Numerical and Real Distinction

by Beth Metcalf

Where is the secondary literature that demonstrates an understanding of Deleuze’s univocity?  Every commentary assumes that Deleuze is talking about numerically distinct and separate objects, parts of objects, or subjective points of view in variable structural relations.  If there is an exception, I haven’t found it yet.  There is usually an effort to reach a transcendental-virtual realm as source of these numerical distinctions of formed substances.  But such an effort can never reach Deleuze’s sub-representative domain of univocality.  I have tried in previous articles to make the case that the numerical distinction of substances has nothing to do with Deleuze’s univocity.  Numerical distinction is never real.  The numerical distinction of substances does not reach Deleuze’s ‘virtual’ as real distinction.  It can never escape the one/many oppositional structure of objects in conceptual identity.  It is still stuck in the very Image of Representational Thought that Deleuze rejects.  This article is another attempt to make the case that Deleuze is saying something really different.

Deleuze is inspired by what he sees as Spinoza’s univocity.  Spinoza’s attributes, thought and extension (as the only two we know), are the heterogeneous parallelism of real distinction.  Thought and extension are really distinct because each is conceived without the aid of the other and deny everything belonging to the concept of the other. This is Deleuze’s inspiration for his intensive coupling of heterogeneity. 

“Every intensity is E – E’, where E itself refers to an e – e’, and e to e – e’ etc.: each intensity is already a coupling (in which each element of the couple refers in turn to couples of elements of another order), thereby revealing the properly qualitative content of quantity.” (Difference & Repetition 222) 

Intensive coupling is empty of empirically formed content.  The heterogeneity of intensive coupling must never be confused with homogeneous form-matter coupling because (DR 275) “…the matter-form couple is already informed…”  Rather, with the intensive coupling of univocity, any expression of thought may be coupled with any expressive designation of unformed matter.  Intensive coupling is the real distinction of unformed Substance.  This unformed Substance is not already actualized in an extensive structure.  Since intensity does not have to conform to a prior conceptual form or causal connection, it can be expressed in any intensive coupling without exclusion.  All is affirmation.  Unformed Substance (empty of empirically formed content) as qualified and expressed in intensive coupling is all real distinction. 

“The distinction between content and expression is always real….It is the double articulation [intensive coupling] that distributes them according to the line it draws in each stratum; it is what constitutes their real distinction.  (On the other hand, there is no real distinction between form and substance….since substances are nothing other than formed matters….)”  (A Thousand Plateaus 44)

However, real distinction is never numerical distinction. Substance is qualified as all real distinction in the attributes. But all real distinction is ontologically one. Yet since qualified substances are really distinct, all are ontologically singular and said in one sense.  Furthermore, all really distinct degrees of intensity say the whole of Being in one sense.  Substance fills space to really different intensive degrees.  Any intensive degree can be joined with, or disjoined from, any other.  In doing so, it becomes a new intensive singularity of real distinction.  Each heterogeneous coupling, in whatever degree of intensity, is the ontological singularity of real distinction.  All say the whole of Being in one sense.  This opens the forms.  It must not be confused with the numerical diversity of substances of already extensive formed matter.  Intensive quantity reveals disparate new forms of quality.  The Substance of Deleuze-Spinoza is not the variable numerical distinction of formed objects.  It is the multiplicity of the real distinction of ontologically intensive singularity.        

Therefore, univocity is not to be confused with the many numerically distinct substances of already formed matter which are totalizable into one conceptual structure of spatialized time.  When we think in terms of such numerically distinct objects, we are still shackled to Representational Thought.  In that case, objects are mistaken to be numerically distinct substances that are totalizable into a unified Transcendent conceptual structure of Identity with no real distinction at all. The "difference" of numerically distinct substances is merely a function of conceptual identity.

