Somers-Hall, (Ch.4), Deleuze’s Difference and Repetition, ‘Chapter 4. Ideas and the Synthesis of Difference’, summary

by Corry Shores
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[The following is summary. All boldface, underlining, and bracketed commentary are my own. Proofreading is incomplete, so please forgive my typos and other distracting mistakes. Somers-Hall is abbreviated SH and Difference and Repetition as DR.]

Summary of

Henry Somers-Hall

Deleuze’s Difference and Repetition:
An Edinburgh Philosophical Guide

Chapter 4. Ideas and the Synthesis of Difference

 

Very brief summary:

Chapter 4 characterizes the sorts thinking that deal with the fundamental intensive level of reality and also the Ideas that are involved in this thinking. An Idea has two important features: 1) it is made of indeterminate parts that are determined by means of a binding differential relation, and 2) it can find many various spatio-temporal actualizations. The differential in calculus is determinate only through reciprocal relations, and it describes the basic structure of Ideas. There are three other examples that more or less fulfill the two criteria of Ideas: 1) Epicurus’ and Lucretius’ atomism, since atoms become determinate only when in vibratory collision and many combinations are possible, 2) Geoffroy’s homological anatomy, where there is a transcendental template whose parts gain sense only in their combined network and many instantiations can be actualized from it, and 3) the Marxist notion that there are invisible networks of relations that underlie and determine the social, political, and economic surface conditions. Learning happens when first we encounter a problematic situation, then on the basis of a question, we gather fragments to form an Idea, implicated within which are many actualizable solutions. The discordant exercise of our faculties is itself a solution to the problem of unrepresentable Difference that we encounter. Also, negation is not a part of the fundamental levels of reality and thinking. It comes about either when we formulate propositions, which are negatable, or in actualization, which generates determinate properties that can oppose one another. Actualization is dramatized, meaning that it begins with intensive variations in the speeds and distributions of development, then secondly these form the extensive and qualitative properties, but all this occurs dramatically in an unpredictable way.


Brief summary: 
Now that we know what thinking should not be like, we look at how Ideas and thinking should be understood. Deleuze thinks that Ideas should not be formulated propositionally, in which case it would take on empirical determinations. Kant’s Ideas at first seem to fulfill this requirement, but in the end they do not. Deleuze characterizes the Idea as having three intrinsically related moments, which are expressed in an unorthodox tradition in calculus. Bordas-Demoulin sees the differential as undetermined, since in the differential formulation for the circle we get the essence of a circle without needing reference to particular circles, as with Descartes’ algebraic formulation. Maimon thinks that the differentials involved in intuitive givenness by themselves are not sensibly determined but gain it when they are differentially related. In this way he describes the conditions for determinability. And Wronski is concerned with notable moments in a variation that are numerically determinable, thus he shows the role of determination. Other fields might have Ideas with this structure, but only calculus looks at the structure itself. Ideas emerge under three conditions: the parts gain determination only through their differential relation, they then lose their independence, and the Idea applies to a variety of spatio-temporal differential relational situations in the world. Deleuze offers three examples. The first is Epicurus’ and Lucretius’ atomism. Here the atoms are insensible until colliding, and they can take many various arrangements of combination. The second is Geoffroy’s homological model of anatomy. Here there is a template of sorts that is really just made of differential relations of parts that take a wide variety of instantiations in the different species. The third is Marxist social ideas. Here we are to think of an invisible network of underlying relations that are responsible for the surface conditions in the political, economic, and social situation. Ideas also have three dimensions: vertical (Ideas can be rearticulated in more basic fields), horizontal (one Idea can find different variations within one area), and depth (one Idea can underly seemingly different Ideas in otherwise incommensurable domains). An Idea is virtual, and it explicates into actuality. It is not possible, since the possible is a deprivation of reality, but the Idea has no such deprivations.  There are three stages in the formulation and actualization of Ideas, and this is learning. First we encounter a problematic situation. Secondly we gather little Idea fragments, which are differential relations, that we combine to form the Idea. We do this in part by means of the question, which creates the framework for how the Idea should be composed and what sorts of actualizations it implicates. Thirdly this Idea is like a map or graph implicated many actualizable solutions, which may find determinate actualization. Our body itself is a solution that evolution has found to certain problems. Our faculties also, insofar as they operate discordantly, are a solution to the problem of the unrepresentable fundamental Difference, which can only be thought about through this discordant exercise. Negation is not found at the levels of the problem or the Idea. It comes about in two ways. The first is when we formulate the problem propositionally, which allows us to negate the sentences. The second is in actualization, which creates determine properties that oppose one another. This actualization however happens by means of dramatization, since development is unpredictable and involves a complicated network of “actors”. Actualization is first spatio-temporally intensive, as it involves intensive variations in developmental speeds and distributions. Then only secondly is it extensive and qualitative.

