Pt2.Ch3.Sb2 Somers-Hall’s Hegel, Deleuze, and the Critique of Representation. ‘Bergson’s Account of Kant and Classical 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 2: Responses to Representation

Chapter 3: Bergsonism

Subdivision 2: Bergson’s Account of Kant and Classical Logic

Very brief summary:

Many theories of our understanding of the world regard there being an isomorphism between the structures of our world and our representations of it. Spencer thinks we evolved to see the world spatially as an adaptation to the way it really is. Kant assumed our representation of space is an a priori representation that conditions our external perceptions so that they are always spatial. Kant also saw an isomorphism between the understanding and the empirical world. Homogeneous space for Bergson is a medium by which atomic things are externally related. Under this analysis, Kant’s transcendental apperception, because it is what allows our understanding to externally relate terms of our judgments, is like homogeneous space. We can trace the concept of homogenous space to Euclid and see it persist throughout the development of physics, to mechanism and to Spencer. But as the Pythagoreans learned when discovering incommensurability, the world does not always match our representations of it. Uncovering this mismatch is a part of Bergson’s method of intuition.

Brief Summary:

To explain our knowledge of the world, many theories throughout the history of philosophy have regarded there being an isomorphism between the structures of our understanding and the world we are trying to understand. We saw this isomorphism with Kant’s transcendental idealism. Here the subject-predicate structure of synthesized concepts is isomorphic to the subject-property structure of synthesized objects of our intuition. But for Kant, our representation of space is isomorphic with the space we perceive, because our representation is a priori and conditions how we perceive objects. We can only perceive them as being external one to the other in a homogenous space. For Spencer’s evolutionary theory, we begin with these a priori structures because we evolved to accurately represent the real spatial world around us for the sake of survival. Bergson’s criticism of Spencer is that he presupposes the space that evolution is supposed to have produced. Bergson thinks that the mind and matter have progressively adapted to each other so to produce our notion of space. His criticism of Kant is that space and the understanding are identical for Kant, because the understanding provides a sort of space for atomic terms to be related externally (in subject-predicate relations). Bergson, then, erroneously thinks that Kant’s notion of space is simply homogenous. However, Bergson is right to note that that each moment of inner awareness [or judgment] is accompanied but an ‘I think’ that represents the same unified ego each time. So Kant’s transcendental ego is like the homogenous space that allows atomic things to take on external relations [especially the parts of judgments]. Russell’s set theory also has such a homogenous space-like medium that allows atomic parts (and sets considered individually) to take on external relations and be examined apart from those relations. Euclid describes a homogenous geometrical space, where the metric is the same everywhere. This homogenized space is kept throughout many of the subsequent major developments of geometry and physics, and it is reflected in philosophy as well. We can think of time as a homogenous space. With time and space both containing parts with determinate external relations, we have Laplace’s dream of determining all past and future states of the world on the basis of knowledge of everything about one moment and a great intellect to make the necessary calculations. Like Spencer, the Pythagoreans thought that our understanding corresponds with the world. In this case, because the mind understands integers and their relations, it can know the parts of the world that are expressible with number. But the discovery of incommensurability shattered that belief, because here there is something numerical that is not understandable with integers and their relations. So our minds and the world did not coincide isomorphically. Bergson’s method of intution, we will see, involves uncovering the mismatch between our representations of the world and the structure of the world.

Summary

Bergson and Deleuze tried to both come to terms with Herbert Spencer’s evolutionary thinking and also show its problems. We will also look at the relation between the structure of knowledge and the structure of the object. We saw how Kant’s system solves this with his transcendental categories. There is an isomorphism between the understanding and the object. Russell also thinks that the object and the system studying it must resemble one another. Russell has an atomistic system, so he solves Zeno’s paradox by saying time is an infinite discrete series. “The resolution of a paradox of thought therefore leads to an alteration of the conception of the object.” (70) In this chapter we will examine this isomorphism in evolutionary theory by looking at a particular concept of homogenous space.

Kant tried to explain how synthetic a priori statements were possible. He applied the subject’s categories to intuition, which conditions experience. “As the same categories play a role in both conditioning experience and conceptualizing it, their application to experience is vouchsafed.” (71) We saw previously how Deleuze wanted to break with this parallelism between empirical and transcendental. “Spencer attempts to provide a genetic interpretation of the development of our categories of thought that would allow us to see exactly why space appears to us in the particular a priori form that it has.” (71) Bergson rejects Spencer’s concept of space, but builds from this analysis. Kant proves the a priori nature of space on the basis of the subject’s ability to represent itself or to conceive the world in certain ways. Kant’s first argument is that in order for us to represent the referents of sensations as being alongside one another (being in different places), we must suppose we already have a representation of space. So we can only have empirical representations on the basis of an a priori representation of space. He second argument is that while we can think of an absence of objects in space, we cannot think of there being an absence of space in the world. This argument “follows a similar structure, placing the weight of the proof on the subject's capacity to conceive of certain relations between space and objects. In other words, what we cannot conceive of, in terms of empirical phenomena, cannot be the case. It is this reliance on the possibilities of representation that at first appears to be the target of evolutionary theory” (71). Evolutionary theory will not argue that we conceive space in accordance to how we condition empirical givenness (as being spatial). Instead, it argues that

our cognitive capacities are based on the fitness of the organism to the environment. Thus, alternative, partial conceptions of space lead to an organism that is not optimally attuned to its environment and therefore has a lower chance of survival than one with a more practical conceptual schema. As natural selection eliminates those organisms with suboptimal | representational schemata, a more optimal scheme becomes sedimented in the organism so that what is a posteriori for the species becomes a priori for the individual. (71-72)

So conceivability seems not to be the support for the argumentation, but rather conceivability becomes a function of fitness. Soon we will see that Spencer’s approach leads to a reversal of this.

What is life for Spencer?

For Spencer, life "in its simplest form is the correspondence of certain inner physico-chemical actions with certain outer physico-chemical actions" so that "each advance to a higher form of life consists in a better preservation of this primary correspondence by the establishment of other correspondences." Evolution is thus characterized by the gradual broadening of the correspondence between the world itself and the set of physico-chemical reactions that lie at the heart of our interactions with the world. (72)

As these correspondences increase, so too does the creature’s milieu. And as the milieu widens, so too does the organism’s subjective representation of the world near coextensity with the world itself. Truth, then, is the accurate correspondence of relations between subject and objects. Error is the absence of this correspondence. More correspondence means more chance to survive, and less means greater chance to die.

Thus, finally, pragmatic truth, when it is applied to a milieu that encompasses the entirety of the real, becomes objective truth. As Spencer considered the evolution of humanity to have reached this endpoint, primarily because of the successes of the scientific enterprise, for him, the validity of the a priori categories is restored, as they now once again correspond to reality (71).

