Individual.’ summary

 
by Corry Shores
[Search Blog Here. Index-tags are found on the bottom of the left column.]

[Central Entry Directory]
[Deleuze Entry Directory]
[Henry Somers-Hall, Entry Directory]
[Hegel, Deleuze, and the Critique of Representation, Entry Directory]

[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 4: Change and the Individual

 

Very Brief Summary:

Aristotle’s notion of alteration does not explain the self-differentiation that is most fundamental to the process of transition, because it regards there being a self-same essence maintaining itself throughout various self-same states. This model does not explain the transitions between states where we might say that something is both itself and not itself, or that something has, simultaneously, temporally incompatible accidental traits.

Brief Summary:

We previously noted one important similarity between (a)Deleuze’s transcendental empiricist notion of the differentiation producing the individuals that are given to us empirically and (b) Aristotle’s logical notion of specific difference in his hierarchical system of classification. This specific difference produces the different species of a genus; for, this difference is inherently essential to the species. In both cases, the difference is inherent and productive of individuals. However, we previously found one main reason Aristotle’s specific difference is incompatible with Deleuze’s difference. Aristotle’s hierarchical system has a highest single genus, being or unity, which means that all things must ultimately be defined or understood on the basis of something self-identical in them, and not by means of a constitutive difference. This proves to be a problem in Aristotle’s account of transition or alteration. Here we are to think of something moving from potentiality to actuality, in a process where matter takes on a new form, all while maintaining a self-same essence that remains undifferentiated throughout the change of accidental traits. On the basis of Aristotle’s concept of essence, we can understand how something remains the same, but we cannot understand how something is in a state of self-differentiation as it changes. There are also non-temporal instances of transition that pose a similar problem, for example ring species. A series of types of gulls are spread out in a chain across the globe. On species in Northern Europe can breed with the type of gull living just east of it, and that one is interbredable with the species just west and east of it, and so on, until the chain reaches its beginning place in Northern Europe. Yet the adjacent species in Europe lying at the beginning and end of the circular chain cannot breed with one another. A hierarchical classification system based on essences cannot determine whether or not these adjacent bird types are the same species or not. If they are, then there are members of a species that cannot interbreed, which goes against the definition of a species. But if we say they are to be grouped into separate species, then where do we draw the line along the chain to say these birds are in one species and these in the other? If we give them all their own species, then we have separate species that are interbreedable, which also goes against the definition of species. So this movement from bird type to bird type is like one thing changing over time. Given that we cannot determine the essence of the bird variations, we cannot explain the relation between adjacent interbreedable ones, just as we cannot explain something’s transition from one state to its adjacent successive state.

 

Summary

 

Previously we examined how difference seems to be the grounding principle of division in Aristotle’s hierarchical classification of things. However, the fact that there is a single category at the top, being or unity, means that Aristotle ultimately must ground his system on something self-identical rather than differential. So even though difference is what produces the various species, this will not serve as a model for Deleuze’s transcendental empiricist notion of difference as what produces the things that are given to us.

 

Now, Somers-Hall (SH) turns to problems with individuals in Aristotle’s hierarchical system. Note how there are potentially infinitely many things, each with its essence. Aristotle’s logic of hierarchical classification “is an attempt to capture the essence of a thing in terms of language, that is, in terms of universal concepts.” (52) But individuals cannot be reduced to universal concepts, because this robs them of their individuality in the world. We also saw how genera can be regarded as species to even higher genera. This can be understood in terms of the form/matter relation. [Consider a genus, ‘Animal’, and a species, ‘Man’. We might think of Man as one way of forming the matter, Animal, for it can be formed into ‘Horse’ as well. But then, Animal can be thought of as itself a form that gives form to the matter, Substance; for, Substance can be informed by ‘Mineral’ as well.]

