Daniel W. Smith’s ‘Essays
On Deleuze’
by Beth Metcalf
Univocity
In Difference and Repetition, Deleuze criticizes what he calls ‘The Dogmatic Image of Thought’. It is the Image of Representation-Analogy with its four iron collars. It is the generalizing structure of negative oppositional relations. Its “difference” is merely the generalizing exchange of particulars. This structure keeps the forms closed inside a principle of conceptual identity. Deleuze contrasts this with his ‘univocity’ that opens the forms by introducing the new “sub-representative” and “extra-propositional” domain. The sub-representative plane of consistency is a plane of univocality that must be included if the forms are to be open with real difference. If that plane is left out, we will not escape that Dogmatic Image of Representation that closes the forms. But many readers of Deleuze have trouble reaching that sub-representative plane. And, if they do not reach that plane, they do not reach univocity. I would like to use Daniel W. Smith’s collection of essays to illustrate this point.
Smith (Essays on Deleuze, 28) quotes Deleuze regarding univocity saying it is “the strangest thought, the most difficult to think, if it has ever been thought.” And, when Smith tries to think this most difficult thought, he runs into several problems.
Smith writes an essay on univocity. After describing his understanding of Spinoza’s univocity of attributes, cause, and modality; Smith concludes (ED 37) that, even in Spinoza, the concept of God has always functioned as a principle of identity. “Even in Spinoza, modes are modification of substance, and the concept of substance (or God) can still be said to maintain the rights of identity over difference…” So, Smith concludes that Deleuze’s univocity is a departure from Spinoza’s univocity. He sees Deleuze’s univocity as a “kind of Spinozism minus substance, a purely modal or differential universe.” Smith says that whereas Spinoza’s univocity still functioned as a principle of identity of substance, Deleuze’s univocity is purely modal differentiation. That is, Spinoza’s univocity of Substance is a monism, while Deleuze makes a detour into pluralism. But Smith does not explain how either side can escape an opposition of the many and the one (which Deleuze tells us does not reach multiplicity). Smith’s reading of Deleuze says that (ED 41-2) Being must account for external difference between beings. It also must account for internal difference of beings. And also the ontological difference between Being and beings must be a non-categorical difference, as well as an internal difference of Being from itself. Therefore, Deleuze’s formula ‘monism = pluralism’ is taken to mean ‘univocity of Being = equivocity of difference’. Smith is still reading Deleuze in a structure of opposition: monism versus pluralism, the one versus the many. And, this is because Smith’s understanding does not reach the sub-representative domain that Deleuze sees in Spinoza’s univocity. Univocity truly is the strangest thought most difficult to think.
Smith looks to Deleuze’s (ED 40) difference as degree of power or intensity to resolve the paradoxical requirements that Deleuze lays out. Smith calls this “a physics of intensive quantities” and states the problem as he sees it, “The power or intensity of a being is its relation to Being….beings that are distinguished solely by their degree of power to realize one and the same univocal Being”. And, at the same time, this degree of power must not be a degree of categorical difference. Smith understands that if difference is thought to be actually or empirically constituted individuals in experience, then we merely fall back into an analogical-representational thought that cannot reach Deleuze’s univocal ontology. He seems to have some insight into the problem but does not know how to resolve it. Individuating differences “are not and must not be.” How do we reach a plane where individual differences are not? How can intensity on the plane of physics reach ‘non-categorical’ difference? Smith seems to know (even if only in the back of his mind) that he cannot fulfill the requirements of univocity that Deleuze lays out. Smith struggles to reach that strangest thought of univocity.
Spinoza’s immanent causality sees cause as remaining in itself, and its effects remain in the cause. That would mean that cause is complicated in God as Substance and the modal effects are explicated in the cause. But Smith says (ED 34) this means that “Spinoza flattened everything on to an absolutely infinite substance that possesses all attributes and comprehends all things as its modes.” Smith says (ED 40) that “Deleuze’s thesis in Difference and Repetition is that only univocity can provide us with a truly collective sense of Being (and not merely a distributive sense) by giving us a comprehension of the play of individuating differences within beings (and not mere generalities in a network of resemblances). But this brings us, precisely, to the fundamental problem of a univocal ontology. If Being is said in one and the same sense of everything that is, then what constitutes the difference between beings?” If there are no representational categories, and we do not distinguish beings by their substance, forms, or genus/species; how do we make distinctions? And, if everything is said in one sense, how can there be any differences? Smith wrestles with these questions.
Deleuze’s Spinoza does not (as Smith asserts) flatten everything onto a substance which possesses all attributes or unifies all modes. To understand what Deleuze sees in Spinoza, we must reach that sub-representative domain of univocality. What does Deleuze mean when he says (Expressionism in Philosophy Chapter 1) that, for Spinoza, real distinction is never numerical and numerical distinction is never real? What does he mean when he says that there cannot be two or more substances of the same attribute? Univocity means that attributes are, each time, a common form that constitutes the essence of Substance while also containing the essences of modes. But this does not mean that essence of Substance and modes are the same. While the attributes are the common and univocal form of Substance and modes, they also complicate the essence of Substance and explicate the essence of the modes. But this means that essence is not the same in Substance and modes. (EiP 48) “…as long as one refuses community of form [i.e., refuses the univocity of attributes in Substance and modes], one is condemned to confuse the essences of creatures [modes] and God [Substance] through analogy. As soon as one posits community of form, one has the means of distinguishing them.” Cause (Substance) and effect (modes) are known through their univocal attributes (common forms) which constitute the essence of their cause and contain the essence of their effects. Ontologically single Substance is Cause that remains in itself, and modes are effects that remain in their cause.