So the reason we cannot imagine their being no space is because our evolution has reached such a point that we are unable to produce an erroneous view of the world’s spatial nature. Thus Spencer’s evolutionary theory also leads to the a priori nature of our representation of space and the categories, but of course for different reasons. (72-73) “The a priori nature of the categories is now grounded in a pragmatic correspondence between the organism and its environment rather than through the conditioning of the object by the subject.” (73)

Although Bergson notes how Spencer avoids the Kantian criticism, he also thinks Spencer failed to provide an adequate alternative to Kant’s theory. Spencer’s theory of evolution presupposes that we are evolving in space. So he begins by presupposes what he will conclude will be the outcome of evolution. “Spencer therefore fails to provide an adequate response to Kant, as his explanation of the genesis of space presupposes an account of a space such as that which Kant gives wherein this genesis takes place.” (73) However, Bergson builds from certain of Spencer’s metaphysical ideas. (a) We need an account of space that does not accept it as ready made. This account would retrace space’s genesis, which he thinks Kant achieves. (b) Bergson will say that Kant’s theory of space does not allow for an account of space’s nature. Bergson looks at the three possible relations between subject and world in Kant. Either [1] the mind is determined by things, [2] things are determined by the mind, or [3] there is some mysterious agreement between the mind and things. Bergson then proposes a fourth possibility: [4] “ ‘intellect and matter have progressively adapted themselves one to the other in order to attain at last a common form’ ( CE, 206).” (73) But this process of progress adaptation cannot precede space, like with Spencer. So Bergson agrees with Kant that space is an ideal feature of the world and also that we cannot use an empiricist account of our conception of space. Bergson notes that Kant does not consider the possibility of degrees of spatiality. For Kant, space is either given or not given. [In order to say that our understanding is connected to both pure space and to its degrees or indeterminate forms, Bergson will have to argue that the understanding is wider than Kant conceived it to be]. Bergson is trying to explain the genesis of space, which highlights a limitation in Kant’s account. First we examine what for Bergson is the connection between homogenous space and the understanding for Kant and Russell. (74)

For Kant, judgments are made through the relations between fully determined terms. The faculty of understanding (which is external to the terms) is what allows the terms to be thought together. So understanding is a third term underlying the unity of judgment. Bergson notes that because we here are conceiving of the elements of consciousness having the subject-predicate form (their being objectival), we are compelled to regard them as united by an artificial bond, “ ‘a formless ego, indifferent and unchangeable, on which it threads the psychic states which it has set up as separate entities’ (CE, 3).” (74) Bergson thinks that Kant’s conception of the atomistic components of judgment is reflected in his conception of the world’s elements, and so he has an atomistic conception of space. We will explore this because it leads to the two forms of multiplicity.

 

In Kant’s transcendental aesthetic, there is a difference between the object insofar as it appears to us and the space that possibilizes its appearing. So space, in Bergson’s view here, is logically prior to the objects that occupy it. Space is the medium that allows objects to relate and interact. Analogously, the ego provides the ‘space’ in which terms relate.

In the cases of both the mind and the understanding of space, therefore, we find the model of a medium through which the elements can interact. The ego enables judgment, and space, in coordination with the categories of the understanding, enables perception of the object. (74)

This spatial metaphor is also at work in Russell’s set theory, because it creates domains that relate to one another.

We saw that set theory provides a hierarchical model of relations, sets being related to others by the relative domains of objects over which they range. Cantor's | definition of the set as "a collection of definite, well discernible objects" emphasizes the use of spatial metaphors at the foundation of the discipline of classical logic, which allows the graphical representation of logical results through, for instance, Venn diagrams. (74-75)

In this set theory, we view the elements of propositions as discrete, and they function in a space that is “inert to their interactions.” This allows us to regard the relations between the members of sets as being purely external to the terms themselves. And in fact, even the relations between sets themselves is seen as external to the sets. Because the relations are external, we can encounter paradoxes of self-referentiality that result when a set has an external relation to itself that is in contradiction with its own definition. But this allows Russell to give an extensive definition of the set, because he could enumerate objects that relate to one another externally on the basis of shared properties, and it also had advantages for analysis. Because relations are external, we can put them aside and merely analyze the terms. Bergson sees something similar in Kant. For Kant, we may examine the parts synthesized into manifolds each individually. This presupposes a spatial understanding of the parts, because they are related by external relations.

Thus, the spatial model allows the method of analysis to develop, where a complex phenomenon can be broken down into its component parts in order to understand the whole through a later process of synthesis. (75)

For Bergson, every homogenous medium is a space. He sees Kant’s faculty of understanding as a homogeneous medium, thus for him, Kant’s understanding and space are identical. Somers-Hall recounts that

In chapter 1, we saw that insofar as Kant takes the empirical to have the same form as the transcendental, he is unable to take account of the generation of the empirical. This led us so see that by privileging the structure of judgment, Kant belonged to the tradition of representation. (75)

Deleuze however sees Kant’s theory of space in less simplistic terms than Bergson.

As Deleuze notes in relation to Kant's argument from incongruent counterparts (DR, 13, 26), Kant recognizes an "inner difference" within space that escapes the understanding. We can further note that spatiotemporal objects for Kant cannot be described 'atomically, ' as "all substances, in so far as they can be perceived to coexist in space, are in thoroughgoing reciprocity" (CPR, B256). [75]

Bergson’s simplification no longer allows us to make his analogy between space and the understanding. However, Bergson’s argument against the limitations of the understanding do still hold, and it will be important for Deleuze’s attack on finite representation. Recall how for Kant, the understanding produces judgments by subsuming representations under other representations. Each term is self-sufficient, so it needs something additionally to relate them, and this is the ‘I think’ whose unity provides the grounds from the representations to come together. So Bergson’s critique applies to the ‘I think’, which can be thought of as like homogeneous space that relates atomic externally related parts.

Leaving aside his argument for this point, given the apparent differences between the structure of the understanding and the structure of space, what will actually be important to Deleuze is the multiplicity that underlies this conception of space and the recognition that it is possible to draw a distinction between extensity and space. (76)

We will now try to understand the importance of space for Bergson. We must first note that we can now formulate different kinds of geometry, Euclidean and non-Euclidean ones. In this chapter we deal with Euclidean, and the next with Riemannian. All of Euclid’s theorems derive from just five axioms, and the fifth interests us here: “through a point not on a given straight line, one and only one line can be drawn that never meets that given line”. (76) [Or, ‘only one line can be drawn through a point parallel to another line.' The basic insight here is that any other line than a parallel one would eventually intersect with the first line.] On the basis of this axiom, we may arrive upon homogenous space. [So if the two lines are parallel, that means the distance we measure at one place will be the same as in any other place. So space has a homogenous metric. We can lift up those parallel lines and move them somewhere else, and still they will not meet, because the metric of space will be the same in that other place as well. The lines are determined, but they are related through a homogenous space. Now consider how Kant’s ego, is homogenous, because it is the same self for every ‘I think’. Euclidean space, as the relational medium between determinate figures, is like Kant’s ego as the homogenous relational medium between instances of inner acts with their accompanying ‘I think’.]

With the fifth axiom, which can be restated as asserting that "through a point not on a given straight line, one and only one line can be drawn that never meets that given line," we arrive at a conception of space as fundamentally homogenous. This means that a particular metric applied at one point within a Euclidean space can equally be applied at any other point. Euclidean space therefore has the fundamental property of measurability, in that we can compare the objects within it by their superposition upon one another. A consequence of this is that an object within a Euclidean space is invariant to transformation by displacement, or in other words, that the space of Euclidean geometry functions as a homogenous medium where position does not affect the constitution of objects within it. Euclidean geometry therefore provides the ideal model of how we are to understand something like the ego as that which allows the relation of already determined concepts. (76)

Descartes invents the algebraic representation of geometry. This, along with his notion of inert matter, further allows for “the conception of physics as the interaction of quantitatively characterized matter within the field of homogenous space defined by this geometry.” (76) “By moving to a purely quantitative definition of matter, Descartes allowed for the application of mathematical concepts to the world, which in tum was to open up the possibility of the mechanics of Newton.” (77) Spencer’s evolution is the closer approximation to this structure of the world.