In Aristotle's hierarchy of genera and species, the genus was considered to be matter, and the difference, form. This meant that, proceeding through the hierarchy, prior differences as differences of a genus shift from form to matter as the difference itself generates a new genus. Thus, while difference provides a formal distinction of the material of the genus when generating species, since these species can themselves be considered as genera of lower species, the formal difference gets incorporated into the matter of the genus. (52)

Now recall how “common difference” can differentiate individuals.

Common difference. [Because of diversity of nature, something differs from another thing by being diversely different from it, and something differs from itself over time in that it diversifies from itself.] “First, common difference defines difference as commonly understood-that is, difference in any way, as, for instance, Socrates differs from Plato (ISA, 42)”. (46d) And also, Socrates differs from himself, as Socrates the boy and Socrates the old man.

In the case of the temporally differentiated Socrates, we might think of boy Socrates as being like a matter that may actualize into the form old man Socrates.

At each stage in this process, the movement from matter to form is therefore characterized as a process of actualization of a potentiality. Thus, throughout the movement between the potentiality and actuality Socrates is asserted as a unity-potentiality is analogous to actuality. While the young Socrates differs from the old Socrates, these differences are purely accidental-they do not affect the actual essence of Socrates himself. (52)

SH now notes two questions.

[1] How do we differentiate Socrates' accidental properties from his essential properties?

[2] How should we understand the process that moves things from potentiality to actuality?

So the first question asks how we might differentiate accidental from essential properties. The Greek term for essence, ti en einai, means “the what it was to be that thing.” (53) What we must note especially here is how an individual’s essence allows it to be reidentified over time despite its alterations. Thus this definition of essence “provides a self-identical underpinning for the thing whose essence we are searching for”. (52, citing Beistegui, Truth and Genesis in ft.20)

Thus essence provides a tool for the selection of properties that are properly definitive of an individual, as opposed to those that 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 accidental states such as this were taken to be definitive, the identity of Socrates himself would break down through the collapse of all continuity. (52-53)

[While something is changing, we do not know what traits will remain while others come-and-go. So,]

While 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. (53, citing Beistegui again in ft.21)

[So there is a process of transformation by which something’s accidents alter]. But what process maintains the individual’s identity as it moves from potentiality to actuality? [In the transformation of boy Socrates to old man Socrates, the boy is the matter through which the form of the old man actualizes. The matter is a potentiality that actualizes as its form. They are two aspects of the same thing. So that ‘same thing’ shared by matter and form, potentiality and actuality, is perhaps what maintains the individual’s identity while it alters.] To answer this question, Aristotle explains: “ ‘the proximate matter and the form are one and the same thing, the one potentially, the other actually. Therefore to ask the cause of their being one is like asking the cause of unity in general; for each thing is a unity, and the potential and the actual are somehow one’ (MP, 1045b)”. [53]
Now recall also the previous discussion on genera. We could not define the genus [because the highest genus is indefinable]. Instead we referred to empirical notions of unity [perhaps how we sense the different ways something can express being and yet all these different senses of being share a focal meaning. But consider when we think of the unity that is found in anything. It refers us to the highest category, being or unity. So unity has a circular definition, perhaps because whenever we define it, we can only appeal to the highest possible genera, which is unity. When we define something, we need to designate something’s genus and specific difference from that genus. However, unity cannot be given any genus other than itself. Perhaps this is what the following passage is saying:]

In discussing the genera, we came across the difficulty of explaining the existence of the paronymous terms, which orbit the concept of being. When we tried to elucidate the concept of unity in our discussion of genera, we found the concept undefined and were referred to empirical notions of unity. When we ask about particular cases of unity, however, we are referred back to the generic concept of unity. Thus, the concept of unity has a circular definition in Aristotle's philosophy. (53)

Now, there are two ways that the question of unity relates to the problem of transition.

[1] Aristotle has no way to explain how the categories are both related but distinct [just as in the case of transition, something, like Socrates, remains unified or related to himself throughout his transition, all while distinguishing himself from himself as he changes.]

[2] We have no way to understand the individual’s self-unity while it changes, so we cannot really understand the individual’s process of change.