So, attributes are common forms that constitute the essence of Substance and contain the essences of modes. But, if the attributes have a common form in Substance and modes, how can the essence of Substance not have the same form as the essences of the modes? It is because, when we reach that domain of sub-representative and extra-propositional forces, the attributes qualify Substance with real distinction, each time. But real distinction is never a numerical distinction. When attributes imply the essence of modes, the modes separate from Substance, and with this division, they change in essence. Actual modes never resemble the virtual Substance they actualize. There is a real difference in essence because Substance and modes have a common form in the attributes.
This means that as long as we remain in
analogical thinking which refuses any form common to Substance
and modes, we will never be able to find difference between the
essence of Substance and the essences of modes. But
Spinoza’s Univocity posits the attributes as form common to
Substance and modes, thereby reaching difference between the
essence of Substance and the essences of modes. Therefore,
Spinoza’s Univocity, far from “flattening”
everything (as Smith claims), gives real difference that analogy
never could. Now, attributes are common forms that
constitute the differentiation of Substance and contain
the differenciation of modes. But this cannot happen
on the level of already constituted individuals. We must
reach a sub-representative domain of pre-individual singularity.
Furthermore, these ‘common forms’ of the attributes also are really different, each time. The attributes open the forms because they are not restricted to a categorical difference of possible experience. Attributes are univocal. This means that they are not equivocal properties distributed by the categories that could be shared by several substances. The univocity of attributes cannot happen without reaching the sub-representative domain of singular difference. Only then can we reach a “parallelism” of heterogeneous attributes, thought and extension, without negative-oppositional correspondences. At this level of sub-representative difference, any intensity of thought may be coupled with any intensity of extension. (See below for a discussion of ‘external relations’.) There is no prior concept to tell us how intensities are to be coupled. But really different couplings of thought and extension cannot be actualized into one unifying formed substance. Spinoza’s Substance is constituted (qualified) in the attributes in real distinction of differentiation. And, numerically distinct modes are contained in the common attributes with each differenciation. With each singular difference in degree of intensity, there is a change in nature. And each singular degree of intensity is said as ontologically one Substance. Each degree of intensity (DR 222) is already a coupling of disparate intensity, “revealing the properly qualitative content of quantity”. But none of this can happen on the plane of already formed substances. We must reach the sub-representative plane of univocality that opens the forms. Substance is qualified in the attributes as a different variety, each time. But then, each time, the attributes are an open form (a new form of real difference) that is common in Substance and in the modes. Deleuze says, (Expressionism in Philosophy 91), “Attributes are conditions common to substance which possesses them collectively and to the modes which imply them distributively.” This univocity of attributes, different each time, constitutes a qualified essence of Substance (a collective variety, singular each time). The attributes, with difference each time, also contain the essence of modes (with a new degree of intensive inseparable variation that changes the nature of the variety, each time). So, Substance and modes have a common form in the attributes. But far from unifying the many modes within one substance, Spinoza’s Substance and modes are now real difference said as Same, because they are all ontological singularity. Deleuze-Spinoza’s univocity can be understood only when we reach that sub-representative domain that opens the forms with real difference.
Smith says (ED 28) that Deleuze’s concept of univocity is short-lived in Deleuze’s writings. I would challenge that. Just because Deleuze rarely uses the term in later writings does not mean he abandons the concept. I contend that we will understand nothing of Deleuze without grappling with this strangest thought. Univocity is the ontology of Being as difference-in-itself. Deleuze never abandons this concept. For Deleuze, real difference is always said in ontologically single sense. Univocity opens the forms of real difference-in-itself said as Same singular sense of all of which it is said. Deleuze later writes in terms of ‘machines’ and ‘flows’, but we will not understand any of his terms without his concept of univocity. Deleuze never abandons this concept that is the strangest ever thought, if it has yet been thought.
Platonism
Smith (ED 14) quotes Deleuze, (D&R 66) “The distinction between the same and the identical bears fruit only if one subjects the Same to a conversion which relates it to the different, while at the same time the things and beings that are distinguished in the different suffer a corresponding radical destruction of their identity. Only on this condition is difference thought in itself, neither represented nor mediated”. In this passage, Deleuze is telling us that in order to overturn Platonism, we must reach univocity. Whereas the usual Image of Representation says Being in several senses while maintaining identity; univocity says Being in a single sense of all real differences that have no identity. The different is said as Same, but the things and beings of which this Same is said are really different. Yet, Smith somehow manages to invert this inversion of Platonism to mean that the Same is related to things through a difference that produces identity --- (ED 19), “…..Identity and resemblance still persist, but they are now merely effects produced by the differential Idea.” He does not reach the forces of the “sub-representative” plane that escape the principle of conceptual identity.
According to Smith’s reading of Deleuze’s inverted Platonism (ED 18), “Difference no longer lies between things and simulacra, since they are the Same; rather, difference is internal to things (things are themselves simulacra). What is required is thus a pure Idea of difference, an Idea that is immanent in things themselves.” So, Smith thinks that Deleuze overturns Platonism through a pure Idea of difference in things --- by saying that things and Idea of simulacra are “the Same”. He thinks that Deleuze’s univocity is a pure Idea of difference in things themselves. But how is Smith’s idea of “difference” in things any different from that Representational Dogmatic Image of generality that is the recognition of identity and resemblance in things? Hasn’t Smith just described ‘conceptual difference’ (D&R 270) that presupposes conceptual identity? Hasn’t Smith described just what Deleuze tells us he is not saying? Deleuze says in a passage Smith quotes (DR 56), “….The object must therefore be in no way identical, but torn asunder in a difference in which the identity of the object as seen by a seeing subject vanishes…” So, whereas Smith thinks Deleuze is talking about relations of variability that maintain a principle of conceptual identity, Deleuze says that the object has no identity but is torn asunder by difference. Smith has not reached univocity --- that strangest of thoughts.