The final stage of Spencer's phylogenie account is the mirroring of an internal world grounded on the invisible thread of consciousness and the external world grounded in the understanding's relations to the homogenous field of space. For Spencer, Newtonian physics therefore represents the final milieu of the development of the organism, one that allows the complete representation of the world to the organism. (77)

This view of a quantifiable metric space of externally related parts helped form Russell’s discrete view of time, and it would help fulfill Laplace’s dream of an unlimited intelligence and knowledge of the state of everything in the universe at one moment being able to determine all past and future moments. “The mathematico-analytic approach therefore allows the analysis of any closed system in a similar fashion, that is, the quantitative”. (77)

This approach creates difficulties for the Pythagoreans, who believe that all knowable things have number. But with the discovery of incommensurable numbers, it was seen that there are numbers which cannot be reduced to integers and their relations. Our understanding of number then did not match the world we are trying to understand.

When Pythagoras' theorem is applied to the square, we find that the length of the diagonal of the square is √ 2 times the length of the side. As the square root of 2 is irrational, the ratio of the length of the side to the diagonal is irresolvable into an integral ratio. The Greek concept of number, built on the idea of the integral numerical progression, was unable to incorporate the idea of a number which could not be reduced to integers or their relations. With the discovery of incommensurable numbers, Pythagoreanism collapsed, the man who disclosed the difficulty being said to have died in a shipwreck as a result. What therefore defeated the Pythagorean model was the discovery of a mismatch between the world and the subject's ability to conceptualize the world. (78)

Just like the Pythagoreans, “Spencer's model of the gradual adequation of the mind to the world produced the corollary that the structure of the mind was isomorphic with the structure of the world.” (78) Bergson’s method of intuition is “a method of recognition of the mismatch between our representation of the world and the structure of the world itself.” (78) We explore this method of intuition in the next section.

 

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

Pt2.Ch3.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 2: Responses to Representation

Chapter 3: Bergsonism

Subdivision 1: Introduction

 

Very brief summary:

Part 2 examines Deleuze’s Bergsonist response and Hegel’s absolute idealistic response to the problem of representation.

Brief Summary:

Part 2, chapters 3 through 5, examine Deleuze’s and Hegel’s responses to representation. Deleuze’s response is largely influenced by Bergson, so much of the Deleuze material is Bergsonist. The chapter on Hegel examines his infinite thought and how he develops his absolute idealism through his examination of the limitations in Kant’s transcendental idealism.

Summary

 

In part 1 we discussed the problematic nature of representation in Kant’s transcendental idealism and in Aristotle’s and Russell’s hierarchical systems of classification. In this next part Somers-Hall (SH) will examine in more detail Deleuze’s and Hegel’s responses to those problems. Bergson is perhaps the most important of Deleuze’s influences. This chapter focuses on that influence. Deleuze is especially concerned with Bergson’s method of intuition and theory of multiplicities.

In making a sharp distinction between space and duration, Bergson was able to provide a theory of the foundations of classical logic, as well as explain why classical logic fails to explain large groups of systems, such as living systems. (69)

In the fifth chapter we examine how Hegel responds to representation with infinite thought and how he develops his absolute idealism “immanently from the limitations he finds in Kant's transcendental idealism. We will see how the introduction of the infinite into his conceptual schema allows him to resolve the problem of representation.” (70)

 

 

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

Pt1 Somers-Hall’s Hegel, Deleuze, and the Critique of Representation. ‘The Problem of Representation’ 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

 

Very brief summary:

We might think of representation as a manner of conceiving matters in terms of self-same unities whose identities and descriptions can be given explicitly and without self-contradiction. Representation has been used as a basic principle for many important theories throughout the history of philosophy. The representational unity of the transcendental apperception in Kant is the basis for our ability to make judgments of the world. But Deleuze’s logic of incompossibility accomplishes the same feat without representational unities. And Aristotle’s and Russell’s hierarchical classification systems are based on an overarching representational principle of identity and the law of excluded middle, but this principle is not representable within their systems. Also, they cannot explain change, cases of ambiguous classification, or paradoxes arising from their principles of class inclusion. Hegel’s solution is to make self-contradiction productive of new concepts, but Deleuze still finds this to have the problems of representation. Deleuze’s solution is non-oppositional difference.

Brief Summary:

The history of philosophy contains tendencies toward building theories and systems on the basis of representation. This means that they make use of principles of self-unity, identity, and the law of excluded middle. There are problems with these approaches. Deleuze and Hegel offer solutions. There are two cases under investigation. The first is the transcendental grounds of our knowledge, specifically, what principle allows us to make judgments of the world? Kant offers a representational theory. It is representational, because it is based on a self-identical a priori unified self that is represented in all inner acts, in their accompanying ‘I think’. This unity unifies the empirical world into things with a subject-property structure, it unifies our concepts into subject-predicate structure, and it unifies our concepts and our intuitions into representable judgments with the subject-predicate structure. Sartre’s critical stance would say that it is really the unity of objects, and not subjects, that comes first and the unity of the self comes secondly. For Deleuze, a unity neither of consciousness, of self, nor of the objects, is what grounds our subject-predicate knowledge of things. Rather, each moment, events can go many different ways, so the same subject now has many various undetermined predicates, and they are incompossible. Because they are contradictory, the predication of a subject is not representable, even though the subject-predicate structure is there. This is Deleuze’s transcendental empiricism. Another case of representation in the history of philosophy is the use of the principle of identity and excluded middle in Aristotle’s and Russell’s theories of classification. For Aristotle, we define species on the basis of their differences. But the highest genus, being or unity, has nothing to differentiate from, no genus above it or species beside it, so it is indeterminate. However, it is the basic principle saying that all beings are self-unified and have identities (and thus also the system is thoroughly representational). The very representational basis of his system is not itself representational. Russell’s theory of class inclusion is also representational. Things are strictly categorized and defined by their groupings. There cannot be contradiction in the system, or instances when something’s identity contradicts its classification. So it cannot have the paradoxical class of all non-self-inclusive classes. Such a class is meaningless, it cannot be represented in the system. And yet, such a class is based on the same notion of inclusion as all the others. Hence class inclusion, as a universal concept that forms the basis of all instances of classification in his system, is not representable in this system. So somehow the nature of inclusion for each level is distinguishable, when in fact it is the same sort of inclusion each time. Also, identities and essences are representable, but moments of self-contradiction do not fit into such representable systems. This means that when something is changing, we cannot represent what is happening in the phase of transition when contradictory properties are coincident (like being both wood and fire in the action of ignition). Hegel’s solution is to make contradiction productive, using internal dialectic, where some concept brings about its own self-contradiction, and out of it comes a new concept not implied in the first. For Deleuze, this solution still has the problems of representation, as we will later see. Deleuze’s solution is a non-oppositional concept of difference.

