Force Relations

by Beth Metcalf


In Expressionism in Philosophy p.131-2, Deleuze-Spinoza says that we should guard against a double mistake.  When we accept a correspondence theory of truth---correspondence of idea with its object---we have no knowledge of a true idea’s form or its content.  For a true idea won’t have any more “internal perfection” than a false one.  There is merely an external relation of idea and object.  It gives us no formal or material definition of truth, but only “extrinsic designation”.  On the other hand, perhaps we may try to reach truth as an internal relation of the concept by using a definition of internal coherence.  But this gives us only representative content, and its form is that of psychological consciousness.  It gives us knowledge of effects or properties of things only in a form of recognition.  Both sides remain in the four requirements of Representation:  identity in the concept, opposition in the predicate, analogy in judgement, and resemblance in perception.  Such Representational theories, with their forces of relations internal or external to the concept, have presented a long history of epistemological problems. 


In Difference & Repetition p.203, Deleuze describes these two forms, internal and external to the concept, as two forms of the negative.  There is opposition and there is limitation.  The former is the opposition of the many to the One.  The later is limitation of the One by the many.  On the one hand, the forces of opposition are internally related.  They are forces that produce a self-unfolding.  But to what are they internally related?  What is it that unfolds of itself?  What is this One which reacts in opposition to the many to produce an unfolding?  This One is the identity internal to the concept.  The many can react in opposition to unfold this concept, but the concept never changes in form no matter how infinite its variability may become.  The concept is conceived in opposition, and can never escape its internal identity.  There can only be mediation through the possibility internal to the concept.  On the other hand, the forces of limitation are externally related as if to something foreign, outside, and wholly other.  This external relation is supposed to be without a concept.  However, Deleuze says that this still presupposes the identity of a concept, albeit externally.  (DR270) Representation distorts repetition.  “Repetition…is represented outside the concept, as though it were a difference without concept, but always with the presupposition of an identical concept”.  Only by appeal to some transcendent miracle can we say how the concept can correspond to something real.  Therefore, both sides of Representational negation consist of negative forces of One/many and never reach Deleuze’s forces of multiplicity.   Both sides have merely conceptual difference mediating the possible.  Opposition is difference internally related to the concept.  Limitation is repetition externally related to the concept.  Neither side escapes the identity of the concept in general.


However, Deleuze says (DR26) “…difference can be internal, yet not conceptual…There are internal differences which dramatise an Idea before representing an object.  Difference here is internal to an Idea, even though it be external to the concept which represents an object.”  (DR27) “In reality, so long as we inscribe difference in the concept in general we have no singular Idea of difference, we remain only with a difference already mediated by representation.”   Therefore, the internal relation of the Idea must not be confused with relations internal to the concept.  The relations internal to the Idea are still external to the concept.  They are without prior concept.  We must reach a field of forces internal to the sub-representative Idea.  At the sub-representative realm of Univocity, Ideas have a logical form that is not the form of psychological consciousness.  Ideas have material content that is not a representative content.  There is an internal conformity between the Idea’s logical form and material content.  Only adequate Ideas (in their sub-representative composition) give us knowledge through causes.  An adequate idea is an idea that expresses its cause.  There is internal conformity between an idea of an idea (in its reflexive form) and the idea as it expresses its material cause.


But what is meant by relations internal or external to their terms?  What is meant by relations with or without a presupposed concept?  On the one hand, there are relations internal or external to a presupposed concept.  For example, ‘A is larger than B’ has the same relation to the concept as ‘B is smaller than A’.  This is because the presupposed concept tells us that the relation of the terms remains the same regardless of appearances.  On the other hand, external relations that are without concept are not determined by the identity of any presupposed concept.  For example, all we can know by way of empirical appearances (without concept) is that sometimes ‘A appears larger than B’ AND sometimes ‘B appears larger than A’.  The terms are external to their relations.  Or, sometimes ‘A appears larger than B’ AND sometimes ‘A appears smaller than B’.  Relations are external to their terms.  From the point of view of a prior concept, external relations are paradoxical.  When relations are external and without concept, elements of sets are prevented from closing into fixed objects.  Nor are there fixed relations between objects.  Relations no longer belong to closed sets of conceptually self-identical or numerically distinct objects.  With external relations without concept, paradox eludes common sense.  Or, perhaps A is larger now.  A was smaller before.  But it is at the same moment that A becomes larger than it was and smaller than it becomes.  This is the simultaneity of becoming (Aion) that eludes the present.  Becoming is the paradox of both directions at once.  Paradox eludes good sense. 