[SH writes, but I cannot explain the first part:]

In both cases, Aristotle lacks the ability to explain change or transition, in the first, through semantic drift, and in the second, temporal change. (53)

Thus

difference for Aristotle merely allows the "extraction or cutting out of generic identities from the flux of a continuous perceptible series" (DR, 34). These identities are extracted at the cost of rendering incomprehensible a certain mode of being, that of the transitional state. [53]

[Perhaps we might look at it this way. An analysis of change in Aristotle’s system would only look at the different states of something that maintains its essence. This does not explain those moments of self-disidentification, those moments of transition when something is between self-identical states, or we might think of transitional moments as being when something is of two contrary states at once, and Aristotle’s philosophy of self-same essence does not help us understand how something can simultaneously both be something with one accident and something with an incompatible accident.] This problem is also found in non-temporal transitions. We might think of something that is in between two species. First consider a man without legs. He still has the essence of man even though he lacks one of his species’ properties. However, an individual can also be trapped between two particular essences. Consider for example “ring species.”

A ring species is a species that contains a series of natural populations, each of which is able to interbreed with its neighbor. As the distance between these various populations increases, genetic differences accumulate, however, to the point where the first species in the sequence cannot interbreed with a species a certain distance away, even though all intermediaries are able to still produce viable offspring. The classic example of this kind of relation is found with the gulls found encircling the higher latitudes of the northern hemisphere. In this case, the Herring gull, which breeds throughout Western Europe and Northern America, is able to interbreed with the Vega Herring gull, which inhabits North-Eastern Russia. This species is in turn able to interbreed with Birula's gull, and so forth, until we reach the lesser blackbacked gull, which is also an inhabitant of Northern Europe. Gulls from this particular community cannot, however, interbreed with our original gull, the Herring gull, even though a continuous path of genetic compatibility around the northern hemisphere can be traced. Thus the problem emerges, one which has not been solved by the current biological classification system, of whether we are here dealing with one or two species. Given the strict method of division that forms the heart of the Aristotelian system, it is clear that the intermediate species must either fall outside of the system of classification or must be incorporated at the cost of the integrity of the categories of species themselves. In examples of this kind, what we seem to be faced with is an objective kind of ambiguity that cannot be solved by simply applying our method more rigorously, an approach we might take in other cases such as the ambiguity in the word sharp in the phrases a sharp knife and a sharp taste. The heart of the problem would therefore seem to be the method of division itself. As we have seen, division for Aristotle is accomplished by the differentiae, and so it seems that the problem is once again the concept of difference at play in Aristotle's work. This is the ground for both the problem of ambiguity in classification and of the ambiguity of | becoming. (54-55)

SH will return to this theme after first exploring “how these difficulties play themselves out in more modern representationalist systems that do not rely on the peculiarities of the Aristotelian metaphysic.” (55)

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

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

by Corry Shores
[Search Blog Here. Index-tags are found on the bottom of the left column.]

[Central Entry Directory]
[Deleuze Entry Directory]
[Henry Somers-Hall, Entry Directory]
[Hegel, Deleuze, and the Critique of Representation, Entry Directory]

[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.

 

Summary

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.

however

[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.

Pt1.Ch2.Sb2 Somers-Hall’s Hegel, Deleuze, and the Critique of Representation. ‘Aristotle.’ summary

by Corry Shores
[Search Blog Here. Index-tags are found on the bottom of the left column.]

[Central Entry Directory]
[Deleuze Entry Directory]
[Henry Somers-Hall, Entry Directory]
[Hegel, Deleuze, and the Critique of Representation, Entry Directory]

[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 2: Aristotle

 

Brief Summary:

We are seeking the transcendental field in Deleuze, which would be the genetic production of individuals [which we might mentally grasp], and for Deleuze this transcendental field is immanent in empirical givenness. One possibility is Aristotle’s concept of species’ difference (specific difference), because it also is genetic. Aristotle categorizes things under three main tier-relations: genus, species, and individual. For example, Animal, Man, Socrates. But animal is also a species of a higher genus, and so on up to the highest genus [, being]. For Aristotle, there is a specific difference that distinguishes one species from another [and thus from the genus itself taken in its generality and not in terms of its internal heterogeneity]. This specific difference does not tell us something accidental about the species but rather something necessary and essential. So man is a rational animal. Because the specific difference is essential to the species, it is inherent to it, and thus it is productive of its differences from the other species in it genus. For, it is not that the genus is divided into things that on account of this division obtain their differences, because the differences were already inherent to the species. Thus the specific differences are what produce the various species in the genus, [and the genus is merely the general category resulting from grouping the species according to what is commonly reducible in all the species.] However, there is a problem with consistency if we were to take species difference as productive of all differences constituting the things we might mentally grasp, because it does not explain the differences between individuals for example, which may be distinguished by inessential accidental traits.

 

Summary

 

Aristotle founded the systematic study of logic, namely, syllogistic logic. Rather than examine syllogistic logic, Somers-Hall (SH) will focus on “the system of organization of genera, species, and individuals which underlies this syllogistic reasoning”. (43) “For Aristotle, the terms operated on by logic have an essentially hierarchical organization, with the lowest term, the individual, being subsumed under an intermediate term, the species, which is itself subsumed under a genus.” (43) Things fall under a genus. When we define these things falling under the genus, the genus itself is a part of that definition, which means that the genus is essential to what is predicated of it. Now consider the genus animal. Socrates is an animal, so the genus animal is predicated of the individual Socrates. [Now consider if each individual of a genus were only definable with that genus and thus having nothing to distinguish one member of the genus from the others. This would mean that there is only a difference in number and not in kind of each member.]

The genus is "what is predicated in [the category of essence] of a number of things exhibiting differences in kind." What this means is that the genus is a part of the definition of whatever falls under it, that is, it is essential to those things of which it is predicated. The second part of this statement refers to that of which the genus is predicated. 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 that 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. (43)

So in between each genus and individual is an intermediary, which is the species, “ ‘that which is predicated of many things which differ in number’ (ISA, 35)”. So Socrates is both a man (species) and an animal (genus). Animal is included in the genus substance, which would then make animal now seem like a genus in relation to man but a species in relation to substance.

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. (44)

This is the first theory of classes.

What is key to recognize in this theory of classes is that it makes possible the definition of the lowest species purely in terms of universals. From the highest genus, we can move through a process of division, whereby at each stage there is a branching of the higher concept into multiple options, allowing the particular entity to be more and more closely specified. Thus Socrates is the final point of an arborescent structure, characterized by a perpetual process of branching in terms of universal properties. (44)

In Aristotle’s system, the universal performs two functions.

[1] The universal “provides the necessary linguistic economy to allow an infinite number of things to be described using a purely finite number of terms.” (44)

[2] The universal allow mirrors structures in the world, which allows logic to match up with the world. “As Aristotle believes that we can truly talk about things within the world, it must be the case that terms such as properties, which have universal application, can find a place within the world. Thus, for Aristotle, the genera and species pick out real features of the world.” (44) But there is a problem with Aristotle’s system. The species and genera need to group things according to criteria that capture something common “to their essence.” (45) So Aristotle distinguishes homonymy, synonymy, and paronymy.

[1] 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 one]

[2] 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.]

[3] 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)

 

Consider for example homonymity. The term animal can refer both to a man and to a picture of a man. So we group two things that should be differentiated. Thus when we define ‘animal’, we are “forced into a definition of a species that does not accurately capture what it is to be that particular thing” (45). Thus “What is important in these definitions is the recognition that certain forms of differentiation of species may not capture what is essential to the species itself.” (45) In fact, there will always be some degree of homonymity, so “much of Aristotle 's logical work consists in a struggle against the possible encroachment of homonymy within the logical system.” (45)

 

Defining terms in Aristotle’s hierarchical model:

A definition contains the genus (because the genus is predicated of the species), so for example the definition of man includes ‘animal.’

to the species will be attributed a difference that allows it to differ both from the genus and from other species that are subsumed under the genus. Thus, the species to which man belongs is a species of animal characterized by its rationality. Man therefore becomes a rational animal. (46)

And because of the hierarchical model, ‘animal’ is further differentiated from other species under its genus, ‘substance.’ These tiers of differentiation allow us to specify the essence of what is under definition.