Summary

 

Part 1 examines developments in the history of philosophy that use identity and unity, more importantly representation, as their basic principle. Somers-Hall then examines how Hegel and Deleuze respond to the problems of these representational philosophies. One question is, on what basis are we able to make judgments about the empirically given world? For Kant, the unity of self-awareness (the transcendental apperception, the a priori self, the ‘I think’  that accompanies all inner acts) is what allows the parts and moments of empirical givenness to belong together and be synthesized with one another. This unity is also what allows us to synthesize the conceptual manifolds of our understanding. And finally it is what allows us to unite our concepts and intuitions. We are then able to make subject-predicate formulated judgments about subject-property structured objects. So the grounds for our knowledge of the empirical world is transcendental, the transcendental ego, and this is his transcendental idealism. Sartre indirectly criticizes the unity of Kant’s transcendental apperception when he critiques Husserl’s transcendental ego. Sartre argues that phenomenal givenness is already given to our awareness in its continuity, and the unity of the objects we perceive is what allows us to secondly unify our consciousness and ego, and not the other way around. For Deleuze, the subject-predicate structure is given without the objects being unified. This is on account of his logic of incompossibility. Here the same something, like Adam, before making the decision to eat the apple, has a plurality of incompossible predicates, like sinner and innocent, because his decision is not yet determined. So the grounds for our being able to make subject-predicate judgments is not representational and it does not rely on a unified subject or object. It is given in the bifurcational logic of the world of empirical givenness. This is Deleuze’s transcendental empiricism. [Deleuze’s theory is not representational, because there is no unified identity involved in it.]

The other representational systems in the history of philosophy are Aristotle’s and Russell’s hierarchical systems of classification. They are based on self-same identity and the law of excluded middle. Aristotle’s highest category, being, cannot be defined, because it has no difference from other other species and no higher genus with which to define it. It is more like a principle of unity shared by all beings falling under it rather than being a category of inclusion. Also, Aristotle’s theory of specific difference does not explain how the individuals on the lower end of the hierarchy can be distinguished, because they are differentiated by accidental and not by essential specific differences. Aquinas says that we can speak not of being (God) but of relations to him based on other relations between genera and species. But this blurs the important differences between relations to God and other sorts of relations between beings. Russell’s representational system is a theory of set classifications. Something is included in a set if it has the property all that set’s members share. [The highest set is the set of all sets. But how are we to conceptualize whether or not this set belongs to itself or not?] Self-inclusion is a problem however. Consider the set of all non-self-inclusive sets. It is impossible to say whether it is included in itself or not. The solution is to say that there is a hierarchy of levels of set inclusion, and one level can only refer to the level below it, and to not other. This means it cannot refer to itself. It also means that we cannot make a universal statement for all levels. And we cannot define a highest class, because this would require one higher to it that refers to it. Both Aristotle’s and Russell’s systems are based on a principle of identity. Contradictions in the system go against their unifying structural principle, that things are self-same and there is nothing whose identity is ambiguous or in self-contradiction. One problem is explaining ambiguous cases of classification like ring species. Another problem is explaining change, because they can account for each moment where something is self-same, but not the transitional phases between when they have contradictory properties. Hegel’s solution is to posit a productive contradiction. Being is purely indeterminate, as the case for the highest categories in Aristotle and Russell, but rather than creating a problem, this is the strength of Hegel’s system and its solution to the problem of representation. Being as indeterminate is indistinguishable from nothingness; the two vanish into one another, and out moves becoming. Thus he can explain change and conceptual ambiguities. Deleuze we will see has the solution of non-oppositional difference.

 

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

Pt1.Ch2 Somers-Hall’s Hegel, Deleuze, and the Critique of Representation. ‘Difference and Identity.’ 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

 

Very brief summary:

There are two important limitations in Aristotle’s and Russell’s representational hierarchies, stemming from them being based on identity and excluding self-contradiction: they cannot explain the motion of change, and they cannot account for ambiguous and paradoxical cases of classification (ring species and the set of all non-self-inclusive sets). Hegel’s solution is productive contradiction, where a concept’s self-contradiction produces something not already implied in it. Later we will see Deleuze’s solution, non-oppositional difference.

Brief Summary:

Aristotle and Russell have hierarchical systems based on a principle of identity, and they enforce the principle of excluded middle. But these systems run into problems, which call for the basic principles in them to be revised. One problem is explaining change, because in systems where individual’s identities are represented in their self-sameness, we cannot explain how one individual in the moment of transition has incompatible properties (like being both wood and fire in the transitional movement of ignition). Aristotle’s system of division into classes is based on specific differences that are the essence of the species. But individuals at the bottom of the hierarchy are not species, and they are not distinguished by essential differences. And being, or unity, at the top of the hierarchy, cannot be defined, because it is not a species with a difference from a higher genus. So the highest genus is more like a principle of self-unity or identity which allows for the unities and identities of all beings classified under it. Aristotle says that there are many senses of the same focal meaning being, which are the different ways that beings express being. But this still assumes a unitary meaning of being, so it does not place difference at the core of the system. Aquinas’ solution is to say that we cannot define the highest category (being, or God), but we can know the relation that beings have to it, by means of analogy from other relations between species and genera. This however reveals that there is an ambiguity in all relations between species and genera [which calls into question the differences that would make each individually itself. Perhaps it suggests that all we can talk about is inclusions, and not about the individuality of things.] Russell deals with set inclusions, and tries to build a system where something is said to belong to a set when that thing shares the property that all members of that set have. This creates a problem at the highest level, because we encounter a paradox with the set of all non-self-including sets. The solution is to say that each level of classification can only apply to the level immediately below it, and not to any other. This way there can be no self-including sets. But that also means we cannot make one universal statement holding for all levels. Instead, when we think we are making such a statement, we are really making a different statement for each level. Here again we have a problematic ambiguity between all levels of the hierarchy. What we note is that in these systems of classification, something either is in a class or it is not, there is no middle or ambiguous status. There cannot be self-contradiction, but this is what leads to problems with explaining ring species and transitions. Hegel’s solution is to embrace contradiction and make it productive. So being as purely indeterminate is indistinguishable from nothingness; they vanish into one another and produce becoming. So Hegel’s productive contradiction is one solution. Later we will see Deleuze’s solution being a non-oppositional sense of difference.

Summary

 

Previously in chapter 1, Somers-Hall (SH) discussed Deleuze’s transcendental empiricism. Kant’s transcendental apperception (the a priori unity of our self-awareness, the ‘I think’ that accompanies all our inner acts) provides the unity on the level of (a) empirical givenness, (b) concepts and understanding, and (c) the relation between these levels. This unity allows us to make subject-predicate formulated judgments of subject-predicate structured objects. Sartre, in his critique of Husserl’s transcendental ego (in defense of Husserl’s phenomenological project on the whole) argues that the self-consistency of phenomenal objects is the basis on which we derive a self-unified ego, and not the other way around. Deleuze also does not take up a unified transcendental ego to explain the grounds of our knowledge of objects. The logic of incompossibility allows there to be a subject with various predicates, depending on the various sorts of branching paths that subject might take in the next moment. So we can have the subject-predicate structure of objects on which to base subject-predicate judgments of them, and yet the predications are not determined. Hence the differential relations in the field of givenness (the bifurcations that create multiplicities of incompossible predications) are both empirically given and yet provide the non-empirical grounds for our knowledge of these objects. This is Deleuze’s transcendental empiricism.

