2 Sept 2015

Somers-Hall, Deleuze’s Difference and Repetition, Summary-Directory

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]


[Somers-Hall is abbreviated SH and Difference and Repetition as DR.]

Henry Somers-Hall

Deleuze’s Difference and Repetition.
An Edinburgh Philosophical Guide


[SH introduces DR. He will focus on the metaphysics of difference, while helping the reader through the challenges DR presents. DR’s structure: 1) First, it formulates a new understanding of difference that conceives it as being more fundamental than identity, and on the basis of this notion, we may reconceptualize repetition. 2) Then, it shows that this new notion is needed for understanding the more fundamental layers of reality (intensity, problems, Ideas), since the older philosophical means which use judgment and representation are inadequate. 3) Finally, it paves ways for this new sort of philosophical thinking. We also note that SH’s text is a handy guide to consult while reading DR, since it summarizes the philosophical argumentation and also provides useful supplements, like a glossary and further reading suggestions.]


Intro sect.1

[This book will discuss the many conceptual strands in Deleuze’s Difference and Repetition, with a focus on its ‘metaphysics of difference.’]

Intro sect.2: Challenges in Reading Deleuze

[Deleuze’s Difference and Repetition is challenging to read, because he uses difficult terminology, he refers to many various other thinkers, and the structure of the book is unclear. Somers-Hall’s guide will present Difference and Repetition in an accessible way by mitigating these problems as best as possible.]

Intro sect.3: The Structure of the Text

[The basic structure of Difference and Repetition begins with a new understanding of these concepts in order to develop a way to understand the world without representation or judgment.]

Intro sect. 4: How to Use this Guide

[Somers-Hall’s guide is best read alongside Deleuze’s Difference and Repetition, however it could also be read alone. Somers-Hall also provides many helpful supplements in the book as well.]

Part 1: A Guide to the Text

[In DR, Deleuze reconceptualizes repetition and difference. He does so in order to enable philosophical thinking to find a new way to operate, which will allow it to explore a more fundamental layer of reality. In this layer, difference’s role is the genesis of variation, while repetition’s role is the perpetuation of variation. They cannot be thought using our normal philosophical tools, because their operations are unrepresentable, meaning that they do not lend themselves to subject-predicate judgments that may define something by determining which properties it has and which it lacks. To understand how all this works, we should distinguish three layers of reality: 1) Ideas, 2) fields of intensive difference, and 3) extensive actuality. In the world, intensive differences enter into situations that present problems. Ideas form in response to those problems, and they are like maps that implicitly suggest an infinity of ways the situation could develop. Those Ideas then interact with the problematic fields of intensive difference in a dramatized (unpredictable) way in which only certain developmental paths are actualized and made explicit in the world. It is just on this explicated level of extensity that we find negation, limitation, opposition, and identity, which is why extensive actuality lends itself to representation. Prior to that, on the levels of difference and intensity, all is affirmative and unrepresentable. Aristotle’s system of classification deals with this representable level of extensity, but it has its own flaws which result from it not acknowledging the more fundamental, non-conceptual sort of difference. Duns Scotus, Spinoza, Nietzsche, Hegel, Leibniz, Merleau-Ponty, and Plato all have to a greater or lesser extent improved upon Aristotle’s model. But to think this unrepresentable difference, our faculties really need to operate discordantly as each deals with an object different in kind from the others. Deleuze’s project in DR was not entirely successful in bringing about this new sort of thinking, but it makes substantial leaps in that direction.]

0 Introduction: Repetition and Difference

[In the Introduction to DR, Deleuze clarifies how true repetition is not generality, and thus it is not the repetition of  artificially equalized things, like the replications of scientific experiments and the mechanically rigid application of moral laws as if each ethical situation were identical. Rather, it can be the reiteration of things with the same conceptual determinations but with non-conceptual differences, like Kant’s incongruent counterparts, words, and atoms, and also it can be the repetition of inconsistent moral commands, like Kierkegaard’s notion of God’s variable moral law.]

0.1 Introduction

[In the Introduction to Deleuze’s Difference and Repetition, he argues repetition is commonly understood in terms of generality and law, when in fact it is not related to these concepts. We are mistaken when we think we encounter repetition in scientific experiment, moral law, and psychological habit. These are generalities and not repetitions.]

0.2 Science and Repetition (1-3/1-4)

[Scientific experimentation seems to repeat situations as if all were equivalent. But this is a mistake. They are not equivalent. They seem so, because by artificially selecting certain parameters and excluding others, the real distinguishing differences go unnoticed. Also, all features of the situation, including qualitative ones, are quantified, which equalizes all these differences in kind to the common system of numerical symbolization, which ignores all individuality of the things being quantified. Also, when laws are formulated on the basis of experimentation, it is always just a hypothesized sameness: ‘given the same circumstances …. [expect these same results]’.]

0.3 Kant’s Moral Law (3–5/4–5)

[It might seem that moral laws which tell us to do the same thing in the same situations are instances of real repetition. But they are really just the application of the mechanistic operation of natural laws into our moral life, and thus they are generalities like scientific laws rather than real repetitions.]

0.4 Kierkegaard (5–9/5–10)

[Kierkegaard presents a notion of repetition in moral life which does not fit the idea of a universal law. Kant says that Abraham should not have assented to God’s request to kill his only son Isaac, since doing so goes against the categorical imperative. Kierkegaard thinks that there is an absolute (God) which is of a higher moral authority than the ethical universal. Repetition in moral life, for Kierkegaard, is not obeying the same law over and over, but rather obeying an absolute whose commands are not homogeneous or self-consistent. What is notable in this conception of repetition is that it is not the reiteration of the same action but rather each time behaving differently in a different situation.]

0.5 Extension and Comprehension (11–16/13–18)

[We might normally think of something repeating as being a reiteration of the same thing. In this sense, we are thinking of repetition in terms of generality, since the thing being repeated is understood as something general that is reiterated in a number of particularities. Yet, Deleuze is formulating a concept of repetition which is not based on generality. Representation is also often understood in terms of generality, and thus representation is not for Deleuze a sort of repetition. There are two processes involving representation that Deleuze addresses: representational memory (which represents objects no longer present) and recognition (which compares present objects with internal representations). These representations often take a structure which makes them only representative of certain objects and not others. This structure can be understood as having a comprehension and extension. The comprehension is the conceptual description which delineates the essential attributes of the thing. The extension are the variety (or singularity) of things that the representation includes.  [“the comprehension of the idea triangle includes extension, figure, three lines, three angles, and the equality of these three angles to two rigid Angles, &c.” and “the idea of triangle in general extends to all the different sorts of triangles” (Arnauld 1850: 49).] The more we add to the comprehension, the more restrictive it gets, and thus more comprehension results in less extension, and vice versa. At the extreme where the extension is one thing, that means the comprehension has expanded to the infinite. Deleuze then addresses a problem this raises when we take into consideration Leibniz’ identity of indiscernables: “if two things share the same properties, they are in fact identical” (15). This implies that two objects cannot share the same properties, as they would really be one identical thing. But if repetition is understood as the reiteration of the same, then this sort of repetition would be impossible. However, if we have a reiteration of things which cannot be conceptually distinguished, then we would have a repetition without them collapsing into one self-same thing. But in order to have Deleuze’s sort of repetition, we need on the one hand to have things which are reiterations but on the other hand not be reiterations of things which conceptually collapse into one another. To progress to such examples, we need first to note the concept of blockages. All things within a generalized concept are the same and thus they all collapse into one another. All mammals if not further specified are conceptually indistinguishable. In order to distinguish some of those mammals from others, we need to stop the application of the term in certain cases, or to put it another way, we need to instate ‘blockages’, which are conceptual determinations. This allows us to have ‘horses’ and ‘cows’ be repetitions of the concept of ‘mammal’. We can further divide horses using other artificially instated blockages. But what we want are natural blockages where the differences are inherent to the things while also they cannot collapse conceptually into one self-same thing.  One case would be things which are conceptually indistinguishable (with that concept having an extension of 1) but differ only in spatial temporal determinations (which cannot be part of the conceptual determination). Atoms for example are like this. Another example of this is using the same word in many cases. They have the same conceptual determination but different contextual variations.]

