§ introduction to the Deleuzian registers and their epistemological correlates: actuality –infinite comprehension, potentiality –finite comprehension, and virtuality –indefinite comprehension
(‘Let us pose a question quid juris [which law applies]:…)
Deleuze inaugurates this portion of the Introduction by explicitly relating his earlier consideration of a 2nd contrast (from the perspective of law) between generality and repetition to now that of a 3rd contrast (from the perspective of the concept or representation). Deleuze poses ‘a question quid juris’ (which law applies). That is, a question arises as to how the 2nd contrast (a concept or theory of value) ‘applies’ a given understanding of the topic of the 3rd contrast (a theory of concepts, or representation). By proposing to ‘pose a question quid juris’, Deleuze is clarifying that our answer to the question of value already implicates a certain presumption about the being of reality –or in other words, it already begs the question of ontology.
We are then incorrectly wording the issue if we say that a materialist theory of value requires an ontology, since it’s the case that any given materialist analysis already is an ontology. To forward an assertion about the coming-into-or-out-of-being of value is to already forward an assertion about what being “is”, i.e. its ontological properties, of how they come and go, of what are being’s registers, etc. In order to get our answers to such questions about value right, we are required to get our ontology right; and in order to get our ontology right, we need to get our questions right.
This assignment drives Deleuze’s thinking on the 3rd contrast –a difference in kind between the orders of generality and repetition, now from the perspective of concepts, or representation. This 3rd contrast of their difference in kind convokes Deleuze’s understanding that there are three registers of reality: actuality, potentiality, and virtuality.
However, our reader will quickly realize that at this portion of DR (pgs. 11-15) Deleuze is merely drawing on the phenomenological consequences that there are three registers of reality, and in doing so proceeds to indirectly unpack some of their basic ontological, epistemological, and logical properties (or “correlates”, as he calls them). Let our reader then be clear that Deleuze’s main objective at this point is not to formally elaborate the registers, as such, but to continue to articulate the difference in kind between the domains of generality and repetition –now from the perspective of concepts, or representation –and only backs his way into a passing consideration of the registers incidental to that purpose. However, our own reader’s full clarity over this part of the Introduction turns on her appreciation that a concept encounters a variety of blockages contingent to the register through which it passes. And because value is our concept of concern herein, without such clarity, she will be unable to follow Deleuze’s opening rumination on the material properties of the synthetic, and in turn the proper materiality of synthetic finance. For this reason, we must briefly overview the three registers.
The three registers of reality and their correlates are as follows:
actuality –a register of extension = 1; is marked by infinite comprehension; herein the concept encounters artificial blockages/logical principles to its representation
potentiality (possibility) –a register of extension = ∞; is marked by finite comprehension (its discrete entities are subject to probability distributions); herein the concept encounters natural blockages to its representation
virtuality –a register of inextension; is marked by indefinite comprehension; herein the concept also encounters natural blockages to its representation, but which are different in kind from the blockages afflicting potentiality
We must briefly consider each, and its significance for our understanding of finance.
§ recap of 2 contrasts between repetition and generality: conduct & law; synopsis of 3rd contrast: concepts, or representation
(‘Repetition and generality are opposed from the point of view of conduct and from the point of view of law. It remains to specify a third opposition from the point of view of concepts or representations.’)
Deleuze closes his introductory comments on operators of repetition, and so for the time being closes his concern with Kierkegaard and Nietzsche. The opening line from the Introduction’s second textual break commences with a recap of the two contrasts already made by Deleuze –that repetition and generality are opposed (i) in conduct (exchange) and (ii) in law (theory of value) – to which he now adds that they are also opposed from the point of view (iii) of concepts, or representations.
Having already cursorily familiarized ourselves with his two prior contrasts, the reader will understand that with this 3rd contrast Deleuze has now introduced to his reader three differences in kind on which pivot his exposition of an ontology of the synthetic, his revaluation of the concept of value, and his advocation of a new materialist political economy. Deleuze’s Introduction is dense, difficult, and at times poorly edited. But if we appreciate that its final aim is to provide us with a rough outline of an ontological disquisition for a synthetic system of exchange founded on difference and repetition, we will feel better prepared to follow his guide. Let us therefore recap Deleuze’s two prior contrasts, and then commence with our initial consideration of his third contrast, as briefly as it’s itemized at this point in DR.
To recap and move forward: there are 3 contrasts to make when distinguishing as different in kind, ontologically-speaking, the domains of repetition and generality (and it’s perhaps worth observing here that Deleuze believes the three contrasts are itemizable in any order):
1st contrast: from the perspective of conduct, i.e. our conduct in exchange, or, the activity of a quasi-causal operator amidst the transformation of economic objects from one to another place in space. The question for Deleuze is one of how we are to regard our conduct in the course of exchange? This is a question of microeconomics.
2nd contrast: from the perspective of law, i.e. if not a theory then at least a concept of value, or, of the change in values of the properties of economic objects. If the spatiotemporal transformation of economic objects is predicated on their symmetry (viz. commensurability, equivalence), the question for Deleuze is what kind of symmetry, where, and what is its relation to value? This is a question of macroeconomics.
And now a 3rd contrast: from the perspective of concepts, or representation, i.e. of the relation of the coming-into-being of value to that of the representation of value, or, of our cognitive and perceptual relation to the registers of reality through which our concept of value passes. For Deleuze, the form of the question of what is value already thoroughly begs an ontological question that demands our better understanding of the relation of epistemology to ontology? This is a question of the relation of ontology and epistemology of finance.