Smith seems to understand that a truly
inverted Platonism would mean that the difference between copy
and simulacrum would be not merely a difference in degree, but a
difference in nature (ED 12). But what does it mean to
reach a real difference in nature? To reach a real
difference in nature with each change in degree of intensity, we
must reach a plane where difference does not maintain a
principle of identity. Singular degrees of intensity that,
with every division, change in nature must not be confused with
the variables that maintain conceptual identity. (D&R173)
The Idea “integrates variation, not as a variable
determination of a supposedly constant relation
(‘variability’) but, on the contrary, as a degree of
variation of the relation itself (‘variety’)…. If
the Idea eliminates variability, this is in favour of what must
be called variety or multiplicity.” We must reach a
sub-representative ‘intensity’ of disparate difference.
That is, we must reach intensive forces of inseparable variation
that, when separated, change in nature. We must not confuse
this with variable relations that, when divided, maintain
identity. If we remain only on the plane of variability
(that turns the concept into a function), we never reach that
sub-representative domain of univocality. We must reach a
sub-representative domain of real difference that is said
as same because all is ontological singularity. Such
repetition of singular difference is not maintenance of
identity.
Smith says (ED 22-3), “The repeated object is a difference that differentiates itself in being repeated. There is indeed, one might say, an “essence” that governs the series….” Smith goes on to tell us that “variations….express differential mechanisms which belong to the essence and origin of what is repeated. There is not an originary “thing” (model) which could eventually be uncovered behind the disguise, displacements, and illusions of repetition (copies); rather, disguise and displacement are the essence of repetition itself, which is in itself an original and positive principle.” But how does this “variation” of essence reach a sub-representative difference of disparate intensity? It is merely the variability of the principle of conceptual identity. It is a principle that never allows any difference in essence. It never reaches the intensive forces of inseparable variation that, in dividing, change essence.
Smith remarks on Deleuze’s description of Plato’s method of division as a selection of claimants in an attempt to distinguish the authentic from the inauthentic participant in the pure Idea. He accurately describes the opposition in this model between the true and the false claimant, and the hierarchical participation [degrees of limitation]. Smith correctly describes that Platonic structure of opposition/limitation. It is this negative structure that holds everything into the four iron collars of the Representation Image. It is this structure that must undergo an inversion if we are to overturn Platonism. However, how does Smith’s variable “difference” as merely the principle of conceptual identity do anything other than maintain this very structure of opposition/limitation? How does it do anything but maintain the closed structure that must undergo an inversion if we are to reach the problematic structure of univocity? Smith does not reach the sub-representative plane that must be included if we are to reach the inverse side of the Image. If we do not reach that sub-representative plane of univocality, the forms will not be opened and Platonism will not be overturned.
Leibniz
Smith writes an essay on Leibniz. However, does he reach the lessons that Deleuze draws from Leibniz? Deleuze says (DR 51) “Leibniz’s only error was to have linked difference to the negative of limitation, because he maintained the dominance of the old principle, because he linked the series to a principle of convergence, without seeing that divergence itself was an object of affirmation, or that the incompossibles belonged to the same world….” Leibniz could have reached univocity had he not made these errors (DR 279). He could have reached the vice-diction that (DR 263) “consists in constructing the essence from the inessential…” Leibniz could have reached the sub-representative process of vice-diction had he affirmed all divergence. (DR 213) “No one has come closer to a movement of vice-diction in the Idea, but no one has better maintained the supposed right of representation, albeit at the price of rendering it infinite.” Leibniz’s ‘incompossibles’ imply divergence. However, all divergent incompossibles must be affirmed if we are to reach vice-diction. Only with vice-diction can we escape the opposition/limitation structures of essence. Without totalizing everything in one unifying essence, vice-diction affirms everything as inessential (DR 45-6). All is affirmed when we reach the ‘intensity’ of Deleuze’s sub-representative forces. Deleuze sees that Leibniz would have reached these forces had he not succumbed to his “errors”. Leibniz could have reached that sub-representative plane of the affirmation of all divergent difference said in one sense.
(DR 213-4) Deleuze tells us that Leibniz builds upon the Cartesian principle of the ‘clear and distinct’. “A clear idea is in itself confused; it is confused in so far as it is clear.” Deleuze says that Leibniz can be interpreted with Cartesian logic. This is the interpretation that Smith makes. But Deleuze also says there is another, more radical, interpretation. The difference between the clear and the distinct may not be just a difference in degree, but in kind. We may understand this to mean that there is a distinct-obscure corresponding to the clear-confused. That is, we could make the traditional interpretation of Leibniz; or, we can include a new sub-representative plane. This second, more radical interpretation would mean “that the little perceptions are themselves distinct and obscure (not clear): distinct because they grasp differential relations and singularities; obscure because they are not yet ‘distinguished’, not yet differenciated [actualized]…..The nature of the Idea is to be distinct and obscure. In other words, the Idea is precisely real without being actual, differentiated without being differenciated, and complete without being entire.” But this more radical interpretation must include the sub-representative plane of the pre-individual singular event --- not to be confused with the extensive individual variable elements of the other plane. So, even though Deleuze rejects Leibniz’s infinite representation of the very small, no less than Hegel’s infinite representation of the very large, he says Leibniz went the ‘farthest’ in his attempt (DR 264).