Summary

(4.1 Introduction: Kant and Ideas) Deleuze seeks a model of thinking where thought does not consist of propositional solutions that relate to empirical objects. So Ideas for Deleuze should not have an extrinsic relation to the empirical world. Instead a) they should be intrinsically related, while b) maintain a difference in kind such that thinking on the level of Ideas is not done using empirical determinations. Kant’s Ideas are problematic since they have no empirical object, but this also means they have no propositional solutions. So they would seem to involve a sort of thinking that deals with problems that are not understood in terms of their possible solutions as articulated in propositions using empirical determinations. However, in the end, the Ideas for Kant receive empirical determinations and thereby extrinsically relate to the empirical world. (4.2 Ideas and the Differential Calculus) Deleuze thinks that the Idea has three intrinsically related moments, namely, indetermination, determinability, and determination. One place where they obtain such a relation is in an unorthodox tradition in the history of calculus that grants the differential its proper metaphysical status. The three main thinkers in this tradition are Bordas-Demoulin, Maimon, and Wronski. They will relate the three moments intrinsically in this way: the differentials dx and dy are by themselves undetermined, but they obtain their determinability when brought into differential relation, which can then be determined numerically. Bordas-Demoulin shows how the differential formulation for the circle gives us its essence, since ydy + xdx = 0 tells us that its points tend back steadily to its point of origin. Descartes’ alternative formulation x² + y² – R² = 0 only tells us what specific values of a circle are, and thus it requires determination. But since the differential formula tells us what circles are without needing to deal with specific ones, it sees the differential as being undetermined. For Maimon, the differential terms dx and dy by themselves cannot receive sensible determination, but they can when they are differentially related. In this way he gives the conditions for determinability. Wronski is concerned with moments in a variation that are drastic while also being numerically determined, thus he supplied the notion of determination. Again, the differentials begin undetermined on their own, but they are determinable when differentially related, which creates a value that may be numerically determined. (4.3 Ideas and the Wider Calculus) The Idea for Deleuze has these structural features, and differential calculus brings that structure to light. Other fields generate Ideas, but unlike calculus they might not explore the structure of Ideas themselves. An Idea is a multiplicity since it is composed of many differential relations. An Idea emerges under three criteria: 1) the parts gain their determination through their differential relation, but they are undetermined prior to this relation, 2) after differentially relating, they lose any independence they might previously have had, and 3) the Idea that emerges applies to a variety of spatio-temporal differential relations in the world. (4.4 First Example: Atomism as a Physical Idea) Deleuze gives three examples in the history of philosophy that seem to fulfill these three criteria for the emergence of the idea. 1) Epicurus’ and Lucretius’ atomism. The atoms that make the world are falling downward too quickly to be perceived, thus on their own the parts are undetermined. They only become sensibly determined when they collide repeatedly and vibrate in a general region. Thus the parts gain their determination through their differential relation. And since they may enter into a variety of relations, they apply to a variety of spatio-temporal configurations. Deleuze is not completely satisfied, since this model understands determination too much as sensible determination. (4.5 Second Example: The Organism as Biological Idea) 2) The second example is Geoffroy Saint-Hilaire’s homological model of evolutionary anatomy. The alternative model by Cuvier, comparative anatomy, gives the same name to different species’ parts that are similar in form and function. Thus a fish fin and a human arm have these different names. But as species evolve there might be evolutionary connections between these parts, even though their form and function mutated. Cuvier’s model will miss these connections. For Geoffroy, however, there is a transcendental structure that is merely a set of relations between parts. All species, then, have these relations, even though their parts differ. Thus it is the same relational juncture in the transcendental structure that in fish takes the form of a fin and in humans an arm. So, the parts in the transcendental model on their own have no sense or conceptual content were they taken on their own, but they gain some conceptual determination when they are understood as occupying their place in the whole total network of differentially related parts, and there are many possible evolutionary instantiations of this transcendental structure. It would seem then that Geoffroy’s model fulfills Deleuze’s requirements for an Idea, but Deleuze thinks that it is still too much tied to actual instantiations. (4.6 Third Example: Are there Social Ideas, in a Marxist Sense?) 3) The third example is Marxist social ideas. There are certain visible surface structures like laborers and means of production. Althusser thinks that Marx is not so concerned with these but more so with deeper, invisible, unspecifiable political and ideological relations that are responsible for the generation of the visible surface structures. These deeper structures also fulfill the three requirements for an Idea, since the parts of these deeper structures have no sense taken independently, but they gain it as a network of such relations, which can take on many different manifestations under different historical circumstances. (4.7 The Relations of Ideas) There are three dimensions of varieties of Ideas. 1) Vertical: an Idea for a problem or solution can be reformulated in a more basic or general domain. So biological ideas might be reformulated using chemistry concepts, which can be reformulated into physics notions, which finally might be reformulated in mere mathematics. 2) Horizontal: here an Idea finds variations of itself within one domain. For example, Geoffrey’s transcendental structure finds many different arrangements (perhaps for creatures with different basic structures, like plants and vertebrates), each being its own Idea. 3) Depth: two systems might seem to be very different and to have very different Ideas might on a deeper level share the same Idea. Geometry and arithmetic for example seem very different, since the one can represent irrational values simply and the other cannot. But on a deeper level they share fundamental structures and thus the same Idea underlies the seemingly different Ideas in each system. (4.8 Essence, Possibility and Virtuality) Ideas for Deleuze become actualized, but we are not to understand them as if there were essences in the traditional sense of the term. For Aristotle the essence is obtained by removing everything that is inessential. The essence for Bergson however is something like the combined network of all actualizable manifestations of the Idea, which are folded in together in a complicated way. His analogy is color. White light is like the essence of color, since it can be broken down into any actualizable color, all of which when recombined form white light. This notion of the Idea involves the concepts of virtual, actual, and possible. The Idea is virtual, and it explicates into actualities. The virtual is not the possible, since the possible is the real deprived of actuality. However the virtual is fully real and lacks nothing, since it implies its infinity of actualizable instantiations. The virtual has three important properties: 1) it is real without being actual, since it is responsible for the genesis of actualities 2) it is complete without being entire, since it contains all actualizable instantiations (making it complete), but since they are infinitely many and various, it can never be exhausted by its actualizations (making it not entire). 3) it is differentiated without being differenciated, since it is composed of a network of differential relations (making it differentiated), but these relations and its terms cannot be ascribed predicates (and so it is not differentiated). (4.9 Learning and the Discord of the Faculties) Learning for Deleuze does not involve drawing inferences from propositions. Instead, we learn when we engage with the problematic situation at hand, then take from many sources little Idea fragments in the form of significant relations in the situation, and combine them into a map or graph of sorts that implies a wide variety of directions to pursue, which is the Idea, then lastly to develop solutions that can change the conditions of the original situation in such a way as to solve its problematic elements. Evolution has already done such a thing, since each of our organs is like a solution to certain problems. Likewise, each faculty is like such a solution. Now, the world is composed fundamentally not of distinct recognizable entities but rather with intensive differences. This means that were our faculties to operate concordantly to recognize a common object, they are not thinking about this fundamental layer of reality. Instead, their discordant exercises, whereby each has its own object of a different kind, enables such a thinking of intensive difference, and thus the discordant exercise of the faculties is like a solution to the problem of Difference itself. (4.10 The Origin of Ideas) So the problem is found in our encounter with an intensive field of differential relations that we cannot process using our given resources. We then formulate an Idea by putting fragments together, and on its basis we find solutions to the problematic situation we originally encountered. What relates the original problematic solution to the Idea we come to form is the question, which sets a particular framework for the construction of the Idea. Deleuze uses the metaphor of the dice throw to illustrate this. The problem is like being in a situation that calls for the throw of the dice, which will be the solution. The dice themselves are the Idea, since they contain the actualizable outcomes, only one of which at a time is in fact actualized. Also, the dice faces can be redesigned, just as the Idea can be reformulated. And the continual reformulation of the Idea is like the repetition of difference. (4.11 The Origin of Negation) For Deleuze, negation is not a part of how things are generated. However, there can be negation after they are generated. The problematic situations do not have negation in them, nor do the Ideas and the actualized solutions. We get negation however when we formulate the problems propositionally, which allows “it is not the case that…” to be affixed to them. This propositional denial is one origin of negation. But it misleads us into thinking that there is negation in the fundamental levels of reality. There is another origin of negation, which is the process of differentiation by which distinct actual states of affairs are generated. But this negation is secondary to the non-representable fundamental structures where there can be no negation. (4.12 Actualisation) Implicated in the Idea are many actualizable instantiations of the Idea, which serve as solutions to problems. But there is dramatization in actualization. It is like the development of egg, where new stages are not predictable from prior ones, and also there are many interrelated parts that interact complicatedly like dramatic actors do. Actualization in this form of dramatized development is initially spatio-temporally intensive, because it involves intensive variations in the accelerations of development and in the distributions of elements. Then, as a result of the intensive spatio-temporal dynamics, extensive and qualitative features come about secondarily.




Citations from:

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

Or if otherwise noted:

DR:
Deleuze, Gilles. Difference and Repetition, trans. Paul Patton, New York: Columbia University Press, 1994/London: Continuum, 2004.

 

 

 

 

Somers-Hall, (4.7), Deleuze’s Difference and Repetition, ‘4.7 The Relations of Ideas (186–7/235–6)’, 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]
[Henry Somers-Hall’s Deleuze’s Difference and Repetition, Entry Directory]

 

[The following is summary. All boldface, underlining, and bracketed commentary are my own. Proofreading is incomplete, so please forgive my typos and other distracting mistakes. Somers-Hall is abbreviated SH and Difference and Repetition as DR.]

Summary of

Henry Somers-Hall

Deleuze’s Difference and Repetition:
An Edinburgh Philosophical Guide

Part 1
A Guide to the Text

Chapter 4. Ideas and the Synthesis of Difference

 

4.7 The Relations of Ideas (186–7/235–6)

 

 

Brief summary: 
For Deleuze, Ideas are varieties including sub-varieties, and there are three possible “dimensions” of these sub-varieties. 1) Vertical: an Idea for some problem/solution can be reformulated in a “higher” (that is, more basic or general) domain; for example, the Ideas of biology can be reformulated in chemistry, which can be reformulated in physics, which can be reformulated in pure mathematics. 2) Horizontal: an Idea for some problem/solution within one domain can be reformulated or re-instantiated within that domain and also within that same problematic, but in so doing produce other Ideas as a result. Thus in Geoffrey’s anatomy, there is one Idea, the transcendental template for the skeletal arrangement of all vertebrates, for example, and each instantiation in actual species is itself a new Idea, since it has different significances to the ways that the parts relate (and thus it has different “singular points” which would define different Ideas). 3) Depth: Two systems which might seem to instantiate different Ideas given their fundamental incompatibilities in fact on a deeper structural level share the same Idea. For example, irrational values make geometry and arithmetic seems fundamentally incommensurable, since geometry can express them as cuts in a line or figure, but in arithmetic the decimals are interminable and thus not so straightforwardly expressible. However, a closer study of the axioms of both systems reveals that on a deeper level they share fundamental structures.