With this third contrast we are given cause to preliminarily concern ourselves with Deleuze’s three registers of reality. We will follow Deleuze’s prefatory sketch of this third contrast, and therein inaugurate our understanding of that which will be more fully developed throughout DR, as Deleuze incrementally but comprehensively elaborates these three registers.
§ 2nd contrast of generality and repetition –from the perspective of conduct; Kierkegaard and Nietzsche: two philosophers of repetition (pg.5-11)
Based on his aforementioned considerations, it is clear for Deleuze that the domain of generality and repetition are not only distinguishable from the perspective of law; for this reason, he again contrasts the domain of repetition to the domain of generality –however, now from the perspective of conduct, i.e. our conduct involved in an act of exchange. This is the 2nd of his three contrasts.
(‘There is a force common to Kierkegaard and Nietzsche…[for each] in his own way makes repetition not only a power peculiar to language and thought, a superior pathos and pathology, but also a fundamental category of a philosophy of the future. To each corresponds a Testament as well as a Theatre, a conception of the theatre, and a hero of repetition as a principle character in this theatre: Job-Abraham, Dionysius-Zarathustra…’)
Deleuze periodically introduces textual breaks throughout DR in order to artificially compartmentalize the subtopics of his chapters –albeit as with the synthetic, attempts to compartmentalize in final prove futile, the synthetic overflows the rafts. Regardless, page 5 is the first of these breaks.
The text picks up with Deleuze’s introductory consideration of Kierkegaard and Nietzsche, two philosophic operators of repetition –or as he calls them, two philosophers of the future. Deleuze asserts that each of these two philosophers in his own way provides a derivative proposition about the same univocal Being, and that each works with the conviction that the value of their work will have been determined and determinable in an as-yet unspecified and to-be-arrived-at future date.
Our reader will learn that just as elements of Euclid-Plato-Hegel’s ontology infuse Marx’s political economic flat space concept of (cardinal) value, so too Nietzsche-Kierkegaard’s ontology work their way into and through Deleuze’s own political economic revaluation of (ordinal) value. Deleuze understands himself to be one more derivative of a philosopher of the future. It is still, however, and of course, a question of knowing what this means –i.e. of what it means to practice a derivative conduct that makes of repetition a category of futures.
(‘What separates [Kierkegaard and Nietzsche] is considerable, evident, and well-known. But nothing can hide this prodigious encounter in relation to a philosophy of repetition: they oppose repetition to all forms of generality. Nor do they take the word “repetition” in a metaphorical sense: on the contrary, they have a way of taking it literally, and introducing it into their style.’)
Deleuze is claiming –and throughout DR will illustrate– that Kierkegaard and Nietzsche, despite an evident, actual separation between the two general orders of their work, nonetheless virtually repeat, and quasi-causally operate on, two different singularities expressive of a univocal Being. Of course, if we were to possess the necessary time and inclination, we could proceed to show that this ‘style’ of difference in repetition marks the entirety of Deleuze’s oeuvre as well –from his initial work on Bergsonism, all the way through his last work with Guattari, What is Philosophy? If we were to perform such a voluminous task, we would witness that Deleuze is constantly making, unmaking, and remaking his ‘concepts along a moving horizon’ of topics and concerns; he was ever thinking and writing ‘from a decentered centre, from an always displaced periphery’ (Preface pg. xxi), in which we are, on the one hand, at first surprised to learn that Deleuze has suddenly and apparently ceased to use a concept whose term had earlier functioned as a protagonist, or was a ‘hero’ in the ‘theatre’ of a particular text, only to later, on the other hand, stumble into an awkward encounter with a repetition of its conceptual content in a different term in some subsequent text (note: the difference in repetition of ‘the Idea’ (DR) –‘rhizome’ (TP) –and ‘philosophical concept’ (WP) is a good example of this). It is as if between or underneath two general orders of actual texts we glimpse a repetition of an earlier Deleuzian concept. We will also see that Deleuze practices this method on a micrological scale in DR –i.e. ‘of taking [repetition] literally, and introducing it into his style.’
Deleuze introduces the principal propositions which, despite different actualities (e.g. in terms of Testaments, Theatres, and Heros) separating them, are coincidental to Kierkegaard and Nietzsche.
(‘We can…list the principal propositions which indicate the points on which they coincide:
1. Make something new of repetition itself: connect it with a test, with a selection or selective test; make it the supreme object of the will and of freedom…
2. In consequence, oppose repetition to the laws of nature…
3. Oppose repetition to moral law, to the point where it becomes the suspension of ethics, a thought beyond good and evil…
4. Oppose repetition not only to generalities of habit but also to the particularities of memory…’)
Deleuze will later more fully elaborate the meaning of these propositions. The reader should try to stay relaxed here. For now, we need merely observe that with these four principals Deleuze seeks to establish the following:
1. First, to ‘make something new of repetition itself’ is to make repetition –which in economics, is always the exchange qua repetition of an object for and into its image of value as money– an economic object, as such; while yet constituting ‘something new of repetition’, i.e. of constituting through repetition a pure difference in itself. To elaborate this is the principle objective of Chapter 1 (Difference in Itself).