0.6 Incongruent Counterparts (13–14/15, 23–7/26–31)

[For there to be repetition, you need a number of instances of something, but they cannot all be one and the same, as you would have one thing never ceasing to be itself rather than repeating. But if there are no conceptually discernible differences between the instances, they would collapse into one another. However, if there are conceptual differences, then they are not reiterations but rather new things altogether each time. So to have repetition, it would seem we need a series of things which are not conceptually distinguishable (and thus do not collapse into one thing) but are also truly unique from one another (so that there is reiteration and not continuation). Deleuze offers examples of such cases. Here we look at Kant’s incongruent counterparts. If we imagine that the first thing invented was a plain and very simple glove, we would not know if it were left or right handed. For, you could flip it over and it could fit the opposite hand. But (assume that) God would only make a glove for either a left or a right hand. It must inherently be one or the other. [It is left handed on account of there being not the relative spatial relations of each part of the glove to the other parts, but rather that the glove takes up some absolute position in space, which perhaps is a place belonging either to a left or a right hand]. So because many things are different (like being left and right hand gloves) without any spatial relations to determine which is which, these incongruent counterparts are examples of repetitions without conceptual distinctions.]

0.7 Conclusion [to the Introduction]: Three Forms of Difference

[We have seen two main types of difference, conceptual and non-conceptual. Deleuze in the first chapter of Difference and Repetition will “perform an enquiry into the principle of difference which neither sees it as conceptual nor sees its non-conceptuality as the end of our enquiry” (21).]

Chapter 1. Difference in Itself

[Chapter 1 of DR critically examines representational systems. They are unable to describe the fundamental world of intensive variation where determinate essential distinctions do not hold. Aristotle’s representational system of genus-species classification also is not even consistent, as it requires that the fundamental category of being be univocally defined while everything else under it equivocally defined. There are four solutions to the problems of representational systems such as Aristotle’s: 1) The univocity being in Duns Scotus, Spinoza, and Nietzsche. 2) The infinite representation of Hegel’s and Leibniz’s systems. 3) The perspectivism of Merleau-Ponty’s phenomenology. And 4) The partial participations in Plato’s system of division. Of these solutions, Spinoza’s and Nietzsche’s are the most successful.]

1.1 Introduction (28–30/36–8)

[We are seeking a more profound notion of difference than what we normally ascribe to it. We operate as though there is a world to which our judgments make differentiations and determinations. We say, ‘this is an x’, and in this way we use the subject-predicate structure to designate things in an otherwise undifferentiated world. But in fact, using such representations will not suffice to explain the grounds of our representational system, which is subrepresentational.]

1.2 Aristotle’s Conception of Difference (30–3/38–42)

[Aristotle’s conception of difference is bound up with his theory of classification. A genus is divided into species, which differ in kind. The division terminates in the individuals, which differ in number and only accidentally [rather than essentially like species do]. The genus-species distinction is relative, such that any genus can be a species to a higher genus, just as any species can be a genus to a lower species. The one exception is the species-individual relation, in which the species cannot again serve as genus, given that there are no species below it; instead there are only individuals. Difference in its truest sense is the difference in kind which distinguishes one species from another.]

1.3 Aristotle’s Conception of Being (32–5/41–4)

[Aristotle’s system of categorization and definition involves designating the essential differences between species within a genus. Thus we might have these definitions and classifications: ‘man (species) is an animal (genus) that reasons (species difference),’ while ‘fish (species) is an animal (genus)  that lives under water (species difference)’. A grave problem this presents to the system is that it undermines its own foundations. All the elements that are classified in the system presuppose a concept of unity or being. As well, the notion of difference which is required to distinguish the parts is also something that has being, and thus it too requires a concept of being for it to be a sensible part of the system. However, being cannot be given a clear conceptualization, since there is no higher genus under which it can be distinguished from other species of its general type. Aristotle’s solution is that there is no one highest genus but rather there are many senses of being that all refer to the same focal concept of being, which is not to be understood as a higher genus. It is like paronymous  meanings, that is, meanings which are related by morphology, like grammarian and grammar. Nonetheless, this solution compromises the coherence of the system, since genus, especially the highest one that encompasses all others, functions by means of a different rule than the species do. Species require univocity in order to be specific and determinate. But genera require equivocity in order to be multiple yet ultimately terminal.]

1.4 Duns Scotus (35–6/44–5, 39–40/48–9)

[The Aristotelian system of genus-species categorization and definition places ‘being’ as the highest category (or highest categories of senses of being). This presents a problem for medieval theologians who want God as the highest category. We note first that the Aristotelian / Aquinian solution is to say that ‘being’ is understood equivocally, in that there is the finite being of our world and the infinite being of God. But being applies to both, since they are analogical (as they have the same cause, God). Duns Scotus objects that we cannot know they are analogical unless we already knew of God’s perfection. Thus our own finite perfection cannot be the basis for us knowing of God’s perfection. Scotus identifies the problem as resulting from making finite and infinite be different in kind rather than different in degree. The infinite being / infinite perfection of God is just a much higher degree of being / perfection than our own. Thus when God’s infinite being is understood intensively, we understand being univocally. It also means that being is not a higher genus than God, since degrees of being / perfection are modes and not properties (and thus not predicates and thus not higher genera) of substances. However, Scotus’ theological position is that, nonetheless, the infinite difference in degree is a difference in kind between God and humanity, which compromises the univocity of his concept of being.]

1.5 Spinoza (40/49–50)

[Spinoza is a philosopher of univocal being, and under Deleuze’s original interpretation, Spinoza is a philosopher of univocal self-differential being. For Spinoza, there is one infinite substance, which is also both God and the world in all its entirety. Since substance is infinite, that means its essence is infinite. In fact, it has infinitely many essences. The essence as our minds understand it would be substance’s ‘attribute’. Our minds are able to comprehend just two of substance’s infinitely many attributes, namely, thought and extension (the ‘realm’ of ideas and the parallel ‘realm’ of physical bodies). There is one substance, but it expresses itself through (at least these) two unique essences. And there are infinitely more. But since there are infinitely many, we cannot characterize substance on the basis of the sum of all its essences, since there is no limit and thus no determinate totality of essence. However, each essence is different from the others. And yet, consider how all of substance’s modifications or determinations are expressed in each attribute. For one attribute to differ from another then, is for substance to internally differ from itself, since each attribute fully contains substance and yet the essences are not identical. Thus, since there are infinitely many essences that fully express all of substance’s determinations, that means there are infinitely many self-differential relations that constitute substance’s essentiality. So instead of conceptualizing substance by means of this or that essence or by means of all essences taken in sum, we can instead conceptualize substance as being infinite self-differentiation. In addition, all of substance’s modal determinations are like intensive degrees and as such are in a way part of an unbroken continuum of variation. Thus both on the levels of essence and determination, substance is a univocal multiplicity: it is one thing but it is thoroughly composed of self-variation (self-differentiation).]