 

 

Summary

Previously Deleuze has been characterizing and exemplifying his notion of the Idea. Now we ask, how do Ideas relate with one another? (SH 148). We first note that Deleuze claims Ideas are varieties containing within them sub-varieties (SH 148, citing DR 187/235). SH says this claim comes from two prior observations. 1) Ideas can be further differentiated to produce Ideas of Ideas, just as differential functions can be further differentiated [although I am not sure yet how this works for Ideas. Perhaps what is discussed below are examples of the further differentiation of Ideas into other Ideas], and 2) Ideas can have various sub-varieties depending on the domain in which they are expressed: “Ideas are related to the domain in which they are solved. This implies that the same Idea can be expressed in different actual situations, depending on what kind of solution we are looking for” (SH 149). Now, Deleuze says there are three dimensions of variety for Ideas: a) a vertical dimension: the Ideas as expressed in one field can be expressed another way in a more basic field [I assume this would be like biology’s problems/solutions being expressed in chemistry, which can then be expressed in physics, which can then be expressed in just mathematics, but I am not sure. This is what SH writes: “there are three ‘dimensions of variety’, the first of which is the ‘vertical dimension’ (DR 187/235). This depends on what the elements and relations we are concerned with are. Depending on whether we conceive of the elements as atoms, bones or relations of production, the solution we arrive at will be expressed in the fields of physics, biology or social theory respectively. While we have here different ‘orders’, these orders are still interrelated, in that Ideas of physics can be ‘dissolved’ in higher order problems such as those of biology, and likewise social theory will find itself ‘reflected’ in the structure of the individuals that compose it” (149).] b) a horizontal dimension: [I do not quite follow this one. Let me quote it first:] “The second, ‘horizontal’ dimension deals with ‘degrees of a differential relation within a given order’ (DR 187/235). As we saw in 4.2, by repeatedly differentiating an equation, we can find ‘singular’ points along a curve where the nature of the curve changes. Now, the same Idea can give rise to Ideas with different singular points. Deleuze gives the example of conic sections to explain this concept. In geometry, we can generate a curve by cutting a cone with a plane, just as if we cut a cylinder in half, we would find, on the surface of the cut (the section), a circle. Now, if we take a section of a cone, depending on the angle to the cone at which we take the section, we will have a different type of curve:

[Image from wiki. Similar to figure 2, SH 149]

| Each of these curves has different singular points (points where the gradient is 0, null or infinite), despite the fact that all of the curves are created from the same fundamental shape. In a non-mathematical field, we can note that Geoffroy’s comparative anatomy relies on the fact that the same structure is to be found in the relations between the bones of all animals. Nevertheless, the singular points will vary within species, so the same bones that attach the jaw to the skull in fish are found in the inner ear in mammals” (149-150). [Although I am not following so well, the basic idea seems to be that what is essential are singular points. It seems in the case of the motion of objects, that when we look at changes in velocity, we are looking at the change of a change (that is, the change of position in relation to time). But when we look at a higher order of differentiation, we are looking at acceleration, which is a change of a change of a change, that is, the variations in velocity are the moments of acceleration. And there will be singular points where that acceleration is significant for some reason. Then there is the example of conic sections, which I am not quite getting. Perhaps it is just a metaphor or analogy. Let us begin with it as that. One singular procedure of cutting gives us various shapes, each with very different singular points in the mathematical sense just described above. Analogously, one Idea has many different instantiations within one field, each having their own analogous sort of singular points, somehow. Perhaps instead the cone example is meant to be taken literally. In that case, perhaps the notion is the following. In geometry, we can think of a geometrical field of variation, like the way that the points on the surface of a cone vary from place to place and relate differently throughout. We have the problem of, what shapes do its cuts make? And we find that different sorts of cuts give different sorts of shapes that each themselves have their own different singular points, meaning that each such cut differentially relates its parts in its own unique way, and thus each is itself an Idea that is a sub-variety of the larger Idea of the cut cone. Then we have the example of Geoffrey’s anatomy. Here we have one Idea, the transcendental structure, but depending on which species it is actualized in, it will have different singular points, which evidently are any given relation between the parts.] c) as dimension of depth [I am not not familiar with the example, so I do not grasp this one in a profound or clear way. The overall idea seems to be that an Idea can have a sub-variety in depth when two fundamentally incompatible systems in fact share deeper structures, and thus the deeper structure would be the Idea of a sub-variety under the dimension of depth. Perhaps the example can be presented in the following way. Consider how geometry seems to be concerned firstly with lines for example, which secondarily can be determined with numerical values assigned to its points. So we have a line, and we arbitrarily assign its left-most point the value zero, and its right-most side the value of 10, and we can further subdivide the line, each time secondarily assigning numerical values corresponding to proportions of the division. So half is 5, half of that 2.5, and so on. However, there are certain divisions which will not produce a numerical determination. For example, if we divide it according to the golden ratio, we will not be able to express it numerically, since the decimals would go on without termination. This tells us there is a fundamental incompatibility between numerical arithmetic and geometry, since geometry works with continuous magnitudes and arithmetic with discrete ones, and the two systems are not commensurable in cases of irrational values. However, the Bourbaki mathematicians also seem to have discovered that underneath the axioms of both systems are certain shared structures, which are like the deeper Ideas that are sub-varieties of the seemingly incompatible Ideas found within each system.]

Deleuze explains the final dimension of variety, that of depth, with an example from the mathematical theory of groups. He gives the example of ‘the addition of real numbers and the composition of displacements’ in this context (DR 187/236). As the structuralist mathematical collective, Bourbaki, noted, the addition of real numbers and the composition of displacements traditionally belong to two very different fields of mathematics, since one involves discrete units, and one continuous measurement [the following up to citation is Bourbaki quotation]:

quite apart from applied mathematics, there has always existed a dualism between the origins of geometry and of arithmetic (certainly in their elementary aspects), since the latter was at the start a science of discrete magnitude, while the former has always been a science of continuous extent; these two aspects have brought about two points of view which have been in opposition to each other since the discovery of irrationals. (Bourbaki 1950: 221–2)

Bourbaki note, however, that underneath the surface structures of the specific axioms of these different branches of mathematics, we can discern structures that occur in both branches, provided the elements of each branch are understood in a sufficiently undefined manner. Thus, certain relations may hold between elements that are obscured by further specifying their nature. Underneath the structures of geometry and arithmetic are deeper structures which they both share.
(150)

Citations from:

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

Or if otherwise noted:

DR:
Deleuze, Gilles. Difference and Repetition, trans. Paul Patton, New York: Columbia University Press, 1994/London: Continuum, 2004.

Bourbaki, Nicholas (1950), ‘The Architecture of Mathematics’, trans. Arnold Dresden, in The American Mathematical Monthly, 57, 221–32.

Image credits:

Conic Section.
https://en.wikipedia.org/wiki/File:Conic_Sections.svg

 

 

 

 

Somers-Hall, (4.5), Deleuze’s Difference and Repetition, ‘4.5 Second Example: The Organism as Biological Idea (184–5/233–4)’, 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]
[Henry Somers-Hall’s Deleuze’s Difference and Repetition, Entry Directory]

 

[The following is summary. All boldface, underlining, and bracketed commentary are my own. Proofreading is incomplete, so please forgive my typos and other distracting mistakes. Somers-Hall is abbreviated SH and Difference and Repetition as DR.]