2. Secondly, to ‘oppose repetition to the laws of nature’ is to oppose repetition in the convocation of value to that which is found in the domain of generality and resemblance. We will later illustrate why it is scientifically-rigorous from the perspective of dynamical systems theory and the sciences of morphogenesis to posit repetition as opposed to the law. But also, insofar as there is no repetition in itself, it will be a matter of examining repetition for itself. To elaborate this is one of the principle objectives of Chapter 2 (Repetition for Itself).
3. Thirdly, to ‘oppose repetition to moral law’ entails a patent rejection of conducting a science of political economy whose impetus is morally-motivated. And yet we must do this without unwittingly backing our way once more into a political-economic-ethical project whose impetus is a morally-motivated purging of morality from our project –that is, the force of our project can neither be ethical, nor an ethic of a ‘suspension of ethics’. To move our conduct in economics ‘beyond good and evil’ is the objective of Chapter 3 (The Image of Thought).
4. Lastly, if we are to ‘oppose repetition not only to generalities of habit but also to the particularities of memory’ we are required to understand the role and relation of virtuality in and to the determination of the actual. Indeed, our financial-economic models exclusively concern themselves with actuality (whose epistemological correlate, as we will discuss below, is infinite comprehension) and potentiality (subject to a probability distribution, and as we will also discuss below, whose epistemological correlate is finite comprehension), while yet neglecting the reality of the virtual (which is neither actual nor subject to a probability distribution, and as we will also discuss below, whose epistemological correlate is indefinite comprehension). To correct this myopia afflicting political economics is the objective of Chapters 4 (Ideas and the Synthesis of Difference) and 5 (Asymmetrical Synthesis of the Sensible).
(‘Kierkegaard and Nietzsche are among those who bring to philosophy a new means of expression. In relation to them we speak readily of an overcoming of philosophy.’)
By practicing the four aforementioned propositions, Deleuze is repeating the move made in philosophy by Kierkegaard and Nietzsche, but now in political economy –a speculative materialist political economy of finance as its method, and a speculative materialist communism as its goal.
(‘Furthermore, in all their work, movement is at issue. Their objection to Hegel is that he does not go beyond false movement –in other words, the abstract logical movement of ‘mediation’.)
This is a theme we see repeated throughout Deleuze’s periodic assessment of Hegel. To be clear, it is not that Deleuze is ‘critical’, as such, of classical exchange –whatever that would mean (i.e. any class of exchange is beyond true or false). Rather, he is critical of those who represent classical exchange as true movement, as the true essence of change. If classical exchange consists of the rigid motions of an object into its image, and if these rigid motions constitute a congruence transformation, whereby the metrical properties of the object remain invariant under their force of motion (i.e. in exchange), how can we call this true movement? For this reason, Deleuze counterposes Kierkegaard, Nietzsche, and his own heterodox political economy of the synthetic against Hegel’s ‘false movement’, ‘the abstract logical movement of mediation’, whereby an economic object is transformed into its image in space, yet without the structure to that space undergoing any transformation whatsoever. Again, this is an ‘empty form of difference’, an ‘invariable form of variation’, a rigid motion whereby nothing truly moves in the course of its transformation –and thus, for Deleuze, this is a ‘false movement’, which operationalizes a far too conservative notion of symmetry. Deleuze aims for a much more radical symmetry –the symmetry of synthetic symmetry. As we will see, this is the symmetry at work in synthetic finance. This is the symmetry operationalized in the course of our exchange of synthetic financial objects.
(‘[Nietzsche and Kierkegaard] want to put metaphysics in motion, in action. They want to make it act, and make it carry out immediate acts. It is not enough, therefore, for them to propose a new representation of movement; representation is already mediation. Rather, it is a question of producing within the work a movement capable of affecting the mind outside of all representation; it is a question of making movement itself a work, without interposition; of substituting direct signs for mediate representation; of inventing vibrations, rotations, whirlings, gravitations, dances or leaps which directly touch the mind. This is the idea of a man in the theatre, the idea of a director before his time. In this sense, something completely new begins with Kierkegaard and Nietzsche.’)
Deleuze clearly understands himself to be working within –i.e. to be repeating in this tradition– but differently than Nietzsche and Kierkegaard, insofar as he is first illuminating for us the metaphysics always-already built into our economic system(s), our acts of exchange; of rethinking that metaphysics; of then putting his own metaphysics ‘in motion, in action’, i.e. of inventing ‘vibrations, rotations, whirlings, gravitations, dances or leaps which directly touch the mind.’ In this sense, and in the study of political economy, ‘something new begins with [Deleuze].’
(‘[M]ovement, the essence and the interiority of movement, is not opposition, not mediation, but repetition. Hegel is denounced [by Kierkegaard and Nietzsche] as the one who proposes an abstract movement of concepts… Hegel substitutes the abstract relation of the particular to the concept in general for the true relation of the singular and the universal in the Idea. He thus remains in the reflected element of “representation”, within simple generality.’)
Pages 8 and 10 contain Deleuze’s first of several passing and periodic treatments of the work of Hegel in DR. One increasingly sees that –with an appreciable amount of nuance, of course– Deleuze ultimately believes that Euclid’s conservative invariance requirements are infused in Plato, that Plato’s model of representation gets reworked and then reproduced in Hegel, and then Hegelian metaphysics terrorizes Marx’s ontology of capital from within, constantly, forever, and as a special form of outer darkness. Our reader is encouraged to be vigilant of this fact on the one hand, when examining Deleuze’s treatment of Hegel, and on the other hand, when attempting to grasp Deleuze’s critique of Hegel from the perspective of his contraposition of the ‘mediated’ domain of generality against the domain of repetition.