Man is defined by the combination of its genus with a difference, the animal that is rational, and the genus is defined similarly, hence animal is further clarified as the substance with animality. Thus man is specified through rationality, animality, and substance. The concept of difference plays an important role, therefore, as difference in kind is essential to Aristotle's system. (46)

 

Hence what distinguishes one species from the others in its genius is some specific difference that captures the essence of that species. So consider the designation man is a rational animal. All the other animals are not rational. We might also think of this designation as indicating the species’ difference from the genus, because the genus does not have ‘rational’ in its essence. The genus ‘animal’ has some other essential trait that distinguishes it from other substances. But in order for it to be essential, the specific difference cannot be accidental. (46) For this purpose, Aristotle introduces some other concepts, one being property. A property is something that can identify what species an individual belongs to. It is a trait that appears in one species [but not in the others in its genus, supposing that is what ‘derivative species’ are (46).] However, not every individual in the species will necessarily have this property and  [so it is for this reason that] they do not define the thing’s essence. [[There are four types of properties. [1] traits found in only one species, but not necessarily in every member of that species, for example, ‘to heal’ or ‘to geometrize’ in man. [2] traits found in all members of a species but are found in other species as well, for example, ‘being a biped’ in man is also in other animals. [3] traits that happen to all members of a species at a certain time, for example turning grey in man. [4] traits that are found only in one species and in all members of that species, for example risibility in man. What will seem to make the important distinction between properties and accidents is that at least some in a species needs to have a property proper to it, where no members of a species need to have an accident.]

a property differs from the kind of difference we have been talking about in that it only occurs within a particular species (although not every individual within a particular species needs to exhibit it), rather than also occurring in derivative species. Examples of properties include "the capacity to laugh in man" or "becoming grey in old age" (ISA, 48) . These properties do not define the essence of a particular thing, although they do, at least in the first case, extensionally define a species so that that which can neigh is a horse, and a horse is that which can neigh. (46)

An accident on the other hand only gives us a trait which need not be found in any member of a species, but very well could or even very commonly is found in them.

Accidents, though similar to properties, "come into being and pass away apart from the substratum" so that "it is possible to conceive of a white crow and of an Ethiopian who has lost his colour apart from the destruction of the substratum" (ISA, 49). (46)

True Aristotelian difference is different from properties and accidents. A property need not be found in all members of a species, and an accident can be removed without destroying the species. However “True Aristotelian difference therefore differs from properties in that it applies to all derivative species and from accidents in that it cannot be removed from a subject without that subject's destruction.” (46) Aristotle uses the concept of difference in three ways.

[1] Common difference. [Because of diversity of nature, something differs from another thing by being diversely different from it, and something differs from itself over time in that it diversifies from itself.] “First, common difference defines difference as commonly understood-that is, difference in any way, as, for instance, Socrates differs from Plato ( ISA, 42)”. (46d)

[2] Proper difference. [Two things might be differentiatable but connected by an inseparable accident. For example, a wound always has blueness (or a wound’s blueness is inseparable from it)]  “Proper difference is difference in terms of an accident.” (47a)

[3] Specific difference. It is a trait that distinguishes one species from another.

“Therefore while the first two lead to a difference in quality, the third leads to a difference in essence.” (47a)

Thus we see the role of difference in Aristotle’s system.

We have now designated the features of Aristotle's system central to our account of Deleuze's argument. Aristotle's system provides a hierarchical arborescent structure through which the essence of a species can be specified through a process of division, from the most general to the specific. Central to this hierarchy is the concept of difference. It is difference that differentiates the different species from the genera, through this process of division. (47)

Deleuze will critique Aristotle’s concept of difference.