In chapter 2, Somers-Hall examines how the prohibition of the principle of excluded middle in Aristotle’s and Russell’s representational, hierarchical systems limits their integrity and their capacity to explain change.

We will later articulate Deleuze’s concept of genetic difference. Aristotle’s system of hierarchical classificatory divisions is based on species difference, and so it would seem like a possible model for genetic differentiation. For Aristotle, there are the three main relational tiers: genus, species, and individual. What distinguishes a species is its special difference, which is its essence. Because it is essential, it precedes the division of the genus, and so it is productive of the different species rather than being something secondary to the division. However, the individuals in a species, like different people, are not distinguishable by what is essential to them, but rather by accidental traits [what makes one man distinct from another are traits they could have lacked, like hair color, and still have been themselves.] So Aristotle’s specific difference is not a model for the genetic production of individuals.

Also, the highest genus, being, is not defined by (essential) specific difference, because there is no higher genus or other fellow species to differentiate from. To define something, we need both genus and species, so the highest genus, being or unity, has no basis to define it. However, the many beings classified under it exhibit their being in various different ways (qualitatively, like being straight, white, etc., quantitatively, being continuous, numerous, etc.). These are not higher categories of being, but are rather different acutalizations of the same focal meaning of being. So, the beings that fall under being (and the senses of being too?) do not have both the same name and the same definition, so they are not homonymous (univocal). Rather, they share a similar name but have different yes related definitions, and are thus are paronymous (derivative).  So, the many senses of being are unified yet diversely applied. Yet, because all the senses revolve around a focal meaning, the core of the system, being, does not seem to be defined by difference.

So Aristotle’s system of divisions (based on specific difference) is organized around the highest category, being, which in a way is implicitly defined tautalogically (being is being, or unity is unity) because there are no differences that distinguish it. The system of difference, then, is based on a central self-identity. But all things fall under the category of being, which means all things are self-identical unities, and this creates a problem for explaining change. So Aristotle’s notion of essence can explain how something remains itself while changing, but it cannot explain how in phases of transition, it has contrary properties (like how an igniting piece of wood is both wood and fire in the same phase of alteration between determinate states). Another problem with Aristotle’s notion of specific difference is that it cannot be used for classifying ‘ring species’: animal type A can breed with B, and B with C, but not A with C. On the basis of specific difference, we cannot really say all three are in the same species, because A and C cannot breed. However, if we say A and C are in different species, then what species is B? Is it in both? And what if each were a different species, what about the fact that pairings can interbred yet are in separate species?

Porphyry shows that Aristotle’s paronymy is a type of homonymity, because in homonymity, there is the same name with different meanings, and paronymy is similar names with related meanings. Aquinas uses Aristotle’s concept of analogy to deal with the problem of characterizing the highest category, being, or God. We cannot determine anything about that category itself, but we can speak of man’s relation to God by analogizing it to isomorphic relations between other genera and species.

Russell deals with problems similar to Aristotle’s. In Russell’s set theory, something is included in a set if it has the property shared by that sets members. [The highest set I would think would be the set of all sets. But this highest set is based on a problematic structure that is revealed in another very high set.] We can define the set by its members or by the criteria for membership in that set. One such criteria might be ‘being a set that has itself as a member’. But this creates a paradox that tells us there is something wrong at the very basis of the system, that this notion of self-identical things contained in self-identical categories is not sound basis for the structure of the organization for all things. The paradox is that if the non-self-inclusive set itself is said to be one of its own members, then it contradicts its own definition of being non-self-inclusive. And if it is not said to be a member of itself, then according to the criteria, we should include it within itself, which goes against the original assumption that it is not included within itself. Russell’s solution is to say that there are different levels of classification, and one level can refer to the next one below it, but not to itself. So ‘a class that includes itself’ has no meaning in Russell’s system. Yet this also means that we cannot make one universal statement that holds for all things. Our statements always are limited to one level. This even means that a property like truth is not the same for all level, it would be ‘truth at level n’ for example. So when we do speak universally about something, we are implicitly making a different statement for all its substrata. Also, like with Aristotle’s hierarchy, we cannot define the highest class in Russell's system.

Both Aristotle’s and Russell’s systems prohibit the excluded middle, so it is always the case that something is P or not-P, but not both. This is why they are unable to explain transitional phases when something expresses contrary properties together and ring species where animal groups seem to both be and not be in the same species.

Hegel’s system, however, not only allows for contradiction, in fact, its coherence and ability to explain change is based on it. And the movement between concepts in Aristotle and Russell is one of implication, so nothing comes out of the movement that was not already there at the beginning. Being vanishes into nothingness, which produces becoming. However, like Aristotle’s and Russell’s systems, Hegel’s movement is not temporal.

Hegel likes how Zeno begins with the notion of multitude to find a contradiction in it, so to conclude that the many cannot be. This is like Hegel’s dialectic, in that contradiction is inherent to the movement, but Hegel goes an additional step with his aufhebung so to derive a new concept from the self-generated self-contradiction. So because being is completely indeterminate, it is indistinguishable from nothingness, so the two vanish into each other, and moving out from that opposition is the notion of becoming. The indeterminacy of being (or the highest category) was a problem for Aristotle and Russell’s systems, but for Hegel, it is one of its strengths, and it allows him to overcome the problems in their systems.

So Hegel’s solution to the problem of representation (in a system) is to apply the notion of productive contradiction. Deleuze’s solution we will see is to use the idea of a non-oppositional difference. Deleuze’s critique of Hegel is that his notion of productive contradiction does not extract him from the problems of a representational system. Hegel can criticize Deleuze’s use of essences, for example in his notion of the virtual.

 

 

 

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

Pt1.Ch2.Sb10 Somers-Hall’s Hegel, Deleuze, and the Critique of Representation. ‘Conclusion.’ 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 10: Conclusion

 

Very brief summary:

There are problems with Aristotle’s and Russell’s classificational systems that arise from them excluding contradiction. Hegel’s solution is productive contradiction. Deleuze’s solution is non-oppositional difference. Deleuze can criticize Hegel for not escaping the limitations of representation, and Hegel can criticize Deleuze’s notion of essence.

Brief Summary:

In Aristotle’s and Russell’s systems of classification, there are deep-rooted problems arising from their use of a deficient concept of difference. They disallow contradiction, which leads to inconsistencies in their systems, and their solutions only further reveal the insufficiencies of the systems’ structures.  Deleuze and Hegel offer solutions. Hegel makes use of a productive opposition, and Deleuze has a non-oppositional sort of difference. We will later see that Deleuze argues that Hegel (unlike with Deleuze’s transcendental notion of difference) still does not escape the limitations in the representationalist paradigm. But Hegel might reply by critiquing Deleuze’s notion of essence as for example in the case of the virtual. The next chapter will be about Bergson.

Summary

 

Previously we saw how Hegel takes up Zeno’s method of finding self contradiction in a concept, and Hegel takes this process further to show how a concept’s self-contradiction, through aufhebung, can lead productively to a new concept. So being, in its pure indeterminacy, is indistinguishable from nothingness. The two vanish into each other and produce becoming. This means that self-contradiction and pure indeterminacy at the most basic level of the system is not a problem as it is for Aristotle’s and Russell’s systems; in fact, it is one of its strengths, because Hegel is able to have a whole consistent system that can explain change, where Aristotle and Russell cannot.