Many a crude commentary on Deleuze has so often dubbed his ontology a “philosophy of becoming”, or “philosophy of movement”, that one will be initially excused for momentarily forgetting the fact that becoming and movement in general rather go without saying –and so the assignation of this label to Deleuze is not so much wrong as it is poorly worded, or at least insufficiently explained. In Deleuze’s treatment of Hegel –and by indirection, the Hegel in Marx– our reader will observe the false movement of “opposition”, since opposition is one of the four shackles of representation, and therefore of the domain of generality. Our analysis of Chapter 5 (Asymmetrical Synthesis of the Sensible) will cause us to observe what, precisely, Deleuze means by ‘the essence and the interiority of movement’ of repetition.
(‘[Hegel] represents concepts instead of dramatizing Ideas; he creates a false theatre, a false drama, a false movement. We must see how Hegel betrays and distorts the immediate in order to ground his dialectic in that incomprehension, and to introduce mediation into a movement which is no more than that of his own thought and its generalities.’)
Deleuze will give full philosophical exposition to this point –and in particular to the drama of Ideas (viz. multiplicities)– in Chapter 4 (Ideas and the Synthesis of Difference). We will clarify therein that markets (and the objects that populate them) are theatres of multiplicities, and that they are marked by a highly peculiar kind of drama –albeit, it is a matter of understanding the ontological difference in kind of the dramas which characterize numerical multiplicities from those which characterize qualitative multiplicities. This is a crucial distinction for Deleuze in elaborating his ontology of the synthetic.
(‘When we say, on the contrary, that movement is repetition and that this is our true theatre, we are not speaking of the effort of the actor who ‘repeats’ because he has not yet learned the part. We have in mind the theatrical space, the emptiness of that space, and the manner in which it is filled and determined by the signs and masks through which the actor plays a role, which plays other roles; we think of how repetition is woven from one distinctive point to another, including the differences within itself.’)
Progressively this will have been a very profound passage as the meaning of it becomes increasingly clear throughout the course of our Guidebook. However, because Deleuze again is getting ahead of himself, the reader’s feeling of puzzlement is only to be expected. We feel yet unprepared to grasp the significance of the ‘emptiness’ of a theatrical space called economic space, wherein that space is distributed along with the coterminous distribution of the objects which comprise and populate it. We will see Deleuze speak of objects which are ‘masks behind which are only other masks’, and assert that their difference is constituted by their derivative repetition from one distinctive point to the next. But perhaps at this early stage (i.e. at pg. 10 of DR) we are still too inculcated with our time-honored political economic ideology of flat space, our dogmatic presumption of a Cartesian-coordinated space of exchange, wherein objects are only ever like actors’ lines insofar as their metrical properties pre-exist their motion, and insofar as they are constantly repeated over and again –and always so that the actor will ‘learn’ his script precisely so that his lines will remain ever-unchanged in their course of motion. Deleuze is saying that we proceed too conservatively with this conception of the distribution of economic space, we act too conservatively when we expect that our economic objects populate a space which is pregiven, when we expect the behavior of those objects to play the role of an actor’s lines, and when we behave with the expectation that our own acting is always a distribution in space rather than the distribution of space. It is true that we always yet expect to see faces behind masks, rather than ‘masks behind which are other masks’. However, the observation of our natural puzzlement over such statements by Deleuze early on is merely a manner of observing that we are unprepared as of yet to fully grasp repetition and difference, we are yet unprepared to critically scrutinize Deleuze’s ontology of the synthetic, and so are therefore unprepared to understand that difference and repetition is truly a radical concept of value predicated on the monstrous power of synthetic symmetry. Deleuze will allow us to clarify our puzzlement over the course of our careful reading of DR if we are prepared to follow his wager for a time.
(‘The theatre of repetition is opposed to the theatre of representation, just as movement is opposed to the concept and to representation which refers it back to the concept. In the theatre of repetition, we experience pure forces, dynamic lines in space which act without intermediary upon the spirit, and link it directly with nature and history, with a language which speaks before words, with gestures which develop before organized bodies, with masks before faces, with specters and phantoms before characters –the whole apparatus of repetition as a “terrible power”.’)
Deleuze continues to illustrate his assertion of the existing isomorphism between the space of the theatre and the space of the market –and that the latter as a space of the representation of value is opposed to a space of repetition as constitutive of value. Deleuze speaks of the latter kind of space as ‘theatre of repetition’. Our reader should be alerted here that in the course of imputing to this space ‘dynamic lines without intermediary’, of ‘a language before words’, of ‘gestures before bodies’, of ‘masks before faces’, and so on, Deleuze is introducing us to the content of the concept of the virtual much earlier in DR than we actually encounter it in its explicit conceptual form. This move is both telling of the way the virtual operates, i.e. its movement, logic, and so on, and is also instructive of the ‘style’ of thought that Deleuze shares in common with Nietzsche and Kierkegaard, as referenced above. The conceptual (i.e. virtual) content of the virtual pre-arrives its conceptual (i.e. actual) invocation precisely because its dynamic lines pre-exist its intermediation by the concept; it is a language formed before words, gestures prior to organized bodies, masks before faces, specters before their corporeal form. Although in truth throughout the whole of DR our reader will observe that Deleuze is performing this methodological exercise of practically illustrating his philosophical exposition of the peculiar phenomenology of the virtual, we will immediately witness this practice as early as the opening of Chapter 1 (Difference in Itself).