(DR 11-2) Deleuze describes a “vulgarized Leibnizianism”. I take this vulgarization to be the first interpretation that accommodates Cartesian logic. It is representation as conceptual mediation. It is that which Leibniz seems to be doing from the point of view of an interpretation that leaves out those forces of vice-diction that Deleuze sees underneath the errors Leibniz made when he did not affirm divergence of incompossibles. But Smith misses Deleuze’s radical interpretation of Leibniz. Smith neglects Leibniz’s vice-diction that Deleuze sees hidden underneath the error. Deleuze tells us that Leibniz is still caught in the Representation of the very small. However, Leibniz’s only error (DR 51, 213, 279) is that he does not include all divergence. Leibniz could have approached the vice-diction of Univocity had he included all divergence of the incompossibles. Smith’s description of Deleuze-Leibniz leaves out the difference between differentiation and differenciation. It cannot even be said that Smith excludes the disjunctions of incompossibles like Leibniz did, because he never reached sub-representative divergence in the first place.
Smith quotes (ED 242) Deleuze (DR xvi) “We tried to constitute a philosophical concept from the mathematical function of differentiation”. But Smith omits the rest of that passage which reads, “….and the biological function of differenciation.” Deleuze says, (DR 220) “The entire Idea is caught up in the mathematical-biological system of different/citation.” However, Smith’s emphasis on calculus leaves out this different/citation. (DR 184-5) Atomism as a physical Idea is the purely anatomical and atomic elements of a ‘reciprocal determination’ that is “still….too much of the aspect of a spatio-temporal relation”. But, Deleuze concludes that “structure [differentiation] reappears on a quite different level, with a completely new [reciprocal] determination of differential elements and ideal connections.” Deleuze uses Geoffroy as an example of that biological function of differenciation that goes beyond a mere “empirical distribution of differences and resemblances”. At another (sub-representative) level there is a different/ciation. Structure is sub-representative and extra-propositional. Genetic differentials are not variable relations between one actual term and another.
So, Smith’s emphasis on calculus leaves out this different/citation. He leaves out (DR 185) structure that is at the level of the sub-representative ideas-problems. Structure (differentiation of problematic Ideas) and genesis (differenciation of intensive degrees) are reconciled when the differentials are different in kind from the relations of solutions. Ideas are differentiated but not differenciated. (DR 187) Ideas are in all coexistent state of ‘perplication’ (real distinction of differentiation) that are obscure because they are not differenciated (not numerically distinct). (DR 190) Vice-diction has two procedures. The first is differentiation in the conditions of problematic structure in specifications of adjunct fields. This is correlative to the second differenciation in the condensation of singularities and the genesis of cases of solution. (DR 191) “It is here that division finds its scope, which is not in breadth in the differenciation of species with the same genus, but in depth in derivation and potentialisation, already a kind of differentiation.” So, to understand Deleuze’s sub-representative and extra-propositional plane, it is not enough to include only differentials of mathematical variables. The problem is different in kind from its solutions. We must reach a problematic differentiation of the Idea, and also the intensive inseparable variation of biological systems of differenciation. There is common form (without prior concept) between these two aspects which are nonetheless different in kind.
(DR 176-8) Deleuze says that the interpretation of differential calculus asks the question of whether infinitesimals are real or fictive. But there is also the question of whether interpretation is to be finite or infinite. Set theory gives a finite interpretation by which the limit takes on only a static variability --- a disjunctive assumption of one value within a discrete interval. Structuralism also makes this disjunctive assumption --- and, “The birth of structuralism….coincides with the death of genetic or dynamic ambitions of calculus.” Therefore, the question is: ‘How are we to reconcile structure and genesis? The alternative between infinite and finite representation becomes an important question. Can infinite representation give a more satisfactory interpretation?
The metaphysical question for calculus asks
why differentials are negligible and must disappear in the
result. Deleuze says, “By ‘problematic’ we
mean the ensemble of the problem and its conditions. If the
differentials disappear in the result, this is to the extent that
the problem-instance differs in kind from the
solution-instance…..the conditions of the problem are the
object of a synthesis in the Idea which cannot be expressed in
the analysis of the propositional concepts constituting cases of
solution.….the problematic element, with its
extra-propositional character, does not fall within
representation…..” So, we must reach a
problematic and its conditions that cannot be analyzed by
propositions at the level of solutions. We must reach the
conditions of the problem at the level of a synthesis of
sub-representative and extra-propositional Ideas. But how
do we reach that domain of problems and their conditions?
The problem and its solution are different in kind. The reason that differentials disappear in the result (i.e. intensive forces tend to be cancelled in the solution), is because the problem is different in kind from its solution. The problem is not negatively related in opposition to its solutions. This means that the oppositional alternatives through which the calculus has been interpreted collapse. Infinitesimals are neither real nor fictive. The finite/infinite alternative also collapses. Infinite representation does not reach dynamic genesis any more than finite interpretation does. (DR 264), “The entire alternative between finite and infinite applies very badly to difference….because both fail to capture the extra-propositional or sub-representative source --- in other words, the ‘problem’ from which the calculus draws its power.” We must not be restricted to oppositional structures of negation. Not even an infinite variability can reconcile structure and genesis, because representation (finite or infinite) still maintains the principle of conceptual identity. Deleuze concludes (DR 178), “What is still missing is the extra-propositional or sub-representative element expressed in the Idea by the differential, precisely in the form of a problem.”
(DR 191) There is no opposition between
event and structure. There is no opposition between
structure and genesis. There is just difference in kind
between two planes: between structure of the problem
(differentiation) and its actualization (differenciation)
in cases of solution. But how do we reach that difference
in kind? We reach it only with univocity. Ideas are
problems. They are sub-representative and
extra-propositional. We cannot put them on the plane of
variables of a function (turning the concept into a function that
produces conceptual identity). (DR 181) Ideas
“are always processes of determinability, of reciprocal
determination and complete determination….”