In order to understand Deleuze, I believe the best way to begin is to come to terms with Chapter 1 of Expressionism in Philosophy.   Deleuze’s Spinozist Substance is the real distinction of unformed matter.  It is not to be confused with a Representational notion of numerically distinct substances of already extended formed matter.  When substance is thought to be already formed, it is differentiated by attributes as categories or properties.  Attributes, then, qualify substance as modes in extension (shapes of bodies) or modes in thought (ideas in the mind).  Modes diversify substances through their attributes.  Substances, qualified by attributes, are diversified into modes. Attributes, then, are properties attributed to a substance (as genus) and modes (as species).  Attributes as differentia make sure genera remain the same while becoming other as species across levels of division (see Difference & Repetition 30-35, describing Aristotle’s finite Representation-Analogy). 

Finite Representation has the generalizing structure of genus and species.  It assumes a matter that is already formed.  If attributes distinguish substances they qualify, then modes distinguish substances of the same attribute.  Attributes constitute the essence of substances they qualify.  However, attributes also constitute the essence of modes sharing the same attribute.  Numerical distinction of modes is mistaken for real distinction of substances.  Substance is a genus, attributes are differentia, and qualified substances (modes) are species.  This treats modes as if they were substances.  Numerically distinct objects are taken to be really distinct substances.  Numerically distinct substances can be totalized into a generalizing structure of identity (genus and species).  But Deleuze warns us that genera and species have nothing whatsoever to do with his process of univocity. 

“Generic and specific differences are tied together by their complicity in representation…” (DR 34)

And yet commentators still try to understand Deleuze through a transcendentalism that resembles empirical substances qualified by categories or properties. They do not reach the heterogeneity of Deleuze-Spinoza's attributes.  They thereby find only numerically distinct substances that can never escape one conceptual form of possibility.  That is, they never reach Deleuze’s real distinction of univocity.  They never escape the generalizing Representational form of genus and species.  In contrast, with univocity, we can make temporary modal uses of disparate generalizing structures of genus and species, but none are to be mistaken for substantial reality, and they are not totalizable into extensive unity.

Representation-Analogy introduces problems.  Substance is that which exists by itself.  But if attributes distinguish substances they qualify, then modes must distinguish substances of the same attribute.  If there are Substances sharing the same attribute, then they would have to be distinguished by their modes.  Such dependence of substance on modes is an absurdity.  Furthermore, two or more substances with the same attribute would be merely numerically distinct.  They could not be really distinct if they share one attribute.  Nor would there be a substantial distinction since one and the same attribute cannot distinguish substance.  If two or more objects are numerically distinct, they cannot be substances because they would have to presuppose an external cause.  This could apply only to modes, not substances.  Therefore, substance can never be numerically distinct objects.  Numerical distinction can only be modal. 

With Representational Thought, substances are mistaken to be numerically distinct and already formed possibilities.  It is assumed that, if substances are not differentiated (formed in extension and numerically distinct) then the only other alternative is an undifferentiated substance – a nothingness.  However, Deleuze rejects this alternative of either a formless and undifferentiated substance, or singularity as numerically distinct already formed substances (see my article Deleuze Versus Hegel). 

In contrast, Spinoza’s Substance is unformed matter.  However, this unformed matter, far from being undifferentiated, is all really distinct differentiation.  And this real distinction of Substance, as unformed and empty of extensive empirical content, is always ontological singularity (i.e. intensity).  Deleuze-Spinoza’s Substance is qualified and differentiated in the univocal attributes as all real distinction that is ontologically one Substance.  The virtuality of Substance is no longer to be confused with already actualized possibilities of numerically distinct formed substances.  Therefore, for univocity, Substance is not undifferentiated, and singularity is not at the level of individual substances thought to be numerically distinct.  Now, the individuation of numerically distinct singularity is pre-individual, intensive, and modal. It is not extensive and substantial.

