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
Substance. 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. Modes are not species. But modes may be distinguished numerically (differenciated) because, in being disjoined, they change in nature. 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.