Summary of

Henry Somers-Hall

Deleuze’s Difference and Repetition:
An Edinburgh Philosophical Guide

Part 1
A Guide to the Text

Chapter 4. Ideas and the Synthesis of Difference

 

4.5 Second Example: The Organism as Biological Idea (184–5/233–4)

 

 

Brief summary: 
There are three critical features of “the Idea”: 1) its parts by themselves are undetermined, but 2)  become so through and by their reciprocal relations, of which 3) there is a great variety of possible spatio-temporal actualizations. The second of Deleuze’s three examples is Geoffroy Saint-Hilaire’s homological model of evolutionary anatomy. In Cuvier’s comparative anatomy, parts that are similar have similar names, but when they have dissimilar form and function, they get different names. Yet, as species evolve from other species, they will have certain parts whose form and function have altered, but which maintain the same relational place in the entire system as their prior instantiation did. So when we only classify the parts based on form and function, we lose a sense of their evolutionary descent. Geoffroy’s alternative model of anatomy, however, keeps these evolutionary links. For him, there is a transcendental structure, which is a template not for the parts themselves but rather for their relations. Each instantiation in different species will have different forms and functions, but the parts will also maintain the same relations to the other parts. So for Cuvier, the fin of a fish and the arm of a man are different anatomical parts, given that they look very different and they serve different roles. However, for Geoffrey, they are analogous in their structural relation to the rest of their respective skeletons, and thus his model allows us to see the evolutionary descent. Geoffrey’s model also exhibits the three traits of the Idea, since 1) the parts have no sensible or conceptual determination on their own in the abstract “transcendental” template, but 2) they gain determination when understood in terms of the basic relations between parts, and 3) many possible instantiations of these relations have and still can actualize in the evolution of species. Deleuze thinks that Geoffrey’s model is still too tied to actual instantiations, but that genetics is an improvement, since it is less so.

 

 

Summary

 

Previously Deleuze gave his first example of the Idea. The second example

is derived from a nineteenth-century debate over the nature of the organism. This was the debate as to whether comparative anatomy should understand the structure of organisms in terms of what are known as analogies or in terms of homologies
(SH 144-145)

[For more on this topic, see these very excellent sections of Somers-Hall’s Hegel, Deleuze, and the Critique of Representation. Dialectics of Negation and Difference: Pt3.Ch8.Sb6 ‘Deleuze, Geoffroy, and Transcendental Anatomy’ and Pt3.Ch8.Sb7 ‘Teratology and Teleology’. Selected parts and more elaboration can be found in the comments section to the entry for section 1.8 of Deleuze’s Difference and Repetition.] SH explains:

For traditional (and pre-evolutionary) comparative anatomy, the names of the parts of animals are, to a certain extent, derived analogically from other animals, archetypally with man. On a model dating back to Aristotle, we define what an organ is by looking at the functional role it plays in allowing the organism to perpetuate itself. Parts are thus defined by their relationship to the whole. The importance of this relationship is made clear by one of the most important comparative anatomists of the nineteenth century, Georges Cuvier, who claims that ‘it is in this dependence of the functions and the aid which they reciprocally lend one another that are founded the laws which determine the relations of their organs and which possess a necessity equal to that of metaphysical or mathematical laws’ (Cuvier, quoted in Coleman 1964: 67). When the function or form of the parts differ, however, a different term must be assigned to the part in question. Thus, although there is a similarity between the fins of a fish and the arm of man, on a teleological account, the functional and structural differences mean that different terms must be applied to each. This teleological account proves itself to be problematic in terms of evolutionary theory, since evolution often involves the change of function of the same structure between different creatures.
(145)

[I might be missing the point, but it seems to be that an evolutionary theory needs to be able to account for the chain of development from one species to another, with (at least some of) the anatomical parts of the descendent being evolutionary variations on those of its ancestor. And, those variant parts may also serve a completely different function. In Cuvier’s system, we would give that anatomical part a different name, but in doing so, we lose a sense of the evolutionary descent from its ancestor. What we  need instead is model of anatomy which allows us to better grasp the lines of evolutionary development despite the stark differences in function and form of the parts from one species to its evolutionary descendent. Geoffroy St. Hilaire had a different way to understand the evolution of the anatomical parts, which proves better for this task. For him, we are to think of a basic template of a structure not for the parts themselves but instead for their relations. Many animals then are variations of this basic template, with drastic variations in the form and function of the parts, while still these parts are analogous to one another. Let us look at a diagram from a book that is making a similar point.

“The hand and the arm of man are similar to the hand and arm of the ape. We find the same plan in the forefoot of the rat, the elephant, the horse and the opossum. We can identify the same parts in the forefoot of the lizard, the frog (fig 3), and even, though less certainly, in the pectoral fins of fishes. Comparison does not end here. We find similarities in the skull and back bones of these same animals; in the brain; in the digestive system; in the heart and blood vessels; in the muscles” (Morton p.8).

“Fig. 3. Limb skeletons of extinct and living animals, showing the homologous bones: 1, salamander; 2, frog; 3, turtle; 4, Aetosaurus; 5, Pleisiosaurus; 6, Ichthyosaurus; 7, Mesosaurus; 8, duck. (After Jordan and Kellogg.)” (Morton p.8)

In this original text, the author is making a point about comparative anatomy, which it seems is different from Geoffrey’s model. However, we still see in this diagram how the anatomical parts each themselves are different in form and function, but their overall relations to one another are maintained in each case. Thus, the same part that becomes a fin on a fish also becomes an arm or leg on a human.]

Now, one of the key conceptual developments that made the theory of evolution possible was Geoffroy St. Hilaire’s positing of homologies between different parts of organisms. Rather than seeing an organism as defined by the form or function of parts, Geoffroy, a contemporary of Cuvier, saw it as defined by the relations between parts. By focusing on relations rather than functions, Geoffroy was able to provide an account that explains one of the key results of evolutionary theory – that the same structure can change its function in different organisms (fins becoming arms, for instance). Geoffroy didn’t relate organisms to one another directly to generate his account of homologies, but rather posited a transcendental structure of an ideal organism that other organisms were instantiations of (he called his approach ‘transcendental anatomy’).(SH 145)

[SH then moves to what Deleuze sees in Geoffroy’s model. I do not follow it perfectly well, so I will quote it below. It seems the point is that the transcendental structure is somehow like a field of differential relations, and as a whole the model has the three traits of an idea: 1) On the abstract level of the “transcendental structure,” each of the “parts” is really like a juncture of relations between possible instantiations. So in the transcendental model there is a relation which would be between parts that in the instantiation of the human is the relation between the arm bones and the rest of the skeleton, while in the instance of the fish the relation stands between the fin and the rest of the skeleton. But these abstract place-holders in the transcendental structure have no meaningful “content” by themselves. Thus the parts are indeterminate on their own, but have some sensible meaning when understood in terms of how they form relations. And so, 2) the elements are determinable only in their reciprocal relations. And 3) there are countless evolutionary variations of these same differential relations. The last point about genetics I am not grasping so well. It seems that Deleuze is saying that for Geoffroy, since the homologies are always actual, that they are too much about the actual to constitute a good example for the Idea. However, the field of genetics perhaps is somehow more about the field of differential variation on the level of coding and thus is a better example for the Idea. Please read to be sure of the meaning:]