Genus, species, and individual are the three levels in Aristotle’s system. Some sort of a difference will be responsible for generating the hierarchy of terms. But it cannot be the differences found between either individuals or genuses. [Consider the differences that distinguish one man from another. One is tall and the other short. One has brown hair the other blond. None of these differences are essential to being human. They are all accidental.] So difference at the level of the individual is accidental, which “will not capture this essence, instead merely reflecting the 'accidental' deviation from the proper form which the essence will exhibit within the particular individual.” (47) [However, consider things that differ in genus, like animals and minerals.The difference between them is so great that they are incomparable. The differences between individuals is too small for comparison. But] The difference between species, specific difference, then provides the greatest difference. “That is, difference between genera can also not be definitive for Aristotle, as the difference between genera cannot define their difference in terms of a higher, common source. Therefore specific difference becomes the greatest difference for Aristotle” (47)

Recall how in the first chapter,

Deleuze's ontology moves away from a Kantian conception of the transcendental by trying to consider the transcendental as generative, as opposed to merely conditioning. Aristotle's conception of difference at first seems to fulfill the criteria of a properly productive concept, which would allow this ideal to be realized (DR, 31). [47]

For Aristotle, a thing’s essence is a formal characteristic of it. [Recall how specific difference is what determines the essential differences between species. So] for Deleuze, specific difference is generative of essence in Aristotle, and it is a formal characteristic of a thing and as such presents itself as a pure difference.  And specific difference, unlike the differences between individuals, “also has a qualitative characteristic, as it defines differences in kind, rather than numerical differences” (48a). Deleuze as well finds Aristotle’s specific difference to be productive and synthetic. The species is composed of both a specific difference [from the others in its genus and thus from the genus itself, taken in its generality] and the genus. Because it is composed of both difference and genus, it is synthetic. And as we saw, the difference is a part of the essence; [it is in the essence of the thing to have its particular difference, thus] the species difference is what is doing the dividing of the genus, rather than the genus being divided into what are then differences as a result of the division. (48a) So difference “plays an active role in defining the species”. (48)

Difference thus has all of the characteristics that were attributed to the concept of difference that Deleuze himself employs, the difference that was outlined in the first chapter. Without the concept of difference, it would be impossible to move from the highest genus to any of its intermediaries. Aristotle's concept of difference is thus, like Deleuze's, directly responsible for the generation of the individual. Division thus appears as differenciation. (48)

Yet, there are still problems with assimilating Aristotle’s species difference with Deleuze’s difference.

[1] Aristotle’s difference is parasitic on a higher identity, because you cannot have a species difference without that species also belonging to a genus. “genera are logically prior to differences and are not logically dependant on them, whereas differences are logically dependant on genera ( that within which they are a difference)” (48)

[2] It is unclear how difference would produce the essence of the highest genus. “The highest genera form the top of the hierarchy of species, from which the species are differenciated by difference. This highest point in the hierarchy, however, cannot itself be the result of differentiation, as, if it was, this would presuppose a higher genus, from which this genus would itself be divided. Given that species and their differentiae are reliant on the preceding genus, the question of the status of difference at the top of the hierarchy now becomes problematic.” (48)

[3] Individuals are distinguished by their differences but they are not the essential differences of species differences. “A similar problem arises at the lowest point, where we have the problem of common difference. To quote Porphyry once again, "[C]ommonly one thing is said to differ from another when by otherness it differs in any way at all from either itself, or from another, for by otherness, Socrates differs from Plato and, indeed, from himself: he was a child and became a man" (ISA, 42) . The second problem is to explain in this Aristotelian system how Socrates can differ from himself and yet remain under the identity of the same concept, given that differentiation takes place in relation to the species and essence, through Aristotle 's focus on specific difference, and not in relation to the individual, which is understood through the contingencies of accidental difference.” (48)  We have the problem then of knowing how to differentiate accidental from essential properties in the individual.