Representational theories remain at the level of formed matter.  Even with infinite variability, there is still only the continuous development of form and the continuous variation of matter.  But the form-matter coupling is never broken.  With Representation, substance is nothing other than formed matter.  Since it cannot break the form-mater coupling, all objects are numerically distinct and separate.  Numerical distinction of substances (formed-matter) holds everything in structural relations of the identity of the concept.  These force relations of formed matter, however variable they may be, lock everything into the infinite variability of conceptual identity, because singularities are at the level of the individual.  Individual singularities hold everything in conceptual identity.  There can be no real distinction, because all relations are determined in all their variability, by the concept in general.  There is only sedentary distribution in proportions determined by the requirements of Representation. 


Everything changes with Univocity.  Only Univocity reaches a sub-representative field beneath form and matter.  Univocity reaches a field where singularity is pre-individual.  Only Univocity breaks the form-matter coupling to escape the internal identity of the concept.  It reaches a force field of unformed and non-subjectified material function in relations of speed and slowness and movement and rest. This is the hecceity of the event in degrees of intensity.  With Univocity there is no longer the numerical separation of substances.  Since there is ontologically single Substance, there can now be really distinct individuation of disparate worlds.  With Univocity, content and expression are really distinct and heterogeneous series.  But they are always ontologically single Substance.  Only Univocity reaches the real forces of universal-singularity.


Therefore, Deleuze follows Spinoza’s Univocity.  All Ideas have real difference, but they all SAY the whole of being in one sense.  All the real distinctions, in whatever degree of power, say the whole of Being in one sense.  We see that this nomadically distributes beings into an open space.  Things/Ideas are distributed into the whole of undistributed Being.  Being is real difference, ontologically one.  Every nomadic distribution is really different from any other, but all say the whole of Being in one sense.  All real worlds are really distinct because they cannot be totalized and do not share the same structure or the same concept.  Because they are all degrees of ontologically single Substance said in one sense, they distribute the open space of the whole of undistributed Being.  All formal and real difference remains in open communication with all others, because they all share the same ontologically single Substance.  They ARE the same Substance ontologically.  Substance in-itself is singular, intensive degrees of real distinction.  Therefore, we see that, instead of sedentarily distributing a closed space to things, there is now a nomadic distribution of things into an open space.  Univocity remains open to a sub-atomic field of intensity beneath formed matter.  With Univocity, there are no negative forces.  All forces are positive and affirmed.  Therefore, there can be no opposition or negation (Spinoza: Practical Philosophy 94-97).  Real distinction is without opposition or limitation.  Forces of Univocity are intensive degrees of power.  There is no opposition to other degrees since they are all singular.  Each is positive, singular intensity.  All intensive forces resonate and communicate without opposition or lack, because they are singular degrees of real distinction, ontologically one.  Intensive degrees cannot divide without changing in nature. Intensive forces can enter into external relations because they are not mediated by the structures internal to a concept of already formed matter.


Forces of intensity are forces of difference itself.  (D&R 222) “Every intensity is E – E’, where E itself refers to an e – e’, and e to ee’ 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.”  This disparate intensity is the condition of the sensible.  With Representational matter-form coupling, matter is already informed and is under the protection of the categories.  Extensive quantities can divide indefinitely without any change in nature.  However, with Deleuze’s Univocity, forces of intensity cannot divide without a real change in nature.  (D&R 237) “An intensive quantity may divide, but not without changing its nature.  In a sense, it is therefore indivisible, but only because no part exists prior to the division and no part retains the same nature after division.”  We can see that this is the case because with the intensive degrees of coupling, distance is not an extensive quantity.  Rather, it is an indivisible asymmetrical relation between heterogeneous terms.  Extensive quantities can divide without changing quality. But intensive quantities are enveloping and enveloped distances.  Intensive quantities are the "numerical" distinction of ontological singularity.  When they divide, they necessarily change the real distinction of their quality.   