But these processes cannot happen on a closed plane of solutions
and variable relations of elements. When we reach that
sub-representative and extra-propositional plane, we will finally
reach a domain where there is (DR 191) “no more opposition
between event and structure or sense and structure than there is
between structure and genesis.” Why? -- Because
sub-representative forces do not exclude divergence. We
reach forces that affirm all ‘incompossible’
disjunctions that, from the point of view of oppositional
structure had to be excluded. We reach multiplicities of
truly dynamic genesis, creating new continuities that were never
thought possible before.
However, what is Smith’s understanding
of Deleuze’s Leibniz? Smith describes
Deleuze-Leibniz’s “perspectivism” (ED 47) as
“point of view through which the individual expresses the
totality of the world”. By this he seems to mean that
there are many perspectives on one unifying world. However,
I contend that Deleuze sees something else in Leibniz’s
perspectivism. Deleuze-Leibniz’s perspectivism is not one
world seen from many subjective points of view. Perspecitivism
is not fully formed individual things or subjective points of
view that can be totalized into one world. Rather, Deleuze
sees in Leibniz, pre-individual singular events that form worlds
that are themselves “perspectives”. The world in
which Adam sinned is not the same world in which Adam did not
sin. They are really different individual-collective worlds
that cannot be compossible. They cannot be totalized into
one universalizing unity. Leibniz’s only error, says
Deleuze, is that he did not affirm all divergent
incompossiblities. Sufficient reason is the
sub-representative problematic expression of individuation.
Differentials are pre-individual singularities that may be
actualized into worlds of non-totalizable difference, said as
same. They are not on the plane of the variable elements of
already formed individuals that would only unify one structure of
generality seen from many perspectives.
But Smith (ED 73-77) traces what he takes to be Leibniz’s arguments, implying that Leibniz had to keep adding more inventions in an attempt to cover up the absurdities “even as he is falling into the abyss”. So Smith acknowledges the absurdity of his reading of Deleuze's Leibniz, but he continues. (ED 45) Smith says that the ‘principle of sufficient reason’ means that “everything has a reason”. That is, all that happens or is predicated is included in the individual notion of the thing. (ED 74) Smith asks, “But how can the principle of sufficient reason allow us to think existing beings?” He answers, “….everything that is predicated of a thing must be included in the concept of the thing…..If we say that what is predicated of a thing is its essence….then there is no difference between the principle of identity and the principle of sufficient reason. But what is said or predicated of a thing is not only the essence of the thing; it is also the totality of events that happen to the thing in its existence.” He concludes that what is predicated of the thing must be its essence and then there is no difference between the principle of identity (essence) and the principle of sufficient reason (existence). Smith thinks that, with the “reciprocity” of the principles of identity and sufficient reason, Leibniz concludes that the totality of events that happen in the thing’s existence connects the thing’s essence to its existence. But isn’t this just an essence/existence opposition that holds everything into identity? (ED 76) Smith’s Leibniz says that the principle of identity determines what is contradictory or not -- what is possible or impossible. But I contend that this does not reach Leibniz’s compossible convergences or incompossible divergences. Although Deleuze says (the Fold 55), “….predication is not an attribution….”, Smith thinks Liebniz's event is a predicate of attribution.
Such “vulgarization”, as Deleuze calls it (DR 11-2), of Leibniz is the result of not reaching that domain of pre-individual singularity of the event that Deleuze sees in Leibniz. (Logic of Sense 110-12) Deleuze says that “each monad expresses the world”. But this does not mean an inherence of predicates in the expressive monad. What is expressed is not the expression (the predicates of a proposition). Rather, once we reach the pre-individual domain of singular events, convergent series of singularities define compossibility as synthesis of a world. Series diverge in incompossible worlds. Singularity is pre-individual. An expressed world exists in individuals as predicates, but it subsists as event (verb) in the series of singular events that constitute individuals. What is expressed is not Adam-the-sinner, but a world (collective and individual) in which ‘to sin’ subsists in the expression of the individual Adam. Expressionism reaches the pre-individiual singularity of the event that constitutes the individuation of the world in which the individual Adam exists. So when a predicate is attributed to a subject, it has no degree of generality. (LoS 112) "....having a color is no more general than being green.” This means that Deleuze sees Leibniz as reaching that ‘sub-representative’ domain of ‘intensity’ without mediation of any degree of generality – if only he had not succumbed to his error of exclusion.
Therefore, Smith’s Leibniz is not
Deleuze’s Leibniz. For Deleuze (LOS 171-2),
“Compossibility does not even presuppose the inherence of
predicates in an individual subject or monad. It is rather
the inverse; inherent predicates are those which correspond to
events from the beginning compossible….” Deleuze-Leibniz’s
‘compossibles’ do not presuppose inherence of
predicates in an individual subject. Rather, predicates
correspond to compossible events. Compossibility is
pre-individual. Deleuze’s Leibniz sees no opposition
between the principle of indiscernibles and the law of
continuity. The principle of indisceribles is a principle
of individuation. However, the divisions established by
individuation, under this principle, are not ruptures of
continuity. The Fold p 64, “Individuation does
not go from a genre to smaller and smaller species, in accord
with a law of differentiation, but goes from singular to singular
under the law of convergence or of prolongation that ties the
individual to one world or another…..Thus the power of the
concept (to become a subject) does not consist in determining a
genre to infinity, but in condensing and in prolonging
singularities. The latter are not generalities but
events…” Structure and genesis are no longer
opposed as they are at the level of fully formed individuals.