1.6 Nietzsche (36–7/45–7, 40–2/50–2, 52–5/63–7)

[If we understand ‘being’ as power rather than as substantiality, then we can grasp it as univocal and affirmative. Deleuze builds from Nietzsche’s notion of subjectivity being a fabrication created by the weak in order to externalize blame for their weakness. In reality there are just competing forces expressing themselves at their fullest and finding relative value in their competitions. This is a nomadic understanding of what makes up the world. It sees the world as made of pure difference, that is, exclusively of differential relations between competing forces. And it is affirmative, since these powers are understood as being as great as they can be and never arbitrarily self-limiting. They are expressions of a pure affirmative will.  A sedentary understanding would instead section off regions in this field of differential power relations and say we have substances with different moral values, depending on how they seemingly choose to dominate others. This sees one thing as being defined by the limits that separate it from other things, thus it is based on negation rather than affirmation. Also, it can only come after the more basic differential field of change and becoming.]

1.7 The Eternal Return (40–2/50–2)

[In Nietzsche’s eternal return, we re-experience every moment of our lives exactly as we have, but infinitely more times throughout eternity. If we view the world as made of delimitable subjects that may make moral choices as to how much power to exert over others, then we would be inclined to think that certain circumstances in our lives could have been better somehow. We therefore would not want to affirm the eternal returnability of every aspect of our lives and self-experience. However, if we saw that fundamentally there are no such substantial divisions in our world but rather just forces competing and always expressing their will and power to their fullest in any instance, given their struggles with other forces, then we would see that every moment of our lives is as perfect as can possibly be. And for that reason, we would want to affirm the eternal returnability of our entire lives. By means of this concept of eternal return, then, we may have a univocal understanding of being, since all being is variations in differential power relations, while also maintaining an intensive view of differences in being.]

1.8 Infinite Representation (42–4/52–4, 48–54/59–65)

[Representational systems may be classified either as finite or infinite. In finite ones, finite forms are limited  by the matter they inform. But in infinite representation, all things are somehow expressions of one infinite concept. (This distinction will be clarified in forthcoming sections.)]

1.9 Hegel (44–6/54–6, 51–3/62–4)

[Hegel’s dialectic is an infinite movement. But it also generates the categories we use in representational thinking. Therefore, it is infinite representation, unlike the finite representation of Aristotle, which fixes things in a stable system of definitional limits. Nonetheless, 1) Hegel’s infinite representation still has a pattern-instance structure similar to Aristotle’s genus-species structure, 2) it makes no room for the uniqueness and singularity of each moment, since each in a sense is contained in or born out of prior states, and 3) the real world is too complicated and full of ambiguity to admit of Hegel’s system of cleanly distinct opposites.]

1.10 Leibniz (43–4/54, 46–52/56–63)

[Leibniz presents an infinite representational system. The world is composed of monads with predicates. This means the world takes on the subject-predicate structure of judgments, and is thus representational. Each monad is in some relation to every other monad, and these relations are expressed in a monad’s predicates. Therefore each monad expresses the world in its entirety. There are infinitely many monads, so there are infinitely many predicates for each one, and thus what each monad represents in its predication is infinite. Since we have a world of coexisting differences, we would think in Leibniz’ system that we might have non-oppositional difference. However, we have just one world with its own defined limits, since it stands opposed to other possible worlds that have inconsistencies and thus were not created. So while within this world there is non-oppositional difference, between this world and the others that God did not create there is in fact an oppositional difference.]

1.11 Phenomenology (55–7/67–9)

[Many philosophical systems explain reality by means of such concepts as limitation, negation, and opposition. Deleuze showed these to be flawed concepts. However, there is a reason they arise. Our knowledge of the things in our world is limited to our perspectival knowledge of them. In perception we can only view an object from our perspective, and we never see it from all possible perspectives at once. Nonetheless, we regard it as a whole thing, even though our phenomenal data can only constitute it partially. Deleuze thinks that the way we do this is by placing the partially constituted object into oppositional relations with other objects, so to define its boundaries and to constitute it negatively. In reality, the object can be no more than our perspective on it. Merleau-Ponty’s perspectival phenomenology could perhaps be not based on identity, but in fact it is, since the body is taken as a center of perception and thus to have a fixed identity.]


1.12 Plato (59–69/71–83)

[Plato has a method of classification that is obtained by jointly dividing general groupings into more specific ones while simultaneously having a (rough) definition for the things to be classified. Aristotle’s system of genus-species classification is similar, since he also divides general to specific. But inclusion for Aristotle is absolute, while for Plato it is relative. A candidate can be more or less faithful to the ideal model it is an instance of. Thus there are ‘imposters’ or ‘pretenders’ that can get mixed up with the good examples of a class of things. Similarly, Deleuze’s project of tracing phenomena to their origins in a field of difference (that is, his project of transcendental empiricism) is like Plato’s project of tracing things’ origins to transcendent ideals. However, Deleuze does not think that the origins lie in a separate world but rather that these origins are immanent yet go unnoticed since we normally fabricate artificial boundaries in the world of intensive variation, when in reality there are none.]

Chapter 2. Repetition for Itself

[Chapter 2 of DR examines the role of repetition in the three syntheses of time and of the psyche. A) The three syntheses of time. The first time synthesis is of habitual contraction, which synthesizes the living present. The second is of the memory, which synthesizes the pure past. The third is of the pure form of time, and it synthesizes the future. This third synthesis is ‘time out of joint’, which takes two forms: time 1) as formal and pre-successive, as with Kant’s a priori intuition of time, 2) as passively synthesized by the eternal return. When we affirm the eternal returnability of the present, we anticipate not the same states of affairs in the future but rather that, like now, the future will be composed of differential intensity. It impregnates the present with the future, which liberates us from the past. B) The three psychic synthesis. The first is the compulsion to repeat, which is a habitual synthesis. The second is the virtual object, which recalls a past experience that never happened, but which satisfies a current need. The third is the death drive, which for Freud tends backward toward a prior inorganic state but for Deleuze tends forward toward a future self-variation.]

2.1 Introduction [Introductory Material For Ch.2]

[In Chapter 2 of DR, Deleuze will elaborate on two themes from the prior text. He will look more at how repetition is possible. The difficulty is that repetition requires a new and different iteration (or else something is continuing and not repeating) while at the same time, the new reiteration needs to be identical to predecessors (for otherwise it will be something new altogether and not something occurring again). The other theme is explaining how the world can be constituted without supposing a unified subject that provides the basis for the coherence of the world.]


2.2 Background: Kant’s Three Syntheses of Time
[Further Introductory Material For Ch.2]

[Kant has three syntheses of time by which object representations are formed. As (1) our senses receive sense data, (2) our imagination constructs the pieces into wholes, by means of (3) the unities of our understanding’s concepts belonging to those wholes. [On the first level (sensibility), we grab onto a chunk of present moments, thereby synthesizing the flowing present. On the second level (imagination), we constitute the past in memory. And on the third level (understanding), we have conceptual structures that allow us to anticipate forthcoming impressions, thereby synthesizing the future.] The foundation for all synthetic unity, especially the unity of moments separated by time, is the unity of the subjectivity that is conscious of those moments. The syntheses of objectivities take the subject-predicate conceptual form of judgment, and thus this is a “representational” system.]

2.3 Deleuze’s First Synthesis of Time: Hume (70–9/90–100)

[We often see pairings of things, like: smoke-fire, smoke-fire, smoke-fire. After a while, when we see smoke, we then call to mind fire and expect to see it, and indeed, after looking below the smoke, we see the fire. This is because we contract all the prior instances of the pairings into one forceful association. Since it unites our past memories with our future anticipated impressions, this is a “contraction,” which somewhat inexplicably Deleuze also terms “contemplation”.  From an empiricist view, we are not some preconstituted subject who performs these contractions. Rather, the contractions happen automatically on a very basic level of experience, by means of a passive synthesis that does not involve our conscious understanding or the use of any concepts. Yet, [somehow] we can see every part of the world performing these contractions, including our hearts (and other organs) and all other things (including rocks, somehow). This means that we are composed of a ‘symphony’ (you might say) of different temporal contractions of past and future. This also means that all the world is such a symphony of selves each with their own temporality. Time then is not a linear, quantifiable sequence of successive events. It is rather a multiplicity of things feeling time in their own way, and is thus qualitative.]