Deleuze’s interpretation of Geoffroy’s work rests on what he calls Geoffroy’s dream, ‘to be the Newton of the infinitely small, to discover “the world of details” or “very short distance” ideal connections beneath the cruder play of sensible and conceptual differences and resemblances’ (DR 185/233). He claims that what Geoffroy is aiming at with his emphasis on connections is a field of differential elements (the ideal correlates of the bones) forming specific types of relations (the connections | which are central to Geoffroy’s account). On this basis, Deleuze claims that Geoffroy’s transcendental anatomy functions like an Idea, with its three characteristics. The elements of the Idea ‘must have neither sensible form nor conceptual signification’, and transcendental anatomy fulfils this requirement due to the fact that what is important is not the sensible properties of the bones, which vary in different creatures, but their relations. Second, ‘these elements must be determined reciprocally’, which means that what is central is not the bones themselves, but the connections they hold with other bones, what Geoffroy calls the ‘unity of composition’. Third, ‘a multiple ideal connection, a differential relation, must be actualised in diverse spatio-temporal relationships, at the same time as its elements are actually incarnated in a variety of terms and forms’. Deleuze emphasises that homologies do not exist directly between actual terms, ‘but are understood as the actualisation of an essence, in accordance with reasons and at speeds determined by the environment, with accelerations and interruptions’ (DR 184/233). That is, we discover a homology between two creatures by recognising that the actual parts of both organisms are actualisations of the same transcendental essence, the unity of composition, rather than by an analogical correlation of actual terms, as in comparative anatomy. As Deleuze notes, this approach finds its parallels in genetic theory, where genes gain their significance from their relations to one another. In fact, genetics represents an advance over Geoffroy’s account in that for him the transcendental correlates of bones, according to Deleuze, ‘still enjoy an actual, or too actual, existence’ (DR 185/233–4). The Idea in this case therefore allows us to determine in what way diverse phenomena (different organisms) are related to one another.
(145-146)

Citations from:

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

Or if otherwise noted:

DR:
Deleuze, Gilles. Difference and Repetition, trans. Paul Patton, New York: Columbia University Press, 1994/London: Continuum, 2004.

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

 

Coleman, William (1964), Georges Cuvier: Zoologist, Cambridge, MA: Harvard University Press.

Morgan, Thomas Hunt. A Critique of the Theory of Evolution. Princeton/London: Princeton University Press / Humphrey Milford Oxford University Press, 1916.
Available at the Internet Archive:
<https://archive.org/details/critiqueoftheory00morgrich>

 

 

 

Somers-Hall’s Hegel, Deleuze, and the Critique 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

 

Very, Very, Very  Brief Summary:

Deleuze’s subrepresentational self-differentiation is superior to Hegel’s infinite representational self-differentiation in solving the problems that self-identity causes in Kant’s and Aristotle’s (likewise Russell’s) representational systems.

 

Very, Very Brief Summary:

Self-identity in representational systems leads to problems in explaining the highest part, the lowest part, and the compositional principle of Kant’s, Aristotle’s (and Russell’s) representational systems. Hegel’s and Deleuze’s principles  of self-difference can solve them. Hegel’s productive self-contradiction and sublation suffices logically but not in application to evolution. Deleuze’s non-oppositional subrepresentational difference however does suffice in this regard.

Very Brief Summary:

A strict view of logical identity leads to problems in Kant’s and Aristotle’s representational systems. The unities of and between concept and intuition that enable our subject-predicate judgments of the world for Kant are based on the unity of a transcendental self. But Sartre shows this is merely a convenient assumption, because for him the unity of consciousness of the object is based on the continuous unity of the object’s givenness. For Deleuze the grounds for our judgments are based on neither the unity of the subject, of the concept, nor of the object, but rather on the unity of incompossible undetermined predicates implying a subject with virtual variations. As it is made of the integration of incompossibilities, it lacks the coherence of self-unity necessary for representation. Another question regards the representational nature of the categories we use for judgment. Aristotle and Russell have hierarchies, but because they exclude self-reference and excluded middle, the very foundations (largest parts), compositions of individuals (smallest parts), and method of composition (division/class inclusion) of their representational systems are problematic and unrepresentable within the systems themselves. Hegel and Deleuze have different ways of solving this by incorporating self-difference into their systems. Hegel’s productive self-opposition creates a genetic line of sublated categories. Deleuze’s Bergsonian continuously integrated heterogeneous multiplicity allows a plurality of differentially related incompossible actualizations to coexist virtually. Hegel’s and Deleuze’s interpretations of differential calculus show us that for Hegel there are ultimately determinate parts that are not finite but make finite values when differentially related; where for Deleuze there are ultimate undetermined parts that are nonetheless determinable as extensive finite values when differentially related. For Hegel the unconditioned (dialectic) and the conditioned (categories it creates) are on the same ontological plane, but for Deleuze the unconditioned (genesis of virtual differentials) and the conditioned (actualization of extensities) are on two different planes, the virtual and the actual, so they cannot succumb to Hegel’s system by being sublated. However, Hegel’s dialectic can be seen within Deleuze’s system as a secondary movement to the genesis of difference. Hegel’s theory cannot explain the creation of variation needed in evolutionary theory, but Deleuze’s can.

Brief Summary:

Deleuze and Hegel offer solutions to the problems of representational systems, which are philosophical systems based on self-unity, identity, and the law of excluded middle. For Kant, our judgments of things have a subject-predicate structure that is parallel to the subject-predicate structure of concepts and intuitive objects (having the subject-property structure). What unifies each themselves and all with each other is the a priori unity of a transcendental self. Sartre thinks the unity of objects precedes that of the self. Deleuze’s transcendental empiricism posits neither the unity of the self nor of the object; things obtain something like a subject-predicate form from incompossibilities being various and indeterminate, but the thing taking these possible predicates is the subject of the judgments. A strict adherence to the principle of identity and the law of excluded middle causes problems in Aristotle’s and Russell’s logical systems of classification. For Aristotle, the highest genus is being or unity. But, as it has no genus above it, it cannot be defined according to the structure of this system of division (the problem of the large) and yet all beings under it are characterized by this unrepresentable classification. The species gives the essence, and under the species is the individual, which is distinguished from other individuals not by essential but by accidental traits. But in moments of change, something with one essence has contradictory accidents, and also we don’t know until after the change what was essential and what was accidental. So the individual cannot be represented properly in this system (the problem of the small). Also there are cases in the natural world, ring species, which cannot be classified using Aristotle’s system of division (the problem of division). Russell also has the problem of the large. He must ban self-reference from his system of set classifications so to avoid the paradox of the set of all non-self-including sets. Yet self-reference is needed to establish identity. Hegel’s dialectic and Deleuze’s philosophy of difference are competing solutions to these problems with representational systems. Deleuze’s system is based on Bergson’s continuously integrated heterogeneous multiplicity. We can understand it using Riemann topographical space. Deleuze’s virtual/actual relation is like topographical phase space portraits, where we can see all possible actual ways a system can behave. All the incompossible actualizations are differentially related yet are continuously integrated. Hegel’s internal dialectic makes use of productive contradiction: from out of a concept arises its contradiction, and from out of that opposition arises a new concept not implied in the first ones. So contraries are located within one another, and there is a genetic chain of production of the categories of understanding. Finite thought like that used in Kant’s and Aristotle’s systems would find such contradiction unthinkable, but Hegel’s infinite thought can think these contradictions. Hegel’s and Deleuze’s interpretations of the differential calculus help us elaborate their positions. For Hegel, the differential is a relation between vanishing values, they are caught in the act of the sublation of the finite and infinite: the values are vanishing and hence are not finite, but their differential ratio is a finite value; and each is constitutive of the other. For Deleuze, the differential values are not determinate, yet they are determinable in differential relation to one another. For, they are subrepresentational, meaning that they are on a level where parts are not externally exclusive like in extensity, so they are not self-identifiable. The important distinction is that for Hegel the terms are representable and determinate, but are only thinkable using infinite thought. In examining Kant’s antimony of the beginning or beginningless of the world, we see that for Kant, we have this antinomy because we mistakenly think the unconditioned is among the conditioned, when in fact it is noumenal; for Hegel the antinomy indicates the sublation of finite (the necessity for a limit) and infinite (the necessity for all limits to be surpassed), and for him the conditioned and unconditioned are on the same level; yet for Deleuze, the conditioned (actual) is on a different level than the unconditioned (virtual) but the virtual is not outside our knowledge, rather it is only knowable outside representational thinking. Hegel could subsume Deleuze’s virtual and actual by sublating them, but that would fail since they are two tendencies of the real and are not really opposites. Deleuze could subsume Hegel’s dialectic by saying it is a secondary movement to genesis of pure difference that happens on the level of actuality and representation. But Hegel could say that from the perspective of logic there is no such thing as Deleuze’s difference. So we test them by seeing how their theories of the composition of the organism suffice in evolutionary theory. Hegel is like Cuvier in thinking that the organism’s parts are matters of how they function in service of the whole (teleological); organ and organism, individual and species are like sublated opposing terms. But this means that deformations are deteriorations in structure and thus cause deficiencies in functionality. But evolutionary theory depends on a positive account of anatomical variations; natural selection needs to pick the best from a variety of mutations. Geoffroy’ s and Deleuze’s view sees variations as different actualizations of a transcendental model, so their view is more compatible with evolutionary theory. Because Hegel’s anatomy is representational, we can see one superiority in Deleuze’s subrepresentational response to representational philosophies as opposed to Hegel’s infinite representational approach.