Now Somers-Hall concludes chapter 2. In this chapter, he showed that one of the problems with representational logic’s structure is that it limits the degree to which the world can be thought as a coherent totality. For Deleuze this is because their systems use a deficient concept of difference. Hegel and Deleuze each offer us their own solutions. Hegel proposes a radical concept of productive opposition, and Deleuze offers a non-oppositional sort of difference. In the next part, Somers-Hall will examine the logics behind these concepts. This will help us understand Deleuze’s critique of Hegel and as well it will allow us to consider a possible reply by Hegel.

To put it simply, Deleuze will argue that in extending the idea of difference to its absolute limit, that of contradiction, Hegel has not truly escaped from the limitations of the representationalist paradigm. Deleuze, on the contrary, by moving to a transcendental notion of difference, hopes to produce a difference that differs in kind from that of Aristotle and Russell. We will also explore the possible Hegelian response that any notion of essence, even a heterodox notion such as the virtual, necessarily collapses into a moment of seeming (Schein) . In the next chapter, we will analyze Bergson's philosophy of duration, with its implicit critique of judgment as spatialization, in order to begin to highlight the grounds of Deleuze's response to representation. (66)

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

Pt1.Ch2.Sb9 Somers-Hall’s Hegel, Deleuze, and the Critique of Representation. ‘Zeno.’ 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 9: Zeno

 

Very brief summary:

Hegel likes Zeno’s internal dialectical method that begins with a concept and then sees how it comes to contradict itself. For example, in Hegel’s aufhebung, being is completely indeterminate (as it is with Aristotle and Russell) and thus indistinguishable with nothingness. They vanish into one another and through this there is a movement to the concept of becoming. Unlike Aristotle and Russell, self contradiction here can not only be inherent to the highest genus, being, it can also be essential for making the system consistent and whole.

Brief Summary:

Hegel likes Zeno’s method of defending Parmenides’ argument that all is one. Zeno does not begin with axioms to come to that conclusion (external dialectic) but rather he begins with the concept of the many and shows it leads to a self-contradiction (internal dialectic). In Hegel’s aufhebung, being is indeterminate and so it is indistinguishable from nothingness, and they vanish into one another, and in that process move to the concept of becoming. So here we have contradiction with respect to the highest genus, being, not leading to a degradation of the integrity of his system, as it is the case for Aristotle and Russell, but rather being one of its strengths. Hegel, unlike Aristotle and Russell, can have a unified system, because he incorporates a productive form of contradiction, and as well, he, unlike them, can explain the process of productive change.

Summary

 

Previously we examined the similarities and differences between (a) Aristotle’s (and Russell’s) hierarchical systems of division and (b) Hegel’s dialectical system. The differences were that (1) Aristotle’s and Russell’s systems obey a strict law of the principle of excluded middle, which does not allow for ambiguous cases of identity like transitional phases between states where mutually exclusive states are coincident, and also for example ‘ring’ species where animal type A can breed with B, and B with C, but not C with A, leaving the species-classifications of these animal types ambiguous, and (2) The ‘movement’ between concepts for Aristotle (and Russell) is one of implication, meaning that the concept moved-to was implied in the first, but in Hegel’s dialectical system, there is a genetic movement when being and nothingness disappear into one another and move to the concept of becoming.

Somers-Hall now turns to Hegel’s reading of Zeno. Hegel’s interest here is the way Zeno arrives at his conclusion that there is no movement. In his analysis, Hegel distinguishes two types of dialectic, external and internal.

Hegel’s External and  Internal Dialectics:

External Dialectic: Here the “ ‘movement is different from the comprehension of the movement.’ (LHP, 1, 264)” (64) It is the dialectic Parmenides uses to prove that “All is one”. Its limitation is that an interlocutor need not take up its assumed axioms. So even if the system built on the axioms is coherent, someone might still find these axioms to be false and exterior. “Thus the debate moves in the wrong direction. I try to prove my case by unfolding the implications of my position, while it is the grounds of the position itself that | are the issue." (64-65) The advantage of it is that it sheds light and reveals reasons. “The result of this is that the object of the debate is criticized, but only from one side, at best merely placing the held assumptions in question”. (65)

Internal Dialectic: This is "‘not a movement of our intelligence, but what proceeds from the nature of the thing itself, i.e. from the pure Notion of the content.’" (64) It “does not reason from alien premises but is itself the movement of the object under discussion.” This is Zeno’s dialectic. Unlike Parmenides, Zeno argues that “the Many cannot be”. It is true dialectic. It " ‘leaves nothing whatever to its object,’ leading it instead to ‘disintegrate itself in the entirety of its nature’ (LHP, 1 , 265). Thus Hegel follows Zeno in arguing that the motor of the philosophical process is contradiction." (65) But Zeno’s internal dialectic cannot move beyond its object’s destruction. So this dialectic results in the null or negative, and the affirmative does not yet appear in it. The negative in this dialectic is how a contradiction leads to the object’s negation; for Zeno, the many is negated. Recall Russell’s problem with his system of classification. He was worried that universality would lead to a contradiction [in his system, to say “the class of all non-self-inclusive classes” would refer only to the order of classes below it. If it were universal, it would refer also to itself, leading to a paradoxical contradiction. But if the system eliminates the distinction between true and false in this way, then all its propositions are simultaneously true and false.]

In talking of an 'affirmative' within contradiction, Hegel is going beyond the structures of classical logic. Russell's paranoia about the possibility that universality would lead to contradiction was grounded in the fact that the existence of a contradiction makes all propositions within a system simultaneously true and false. Thus, what Hegel is seeking is something between the mad proliferation of propositions within a system and the skepticism that "ends up with the bare abstraction of nothingness or emptiness and cannot get any further than there, but must wait to see whether something new comes along and what it is, in order to throw it too into the same empty abyss" (PS, 51). (65)

To do this, we need to regard the negation of the contradictory concept as a determinate negation,

meaning that in showing a particular object to be contradictory, we do not simply reject it, but trace out the path that its own rejection forces us to take. In this way, Hegel moves beyond a purely formal logic to one in which the content itself opens up a determinate movement beyond the impasse that contradiction leads to in earlier systems.  (65)

[So if Hegel were just using formal logic, contradiction is not generative of new concepts. In formal logic, there are only conceptual movements of implication, when one concept emerges from another.]

Thus, in the case of the problematic concepts of being and nothingness, we are led not to a skepticism concerning these concepts, but rather to a further concept of becoming. Furthermore, the concept of becoming does not result from the destruction of these prior categories, but is instead the result of the resolution of this contradiction at a higher level. The contradiction is aufgehoben, that is, simultaneously surpassed and preserved. (65)

[In the case of Russell’s formal logic, a contradiction means that any conclusion could result. But in Hegel’s aufhebung, there is a determinate result.]

In this movement, the force of Russell's anxiety in the face of contradiction is removed. Instead of leading to an indeterminate proliferation of concepts, the unfolding of the contradiction is determinate and productive. (65)

[Before in Russell’s paradox of the non-self-inclusive class, what could be a highest genus here creates a contradiction whose resolution creates such deep problems as to call into question the integrity of the whole system. In Hegel’s system, being, the highest genus, is indeterminate and it intermixes with nothingness. This contradiction however leads to a new concept. This means that Hegel’s system solves important problems in the Aristotle/Russell systems. Their systems could not explain the movement of concepts, and it could not allow for contradictions involved in such cases as phases of transition. Here Hegel’s dialectic can still have a highest class of being (in its pure indeterminacy), and yet it does not have these problems.]