2.4 Deleuze’s Second Synthesis: Bergson (79–85/100–7)

[The second synthesis is based on Bergson’s theory of time. It synthesizes the past with the present. Both of which are cotemporal. Why? If a new moment supplants the current one, there needs to be a place for the new one to settle into. There can only be such a place if the present one is already in the past. The solution is to say that the present moment is already in the past, and this is because as soon as new moments are experienced, they are already registered or entered in our memory. For Bergson, the past and all the present are one large entity with no discrete parts. When we recall something, it may seem like we remember a discrete moment in time. Really it is just a part of the whole of memory that is expanded. Every moment of our lives we carry all our memory with us. Sometimes we act in the moment, and all past memories express themselves in how we act, like when performing something we previously practiced many times. Other times we sit back and expand moments, like recalling one memorable practice session. The past is inserted in the present and determines it. But we are free to choose which parts to expand and when to expand them and to what degree to expand them. This mixture of the past’s determinacy without our current freedom of choosing how to experience the past in the present Deleuze calls Destiny.]

2.5 The Third Synthesis 1: The Pure Form of Time (85–9/107–11)

[For Deleuze, time is something that is synthesized, and there are three ways it is synthesized. Perhaps the most important and the most difficult to conceptualize is the third synthesis. The basic idea here [it seems] is that time is most fundamentally a pure form rather than an actual activity or process. To elaborate this notion, Deleuze says that in this synthesis, time “comes out of joint.” An analog clock-hand has a central spinning “joint” or “hinge,” in the sense of a 360-degree door hinge, as in a turnstile. Similarly, the stars in the sky seem to circulate yearly in perfect circles around the north star, and the sun seems to wheel around the world circularly each day. These regular motions give value to one another by means of ratios. For example, the sun makes about 365 turns around the sky by the time a star returns to its original position in the night sky (when we observe the star the same time each night). This is time that is “in joint,” perhaps meaning that it is time formed or conceived by means of motional regularities whose ratio comparisons produce a measure for a linear, progressive, and steady flow of time. Such an ongoing, steadily-moving sort of time is one of succession, where we have one day coming after the other, one year following another, and so on. One way to understand how time is out of joint is to remove this concept of successivity. Deleuze, then, turns to Kant’s notion of the pure a priori intuition of time. Before we can even experience time as a succession of moments – that is, as having a linear order and a sequence that can be enumerated as ‘moment one, moment two, moment three, and so on’ – we first need a basic mode of receptivity which would allow us to experience something as temporal in the first place. Then somehow secondly we may give temporal order and measure to our experiences.]

2.6 The Third Synthesis 2: Two Different Paralogisms (85–7/107–10)

[For Deleuze, there are three syntheses of time, and the third is the synthesis of the pure empty form of time, which he elaborates with his notion of ‘time is out of joint’. One way he further develops this concept is by commenting on Kant’s critique of Descartes’ cogito argument: I think, therefore I am. Descartes might be saying that because at this moment you are thinking, that means you know there is an I who is doing that thinking. And furthermore, this I [for some reason] is self-same and self-identical, and thus it does not vary over the course of time. Kant observes that Descartes is forgetting that in order to determine ourselves, that is, to determine our ‘I’ as being because it is thinking, we need some determination. Now, our ‘I’ formally speaking is no more than the unity that provides the glue for all variations through time we experience in the world and in our own selves. So this formal unity itself does not tell us more about who we are. Instead, in order to find out about and thus determine ourselves, we need to actuallty experience ourselves. [Recall also that for Kant, concepts require intuitions for there to be cognitions. We can only have cognitions of ourselves if we also have intuitions of ourselves.] Yet, we can only have such self-experiences in a flow of continuously varying experience. This means that we are never self-same from moment to moment. This also means that we never actually cognize that pure formal self that Descartes seems to think we have mental access to. That formal self is what actively syntheses all empirically given variations, including both intuitions of the world and of ourselves. Deleuze, however, does not think that we and the world are synthesized actively by some transcendental self. Rather, we will see that the unity of both ourselves and the world are the product of some passive synthesis.]

2.7 The Third Synthesis 3: Hamlet and the Symbol of the Third Synthesis (88–92/111–16)

[Another way that Deleuze elaborates his third synthesis of time, where ‘time is out of joint,’ is by discussing Hamlet and Zarathustra. Hamlet begins with the title character not deciding whether or not to take a serious action (avenging his father’s death by killing the murderer, Claudius). But without such actions, we are unable to organize Hamlet’s actions as being either conforming to the law or not. So the temporality of the first part of Hamlet is out of joint, because its events cannot be organized. Also, Hamlet in a way lives in a suspended present, since he cannot advance into his future drastic action, and this is also him being stuck in the past, back when he first was charged with the task of seeking vengeance. Furthermore, this lingering past and suspended present obtain their significance in relation to a future that they anticipate. We see something similar with Zarathustra. The title character at first is concerned with revenge and thus is stuck in the past. But when he comes to acknowledge the eternal return, he can live life unconditionally affirming the value of each moment and thus having no need to linger on the past and instead to see each present anticipatable eternally in the future.]

2.8 The Third Synthesis 4: The Esoteric Doctrine of the Eternal Return (90/113, 93–6/117–19)

[Kant makes an interesting move. He says that time is different in kind than the understanding. He could have further developed this insight by seeing how time synthesizes passively in habit and memory. But instead he holds to the authority of an active subject who performs a synthesizing operation on time. Deleuze likewise sees time as different in kind from the understanding. But for him, the synthesis comes about automatically, since the intensive differential relation (the pure empty form of time understood as the eternal return) that is responsible for the newness of successive moments is also what synthesizes them together. Thus for Deleuze, time can be synthesized without the help of a transcendental ego.]

2.9 Freud (16–19/18–22, 96/119–20)

[Deleuze is interested in non-representational repetition. Similarly, Freud is interested in repetitions of past traumas in our behaviors and psychic life that result from an experience that is non-representational, since it has been repressed. But while for Freud the compulsion to repeat is the brute repetition of matter, for Deleuze it is the intensive repetition of difference. In Freud’s account, the psyche is understood as a system that manages excitations, trying to keep itself in dynamic balance. Minimizing or keeping constant the levels of excitation leads to pleasure, and this is called the pleasure principle or a principle of homeostasis. Sometimes there is more excitation than it can handle, as in traumatic experiences, which leads to unpleasure. Yet, at times we now defer pleasure for greater pleasure in the future. This is the reality principle. But the repetition of past traumatic events cannot be explained by the pleasure principle.]

2.10 Freud’s First Synthesis (96–8/119–22, 111–14/136–40)

[In Freud’s model, an organic system has a relatively ordered dynamics, which can be disrupted by an excess of external excitations. One way it deals with this threatening excess is to habitually contract it into the system, which then has its ways of minimizing its destructive influence. [For example, if we suffer a trauma, we have an excess of disruptive excitation in our systems. Then we relive it for example repeatedly in our dreams, which use associations to distribute it relatively safely throughout the rest of our psyche]. This tendency to incorporate the surplus energy habitually is the compulsion to repeat and as well the libido. The pleasure principle is the tendency of the system to take that already contacted surplus energy and to manage it. The more it can be minimized or kept under control, the more pleasure we feel. However, the more it disrupts the system, the more unpleasure we experience. Thus the pleasure principle must be understood as distinct from the compulsion to repeat, since they are performing different actions. This can explain why it is we repeat traumas even though they are unpleasant; for, the compulsion to repeat them does not operate according to the pleasure principle. It is merely a mechanical feature of the organic system, and it is like the first passive synthesis of contracted habit. The contraction habit is a self-preservation drive, but it is a variation on the death drive. This is because the compulsion to repeat is an expression of a movement away from evolution toward the creature’s inorganic evolutionary origins.]