 

Summary

Henry Somers-Hall will examine how Deleuze and Hegel respond to the shared problematic of representation in philosophy. He then pits them against one another, and applies them to the role of the structure of the organism in evolution, to evaluate them with respect to one another.

 

In the first part, we begin by seeing how 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.

 

 

In the second part, we formulate Deleuze’s and Hegel’s alternate proposals. Deleuze’s is based on Bergson’s duration, which is a continuously-integrated heterogeneous multiplicity, unlike the discrete multiplicity of externally related extensive parts characterizing homogeneous space. Bergson’s heterogeneous multiplicity better explains living systems.

Deleuze then uses Bergson’s continuously integrated heterogeneous multiplicity to characterize the Idea, the problem, and the concept. In all cases, they are terrains of virtual differential incompossibly-actualizeable paths of developmental explication. We can understand them with the model of topographical phase space portraits. They indicate all the tendencies for a system’s development using terrain features. This describes the system’s behavior on a whole, but in each instantiation only one possible line of development indicated in the map is actualized, because all the lines are incompossible yet coincident in this virtual form. They explicate into extensity. And any one actualization implicates the totality of the whole ‘problematic’.

Hegel’s dialectical movement brings contraries within one another, and also unites them on the basis of their genetic productions of one another. This allows him to go beyond Kant’s finite thought, and also to have totality to his system and an account of change, which is lacking in Aristotle’s system.  Kant cannot go beyond finite thought, because it cannot think contraries together, like Hegel’s infinite thought can. And because Hegel’s concepts are united genetically, differences are inherently linked, and thus he can have totality to a system of differences without the need of some generic category to encompass them all, which was a source of a problem for Aristotle. Rather, their genetic process of unfolding is the glue uniting the differences. Thus Hegel can also explain the process of change, as he has accounted for the process that generates and unites the diverse contradictory changes when something alters.

 

Now in this final part, we examine how Deleuze and Hegel propose theories that try to overcome the problems of representational theories like the ones we saw in the first part, and we pit the theories against one another and apply them to evolution so to better evaluation them. First we examined how Deleuze’s and Hegel’s responses to classical representationalist philosophical can be compared on the basis of their different interpretations of differential calculus and Kant’s antinomies. We found that for Deleuze we have an unconditioned ground of sensible and intelligible things that is subrepresentational, and for Hegel it is representable, using infinite thought. The calculus differential determines the varying relation between variables that vary with respect to one another. Leibniz saw it as the relation between infinitesimal magnitudes but there are formal problems with this. Newton saw it in terms of vanishing values. Hegel regards the vanishing values as being determinate values that combine finite and infinite, and being and nothingness. This contradiction is only thinkable with infinite thought. For Deleuze the terms of the differential relation are undetermined and subrepresentational, but they are determinable in relation to one another and are the unconditioned condition of conditioned actual determinations. Kant thinks we arrive at antinomous theories regarding whether there is a temporal beginning to the world because our understanding is unable to grasp the unconditioned, the thing in itself, with its categories. Hegel thinks the antinomies go together. Together they express the genuine infinite, because they affirm both that there is a limit and also that it is surpassed. For Hegel the unconditioned, the dialectical contradiction, is representable with infinite thought. Deleuze thinks that the unconditioned is thinkable but not using representational thought but rather using the logic of incompossibility.

We then saw how Deleuze’s philosophy of difference is more resilient to attack than Hegel’s, when both are pitted against one another. If Hegel wanted to critique Deleuze’s philosophy of difference, he would show how Deleuze’s virtual and actual as contraries dialectically sublate, which collapses the basic distinction of Deleuze’s ontology. However, because Deleuze’s virtual and actual are two tendencies of the real and not contraries, such a Hegelian critique would not hold. From a Deleuzean perspective, Hegel’s dialectic could be viewed as a false movement, with Deleuze’s genesis of difference being the real movement. Yet Hegel purely from a logical standpoint might say that Deleuze’s difference does not exist.

So we then applied Deleuze’s and Hegel’s responses to representation to evolutionary theory to see which one is more compatible and also to see if Deleuze’s three criticisms of Hegel still hold: [1] Hegel’s is a false movement, [2] Hegel’s logic revolves around a single center, and [3] Hegel’s dialectic does not provide enough precision for characterizing the world. For Hegel, nature is the one totality and it externalizes into multiplicity, but these form unified systems where parts and their whole are reciprocally determining. Hegel’s dialectic is  not temporal, so it does not describe an evolutionary progress through time. The structure of the organism is the reciprocally determining relation between organism and organs, which are opposing dialectical pairs like the one and the many. Individuals and species bear this organ/organism relation too for Hegel. Hegel’s structure of the organism is more closely tied to Cuvier’s anatomy, which is functional and teleological, meaning that organisms’ anatomical structures can be understood in terms of their functional purposes. Geoffroy’s homological theory of the unity of composition does not identify anatomical parts on the basis of their functions. Rather, he looks to see if the relations between the parts are isomorphic to a transcendental model which is so abstract that it can actualize in a wide variety of forms, such that a fin can be identified with an arm. This is compatible with Deleuze’s transcendental empiricism and theory of the virtual, which sees there being a transcendental level that is actualized in various ways. Cuvier’s and Hegel’s theories, as teleological, regard deformations or mutations in negative terms, as degradations of the organism’s structure and thus functioning as well. But evolutionary theory needs a positive view of aberrations. Geoffrey’s and Deleuze’s theories see variation positively, because variations are considered novel actualizations of the virtual model. Thus Deleuze’s response to the problems of representational theories is better than Hegel’s at least with regard to its application in evolutionary theory. We also see that Deleuze’s three criticism’s hold, because [1] Hegel’s movement is a matter of (infinite) representation, but because it cannot explain novel evolutionary variations, there is no real evolutionary movement involved. [2] Hegel’s structure of the organism has a teleological unity, and so there is a ‘monocentering of circles’ [around the organic unity of the organism.] [3] Hegel’s account is not precise enough. Because it understands the differentiation in the natural world in terms of determinate oppositions, Hegel’s dialectic too strongly divides the world rather than seeing the blurrings of boundary that allow for evolutionary variation.