Because we are now considering the concept of virtuality, we must specifically draw our reader’s attention to a consideration of the context, meaning, and reason for the final line of the above-quote, insofar as it serves as a quilting point for the whole project of DR. Following Deleuze’s preliminarily rumination on the functional role of the virtual as the distribution in and of the space of repetition, he calls ‘the whole apparatus of repetition’ ‘a terrible power’. Why? This is neither a passing hyperbole nor cheeky-comment. One of Deleuze’s principal philosophical leaping points in DR is to investigate the historical, multidiscursive, moral disrepute befalling the synthetic as a realm of simulacra. Deleuze pokes at this topic as one pokes at a strange animal lying prone to see if it will move. As we know, for Deleuze the movement of this animal is the history of western philosophy; and when it moves, Deleuze shows us that at its inaugural canonical moment, i.e. with Plato’s Socrates, philosophical thought has already assumed a morally-motivated critical disposition against the synthetic as an instantiated bad-copy of model, a perversion of nature, her essence and organicism, i.e. a virtual truth which is no actual truth at all. We will consider this, as Deleuze does, near the end of Chapters 1 (Difference in Itself) and 2 (Repetition for Itself).
Of course, while Deleuze probes a widespread opposition to the synthetic in its modality of western philosophy, the reader will also know that the modality of our own examination of this pathology is political economy’s morally-motivated ill-regard of derivatives as an evil realm of simulacra, of simulated capital, a bad copy of a model of value, a perversion of the commodity, her concrete essence and organicism, i.e. a virtual commodity which is no actual commodity at all –and above all else, the outstanding poor regard of this derivation of classical exchange that yet falls short of the representation of “true” value. This is the ‘terrible power’ of the ‘whole apparatus of repetition’: it is such a power of synthetic exchange our Guidebook seeks to examine anew, for purposes of it’s a radical revaluation by and for a project of political economics –a new materialist political economics in an age of synthetic capital.
§ 1st contrast of generality and repetition –from the perspective of law; flat space equivalence classes; introduction to classical symmetry, which is conservative, and synthetic symmetry, which is transgressive; introduction to a critique of representation (pg.2-5)
What is the nature of the differences between these two economic orders, between the domains of generality and repetition? Deleuze begins by warning his reader that while the transition from one to the other can be perceived to occur by linear progression, we should not mistake that there is in fact a difference in kind (i.e. ontologically) between the two domains, rather than merely or exclusively a difference in degree (i.e. historically).
(‘Repetition can always be “represented” as extreme resemblance or perfect equivalence, but the fact that one can pass by degrees from one thing to another doesn’t prevent their being different in kind.’)
It is difficult to overstate the importance of this point for the purposes of our future elaboration of dynamical systems theory. Deleuze, however, is perhaps getting a little bit ahead of himself here. We will not follow his cue too far by equally getting ahead of ourselves. However, one brief point of explanation may prove helpful.
Deleuze is saying here –and in DR will ultimately illustrate– that, for instance, just because one sees in the progressive differentiation of the ‘domains’ we call ‘markets’ a passage by degrees does not mean that the objects populating such domains do not differ in kind. That conduction and convection and turbulence all proceed by degrees does not prevent their being different in kind. And so too though we observe the linear development from a set of markets populated by numerical multiplicities –actualized as classical objects and generic financial objects (the objects populating flat space)– to those populated by qualitative multiplicities –actualized as synthetic financial objects (the objects populating curved space) doesn’t mean that their systems of exchange don’t differ in kind. Numerical multiplicities and qualitative multiplicities differ in kind; they differ as objects, and they differ as domains of action.
In the modality of economics such ‘domains of action’ (as the geometer calls them) are quite obviously markets. There is an order of generality, and there is an order of repetition; we may witness the passage by degrees from one order to the other; and the two orders may even resemble one another; but there is an important ontological-economic difference between them. It is merely a matter for us to follow Deleuze’s analysis further in DR so as to find out what is the precise ontological character of this difference, and to understand how different markets which resemble each other, and pass by degrees from one to the other, might actually differ in kind.
(‘…Generality belongs to the order of laws…It condemns [particulars] to change…[and yet is] an empty form of difference, an invariable form of variation.’)
The 1st of 3 contrasts Deleuze makes between generality and repetition is from the perspective of law. And in the modality of political economics, “the law”, which is thought to generally order the values of change, is said to manifest itself in and through the becoming, or change, in value –or what political economics has historically understood to be a theory of value for economic objects.