2.11 Freud’s Second Synthesis (98–111/122–35)

[The pleasure principle is what makes our inner workings manage surplus excitations, trying to minimize their harmful effect. But sometimes doing so blindly leads to more damage to the system. A hungry child without its mother present might become traumatized by the distress of concluding that they will die. So the active syntheses that manage the excitations need a further principle to govern them more effectively. They need the reality principle, which defers gratification. But this requires an active interaction with the external world of objects. The child must recognize that the mother comes and goes. So her breast will arrive at some point in the future. In the meantime, the child sucks its fingers. This is a virtual object which provides excitations that lessen the inner distress. Because it is linked to a past experience of breast-feeding that it substitutes, it is a shred of the past. This past is pure, because there never was a real event when the fingers provided the nourishment they are substituting. Also, virtual objects are what link past and present “associatively,” since what is shared by such linked events of different times is not resemblances each have to the others but rather that all somehow share the same virtual object.]

2.12 Freud’s Third Synthesis: The Death Drive (110–14/135–40)

[Freud’s death drive tends toward a supposed prior pre-evolutionary state when the organism was inanimate matter. So it is a material repetition. Deleuze disagrees. The compulsion to repeat is a variation on the death drive, since they both tend toward a past status. This harkening back to the past is achieved by creating and repeatedly re-experiencing a virtual object, which substitutes for an external object that was once experienced but is now lacking. However, as there never was an actual experience where the virtual object fully supplied the person’s needs, it is not harkening back to an actual event but rather to the pure past in general. So for Deleuze, the death drive results in a spiritual rather than a material repetition. There is another difference between these two thinkers’ views on the death drive. Death for Freud is a personal loss. For Deleuze, this death is the instability and temporariness of identity in pure self-variational “intensive” becoming. Here, the organism is in a constant state of vital dying, since by means of its self-variation it is adapting, evolving, and self-perpetuating under new guises.]

Chapter 3. The Image of Thought

[Philosophy so far has failed to think about the intensive and differential basis of the world, because it has been using a representational model of thinking that cannot deal with this non-representational level of reality. Deleuze characterizes this traditional image of thought by discussing its eight “postulates”: 1) good sense (reason alone is adequate for thinking), 2) common sense (the faculties cooperatively deal with a common object), 3) recognition (thereby they recognize an object), 4) representation (its means and product are representational, since it has the four features of representation, namely, identity, analogy, opposition, and resemblance), 5) error (as misrecognition), 6) proposition (propositions bear truth), 7) solutions (problems are understood in terms of possible solutions in propositional form), 8) knowledge (as being propositional rather than the learning process). For Deleuze, in order to think about the intensive grounds, our faculties need to operate discordantly while having objects that differ in kind. Kant’s sublime experiences are partly like this, since the faculties have different objects that do not conform to one another. Also Plato’s experiences of inconsistency involve sense data of an imperfect idea and a mental recollection of a pure Idea, which differ in kind. But Kant thinks that reason finally supplies a representation, and Plato traces the origins of thinking to another realm of Ideas rather than to the immediate intensive situation.]

3.1 Introduction

[In chapter 3, Deleuze will give a critical account of philosophy’s “dogmatic image of thought”. The main problem he has with this conception is that the foundations of thought cannot be found within its structure of judgment, as the dogmatic image conceives them to be.]

3.2 Feuerbach and the Postulate of the Principle (129–33/164–8)

[The “dogmatic image of thought” is the problematic way that philosophy understands philosophical thinking. Deleuze discusses eight “postulates” of it. The first is the belief that rational thought itself is good-willed and trustable for the task of arriving at truth, since it supposedly can be utilized without any other presuppositions that might contaminate the inquiry. Thus Descartes thinks that the method of doubt can lead all people to rational thinking itself, on the basis of which we may safely and fruitfully conduct our philosophical inquiries. Hegel as well begins with thought itself. Feuerbach criticizes this notion, since it forgets that such methodologies assume many things, like the philosopher is speaking the truth, as this is required to understand what she is saying in the first place. Instead, Feuerbach argues, philosophical thinking must go outside reason to encounter pure sensuous intuition. Deleuze agrees that philosophical thinking must encounter something outside reason, but it would not be sensuous intuition. Rather, it would be the transcendental ground for the passive synthesis of sensuous intuition, which is not a transcendental active ego like in Kant.]

3.3 Descartes and the Postulates of Common Sense and Recognition (132–4/168–70)

[Deleuze’s first postulate that describes traditional philosophy’s problematic “image of thought” was good sense, that is, the belief that our methods of reasoning are sufficient in themselves for finding truth and for philosophical thinking in general. The second is common sense, which has two meanings of “commonality:” 1) all our faculties work in common to synthesize givens into a common object, which we may recognize by judging what it is, and 2) all people commonly share this ability to organize coherently their givens. This common sense is always at work. But in cases of misrecognition, our reason might incorrectly judge the organized givens as something which they really are not.]

3.4 Kant and the Postulate of Representation (134–8/170–4)

[We see the first four postulates of the problematic image of thought in Kant: 1) good sense: reason is adequate to thinking, with the limitation that it can only think by means of intuitions of the things themselves and not think those things themselves as themselves, as in Descartes. 2) common sense: the faculties operate cooperatively to synthesize the cognized object, although this is enabled by the transcendental unity of the self and not by the powers of reason, as in Descartes. 3) recognition: by means of the common sense operation of the faculties, we may recognize the object. 4) representation: the faculties recognize the object as a representation with the four problematic qualities of representations, namely, a) identity: that an object has a self-same unified identity to which the determinations relate, b) analogy: the determinations are grasped as belonging to that object by means of an analogy between their intuitive and their conceptual manifestations, c) opposition: the object’s determinations are selected in part by knowing which ones are opposed to it, and d) resemblance: and they are selected also on the basis of knowing which ones resemble one another in their common belonging to that object.]

3.5 Plato and the Encounter (138–45/175–83)

[Deleuze is against representation as being the basis for a model of thought, and he has found this to be a problem in Descartes and Kant, for example. One problem they have is that they think the faculties work together to recognize a common object. Deleuze thinks it would be better if the object each faculty deals with were different in kind and that all the faculties worked discordantly. Plato seems perhaps to be closer to what Deleuze is looking for. For Plato, we have the faculties of sense experience and of conceptual thinking. Sense experience sometimes gives us contradictory properties for the same object. For example, two things that appear equal in length when next to one another may appear unequal when one is further away from us. Plato thinks that this experience leads us to recall a supposed experience our soul had before our bodies were born, when we experienced the pure Idea of equality. So when we see unequal things, it seems we are dealing with different objects, namely, a visual impression of imperfect equality and an intellectual recollection of pure equality, and also that our faculties are not working concordantly, since they are dealing with incompatible notions (equality as a concept is not variable, but the equality of things sometimes holds and other times does not). However, the problem is that both the supposed recalled experience and the actual one are taken by Plato to be the same sort of experience, just with the supposed prior one being better at giving us the pure Idea. Also, his model has the four properties of representational thought, namely identity (the Idea is self-same), analogy (our knowledge of things is analogous to our knowledge of Ideas), opposition (we recall Ideas when encountering oppositional properties in things), and resemblance (the imperfectly equal resembles the absolutely equal, which is how the first recalls the second).]