 

 

 

 

 

 

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

Pt3.Ch8 Somers-Hall’s Hegel, Deleuze, and the Critique of Representation. ‘Hegel, Deleuze, and the Structure of the Organism.’ 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 3: Beyond Representation

Chapter 8: Hegel, Deleuze, and the Structure of the Organism

Very Brief Summary:

Deleuze’s response to representational philosophy, and not Hegel’s, is compatible with evolutionary theory. For, Deleuze’s virtual explains novel variation in the organism’s structure, but Hegel’s dialectic does not. Also, Deleuze’s three criticisms of Hegel exhibit themselves when we relate Hegel’s ideas to evolution: [1] dialectical movement would halt evolutionary movement, [2] Hegel’s logic circles around a center, the sublation of organ and organism, which blocks evolutionary progress, and [3] Hegel’s account misses the ambiguities and variations that are vital to evolution.

Brief Summary:

We will apply Deleuze’s and Hegel’s responses to representation to evolutionary theory to see which one is more compatible and also to see if Deleuze’s three criticisms of Hegel still hold: [1] Hegel’s is a false movement, [2] Hegel’s logic revolves around a single center, and [3] Hegel’s dialectic does not provide enough precision for characterizing the world. For Hegel, nature is the one totality and it externalizes into multiplicity, but these form unified systems where parts and their whole are reciprocally determining. Hegel’s dialectic is  not temporal, so it does not describe an evolutionary progress through time. The structure of the organism is the reciprocally determining relation between organism and organs, which are opposing dialectical pairs like the one and the many. Individuals and species bear this organ/organism relation too for Hegel. Hegel’s structure of the organism is more closely tied to Cuvier’s anatomy, which is functional and teleological, meaning that organisms’ anatomical structures can be understood in terms of their functional purposes. Geoffroy’s homological theory of the unity of composition does not identify anatomical parts on the basis of their functions. Rather, he looks to see if the relations between the parts are isomorphic to a transcendental model which is so abstract that it can actualize in a wide variety of forms, such that a fin can be identified with an arm. This is compatible with Deleuze’s transcendental empiricism and theory of the virtual, which sees there being a transcendental level that is actualized in various ways. Cuvier’s and Hegel’s theories, as teleological, regard deformations or mutations in negative terms, as degradations of the organism’s structure and thus functioning as well. But evolutionary theory needs a positive view of aberrations. Geoffrey’s and Deleuze’s theories see variation positively, because variations are considered novel actualizations of the virtual model. Thus Deleuze’s response to the problems of representational theories is better than Hegel’s at least with regard to its application in evolutionary theory. We also see that Deleuze’s three criticism’s hold, because [1] Hegel’s movement is a matter of (infinite) representation, but because it cannot explain novel evolutionary variations, there is no real evolutionary movement involved. [2] Hegel’s structure of the organism has a teleological unity, and so there is a ‘monocentering of circles’ [around the organic unity of the organism.] [3] Hegel’s account is not precise enough. Because it understands the differentiation in the natural world in terms of determinate oppositions, Hegel’s dialectic too strongly divides the world rather than seeing the blurrings of boundary that allow for evolutionary variation.

 

Summary

Previously we saw that if Hegel wanted to critique Deleuze’s philosophy of difference, he would show how Deleuze’s virtual and actual as contraries dialectically sublate, which collapses the basic distinction of Deleuze’s ontology. However, because Deleuze’s virtual and actual are two tendencies of the real and not contraries, such a Hegelian critique would not hold. From a Deleuzean perspective, Hegel’s dialectic could be viewed as a false movement, with Deleuze’s genesis of difference being the real movement. Yet Hegel purely from a logical standpoint might say that Deleuze’s difference does not exist.

So in this chapter we will apply their theories to a field outside logic, something that is a real phenomenon in the world, evolution. This is the chapter’s aim, and also to see if in this application Deleuze’s three criticisms of Hegel hold: [1] Hegel’s is a false movement, [2] Hegel’s logic revolves around a single center, and [3] Hegel’s dialectic provides enough precision for characterizing the world.

We then saw that for Hegel, the Idea is The One Totality and it is self-determining reason. This totality is nature, but it becomes other to itself as externality and multiplicity. Nature is rational. The movement in nature involves the identity of difference and identity. So while there are multiplicities of bodies, they form whole systems. In physics bodies form indifferent relations to one another. In chemistry chemicals combine and transform, but their processes are not self-perpetuation. They are however in organic life. Here we have unity and difference in the form of the unity of the organism being constituted through the differences of its organs, and its processes are self-perpetuated.

Now, Hegel’s ideas on the dialectical movement in nature might suggest a compatibility with evolutionary theory, even though Hegel’s thinking precedes Darwin. However, evolution as a theory precedes Hegel. For Hegel, the dialectical movement in nature is not to be seen as something unfolding in time. So Hegel’s philosophy of nature is not easily seen as compatible with evolutionary theory.

However, we can still examine his philosophy of the structure of the organism, which is based on his dialectic, to see if it is compatible with evolutionary theory. For Hegel, we cannot understand the organism as a mechanically related set of indifferent material parts, because it maintains a characteristic unity and acts spontaneously. Instead the organism is structured on the integration of unity and multiplicity, identity and difference, part and whole, one and many; for, it is organ and organism, with the two mutually dependent on each other [each organ is reciprocally determinate with the others, but also the organism and its organs are reciprocally determining]. The best model for the structure of the organism would be one with the greatest differentiation that is still unified. Plants can be divided and the parts regenerate new plants, so they were not organs so much. Animals go up a scale of differentiation, with humans at the top, because they also have the greatest sense of how each individual is an organ in a social body.

 

We will compare and contrast by relating Hegel’s and Deleuze’s ideas on the organism’s structure to Cuvier and Geoffrey. Cuvier, like Hegel, thinks that animals should not be classified in terms of differences of degree. Unlike Hegel, he uses a non-unified system, one with four branches. Nonetheless, like Hegel, Cuvier’s system is functional and teleological, meaning that organisms’ anatomical structures can be understood in terms of their functional purposes.

Geoffroy, on the contrary, offers a theory of anatomy based on homology. There is a transcendental unity of parts to which actual empirical cases correspond isomorphically. The theory was most demonstrable in application to embryonic forms. Thus both fish and human embryonic skeleton’s share a one-to-one correspondence to a transcendental arrangement of parts. This goes against Cuvier’s anatomy, and Hegel’s as well, because for them, anatomical parts are understood teleologically, in terms of their purposes or functions for the organism. So a fin and arm in Cuvier’s and Hegel’s approaches would not share the same designation, because their functions are different, however in Geoffrey’s they will. The relation between transcendental and empirical resonates with Deleuze’s transcendental empiricism.

We then noted that Geoffroy’s homological theory provides an account of the variations in anatomy, which becomes central to the theory of evolution. For Darwin different species have homologous forms on account of common ancestors. And anatomical parts can evolve according to how their functions alter. Cuvier's teleological theory of anatomy is not compatible with evolution, [because were a part’s function to change, it is no longer the same part, and thus such an evolutionary connection cannot be observed using this approach.] Also, Geoffrey’s homology or unity of composition is like Deleuze’s Idea.

 

We then saw how these theories of the structure of the organism apply in evolutionary theory. To explain evolution, we need an account of accidental, contingent variations. These can be seen either positively or negatively. A theory of anatomy like Cuvier’s or Hegel’s is teleological, meaning that it identifies anatomical parts in terms of their functionality, their purpose in the function of the organism. This means that if there were to be a deviation, a slight mutation, then this changes the structure of the organism’s functioning and thus degrades its functioning. Geoffrey’s homological theory of anatomy does not regard anatomical parts in terms of their purposes but rather in terms of how their interrelations correspond isomorphically to an abstract or transcendental model. This means that parts can change both form and function so long as their structural relations match the mold. A deformity then is the model expressing itself in another way, so this would be a positive account of variation rather than a negative one. This notion of homologous variation is central to evolution which is a process of the natural selection from a pool of variations.