Now, it is important to observe here that Deleuze and why Deleuze discusses generality in strict Euclidean terms. If we do not understand this fundamental point we will misunderstand Difference and Repetition from the beginning. Our reader will be reminded that generality has now been established as the domain of action of resemblance and equivalence. And so if in turn we keep in mind that in Marx’s ontological schema, resemblance and equivalence are the qualitative and quantitative orders of classical exchange and generic finance, then it follows that Deleuze is ontologically collapsing these two classes of exchange into Euclidean geometry –or rather, more correctly, he’s identifying an isomorphism between geometric equivalence classes and classes of exchange. Classical exchange and generic finance are flat space equivalence classes of exchange. Such equivalence classes and Euclidean geometry are of different modalities, i.e. one is of economics and the other is of mathematics, but they are both of the same order of generality. Let us consider why.
congruent motions, i.e. classical exchange
Euclidean geometry defines a congruent transformation as the rigid motion of a geometric object into its image, with all its metrical properties remaining absolute and invariant in the course of its transformation: an object is set in motion as it moves from one to another place in space; and this object will subsequently occupy different Cartesian coordinates; but all properties of the object remain unchanged, invariant, and indifferent to the difference of their new position in space. Additionally, Euclidean geometry defines a similarity transformation as the rigid motion of a geometric object into its image with all metrical properties except its lengths of sides, and consequently its volume, remaining absolute and invariant: an object is set in motion as it moves from one to another place in space; and this object will subsequently occupy different Cartesian coordinates; but all properties of the object except for its lengths of sides and volume remain unchanged, invariant, and indifferent to the difference of their new position in space. Euclidean space is a flat space. Flat space is populated by sedentary objects, whose transformations into their image either effects no or else very little alteration to their metrical properties. Objects transformed in Euclidean space –whether by congruence or similarity– therefore effect an ‘invariable form of variation’, ‘an empty form of difference’ in their space of transformation. The technical term given by geometry to such invariance to change is symmetry.
generic finance (debt & equity)
We explain this so that the reader of DR does not miss the decisive move made by Deleuze when he later begins to give philosophical transformation to these mathematical concepts. Deleuze is often mistakenly regarded as a common poststructuralist by those who are oblivious that group theory and non-Euclidean geometry –among other mathematical and scientific insights– are of much greater methodological predominance in his work. Of course because DR is giving philosophical transformation to these mathematical concepts, we will see Deleuze modify the Euclidean understanding of symmetry that is surreptitiously imported into our political economics: this is the kind of symmetry that is classical symmetry. In DR we see Deleuze counterpose classical symmetry with a second kind of symmetry, which is synthetic symmetry. DR provides a thorough exposition of the ontological differences between these two symmetries that so differ in kind. And remarkably, he will illustrate that this second kind of symmetry is at the heart of the first –which, our reader will learn (or may know already), is originally a group-theoretic insight about the ontological relation of the non-Euclidean equivalence classes to Euclidean transformations (We will have occasion to discuss the contributions of the group theorists Evariste Galois and Felix Klein sometime later).
(‘If repetition is possible, it is…against the similar form and equivalent content of law.’)
We have said Deleuze is observing that the equivalence classes of Euclidean geometry are isomorphic to the flat space equivalence classes of classical symmetry in economics: congruence transformations are to classical exchange what similarity transformations are to generic finance, insofar as transformations of classical objects effect no change to their metrical properties, while transformations of generic financial objects allow for their length of tenure and volume of image of value to shrink or grow over the course of the exchange, but otherwise effect no change to their metrical properties. (More on this point will be developed later; however, for more immediately on the isomorphism between geometric transformations and economic transformations, see the Appendix in Of Synthetic Finance)
Deleuze wants to make clear that as flat space equivalence classes of exchange, both of these aforementioned equivalence classes are populated by objects whose domain of action is the order of generality. This is why Deleuze opposes repetition to generality (i.e. its ‘similar form and equivalent content’). Repetition is the domain of action of synthetic transformations, and is predicated on the actualization of synthetic symmetry. Generality is the domain of action for congruence and similarity transformations, and is predicated on the actualization of classical symmetry. Deleuze upholds synthetic symmetry over classical symmetry, and because of this he opposes difference and repetition to resemblance and generality. And why? For what purpose? To what effect? In short, he does this precisely because he seeks to upend our traditional and flat space understanding of a system of economic transformations (viz. exchange) whereby nothing is transformed in the course of exchange; he seeks to elude reproducing this ‘empty form of difference’, the ‘invariable form of variation’ of classical symmetry, whereby everything remains the same in the course of its ostensible change, whereby a conservative invariance requirement on economic transformations is morally maintained in the face a more radical potentiality for change. This is his wager for thinking the ontology of the synthetic.
It is therefore highly thought-provoking to stand back here, already on the opening pages of the Introduction to DR, and reflect on the project at hand. Deleuze is engaged in a critique, an exposition of the internal limits of representation in philosophy: this is the avowed, ostensible, and actual project of DR. But there is a virtual project going on here as well. It is compelling to realize that the very same philosophical concept of representation that is the actual object of critique in DR is always already virtually operationalized in our classical political economic understanding of value, as it’s employed in our flat space equivalence classes of exchange (i.e. in congruence and similarity transformations), and at work in the actualization of classical symmetry. Our wager here, then, is to follow Deleuze en route to using the concepts of difference and repetition to think the ontological property of the synthetic –a synthetic symmetry– at the same time that we use synthetic symmetry to help us to rethink the political economic concept of value…And ultimately to therein tap an infinite leverage to actualize a mode of nomadic distribution.