Through this moment of Aufhebung, the problems that occurred within the earlier representational systems are resolved. The contradictory nature of the highest genus, being, becomes instead positive | and productive. (65-66)

[So let’s recap. Zeno argues not that All Is One but rather that The Many Cannot Be. He uses an internal dialectic, (which means that he begins with the notion of the many, and shows that its implications are inconsistent, and hence it contradicts itself.) Hegel likewise sees negation and contradiction to be the motor of the philosophical process, but Hegel invents the aufhebung, which is a productive contradiction. Also, this process for Hegel comes out of the concept itself.]

The further lesson that Hegel draws from Zeno is that this dialectical process is not an imposition on the object (object in the sense of that which is analyzed-dialectic does not presume that the analysand must always be objectival), but rather the natural development of the object itself. For Hegel, this means that the method of dialectic itself is a product of the dialectic of the object itself, rather than being a presupposition of the analysis. Further, we saw that for Russell, unity and contradiction imply one another, hence the need to reject the former to safeguard against the latter. For Hegel, accepting the possibility of contradiction means opening the possibility of a unified, total system. (66)

Somers-Hall will return to Hegel’s philosophy to discuss it further in chapter 5.

 

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

Pt1.Ch2.Sb8 Somers-Hall’s Hegel, Deleuze, and the Critique of Representation. ‘Hegel and 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 8: Hegel and Aristotle

 

Very brief summary:

Hegel’s system is different from Aristotle’s and Russell’s systems in that for Hegel, there is (1) an ambiguity of concepts that breeches the law of the excluded middle, and (2) there is a generative motion between unimplicated concepts. However, like Aristotle and Russell, this movement is not temporal.

Brief Summary:

We will further explore the problems of Aristotle’s and Russell’s hierarchies by examining similar issues in Hegel. There are important similarities between Hegel’s and Aristotle’s systems. For both, a thorough analysis of the empirical leads us to the speculative. Both their systems begin with a necessarily indeterminate concept of being. And for both there is a process of increasing determination. Yet there are important differences between their systems. (1) Aristotle’s unmoved mover is difference from Hegel’s self-movement of being. (2) For Aristotle movement between concepts is no more than that of implication, but there is more generation in Hegel’s sense of the intervanishing of being and nothingness moving to becoming.  So, in Aristotle’s and Russell’s hierarchies, there is no transition or contradiction, where in Hegel, being as indeterminate is not differentiatable from nothingness, and this mixing leads to a movement to a new unimplicated concept of becoming (hence a sort of ambiguity or breach of excluded middle that is not allowable in Aristotle and Russell, and also an account of transition). However, like Aristotle and Russell, Hegel’s movement is not temporal.

Summary

 

Previously we saw how Russell’s and Aristotle’s hierarchical systems rely too much on the principle of excluded middle. This prevents them from being able to explain transition and ring species.

Now Somers-Hall  (SH) turns to Hegel, and he begins by looking at his relations to Aristotle.

Hegel, in his analysis of Aristotle, | forms an image of Aristotle that is very close to that which one might draw of Hegel himself. While Aristotle's system "does not give the impression of its being in construction a self-systemised whole" (LHP, 2, 118), its parts "still form a totality of truly speculative philosophy." Aristotle is "the perfect empiricist" (LHP, 2, 133), in that through an absolutely thorough analysis of the empirical world, we are led back to the idea of the speculative notion. The Aristotle of Hegel is therefore an empiricist who pushes empiricism so far as to arrive at a truly speculative form of knowledge. (62-63)

Also, there important structural similarities between their systems. For both of them, speculative thought begins with the concept of being, and for both of them this concept is necessarily indeterminate. “The Science of Logic begins its deduction with the concept of ‘Being, pure being’ (SL, 82) which, like that of Aristotle is, for thought, ‘pure indeterminateness and emptiness’ (SL, 82).” (63) In Aristotle’s classificational divisions, there is also a dialectic that is

a process of increasing determination, through the addition of differentiae, to the point at which the lowest species can be specified in its essence. This too is the movement of the Science of Logic. The progressive accumulation of determinations allows us to move from the purest, but also the emptiest, of notions, to one that is adequate to the conception of being. (63)

[Recall that in paronymy, things have similar names and similar meanings, even though they are not exactly the same. Paronymy is a type of homonymity (also called equivocity), which is when things share the same name but different meanings. For Aristotle, being and its beings are paronymous, thus also equivocal.] So, SH wonders, is Hegel’s being equivocal like Aristotle’s being?
But Hegel never refers to Aristotle’s problem of the highest genus. In fact, we can find important differences between their systems.

Differences between Aristotle’s and Hegel’s systems:

1) Aristotle’s unmoved mover is very different from the Hegel’s self-movement of being.

2) Aristotle’s implicatory movement between concepts and Hegel’s being and nothingness vanishing into one another and moving to becoming.

We have emphasized how Aristotle's system eliminates the possibility of movement through what Deleuze will call a "mediated concept of difference," but reading the problem of the highest genus in the light of the Principia Mathematica, we also see that this move eliminates the possibility of contradiction. Hegel, on the contrary, is willing to push the question of the indeterminate notion of being to the point where this very notion itself breaks down. Thus, if being is such that "there is nothing intuited in it," this very concept itself will vanish into nothingness: being, as indeterminate, is impossible to differentiate from nothingness. The instability of being, however, is paralleled by a similar indeterminacy of nothingness, which in turn vanishes into being. Thus, in this process of vanishing, a further concept is developed, that of becoming, the movement between the two prior concepts, which shows that the provisional meaning of being and of nothing is for both to be simply this vanishing of one into the other. This provisional result will itself be qualified, since becoming, the unstable unity | of being and nothing, gives way to determinate being, which is a resolved unity of both. Now, what has been presented here is a certain movement between concepts. Of course, in the logics of Aristotle and Russell, movement between concepts is possible, but this movement must purely be one of implication, that is, nothing not already present in the concept can emerge from it. Hegel himself recognizes this distinction between his own system and that of Aristotle. While for Hegel, the movement of the system is a progressive determination of the concept of being, for Aristotle, the process by which the indeterminate concept is reached is one of enumeration and abstraction. (63-64)

But one similarity we might draw between Hegel’s and Aristotle’s and Russell’s systems is that Hegel’s movement is not temporal, as the notion of pure being is logically prior to temporality.

Similarly, while the inability of either Russell or Aristotle to deal adequately with the notion of temporality is an indication for Deleuze of the problematic nature of their systems, we saw that the real root of the problem was not itself temporal. What exactly is driving the Hegelian dialectic becomes clear when we look at Hegel's comments on Zeno's dialectic and compare them with those of Russell. (63)

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

Pt1.Ch2.Sb7 Somers-Hall’s Hegel, Deleuze, and the Critique of Representation. ‘Preliminary Conclusions.’ 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 7: Preliminary Conclusions

 

Very brief summary:

Aristotle and Russell construct hierarchies whose problems derive from the fact that their systems omit a form of difference which would explain cases where the principle of excluded middle does not hold, of example (a) in transitional phases when something has mutually exclusive states (like something being both wood and fire in the transitional phase of its ignition) and (b) ring species where creature A can interbreed with B, and B with C, but not C with A.