“No, singularities are not imprisoned within individuals and persons; and one does not fall into an undifferentiated ground, into groundless depth, when one undoes the individual and the person. The impersonal and pre-individual are the free nomadic singularities….” (Logic of Sense 140-1) 

Deleuze tells us that when objects are frozen into numerically distinct substances, then movement is suspended.  The object becomes the mould of a perceptible image in an intelligible structure (Cinema 2, 26-28).  Therefore, Spinoza’s Substance (unformed matter) is not to be confused with a Representational notion of substance (formed matter).  The numerical distinction of substances is an oppositional form/matter coupling.  It is differentiated without any real distinction at all.  In contrast, Spinoza’s Substance is unformed singularity yet it is not undifferentiated.  Substance is differentiated as real and formal distinction.  Singularity is intensive and pre-individual difference.

Nonetheless, Deleuze is still misunderstood to be working within the Representational model of genus and species.  It always seems to be supposed that the only way to avoid an undifferentiated nothingness is to accept Representational model of numerically distinct individuations of substance.  Nor does Infinite Representation solve the problem.  It merely opens the categories and puts subjects and objects in a constant relation of variability of one spatialized-time.  It never escapes one form-matter coupling because it never reaches sub-representative intensity.  It never escapes one extensive structure.  Infinite variability is still one unifying conceptual form of the many numerically distinct substances.  It is the infinite diversity of already formed matters. It never reaches disparate intensity. Deleuze’s univocity refuses the alternative of both finite and infinite representation.

“We refuse the general alternative proposed by infinite representation: the indeterminate, the indifferent, the undifferenciated or a difference already determined as negation, implying and enveloping the negative (by the same token, we also refuse the particular alternative: negative of limitation or negative of opposition).  In its essence, difference is the object of affirmation or affirmation itself.  In its essence, affirmation is itself difference.”   (Difference & Repetition 52)

There is another problem.  Although most Representational thinkers understand that things conceived as really distinct in the mode of thought must not be confused with really distinct things in the mode of extension, Representational Thought still sees a passage from one to the other through a Transcendent Ground that mediates between really distinct substances (in the mode of extension) and the mind’s way of conceiving them possible (in the mode of thought).  Representation-Analogy needs a Transcendent Ground between substance conceived as really distinct (in the mode of thought) and really distinct things (in the mode of extension).  Both the transcendental virtual and the actual are then misunderstood to be in a structure of resemblance between really distinct substances and the mind’s manner of thinking them possible. 

Although Representational thinkers usually understand that things conceived as really distinct must not be confused with really distinct things, many seem to think that Deleuze is a proponent of a kind of metaphysical realism (or objectivism) of numerically distinct objects. They think they avoid Representational Thought through a realism of objects that somehow is supposed to eliminate representation to subjectivity. That is, they believe Deleuze is saying that relations among numerically distinct elements or objects (taken as really distinct substances) can be known in themselves apart from representation (conceived as really distinct) to a knowing and perceiving subject. This is very far from having anything to do with what Deleuze is saying. In fact, if these 'speculative realists' want to avoid naive realism, they must explain how they can know or conceive a relational structure of numerically distinct substances without any prior concept or resemblance represented to their subjectivity. That is, how can they know identities and differences of elements and objects (taken as really distinct substances) apart from representation of identities and differences of elements and objects (conceived as really distinct)? In any case, this metaphysical realism is still the opposition of subject and object that cannot escape the epistemological problems of Representational Thought. It is still the formed matter variability of structural relations. It is still the numerical distinction of substantial objects that excludes real distinction, according to Deleuze.

Deleuze sees univocity as Spinoza’s attempt to address these problems.  Univocity is really different from our common sense Representations.  Attributes are not attributed to generic substances or to specific modes.  Attributes no longer constitute the essence of both substance and modes.  Rather, attributes are now attributive.  Each attribute expresses an essence and attributes it to substance.  Univocity is not a generalizing structure of genus and species.  Univocity is expressive.