This is a timely project, indeed. We set out with Deleuze’s Guidebook to do this at the very moment that synthetic finance is progressively differentiating itself within the system of exchange that is finance; we do this at the moment that an order of generality is progressively passing by degrees into an order of repetition –and yet we are seeing that these two orders differ in kind. That is to say, we do this at the very moment that –to put it in Deleuze’s terms– the virtual is progressively getting refracted through itself and now dumped out into actuality.
Deleuze further articulates some ontological properties of repetition in the modality of economics that distinguish it from the domain of generality from the perspective of law.
(‘If repetition is possible, it is due to miracle rather than law. If repetition can be found, even in nature, it is in the name of a power which affirms itself against the law, which works underneath the laws, perhaps superior to laws. If repetition exists, it expresses at once a singularity opposed to the general, a universality opposed to the particular, a distinctive opposed to the ordinary, an instantaneity opposed to variation, and an eternity opposed to permanence. In every respect, repetition is a transgression. It puts law into question, it denounces its nominal or general character in favor of a more profound and more artistic reality.’)
There is much in this statement that will need to be comprehensively unpacked when we periodically return to these topics in their more thorough incarnations in DR later on. However, as the reader can see, Deleuze is issuing a bold proposition right away in DR, and from which a bold promise follows. He is proposing that we radically rethink our political economic concept of value. And he suggests that doing so convokes the possibility of constructing an alternative and radically different system of exchange. He’s talking about distributing a different space for the circulation of capital –a distributive systemic-space founded on repetition, and working ‘underneath the laws’; one that that is ‘distinctive’, ‘singular’, ‘universal’, ‘eternal’, ‘transgressive’, and always in the service of ‘a more profound and more artistic reality.’ We will see Deleuze resume his elaboration of this notion as soon as Chapter 1 (Difference In Itself).
Of course, the question always arises here of how we arrive at such a ‘reality’? A question for Deleuze to address in DR is how, if an order of generality will pass by degrees into an order of repetition, one can ever observe the achievement of repetition “in-itself”? In his Introduction he alludes to this issue, which he will more fully treat in Chapter 2 (Repetition For Itself), and then in later chapters in even more depth.
(‘Repetition appears…only in the passage from one order of generality to another, emerging with the help of –or on the occasion of– this passage. It is as if repetition momentarily appeared between or underneath the two generalities. Here too, however, there is a risk of mistaking a difference in kind for a difference in degree.’)
Let us work backwards here towards the beginning of this passage.
First, we see Deleuze again remind his reader –when sketching his opening comments on the proprietary differences between generality and repetition– that the character of these differences may be perceived to be a mere matter of degrees, that they may appear to us as spatially-progressive and temporally-linear. However, Deleuze reiterates that these differences are ontological: they are different in kind, extremely so; and that we would be remiss to mistake our linear perception of a difference in degree for what is in fact nonlinear and ontologically different in kind. As we have said, this is a consistent and important theme threading its way throughout DR to which we will periodically return, insofar as, on the one hand, we must grasp what it means that different economical objects and the markets they populate are ontologically different in kind; and on the other hand, we will come to know such statements as instructive of the peculiar and highly original methodology developed by Deleuze for the task at hand. Deleuze rejects naïve realism, and yet is obviously not an idealist in any sense of the term. We can call Deleuze a speculative materialist (if we find ourselves psychologically requiring some label to attach to his style of analytically proceeding) –since he does indeed proceed as a “materialist”, i.e. as one who aims to think the registers of reality as material reality; but he does so by way of an analysis of a register of reality he labels “virtuality”; and so we must at least concede that he’s a new and peculiar kind of materialist. Also, as we will discuss later, Deleuze emphasizes the analytical power of “speculation”, much like Copernicus did when speculating about that which and where his sensible perceptions either could not go, or else when they led him astray; but Deleuze appears to even regard this kind of speculative practice as a radical empiricism. We will consider several features of Deleuze’s methodology in Chapter 3 (The Image of Thought).
Secondly, then, when we are examining Deleuze’s assertion that ‘[r]epetition appears…only in the passage from one order of generality to another’, and that ‘it is as if repetition momentarily appear[s] between or underneath’ the two domains of generality, we should proceed under the color of our earlier observation that Deleuze is preparing his reader for a full-scale philosophical exposition of the concepts of difference and repetition, and that the latter is merely a necessary inaugural step towards thinking a concept of value radically independent of the Euclidean model of representation infusing Marx’s critique of political economy. By proceeding in this manner, we immediately find Deleuze’s aforementioned claim to be very thought-provoking and seductive –if still, at this point, admittingly somewhat nebulous for even his most earnest reader.
For instance, if classical symmetry is of the domain of generality, and in practical terms is constrained by ‘the shackles of representation’, what does it mean that repetition is ‘momentarily’ revealed ‘between or underneath’ its domain of action –especially when these domains of action are the markets populated by financial objects? Or, how can we witness such a repetition if it remains unmediated by ‘the shackles’ of representation? Is this not merely an obtuse manner of ascribing an unrepresentability to that which we have simply asserted to exist, albeit now merely switched-out for the old term ‘representation’ the new term ‘revealed’? We will return to these questions and examine assertions made by Deleuze of just this sort after we have prepared ourselves, by close analysis of the text, to understand its meaning.
§ the order of generality and the order of repetition: a difference in kind; introduction to the value-form (pg.1)
Deleuze begins by distinguishing generality and repetition as two orders that are different in kind.