Brief Summary:

So far in this chapter we have seen the problems with Aristotle’s and Russell’s hierarchies. For example, it is difficult to speak of the highest category. For Deleuze, these problems arise from the four shackles of mediation: identity (what allows classificational grouping), analogy (comparable relations between concepts), opposition (maximal differences allowing differentiation between species), and resemblance (variational similarities allowing differentiation of individuals in a species). These shackles result from common sense (which calls for partitions between concepts) and good sense (which calls for hierarchical subsumptions). For Deleuze, all four cases miss his notion of a deeper sort of difference. Common sense wants general concepts that are distinguishable from others. This requires clear demarcations, or maximal difference, following the principle of excluded middle, ‘either P or not-P but not both’ (P v –P). This means there is no ambiguity between concepts. However, there are two important cases where this principle does not hold, namely, transition (when something is between states and thus has two mutually exclusive determinations together) and ring species (where a first species can interbred with a middle species, which can interbred with a third species, and yet the first and third cannot interbred. So how do we classify their species?)

Summary

 

Previously we examined Russell’s solution to the paradox of the class of all non-self-inclusive classes. We saw that he distinguishes levels of classification, and one level can only refer to the level below it, and not to itself.

Now Somers-Hall makes some preliminary conclusions. In Aristotle’s system, we cannot define the highest genus, being, because definition requires giving the genus and species, but the highest genus has no greater genus for its definition. [Yet we call both the highest genus ‘being’ and all its members ‘beings.’ Does this mean that ‘being’ and ‘beings’ are synonymous, on account of them sharing both the same name and the same definition? Aristotle instead says they share related meanings and a similar name. They are paronymous.] But we found in our examination of Russell’s and Whitehead’s Principia Mathematica that the problem runs even deeper. For in this case, in order to make a system of classification consistent, it needs to rectify the paradox of the class of all non-self-inclusive sets. Russell’s solution is to say that one level can refer to the one below it, but not to itself. But this makes it impossible to designate a highest class and also to make a universal statement regarding all classes. And when we say we are speaking of all properties of a class, we are implicitly making just as many statements as there are levels under that class.

While Aristotle's logic may prevent the determination of the highest genus, our discussion of the Principia showed that this difficulty is in fact far more serious than it appears in Aristotle's work, as if this highest genus could be specified, then the concept of the totality of the system could only be achieved at the cost of consistency. Thus, within representational logic from Aristotle to Russell and Whitehead, totality and consistency remain mutually exclusive. (61)

[So for Russell, as we noted, when we speak of all the properties of a class, we are implicitly making a statement for every class below it. This means that there is an ambiguity between the levels that allows for one statement to refer to all of them indirectly. In Aquinas, we are not able to define God, or being, the highest category; however, we can specify the relation of beings to being, using analogy. Just as some species is to some genius, so to are beings (or Man) to God.]

As both Aquinas and Russell make clear, and without Aquinas having any direct influence on Russell, the concept of a totalized thinking of being remains a necessity, so in both cases the notion of analogy is brought in to provide the same kind of pseudototalizing effect on the systems. For Aquinas, this allows us to talk of God and man in the same terms, regardless of their differences in being. For Russell, systematic ambiguity allowed us to refer to a series of statements of different types as if they were one universal statement through structural analogies between them. (61)

We also saw that both Aristotle and Russell were unable to explain change, because there were only able to say something about states at some moment, and not about the transition between states.  
For Deleuze, these issues spring from what he calls the “four shackles of mediation (DR 29)” (61): identity, analogy, opposition, and resemblance.

Deleuze’s Four Shackles of Mediation:

1) Identity: the undetermined concept that unifies the system and is presupposed in the form of the highest genus [perhaps it is something like the principle that allows anything to be a class, like saying, things can be unified into groups as if there is a higher identity for all of them, even though there can be no explicit specific highest identity unifying them all.] "This is present for Russell as the universal statement that cannot be more than a verbal pronouncement, one that is comprehensible but cannot be explained through the system itself.” (61)

2) Analogy: the “relation between the ultimate determinable concepts, that is, the categories for Aristotle or the isomorphic statements of variable type for Russell” (61).

3) Opposition: [what distinguishes things from one another] “Opposition deals with the relations between determinations within concepts and thus refers to the differentiae, which relate the determinations of the genus to each other through a process of exclusion, and to the clear specification of the predicate for Russell, which delimits a class from other classes through purely bivalent criteria.” (61)

4) Resemblance: Resemblance allows for the differentiation of individuals sharing the same species. For Aristotle, essence is what allows for this sort of resemblance, and we see something similar in Russell’s theory of change, which explains how the same thing differs at different moments of time. (61d)

Deleuze says that the source of these problems is common sense and good sense, which we discussed earlier when discussing Kant. Common sense again refers to the partitions of concepts. In the context of Kant, good sense referred to subsumption of the predicate under the subject, but now in this context it refers to the construction of hierarchy itself (62).  The two functions are both present in Aristotle and Russell. But in both cases there are problems with what does not fit explicitly in their systems.

What is at issue in both Russell and Aristotle is what is absent from their systems. Identity provides a concept that is inexplicable, analogy provides an isomorphism between elements within a totality that cannot be defined, opposition provides a stability that is contradicted by phenomena such as ring distributions of species, and resemblance merely shows the gap between differing temporal individuals rather than explaining it. (62)

For Deleuze, the element getting overlooked in all four cases is the concept of difference. Common sense wants a general concepts. This requires a clear demarcation between concepts.  In order for the demarcation between concepts to be clear, we need the law of excluded middle (Either P or not-P, but not both) P v –P, which makes use of maximal difference [because they are mutually exclusive, the terms could not be more clearly different, for otherwise they would be ambiguous]. [But change involves the ambiguity of states. In the transition from one state to the next, something is predicated simultaneously with two mutually exclusive states. Also, there are cases like the ring species that also make it unclear whether or not one animal is clearly the same species as another. For, A is a fellow species with B, and B is a fellow species with C, but A and C cannot interbred. So if A and C are in separate species, then what species is B in? But how can two types of animals A and C be in the same species but be unable to interbreed? So there does seem to be ambiguous cases of classification where something is both P and not-P at the same time. There is a sort of middle that must be included. There is the transitional state between P and not-P when something is both at the same time, and there is the intermediary links in ring species that are both in and not in the species on either end of the chain.]

This makes difference essentially oppositional and prevents the understanding of temporality, as well as the diversity present in indeterminate species ( the issue of ring distributions applies just as much to Russell's system as to Aristotle's) . Static states form the entirety of the system, leaving no space for either generation or transition. The points where true difference shows itself are in the places where representational logic breaks down, in the movement between these oppositional points, in the chasms that appear within the system . "Difference ceases to be reflexive and recovers an effectively real concept only to the extent that it designates catastrophes: either breaks of continuity of the series of resemblances or impassable fissures between analogical structures" (DR, 35). (62)

Deleuze’s difference is not oppositional or maximally different as with the difference in the law of the excluded middle. We will discuss Deleuze’s difference in chapter 6. Now we turn to Hegel’s possible response to the systems of identity in Aristotle and Russell. (62)

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