3.6 The Kantian Sublime and the Discordant Relation of the Faculties (145–6/183–4)

[Deleuze wants an account of thinking where Ideas are a product of the discordant operation of our faculties. Kant has something similar in his analysis of the sublime. Consider if we are standing before a gigantic mountain. We have a stream of intuitions, but our imagination cannot retain enough of them and process the information sufficiently to take in the whole mountain at once. But our faculty of reason has the idea of totality, and so it forces our other faculties to keep working even though they will never succeed. Each faculty has something different as its object, and they continue communicating with each other in their effort to synthesize a common object, so they are working discordantly. However, Deleuze is not fully satisfied with this model, since the Idea comes from one particular faculty, the reason, rather than coming from the discord itself between the faculties.]

3.7 Descartes on the Postulate of the Negative or Error (146–53/184–91)

[The fifth postulate of the problematic image of thought is of error. It is the notion that error results simply from misrecognition. Error for Descartes is a failure of the good sense: the faculties work together in processing a common object, but the reason fails to make the proper judgment about it and thereby misrecognizes it. For Kant, however, error arises when our reason incorrectly assumes it can know everything, since it can always supply ideas to compensate when the other faculties are beyond their capacities. But these ideas are  insufficient, since a total system of knowledge would require thinking about things which go beyond possible experience, and thus still the other faculties need to be involved. Reason’s mistaken view of its own powers is what Kant calls “the transcendental illusion.”]

3.8 The Postulate of the Proposition (153–6/191–5)

[The sixth postulate of the problematic image of thought is of logical function or of the proposition. Consider the proposition, “it is raining” outside. If it is true, then it corresponds to the state of affairs of it actually raining outside. If it is false, it does not correspond, since outside it is not raining. This correspondence to a true state of affairs is its denotation or designation. This assertion also has a “sense,” which refers to the belief of the speaker that it is raining. The sentence has sense even if it is false, since the speaker supposedly does in fact have the belief that it is raining. This also means that the sense is broader than the denotation, since the sense refers more generally to possible states of affairs (either that it is or is not raining) while the designation refers supposedly only to one actual state of affairs. In the sixth postulate, designation is problematically given the primary status, and so sense is understood in terms of how it may be captured in propositional form. But this creates various problems. One is that we already said that sense is broader and thus more fundamental than the proposition, so we cannot ground sense in it. The other problem comes if we explicate sense in propositional form. This will produce a sentence with yet a new sense. The regress either terminates in a fundamental proposition like Descartes’ cogito, which as we noted in a prior section is problematic. Or the regress is infinite and thus fails to find a ground.]

3.9 The Postulate of Modality or Solutions (156–64/195–204)

[The seventh postulate of the problematic image of thought is of solutions or of modality. Here problems are understood in terms of propositions and the possibility of the problems being solved. For example, a referendum is based on a possible policy change, which can be stated as a proposition or as a question like, “Yes or no, should the possible change be made?” Deleuze’s criticism is that understanding problems this way only helps us grasp what conditions them and not what generates them, and therefore it does not provide an adequate model for accounting for thinking itself.]

3.10 Conclusion: The Postulate of Knowledge (164–7/204–8)

[The eighth postulate of the problematic image of thought is of knowledge. It regards knowledge as propositional solutions obtained by dealing with problems put into propositional form. For Deleuze, what is more important for thinking is the process of learning when we are struggling with the problems.]

Chapter 4. Ideas and the Synthesis of Difference

[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.]

4.1 Introduction: Kant and Ideas (168–71/214–17)

[Deleuze is looking for a way to understand thinking and the problems it deals with that does not do so in terms of propositional solutions relating to empirical objects. Kant’s notion of the Idea seems at first to succeed at this. For Kant, our reason wants a systematized knowledge of the world. But knowledge normally requires empirical intuitions. However, some things that are important for a total system of knowledge cannot be given in intuition. For example, we cannot experience the temporal origin of the world, nor does the ground of all appearances (the Idea of God) itself appear to us. So such Ideas as the Idea of God seem to allow us to think without relation to empirical objects. Nonetheless, in the end, for Kant, these ideas do come to obtain empirical determinations, and so they fail to satisfy Deleuze’s requirements. Instead, he wants “an account that intrinsically relates Ideas to the empirical world, while allowing them to maintain their difference in kind” (131).]

4.2 Ideas and the Differential Calculus (170–82/217–30)

[For Deleuze, the Idea has three intrinsically related moments, indetermination, determinability, and determination. He sees their relation expressed in a non-orthodox tradition in the history of the calculus which grants the differential its proper metaphysical status. Bordas-Demoulin shows how the differential gives us the the essence of something rather than a description of any of its particular instances. For example, Descartes’ formula for the circumference of a circle, x2 + y2 – R2 = 0, only tells us how we would expect the x and y variables to relate for some given point on the circumference of some one circle or another. But the differential formulation, ydy + xdx = 0 tells us more what it means to be a circumference, since it tells us that the tendency of variation in the curve of the circumference is of such a sort that it will eventually return to any point of origin. Also in such a differential formulation, we have the undetermined, since it is more about circumference in general and not about the determinate relations of particular circles.  For Maimon, the differentials dx  and dy each by themselves cannot be given a sensible interpretation, however, the differential relation of the two can. In this way Maimon gives the conditions for determinability. Wronski thinks that the differentials are real, but they fall under a different kind of knowledge than finite values. He is also concerned with moments in a function’s variation where the change is drastic and as well where the value of that change can be numerically determined. Thus we have the three moments intrinsically related: 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.]

4.3 Ideas and the Wider Calculus (178–84/226–32)

[Deleuze has been discussing how differential calculus allows us to understand certain structural features of his notion of the Idea. However, other fields (including physics, biology, psychology, and sociology) as well generate Ideas in response to problems. The important difference is that differential calculus also deals with the issue of the grounds for a problem to be determinable, namely, with the differential relations between undetermined, reciprocally related parts. Since Ideas are composed of many such differential relations, they are multiplicities. There are three criteria for the emergence of an Idea: 1) the parts are determined only through their differential reciprocal relations, and thus they are not determined prior to those relations, 2) when the differential elements are reciprocally related, they lose any sort of independence they may previously have had, 3) the Idea must apply to a variety of spatio-temporal differential relations in the world.]

4.4 First Example: Atomism as a Physical Idea (184/232–3)

[For Deleuze, differential calculus exhibits certain critical features of “the Idea”: 1) the parts are determined through (and not prior to) their differential reciprocal relations, 2) the parts become determined only together by and as these reciprocal relations, and 3) there must be a variety of possible ways these spatio-temporal relations can manifest. Deleuze gives three examples in philosophy which seem to fulfill these criteria. The first is Epicurus’ and Lucretius’ atomistic model of the world. They say the world is made of atoms which move so fast downward through a void that their motions cannot even be perceived. And the atoms would never interact were it not for their tendency to make spontaneous deviations (clinamen) from their directly downward course, which causes them to collide into one another. Such mutually colliding atoms might continue doing so, forming a compound. Their collisions cause them somehow to appear to vibrate at a speed slower enough to be perceptible, and this is how atoms can generate the sensible qualities of the objects they compose. Thus we see how this model satisfies the three criteria for Ideas: 1) on their own, the atoms are not sensibly determinable; 2) but they can become so when they enter into differential relations with one another; and 3) there are many spatio-temporal ways they may enter into such reciprocal relations. Yet, because their relations are understood too much in terms of sensible determinations, this model does not fully exemplify Deleuze’s notion of the Idea.]

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

[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.]