SH concludes by leading us into the next chapter section:

Aristotle's concept of difference therefore seems to be problematic on both sides. As Deleuze | puts it, "[S]pecific difference refers only to an entirely relative maximum, a point of accommodation for the Greek eye which sees the mean, and has lost the sense of Dionysian transports and metamorphoses" (DR, 32) . The failure to find a truly Deleuzian concept of difference in Aristotle's logic may be indicative of problems, but it is not in its own right problematic itself. We therefore need to look at these two problems in further detail, that of the genus, and that of the individual. (48-49)

 

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

Pt1.Ch2.Sb1 Somers-Hall’s Hegel, Deleuze, and the Critique of Representation. ‘Introduction.’ summary

by Corry Shores
[Search Blog Here. Index-tags are found on the bottom of the left column.]

[Central Entry Directory]
[Deleuze Entry Directory]
[Henry Somers-Hall, Entry Directory]
[Hegel, Deleuze, and the Critique of Representation, Entry Directory]

[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 1: Introduction

 

Brief Summary: In chapter 2, Somers-Hall will examine the limitations of representation and Hegel’s and Deleuze’s treatments of it.

Summary

Previously Somers-Hall (SH)

explored the extent to which Deleuze tries to overcome what he considers to be the limitations of the Kantian approach to philosophy. Kant's approach essentially required predication to take place through a third term, the understanding, that provides a common ground upon which the autonomous elements of the judgment can take a common form. (41)

We also saw how Deleuze is situated in the post-Kantian tradition. But “the success of Deleuze's deduction was limited, in that Sartre's 'decisive' new concept of the transcendental field itself presupposed a structure analogous to that employed by Kant” (40). Now in this chapter SH will examine the more general problem of representations by looking at Aristotle’s and Russel’s logics, which will show us the limitations of representation. “After having done so, we will sketch the general approaches of both Hegel and Deleuze to the problems thrown up by the representational approach to philosophy. The key issues we will address are the problems of transition and of univocity.” (40)

For Deleuze, the issue here revolves around 2 interrelated questions.

[1] What is the position of the concept of difference within the tradition. (41) Deleuze notes how philosophers, especially Aristotle, have so far conceived of difference as a difference between concepts. But this subordinates difference to identity, which hindered a formulation of a concept of difference itself.
[2] What about the homonymy of being? ‘Being’ is used in many ways.

Thus the unity of phenomena is lost within Aristotle's analysis. We will begin from the analysis of being in terms of species and genera put forward by Aristotle, as it is here that the problem of the univocity of being is first discovered in the form of the problematic of homonymy, synonymy, and paronymy. (42)

For Deleuze, Aristotle and his successors used an illegitimate concept of difference. The result is that several phenomena, including temporality and unity, have been misunderstood. “These points of silence Deleuze will call the catastrophes of representational thought-the points where difference shows through in spite of the limitations placed on it by identity.” (42) SH will then move to Porphyry the Phoenician’s formalized Aristotelianism and afterward will move to the problem of analogy in Aquinas. He will then analyze the problem of univocity in terms of the calculus of the Whitehead and Russel’s Principia Mathematica.

We will see that this purely formal description cannot, however, avoid a fall into an equivocal concept of being. Formal logic, therefore, and those schools of philosophy that define themselves in terms of the rigor of formal deduction that it provides, are themselves fundamentally tied to a metaphysical interpretation of being from which they cannot escape, since this interpretation is not even an axiom of the system but, and prior to this, a function of the very laws through which the axioms themselves are interpreted. (42)

SH will conclude by turning to the problem of the univocity of being in its connection to Hegel’s philosophy.

The problem will be to reconcile Hegel's often stated love of Aristotle with the difference between Aristotle's dialectic and his own. Important in this regard is the opening to the Science of Logic where the concept of being is introduced, and Hegel's understanding of contradiction, which differs both from the concept of contradiction as conceived of by Russell, and the concept of difference thought by Deleuze. (42)

 

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