 

So Deleuze’s ideas are more compatible than Hegel’s for explaining evolution. Deleuze’s three criticisms also hold in this context of evolution. [1] Hegel’s movement is created with words and representations, so nothing follows. [The movement of evolution cannot be explained with the infinite representation of the contraries organ and organism, individual and species being thought together.] [2] Hegel’s structure of the organism has a teleological unity, and so there is a ‘monocentering of circles’ [around the organic unity of the organism.] [3] Hegel’s account is not precise enough. [Because it understands the differentiation in the natural world in terms of determinate oppositions, Hegel’s dialectic too strongly divides the world rather than seeing the blurrings of boundary that allow for evolutionary variation.]

 

 

 

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

Pt3.Ch8.Sb9 Somers-Hall’s Hegel, Deleuze, and the Critique of Representation. ‘Conclusion’. summary

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

 

Henry Somers-Hall

 

Hegel, Deleuze, and the Critique of Representation.

Dialectics of Negation and Difference

 

Part 3: Beyond Representation

Chapter 8: Hegel, Deleuze, and the Structure of the Organism

Subdivision 9: Conclusion

Brief Summary:

Deleuze’s response to representational philosophy, and not Hegel’s, is compatible with evolutionary theory. For, Deleuze’s virtual explains novel variation in the organism’s structure, but Hegel’s dialectic does not.

Explanatory Summary:

Hegel’s theory of the organism’s structure is based on the dialectical relation between part and whole, that is, between organ and organisms (and individual and species). It is a teleological view, like with Cuvier, that regards the structure as being divided according to the functioning of the parts. But this means that a deformity would be understood negatively, as  a degradation of the structure and thus functioning of the organism. Evolutionary theory, however, presupposes a positive view of anatomical variation. It would see mutations as novelties from which natural selection can chose the most adapted. This positive view of evolutionary theory we see in Geoffroy’s homological theory of anatomy, the unity of composition. Here we can consider functionally different parts between different species as expressing the same part in an abstract, transcendental, unrepresentable model. For Cuvier and thus also for Hegel, a human leg and a dog leg can have the same name because they have the same function. Not so for an arm and a fin. But for Geoffroy, we see how the arm relates to the rest of the parts in its body, and how the fin relates to the rest of the parts in its body, and see if both of them can related to a third abstract model which is not expressed or drawn but merely implied in unifiability of the relational structures between the different species. So we might imagine a mutation in the fish where the fins take on the shape of arms, and allow the fish to craw on surfaces. This is just another expression of the same representable blue print. [However if the fish’s fins removed from their locations and reappeared inserted themselves in very different places, this would not be a homology, because it is no longer isomorphic with the abstract arrangement.] So because Hegel’s theory of the structure of the organism is dialectic, that makes it teleological, and that makes aberrations degradations rather than potentially useful novelties. Thus Hegel’s dialectic was a response to the problems of traditional representational systems, so his response to representational systems does not apply to a real world phenomenon, evolution. However, Deleuze’s transcendental empiricism functions like Geoffroy’s homology. For Deleuze, actuality is one explicit expression from a field of differentially related incompossible virtual possibilities. All the different ways a pendulum actually might swing are homologous to the phase portrait which depicts all possibilities in a non-representational form. So for Deleuze, organisms also express a certain unity of composition, as they are expression of the Idea, so Deleuze’s response to representational systems, the subrepresentationality of virtuality, does in fact apply to the real world phenomenon of evolution. Hence Deleuze’s response to representational systems is superior to Hegel’s.

Summary

The previous chapter discussed Deleuze’s three main criticisms of Hegel’s philosophy:

[1] its reliance on false movement,

[2] its focus on movement around a center, and

[3] its use of concepts that are too general to capture the particularity of the world.

We saw that if remained on merely the logical level, Hegel’s infinite representation, his solution to the problems of representation, remains consistent. So we needed to apply Deleuze’s and Hegel’s philosophies to a subject outside logic to better see if Deleuze’s criticisms hold, and in this chapter we applied them to theories of the structure of the organism. For Hegel, organs can only exist in their relation to the whole [and vice versa.] This is the movement of the infinite [because it is a sublation of contraries.] But this part/whole relation is still representable, even if with infinite thought/representation. Deleuze instead prefers to see the structure of the organism in terms of homology and the unity of composition. It escapes representation [because it is not a matter of identifying parts between species more rather a matter of saying that the relations between parts in organisms of different species is isomorphic to an abstract model that must remain unrepresented, because it can only manifest in its various actualizations.]

Just as with the calculus, the accounts of the organism offered by Hegel and Deleuze provided concrete exemplars of their logical positions. Thus, for Hegel, the organism represents the movement of the infinite, or of contradiction, with the particular organs only existing within the relationship to the whole. For Deleuze, what is required to explain the organism is the moment that escapes representation, the unity of composition that functions as a transcendental condition for the organism. Thus, for him, the virtual/actual distinction is vital to our understanding of the organism. (237)

So these accounts are implied in Hegel’s and Deleuze’s different responses to the problems of representation. And there are problems with Hegel’s account. Hegel himself rejects an evolutionary theory. But this evolutionary theory he describes can be seen merely as a description of the structure of organisms and not of their temporal genesis (there is an increasing scale of perfection). But, we still cannot resolve the conflict between Hegel’s dialectic, which is teleological, and teratology, which is a precondition of evolution; it is the study of variations, and under the teleological account, these variations are degradations in functioning  rather than evolutionary improvements. Evolutionary theory needs an account of variations leading to novel structures that can be naturally selected, so we need a positive account of aberration. Teratology tells us about the organism’s development and thus also about its structure. So we return to Deleuze’s three criticisms of Hegel now in this context of the organism’s structure. [1] Hegel’s movement is created with words and representations, so nothing follows. [Hegel’s movement of the infinite sees the dialectical relation between organ and organism, individual and species. However, these relations are representable. The structure of the specie’s anatomy is representable. But this is on account of the teleology, the purpose of the parts in the functioning of the whole. This cannot explain evolution, we noted, so Hegel’s infinite movement leads to a false movement and not the true movement of evolution.] [2] Hegel’s structure of the organism has a teleological unity, and so there is a ‘monocentering of circles’ [around the organic unity of the organism.] However, it cannot explain the evolutionary development that builds from aberrations. The individual itself, were it to vary from the species, would be [a non-functional monstrosity,] a “failure to embody the Idea in nature.” (237) Also, for Hegel, the boundary between the organism and the world is “too effective,” and so he cannot explain the transversal relations between organisms that brings about the variations that provide the novelty for natural selection to choose from. [3] Hegel’s account is not precise enough.

"Oppositions are roughly cut from a delicate milieu of overlapping perspectives, of communicating distances, divergences and disparities, of heterogeneous potentials and intensities" (DR, 50). In this sense, what Hegel calls the "impotence of nature" could be characterized by the Deleuzian as the impotence of dialectic itself, since it is unable to explain positively the contingency of nature, which is vital to our modern understanding of the world. (238)

[So because it understands the differentiation in the natural world in terms of determinate oppositions, Hegel’s dialectic too strongly divides the world rather than seeing the blurrings of boundary that allow for evolutionary variation.]

We cannot, therefore, follow the strategy of some Hegelian commentators of accepting the weakness of Hegel's position on evolution, before isolating this position from the rest of Hegel's philosophy. Instead, the limitations of Hegel's account of the organism must be seen as stemming from limitations of the more abstract metaphysical categories discussed in the preceding chapters of this book. (238)

 

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