4.6 Third Example: Are there Social Ideas, in a Marxist Sense? (186/234–5)

[For Deleuze, “the Idea” has three critical features: it has 1)  undetermined parts that 2)  are determinable only through and as reciprocal relations for which 3) there can be various spatio-temporal actualizations. The third of Deleuze’s three examples is Marxist social ideas. Under Althusser’s interpretation, Marx is concerned less with visible entities like laborers and means of production and more with deeper, invisible, and non-specifiable political and ideological social relations that are responsible for the generation of the surface structures. There are certain such structural relations at work below the surface, which under some historical circumstances manifest in one way and under others manifest another way. Thus the model fulfills the three requirements for an Idea: 1) the deeper structural elements on their own have no meaningful sense but 2) obtain one when they enter into relations with one another, which 3) can take on many actual instantiations under different economic, social, and political circumstances.]

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

[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.]

4.8 Essence, Possibility and Virtuality (186–8/235–7, 208–14/260–6)

[For Deleuze, Ideas are actualized, but they are not essences in the conventional sense of the term. Deleuze, following Bergson, notes two ways we may understand essences. The first is the Aristotelian way of removing everything non-essential. So if we wanted to know the essence of color, we would remove each of their accidental traits. But this gives us only an abstract and empty notion of color. The other way to understand the Idea as an essence is to consider how it implicates complicatedly (that is, how it ‘perplicates’) all actualizations it can take. To make an analogy, the essence of color under this view would be like white light, since we can break white light down into every actualizable color of the spectrum and also recompose that white light by recombining all actual light colors. This notion of the Idea is tied to the distinction between the virtual, actual, and the possible. The Idea is virtual, and the instantiations in spatio-temporal reality that the Idea somehow generates are actual. The virtual is not the possible, since the possible is a deprivation of the existant and also since the possible is not “real,” while instead the virtual is real and is also not deprived. The virtual, then, has three important features. 1) The virtual is real without being actual, since “it provides the structure responsible for the genesis of the qualities we find in actual entities”. 2) The virtual is complete without being entire, because it implies all actualizable determinations and thus is lacking nothing (it is complete), but at the same time, it is infinitely rich in such implications, and thus it can never be exhausted by its actualizations (it is not entire). 3) The Idea is differentiated without being differenciated, since it is composed of differential relations (it is differentiated) whose related parts are by themselves undetermined, meaning they lack an identity to which predicates may be ascribed (it is not, then, differenciated).]

4.9 Learning and the Discord of the Faculties (188–97/237–47)

[For Deleuze, learning is not a matter of drawing inferences from propositions. Instead, it occurs when 1) we deal with the problematic situation in current states of affairs, then 2) gather together Idea fragments from a variety of sources to devise a ‘map’, so to speak, of the important relations in the situation, which is the Idea, and then 3) develop solutions which would change those states of affairs in ways which solve the problems. In an evolutionary sense, each bodily organ is itself like such a solution to certain problems, since for example the eye is the solution to the problem of light. Likewise, each faculty is a solution or Idea on its own. The reproductive imagination (or memory) for example could be the solution to the problem of intuitions (or perceptions) continually being lost due to the passage of time. Now, in those confusing moments while we are learning something very new, our faculties are working together discordantly, meaning that they each have their own object that is different from the other faculties’ objects. But this discordant relation of the faculties, since it is what allows us to learn, is a solution to the problem of Difference itself, which is what presents to us the many problematic situations that call for us to reconfigure our minds and workings in order to continually adapt to a complicated and changing world.]

4.10 The Origin of Ideas (195–202/244–52)

[Ideas for Deleuze are bound up with problems, solutions, and questions. The problem is an encounter with an intensive field of differential relations that we cannot process using our given resources. It causes us to put together Idea fragments to formulate an Idea on the basis of which we find solutions. The question is what relates the Idea as a basis for a solution to the problematic situation. So consider if we without ever swimming before are thrown in rough waters. We encounter the intensive field of differential relations of the waves, which threaten our survival, and in response we pose the question, “how do I not drown?” On the basis of how we come to understand the particulars of the problematic situation, we formulate our own particular arrangement of Idea fragments to make an Idea. This Idea then serves as the basis for the particular kind of solution we find, which would be one of many possible swimming strokes we spontaneously learn to enact to save ourselves from drowning. Deleuze uses the metaphor of the dice throw to illustrate. So again, when we learn, we encounter a problematic situation that presents to us a question (we are handed dice to throw). But how we understand the problematic situation and formulate the Idea for its solutions is a matter of chance, since we could have made many other arrangements of Idea fragments but we happened in this case to choose certain ones (the faces of the dice in a way are as such by chance and rolling them and getting some particular outcome is the affirmation of chance). Our Idea for the solution can in fact find many different kinds of solutions (there are many combinations that can be rolled). But only one solution is found at a time (we in fact roll one particular combination). However, we could have devised many other solutions from the same Idea, and also the Idea could have been formed differently depending on the different components we use to form it, and thus there is the repetition of difference built into the system (we can roll many other times or we can obtain different dice and repeat the process of solving problems).]

4.11 The Origin of Negation (202–4/253–5, 206–8/257–60)

[Negation for Deleuze is not fundamental to the genesis of things; however, it can result from that genesis. There is no negation inherent to the problematic situations on whose basis we form Ideas, nor is negation found within those Ideas formed from and in response to the problems, since both the problems and the Ideas affirmatively interrelate differential relations. There is also no negation when those Ideas are actualized into solutions, since these solutions affirm one of the actualizable instantiations implied in the Idea. But when we incorrectly understand problems in propositional terms, we might affix to one proposition ‘this is not the case’, since we affirm some opposite proposition to in fact instead be the case. However, the problems really do not lend themselves to propositional explanations, since they exist on a sub-representational level. So this notion of propositional denial is one origin of negation, but it leads to the false understanding of reality that negation is inherent to it. The other origin of negation is the process of differenciation, which generates actual distinct states of affairs that could have been many other actualizations. But this negation is secondary to their genesis and to their more fundamental structures, and thus still negation is not fundamental to reality, for Deleuze.]

4.12 Actualisation (214–21/266–74)

[For Deleuze, actualization is the movement from the virtuality of the Idea to the actualities implicated in the Idea as solutions to problems. But actualization is not predictable. It rather unfolds by means of ‘dramatization’ like with the development of an egg, since what comes about is not overtly implied in prior states of the development, and thus it surprises us in a dramatic way, and also, that development involves interrelated parts that interact much like actors do in a drama. The development is initially spatio-temporally intensive, since it involves firstly intensive variations in accelerations and distributions of the development. Then, secondarily as a result of those intensive spatio-temporal dynamisms are the extensive quantitative and qualitative features of the organism that result. Thus extensive spatio-temporal features are only secondary to the intensive spatio-temporal dynamisms of the development.]

Chapter 5. The Asymmetrical Synthesis of the Sensible

[In Chapter 5, Deleuze examines how intensive difference is found in the extensive world and is at work in the productions of extensive properties and qualities. The Idea colludes with fields of intensity in the world so to explicate actualizable paths of development implicated in the Idea. On account of intensity’s “depth”, it cannot be represented, and also, it is a wellspring that continually injects difference, variety, and energy into the world by constantly generating differential relations. This depth is also at work in individuation, which is the fundamental process that produces the structures that secondarily come to be our subjectivity, ego, I, etc.  In efforts to represent intensity’s depth, we posit an Other as the grounds of representation, but it is an erroneous concept.]

5.1 Introduction

[In chapter 5 Deleuze will examine the role of intensive difference in space, which he will do through a critical reading of thermodynamics and by further applying his notion of the Idea.]