(‘Repetition is not generality. Repetition and generality must be distinguished in several ways. Every formula which implies their confusion is regrettable…Repetition and resemblance are different in kind –extremely so.’)
He defines the order of generality.
(‘Generality present two major orders: the qualitative order of resemblances and the quantitative order of equivalences…[G]enerality expresses a point of view according to which one term may be exchanged or substituted for another. The exchange or substitution of particulars defines our conduct in relation to generality.’)
He then contrasts the order of generality with the order of repetition.
(‘By contrast, we can see that repetition is a necessary and justified conduct only in relation to that which cannot be replaced. Repetition as a conduct and as a point of view concerns non-exchangeable and non-substitutable singularities. Reflections, echoes, doubles, and souls do not belong to the domain of resemblance or equivalence.’)
We have said that Deleuze’s inaugural distinction between these two orders is made to alert the reader that s/he will be encountering an ontological disquisition on political economics –a political economic revaluation of value by way of an ontological analysis of synthetic finance. On the one hand, Deleuze associates the order of generality with the phenomena of resemblance (qualitative) and equivalence (quantitative). On the other hand, he associates the order of repetition with the phenomena of nonresemblance (qualitatively) and nonequivalence (quantitatively) –or as he says, ‘of non-exchangeable and non-substitutable singularities’; and to this latter ‘order’ or ‘domain’ belong ‘reflections, echoes, doubles, and souls’ –Deleuze might have added ‘synthetic financial assets’ and ‘synthetic securitization’ to this list as well, for the domain of action of synthetic financial markets comprise an order of nonresemblance and nonequivalence. We will see that and why the objects populating these markets are images of objects without likeness.
Deleuze makes this inaugural distinction as a way of alluding to Marx’s profound analysis of the ontological properties of an economical object (viz. the commodity) in the Part I (Commodities and Money) of Book I (The Process of the Production of Capital) of Volume I of Capital. In Book I, which comprises the first 100 pages or so of Capital, Marx distinguishes value from the value-form, and then imputes to the latter the quality of generality. To truly appreciate Deleuze’s opening rumination on the ontological distinction between generality and repetition, our reader is encouraged to revisit the first 100 pages or so of Capital.
the rigid motion of translation (the relative form of value)
For Marx, classical exchange is an equivalence class of flat space; flat space is a domain of generality; and the value-form is the great generalizer. The value-form is that which performs the ‘magical’ or ‘metaphysical’ feat of translating all qualitative differences in and of value into the property of ‘the same’ –i.e. the same ‘form’ of value, or, ‘the value-form’. The value-form renders qualitatively singular objects of value identical; in the value form all disparate values suddenly resemble one another; two or more objects of value are opposed to one another in the act of exchange; in the act of exchange all objects are analogous (note: our reader will come to know that identity-resemblance-opposition-analogy are what Deleuze labels ‘the four shackles of representation’, which we later discuss). The value-form, then, is that which renders all dissimilar quantities of qualitatively distinct objects commensurable, such that that they are exchangeable: asymmetrical objects of value become symmetrical images of value in the value-form. Marx depicts the value-form as a kind of warped reflection, a deceitful echo, an imagistic double, a bad copy of the true soul of value. This is why, for Marx, the domain of classical exchange is the domain of resemblance and equivalence. In such resemblance and equivalence, objects will achieve their perceived commensurability so as to be rendered exchangeable for one another. But then again, for Marx, this is precisely what is so fetishistically horrifying about the value-form: he proceeds to illustrate that value can only ever express itself, i.e. can only ever be represented to us in this derived form; and so looked at from this perspective, the conversion of an object’s “true” value into the value-form, its transubstantiation into a derivative image or bad copy of value, is the price paid by the object qua natural object for its transformation into an object qua economical object, such that it now becomes exchangeable for other objects.
“So let’s just strip-out this derivative of value?”, we think. “Let us cut from exchange this mediated and imagistic step, and we will resolve ourselves to access the model (value) of the copy (the value-form) directly?Indeed, shall we not simply purge the image of value (value-form) from exchange, and go straightaway to the essence (value)? Let us agree to a system of exchange whereby we exchange objects of value as value in-itself?” No, Marx quickly points out, we cannot. For the problem is, without this mediating step, i.e. without the conversion of an object of value into the image of its value-form, there is no representation of value, no commensurability between objects will even be arrived at, and therefore no exchange will occur. This is why, for Marx, already in the first instance of classical exchange something has gone horribly wrong. Already the object as value is a mere image of value in the value-form. Already the economical object is perverted, synthetic, derived, a bad copy of “true” value. Moreover, it is rather difficult to see how the world of exchange could be otherwise, since such mediation, such representation of value in the value-form, is the very condition of its alienation –a kind of image set free of its object, but which then returns to dominate the object from which it has been emancipated.
This is the political economic backdrop to DR. Deleuze’s opening distinction here between the orders of generality and repetition convokes this aforementioned Marxian ontological lineage: resemblance and equivalence are of the order of generality, and classical exchange is a matter of resemblance and equivalence. This is why Deleuze contrasts generality and repetition as a difference in kind that is most clearly witnessed in the modality of economics.
(‘Generality, as generality of the particular, thus stands opposed to repetition as a universality of the singular…If exchange is the criterion of generality, theft and gift are those of repetition. There is, therefore, an economic difference between the two.’)
taken from speculative materialism
Deleuze, derivate, difference, finance, money, repetition