Deleuze says (Logic of Sense p.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.”  In D&R p. 268, Deleuze speaks about the ouk-on (non-being of the negative) and me-on (the non-being of the problematic).*  We see that Representational Thought is ouk-on when it is cut off from its source me-on.  When ouk-on is cut off from me-on it closes into forces of negation (opposition or limitation).  Then there are only forces of binary opposition closed in the identity of the concept in general.  There is only conceptual difference.  It is confined to the plane of transcendence.  It never reaches Univocity’s non-being of the problematic (me-on).  It never reaches the sub-representative plane of immanence which is included, along with the plane of transcendence, in Univocity.  Therefore, when it is cut off from me-on, ouk-on is the closed form of conceptual possibility in Representational Thought.  DR207 “Forms of the negative do indeed appear in actual terms and real relations, but only in so far as these are cut off from the virtuality which they actualize, and from the movement of their actualization.  Then, and only then, do the finite affirmations appear limited in themselves, opposed to one another, and suffering from lack or privation.”  However, Univocity includes both a plane of transcendence and a plane of immanence.  Now, the plane of transcendence is not cut off from its source.  With Univocity, representation is actualized in worlds that remain open to all the singular forces of intensity. 


Therefore, Deleuze is not envisioning an end to representation.  Actualizations within Univocity are always fragile and temporary “uses” of representation (LoS144-147); open, fragile, and temporary “uses” of ouk on.  However, Deleuze warns us that the process of actualization of the virtual must never be confused with mere conceptual possibilities.  The dogmatic image of thought is merely the conceptually possible.  The dogmatic image of thought involves no actualization of the virtual at all.  This means that the Representational image of thought mistakes representations to be something more than fragile and temporary “uses”.  It sees them as universal generality.  Deleuze is not envisioning an end to “uses” of representations as actualizations of the virtual.  Rather, he rejects Representation that restricts thought to prior possibilities of its conceptual image.  Immanence is a process of the actualization of the virtual-real.  This process of actualization is therefore creative, because it is not merely restricted to prior conceptual possibility.


Therefore, Deleuze warns us (DR211) against the danger of confusing the virtual-real with the possible.  Deleuze is saying that the Representational image of thought is not real---it is merely conceptual possibility.  He says that the virtual is real, but the possible is not real.  But how can Deleuze say that the conceptual image of thought is not real?  Wouldn’t that just create a new dualism between the real and the conceptual?  Wouldn’t that dualism mean that thought is not included in the real?  How can immanence leave out the image of thought?  If immanence excludes something, wouldn’t that just set up a new dualism?  However, Deleuze is saying that it is the Representational Image of Thought itself that excludes the real and remains closed in the dualism of conceptual forces of opposition and limitation.  The dualism of Representational Thought excludes anything that is outside its conceptual image.  But Univocity says that ALL real distinction is included and affirmed.  Nothing is excluded.  Univocity does not exclude representation.  All incorporeal events may become actualized as “uses” of representation (LoS144-147).  Univocity includes ALL real distinction said in ONE sense (The One-All of Univocity DR37).  This is in contrast to the Representational Image of Thought that excludes everything outside the possibility of the concept and unifies the Many numerically distinct substances into One conceptual totality (the Many/One opposition of Representation DR182).  The dualism of Representational Many/One is not to be confused with the Univocity of One-All. 


Therefore, we see that forces of negation (opposition or limitation) are not Deleuze’s forces of multiplictity.  Multiplicity is the positive forces of affirmation.  It does not exclude anything.  It doesn’t even exclude the Representational Image of Thought.  Rather, it vice-dicts it.  All really distinct forces are included.  Forces are externally related without concept.  There can be all really distinct “uses” of representation---this one AND that one AND another….AND another….  There can be no dualism, contradiction, negation, limitation, or lack.  All becomings are now possible---even those that are deemed impossible by the Representational Image of Thought.


*Traditionally, me-on and ouk-on have been terms of opposition on the plane of representation. But Deleuze changes the sense of these terms. Ouk on, now, is the representational plane of oppositions (being in opposition to negative non-being). Me-on, now, is the sub-representative plane as the non-being of the problematic.

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