Rather, we can have both structure (differentiation)
and dynamic genesis (differenciation) because we
reach a process of vice-diction at the sub-representative and
extra-propositional level.
The New
Smith understands that Deleuze’s concept of the ‘new’ is something different from a mere rearrangement of already existent formed matter. He understands that conditions of the new cannot be conditions of the already possible. Conditions of the real cannot be conditions of logical or transcendental possibilities. But then, Smith should also understand that conditions of real genesis should be different in kind from the conditions that merely maintain conceptual identity. As Deleuze says (LOS 68), “…it is futile to go from the conditioned to the condition in order to think the condition in the image of the conditioned as the simple form of possibility. The condition cannot have with its negative the same kind of relation that the conditioned has with its negative.” Smith says that Deleuze, informed by Maimon’s critique of Kant, attempts to reach the conditions of real experience. However, does Smith reach a process of real genesis whose conditions are different in kind from conditions of possible experience? The way forward seems to be, according to Smith’s reading of Deleuze, a post-Kantianism corrected by Maimon’s critique of Kant. Smith says (ED 247) “When a differential relation reciprocally determines two (or more) elements, it produces what is called a singularity, a singular point….singularities are precisely those points where something “happens” within the multiplicity (an event)….causing it to change in nature and produce something new.” But, as I contend, this can only “happen” if we reach that sub-representative plane of pre-individual singular difference. Only then can we reach the conditions of real genesis and real novelty. Does Smith reach that plane? He thinks he reaches the conditions of the real with his understanding of ‘external relations’.
Smith explains his understanding of ‘external relations’ by saying (ED 243-5) “When I say, “Peter is smaller than Paul,” this relation is not a property of Peter, nor a property of Paul; rather, it is something between the two.” He continues, “While properties are internal to the terms to which they are attributed, relations are exteriorities…” But if properties are internal to their terms, aren’t we still stuck in that already formed matter whose changes are still determined by the mere variable relations of a function? Aren’t terms and relations, then, closed into prior possibilities by the representational categories of attribution? I contend that, if we are to reach Deleuze’s ‘external relations’ we must reach that sub-representative and extra-propositional domain of intensive difference that does not conform to the possibilities of a prior concept that maintains identity. Deleuze-Hume’s ‘external relations’ must not presuppose an image of what things are or how they can possibly be related. Terms, if they are not to be determined by the categories, must be external and heterogeneous to their relations AND relations must be external and heterogeneous to their terms. Otherwise, we still have a prior concept of what things are and how things can possibly be related. External relations can only happen at the sub-representative level of disparate intensity. If we see only a “becoming” of variable terms and relations of already formed-matter, we do not reach univocity. Only forces of sub-representative intensity can couple any singularity with any other to reach a new singular ‘becoming’ that changes in nature, each time. External relations are constituted in parallel series of heterogeneous terms and relations. They are not oppositions of homogeneous variability of relations and terms. If properties are still internal to their terms, as Smith thinks, then difference would still be categorical and relations between them would still be mediated by a principle of conceptual identity. Terms and relations would still be internally related in a prior concept.
It is important to realize that (DR 304) “Opening is an essential feature of univocity.” Smith writes an essay ‘The Open’. But does he reach the opening of the forms? Does he reach ‘external relations’ in Deleuze-Hume’s sense? Smith says (ED 266), “Properties may be internal to the terms to which they are attributed, but relations are exteriorities.” And, Smith continues, “….it is not possible to think relations without thinking of a becoming….the relation cannot change without the concepts changing….Whereas properties are solid, relations are fragile…” But when these “fragile” relations of solid properties change they are merely variable relations that maintain conceptual identity. There is no real change in nature. There is only a rearrangement of already formed matter that Smith himself noticed cannot be the conditions of the new. If properties are solid, how can they reach a non-categorical difference? If relations are really fragile, how can they still maintain conceptual identity? If we are to reach the conditions of real experience, we must reach the sub-representative intensive forces that are not mere variables of a function, but the inseparable variation of disparate intensive difference. If we are to reach the new, we must reach a real difference that is not merely a difference of possible conceptual terms and relations that maintain identity. With Deleuze’s ‘external relations’ of univocity, intensive forces may couple in any way because there is no prior concept to tell us what things are or how they can possibly be related. Any intensive singularity may be related to any other to form a really new inseparable singular difference each time --- to be actualized in a really new singular world, each time. The external relations of univocity are the conditions of the new. But to reach them, we must reach the sub-representative singular differentials of disparate intensity.
How is Smith’s sense of “becoming” any different from the variability inside the identity of a concept (turning the concept into a function)? How does this reach the intensive forces of inseparable variation of the sub-representative problematic concept? How does this reach the real ‘becoming’ of univocity that opens the forms into continuous variation without exclusive disjunction? Smith does not reach the ‘external relations’ that break with the logical categories of attribution as he intends. His “external relations” are merely the “becoming” of terms in a variable relation of possible experience. Because Smith does not reach sub-representative forces of intensive inseparable variation, he has turned the concept into a function of variability that maintains identity. Smith is still thinking according to internal relations because he does not know how to reach that sub-representative plane of univocality.
If ideas contain no more than what is given in sensory impressions, as empiricism claims, then this is because relations are external and heterogeneous to their terms. This is not a relation of oppositional difference between ideas and impressions. External relations are between impressions or ideas of terms and impressions or ideas of relations. We must reach the sub-representative forces of heterogeneous parallelism, not homogeneous opposition with correspondences. This externality of relations cannot happen at the level of functions and their variable relation. This can only happen on the sub-representative and extra-propositional plane where terms are singularities of real difference and relations are external bridges that have no prior coupling with which to conform. Only when we reach the sub-representative genetic forces do we reach the conditions of real experience that are not to be confused with the conditions of possible experience.