“In short, what is expressed everywhere intervenes as a third term that transforms dualities.  Beyond real causality, beyond ideal representation, what is expressed is discovered as a third term that makes distinctions infinitely more real and identity infinitely better thought.  What is expressed is sense: deeper that the relation of causality, deeper than the relation of representation.”  Expressionism in Philosophy 335   

With univocity, attributes are univocal forms common to substance and to modes.  But now the essence of substance and modes are no longer analogous --- they are really different.  Attributes constitute the essence of substance, but do not constitute the essences of modes because, when modal essence disjoins qualified substance, there is a change in nature.  Representation-Analogy, in denying common univocal forms of real distinction, must speak of analogy between the essence of modes and the essence of substance.  This results in a negative structure of opposition and limitation with no real distinction.   

“The analogical method denies that there are forms common to God [Substance] and to creatures [modes] but, far from escaping the mistake it denounces, it constantly confuses the essences of creatures with the essence of God.” Expressionism in Philosophy 46-7

With univocity, (DR 303-4) attributes are not categories, because although they are really and formally distinct, they are ontologically one and introduce no division into Substance.  The real distinction (differentiation) of qualified substances cannot be distinguished numerically (differenciated).  Modes are not species.  But modes may be distinguished numerically (differenciated) because, in being disjoined from substances, they immediately relate to ontologically singular Substance.  Substance, although unformed and empty of empirical content, is not undifferentiated.  Substance is qualified as really distinct (differentiated) in the attributes.  Attributes are no longer properties or qualities.  Attributes are now expressed as forms common to substance and modes.  Substance and modes are now said (expressed) in one ontological sense in the common form of attributes.  But this now allows the essence of modes, in being disjoined from substance, to be really different from the essence of substance.  There is no need of a Transcendent Ground because all substances, qualified by the attributes as really distinct, are ontologically one.  Bodies are no longer modes of extension.  Minds are no longer modes of thought.  Now, thought and extension are attributes that are the heterogeneous parallelism of real distinction.  That is, as expressed, they are not cause of one another.  Any expression of thought may be coupled with any expressive content to form a new singular concept of real difference, each time. 

Univocity solves the problems that lead to internal contradictions of Representational Thought.  Attributes are no longer modes (subjective thought in opposition to objective extension) sharing a prior Transcendent Ground of unification.  Thought and extension are now immanent attributes of real distinction.   Substances are never numerically distinct or divisible into parts.  Substance is not a genus that could contain nested hierarchies of modes as numerically distinct sets of objects or elements.  Such sets, in dividing, could never change the quality of real distinction.  Only intensive modes change nature in dividing.  Actualized formed matters are temporary existing modes and are not substantial essences.  They can never be totalized, because there is no Transcendent Ground that mediates conceptual unity.  Virtual Substance is no longer a unifying Ground of Transcendent possibility (the One) from which actualizations of objects (the Many) may become totalized.

Representation-Analogy confuses the real distinction of substances (as genera) with numerical distinction of modes (as species).  It confuses modal distinction with substantial distinction.  It sees many numerically distinct objects as substances and unifies everything into conceptual identity through an external Transcendent Ground.  In contrast, univocity is the real distinction of immanence.  For Deleuze’s Spinozist univocity, two or more substances cannot share the same attribute.  There is one substance per attribute.  Numerical distinction is never real.  Furthermore, there is only one substance for all attributes.  Real distinction is never numerical.  Substance is qualitatively distinct.  But it is not quantitatively distinct.  It escapes the unifying Transcendent structure of conceptual identity that is the Image of Representation-Analogy.

Some commentators agree with Deleuze.  Others disagree with Deleuze.  However, they really can do neither until they begin to grapple with Deleuze’s concept of univocity.  The only way to begin to understand Deleuze is to admit we do not yet understand him.  Now, I realize that the model of Representation (including Infinite Representation) is much easier to understand than Deleuze’s univocity.  And it is unfortunate that the problems of Representational Thought have made it necessary to abandon the conveniences of our common sense and good sense.  But Deleuze must be taken seriously when he tells us that his univocity is real difference that requires us to think differently.     

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