5.2 Thermodynamics and Transcendental Illusion (222–9/280–8)

[For Deleuze, difference is difference in intensity. We see in Carnot’s thermodynamic ideas, particularly the second law of thermodynamics, the energetic power of intensive differentials. A thermodynamic system has more power to perform its work when there is a greater difference of temperature between its input heat and its output or environmental cold. However, in other ways, thermodynamics is fundamentally incompatible with Deleuze’s metaphysics. Thermodynamics thinks there is entropy in thermodynamic systems whereby heat differentials tend to equalize over time as systems tend toward a state of homogenized disorder. But Deleuze notes that there is another factor that thermodynamics is missing, which is the generation of the intensive differentials. Thermodynamics cannot for example explain the generation of life, in which there is movement toward more and greater differentials as the organism diversifies and becomes increasingly heterogeneous and organized rather than homogeneously disordered.]

5.3 Merleau-Ponty and Depth (229–32/288–91, 241–4/302–5)

[Parallel to Deleuze’s three syntheses of time are his three spatial syntheses. 1) Intensive differences are localized by being distributed into various spatial locations, and they move from place to place according to how they interrelate and interact (in thermodynamics, for example, heat moves from its location to where cold is located, normally). 2) The extensive space into which these intensities are distributed and the qualities belonging to those things in extensive space come about somehow by means of intensive depth. 3) These distributions of intensities and their explications into extensive properties and other qualities continues to remain fresh and in a perpetual state of renewal. This is because the intensive depth responsible for them returns eternally, that is, it never ceases to inject newness and variety into the system, counteracting the entropy which would otherwise cause the system to eventually die.]

5.4 The Three Characteristics of Intensity (232–40/291–300)

[Extensity, which is of the realm of the extensum, is fundamentally different from intensity, which is of the realm of the spatium. The most important difference is that intensity is more fundamental than extensity, since extensity takes on its features as a result of intensity explicating into certain extensive expressions. The main distinguishing feature is their divisibility: The extensum, as it is extensive, is a multiplicity that is homogeneously divisible, meaning that each division produces parts that are of the same nature. Two meters (of something) can be divided into two equal (and identical) parts. The spatium, as it is intensive, is a multiplicity that is heterogeneously divisible, meaning that each division produces parts that are of a different nature. Each moment, our consciousness synthesizes the past with the present into a whole mental state. But each successive moment of consciousness is qualitatively different from prior ones. For example, with each new note of a melody, the character of that melody as a whole changes. Were we to divide our consciousness between the way it once was when we heard a prior note with the way it is now, having heard more notes that have altered the melody’s character, we would have two parts of consciousness that differ qualitatively. Thus, they differ in nature. Deleuze emphasizes three important features of intensity: 1) because it is not metrically homogeneous like extensity, it does not divide into equal parts, and thus intensity includes the unequal in itself; 2) since an intensive difference does not involve one thing being the negation or denial of another, but rather is a matter of pure differential relations, intensity affirms differences; and 3) because it explicates into extensities, intensity is an implicated, enveloped, or embryonized quantity.]

5.5 Individuation (244–56/305–19)

[For Deleuze, we have a realm of extensity. It is our familiar world we experience, and it has spatial features and other determinate qualities. One view would say that the states of affairs in this realm of extensity are determined by other extensive factors in prior moments, in a mechanistic sort of model. Deleuze, however, thinks that something more is at work. For him, there is another layer  of reality couched within the extensive world. There are not just extensive relations, like one thing being beside another. There are also intensive ones, like the “potential differences” that physics studies. We might for example have an electrical charge in the clouds and another in the ground. We could talk about extensive relations and say that the sky sits above the ground, but this will not explain to us much about why and how the coming lightning bolt will shoot between them. The charges or “potentials” in each region are such only in their differential relation to one another. That difference itself, which is relationally “between” them but not spatially interposed between them, is an intensive difference. Many varieties of intensities are couched in the extensive world, and they help shape it. The intensive difference between the charges shapes the extensive world by sending a powerful and destructive lightning bolt through the intervening region between the clouds and the ground. This transformation of the extensive world by means of intensive difference is called “explication:” certain actualizable outcomes are implicit in the intensive situation, and they become explicit through explication, meaning that they manifest overtly in the extensive world. The way that intensive relations explicate has to do with their interactions with “Ideas.” An Idea is a network of pure differential relations that might find one actualization or another when they are explicated. Perhaps all vertebrate organisms now and going way back in evolution have skeletons that are isomorphic. One explanation is that there is a transcendental template that is merely a fixed set of relations which may manifest in a wide variety of ways in different organisms. So the template of relations is an Idea. Any of many various organisms expressing it is an explication. Now also, the physical intensive conditions surrounding the organism’s embryonic development are the “field of intensities,” which is a notion that is important when understanding how creatures develop uniquely from nearly identical embryos. In fact, the embryos are never identical, even if the DNA is. For, there are contingent features in the actual situation, like the chemical composition of the embryo’s cytoplasm. They cause one embryo to follow one path of division and another embryo to follow a different developmental course. What happens is the fixed DNA code colludes with the variable intensive relations of the actual situation, and thus the development is dramatized rather than mechanistically predictable.]

5.6 The Other (256–61/319–25, 281–2/351–2)

[For Deleuze, the individual is not the self, ego, subject, or “I.” Rather, the individual is bound up in generative processes that create the conditions for these other structures to arise. So, couched within your self, that is, within the self that you recognize as being you, is an indeterminate, pre-subjective process that is variable and structured only by difference itself. And perhaps this variational dynamic causes you to mutate, despite your beliefs that you are still the same person throughout your life. Now note that it is our faculties that recognize our representational self (the ego or “I”). But they cannot recognize our sub-representational individual. This is because our faculties can only work with representations, but our deeper individual cannot be represented. However, our faculties can be aware of this problem. But their solution does not succeed. They seek a notion of something un-representable which can be the basis for representation. Now consider that the only way our faculties have to deal with the world is limited by their spatial and temporal perspectives. Nonetheless, they regard the fragmented world of perception as being composed of complete objects. They do this by supposing that were every other perspective given, then the object in its completeness would become directly apparent. Since this omni-perspectival view is not possible for any one subjectivity, it belongs to no one and is thus the Other. And yet, this Other is the grounds for us to see the world as being made coherently with complete objects, and it is also the basis for objectively finding common grounds and for settling disagreements. Thus it is seen as the basis for representation. However, this Other as it is understood in this way is not really un-representable, which it needs to be in order to account for representation’s origins. For, it is only unrepresentable because humans happen to have perspectival limitations. But, it is still potentially representable by an intellect lacking these limitations, and thus it is not fundamentally un-representable. Deleuze then says that since philosophical thinking takes us to the pre-subjective structures of reality, it is a solitary and solipsistic exercise.]

The Two Prefaces: After Difference and Repetition (xv–xxii/xiii–xx)

[Deleuze’s Difference and Repetition has two prefaces. We learn from them that Deleuze was attempting to revolutionize philosophical thinking by liberating it from the constrictions placed on it by its conventional subordination of difference to identity. DR does not succeed entirely, since his notions of intensity and simulacra are still too closely tied to former conceptual structures. However, the third chapter acts as a guide for finding a new way to think philosophically, which Deleuze later accomplishes with Guattari in their rethinking of the concept of multiplicity.]

Part 2: A Guide to the Text

[After his summarization of DR in section 1, SH follows with another, brief section of study aids for those who would like to work more with DR. There is a very useful glossary with 35 important terms. He suggests a  number of commentaries on DR, mentioning the particular usefulness of each. As well he gives recommendations for further reading of philosophical texts Deleuze refers too, going section by section. And finally he provides excellent tips for writing more successfully about Deleuze and DR.]


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