Smith says (ED 246), “normally” or “empirically” difference is a relation between things that have a prior identity. However, Smith says, Deleuze’s ‘difference’ is on a transcendental level where relations do not depend on their terms. So, he thinks he is describing external relations where “the elements are reciprocally determined by the relations themselves…..Difference here becomes constitutive of identity --- that is, it becomes productive and genetic, thus fulfilling Maimon’s demand…” So, Smith’s “reciprocally determined” terms have an internal relation of variability that maintains identity. Difference becomes constitutive of identity. Variables remain on the level of conceptual identity (turning the concept into a function of variability). He does not reach the sub-representative and extra-propositional conditions of real experience. He does not reach the reciprocal determination of intensive inseparable variation of parallel series that couple any singularity with any other in external relations without a prior concept. He does not reach the disparate intensive forces of inseparable variation that, with each division, change in nature. Smith’s variable relations can only change within a prior concept of what is possible in order to maintain identity. How is this anything other than the transcendental conditions of possible experience? Smith does not reach the sub-representative transcendental conditions of real experience. He sees only the variable changes from one actual term to another that merely mediate conceptual identity.
How can we reach the conditions of real
experience that are no broader than what is conditioned? Something
unconditioned must determine both the condition and the
conditioned together so that they are not negatively mediated in
a prior conceptual relation of what is possible in order
to maintain identity. But how can we reach that
unconditioned something? We must reach a sub-representative
domain beneath the conditioned and its conditions of possibility.
The conditioned must not resemble its conditions. We must not be
restricted to the prior possibility of a conceptual image that
maintains identity.
Hegel and Post-Kantianism
Deleuze calls his ‘Kant’s
Critical Philosophy’ a “book on an enemy” and
yet, Smith remarks (ED 64-5) Deleuze also finds immanence in
Kant. Likewise, Deleuze is not “anti-Bergson” or
“anti-Leibniz" just because he has disagreements with
them. So, Smith insists, Deleuze is not “simply
anti-Hegel” either. Smith seems to be looking for some
common becoming in terms of historical causality between Deleuze
and Hegel --- in terms of species of a common genus. But
that is not what Deleuze means by “becoming”. For
Deleuze, “becoming” must reach a ‘common
notion’ or a 'zone of indiscernibility' with a common degree
of intensity that, with every new degree, changes nature. Deleuze
was able to enter into a ‘becoming’ with Spinoza, Hume,
Kant, Bergson, Leibniz….etc. because, by finding with them a
common degree of intensity, he could change the nature of
thought. Deleuze could find in each of them something of
the sub-representative and extra-propositional with which he
could enter into a becoming of the new. He could find
something of immanence underneath the traditional readings of
certain philosophers, despite disagreements he may have had with
them. He could enter into a ‘becoming’ with those
philosophers because of that domain he found hidden beneath the
historical strata. He could find nothing like that in
Hegel. Hegel is included in Deleuze’s text as the
enemy. So, when Smith tries to make compromises between
Deleuze and Hegel, he is not entering into a becoming with
Deleuze’s text. He does not allow himself to see Hegel
from the light of Deleuze’s plane of consistency. He
prevents himself from ever seeing how Hegel appears from the
perspective of Deleuze’s univocity. He prevents
himself from ever reaching any understanding of univocity (that
new and strangest of thought) that changes the light of how
things appear.
Why does everyone (Smith included) seem to see Hegel in Deleuze? It is because they can see no way out for Deleuze. Smith says (ED 65) citing Derrida, “it is impossible to oppose Hegel, because opposition is the motor of the Hegelian system and to oppose Hegel is to become part of the system.” But Smith seems to be saying that this critique of “binary oppositions” or “closure” is not found in Deleuze’s critique. But, of course, it is; and it must be. This is a problem Deleuze must address. Deleuze’s critique of Hegel is the critique of that closed oppositional system from which nothing can escape. Deleuze must address the problem of how to oppose Hegel’s oppositional system of exclusive closure. But Deleuze understands the paradoxical nature of this problem. Any resolution must have no relation to Hegel’s negative-oppositional relations. This means we must reach something that has no relation with Hegel -- not even an oppositional relation; for if it did, the relation would fall right back into a generalizing structure of opposition and there would be no way out. Everything would close into a system that maintains the principle of conceptual identity. Yet, at the same time, any resolution to the paradox must exclude nothing. It must have no relation to any negative system (such as Hegel’s) and yet must leave nothing out. These are the paradoxical requirements that Deleuze must address if he is to escape that essence of the Dogmatic Image that Hegel Represents.
Therefore, the paradoxical problem Deleuze addresses with his univocity is, ‘How to oppose an oppositional system without using oppositional relations’ --- ‘How to oppose Hegel’s exclusive system of closure while still affirming everything.’ ‘How do we reach forces that had been excluded by Hegel’s oppositional system?’ ‘How do we escape Hegel’s exclusive closure without excluding anything?’ Deleuze finds resolution to this paradox in the concept of ‘vice-diction’ (DR 45-6). But to reach vice-diction, we must reach the sub-representative domain of univocality. Hegel’s infinitely large excludes the inessential forces. But infinitely small inessential forces vice-dict essential elements, thereby including in the inessential case what it excludes as essence. So, Deleuze’s univocity has no relation to Hegel’s system of exclusive essences, even as it includes everything in the inessential case. So, in order to escape from Hegel’s closed oppositional system, Deleuze’s univocity must be really distinct from Hegel’s generalizing structure of identity. That is, there must be no relation. There must be no relations of opposition, genus/species, identity, etc., for if there were, everything would be absorbed back into a generalizing Image of what is “possible”. Deleuze’s univocity is really distinct from Hegel’s infinite variability that maintains a principle of identity. Smith cannot believe it possible that Deleuze has no relation to Hegel, because he has not reached Deleuze’s sub-representative forces of univocal vice-diction.
Whenever we try to make compromises between Deleuze and Hegel, we prevent ourselves from even beginning to understand Deleuze. Deleuze makes a real rupture with the historical-causal interpretations of traditional philosophy. Deleuze adds a new degree of intensity to the history of thought that changes the nature of philosophy. But Smith can see no such rupture. He sees both Deleuze and Hegel as just two species of post-Kantianism. But Deleuze sees something new in Kant --- a never fulfilled initiative --- through which he could enter into a becoming with him. He could do nothing like that with Hegel. Deleuze could find no ‘common notion’ with Hegel as he could with some others. If we want to understand Deleuze’s ‘difference’, we must see Hegel as he appears from the perspective of Deleuze’s plane of immanence. It does no good to argue with Deleuze’s text if we want to understand Deleuze’s plane of consistency. Deleuze is telling us that, from his point of view, there is no way to reach a becoming with Hegel’s closed system of essence. However, Deleuze does vice-dict Hegel by reaching the sub-representative inessential difference that excludes nothing.
When we reduce Deleuze's thought to a mere calculus of variables and the possibility of their infinitely variable rearrangements, we miss the rupture in the history of thought brought about by Deleuze’s forces of sub-representative vice-diction. What is the newly created concept that makes Deleuze’s philosophy really different in nature from the Kantian tradition --- and yet is also the concept through which Deleuze entered into a new becoming with Kant? To answer this question, we must look to Deleuze’s own reading of Kant. (See my 'Deleuze's Repetition of Kant'.)
So, what was it that Deleuze saw hidden in Kant through which they could enter into a becoming? Deleuze tells us that Kant’s ‘time’ is the form of everything that changes and moves, but it is an immutable Form which does not change” (‘Kant’s Critical Philosophy’ vii-viii). Deleuze tells us that Kant freed time from its subordination to movement. But according to Smith (ED 133-4), when Deleuze says that time is no longer the cardinal measure of movement, it means that “….time no longer measures movement, but movement itself….now takes place within time.” Smith explains his understanding of this ‘pure and empty form’ by saying “…..the pure form of change, time itself is defined by its infinite variability…” all according to a Kantian synthesis. Smith does not seem to notice that what he describes happens on the plane of the time that Deleuze calls ‘Chronos’. He still leaves out the sub-representative plane of Aion that Deleuze calls the ‘pure and empty form of time’ (D&R 87).
So, Smith reads Deleuze-Kant to say that there is an a priori image of infinite variability in time. Smith describes his understanding of this “empty form of time” as the subjective synthesis in a variable present that contracts past into the future. But what has Smith done but describe time as merely that which Deleuze has called ‘Chronos’ (time subordinate to movement)? It is still the traditional understanding of Kant that leaves out what Deleuze calls the ‘empty form of time’ (Aion) that must be included (along with Chronos) if movement is to be subordinate to time. That is, Smith’s Kant leaves out the sub-representative empty form of time (Aion) that is the ‘form of the determinable’--- the univocity of time.
Smith’s understanding of the
‘empty form of time’ is not empty. It is the a
priori Image of possible empirical content in the
synthesizing apprehension of the transcendental subject. It
closes the forms in the variability of conceptual identity.
This traditional interpretation of Kant leaves out what Deleuze
sees in Kant. It leaves out the ‘form of the
determinable’ which is no longer merely a direct
determination of an empirical difference between determination
and the undetermined. Deleuze says (DR 85-7), “to the
determined and the undetermined must be added the form of the
determinable, namely time….” And, Deleuze thought
that Kant would have reached that sub-representative empty form
of time --- the form of the determinable that is empty of
empirical content --- had he not aborted this initiative with a
“practical resurrection”. Deleuze sees
Kant’s Copernican Revolution as an initiative which could
have opened thought to that sub-representative empty form of
time. He sees that Kant might have reached the
sub-representative univocality of time --- that would have
overcome the transcendental illusions of Self, World, and God ---
if only Kant would have pursued his initiative. But Kant
put time back on its cardinal hinges, subordinating time to
movement. Deleuze takes up Kant’s aborted initiative
to reach the univocity of time --- to reach that
sub-representative empty form that nomadically distributes
incorporeal content. But the empty form of time (Aion)
itself does not change. Time is the form of everything that
changes and moves, but time is immutable Form which does not
change. It is not an eternal form of variability. Rather,
it is the immutable form of change and movement of the univocal
dice game. (See my article, ‘The Empty Form of Time
--- The Eternal Return’.)
Conclusion
Deleuze says (D&R 262), “In any case, difference in itself appears to exclude any relation between different and different which would allow it to be thought. It seems that it can become thinkable only when tamed – in other words, when subject to the four iron collars of representation: identity in the concept, opposition in the predicate, analogy in judgment and resemblance in perception.” But how do Smith’s variable relations that maintain identity do anything other than tame thought? How does Smith reach anything other than these four iron collars that Deleuze criticizes? When Smith quotes Deleuze as saying (ED 28) univocity is “the strangest thought, the most difficult to think, if it has ever been thought”; does he really believe he has reached a thought that is in any way strange, new, or untamed? I contend that if we are to begin to understand Deleuze, we must begin to grapple with the most difficult thought of univocity. But to do that, we must reach an encounter that requires us to think differently.