by Corry Shores
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[Note: All boldface and underlining is my own. It is intended for skimming purposes. Bracketed comments are also my own explanations or interpretations.]
Henry Somers-Hall
Hegel, Deleuze, and the Critique of Representation.
Dialectics of Negation and Difference
Part 3: Beyond Representation
Chapter 6: Hegel and Deleuze on Ontology and the Calculus
Subdivision 7: The Kantian Antinomies
Very Brief Summary:
Kant’s antinomies of reason for Kant indicate that there is an unconditioned noumenal world that is beyond our understanding. For Hegel the antinomies demonstrate the sublation of infinite thinking, although it is still a representational thinking. For Deleuze the antinomies show that the unconditioned is subrepresentational yet still determinable.
Brief Summary:
One of Kant’s antinomies is about whether or not there is a beginning to the world. There are two equally valid yet opposing arguments. The dogmatic view says that there must be a beginning to the world. If there were not, then there would be an endless series of moments before the present one, but that means we never could have gotten to the present, because the progress of time would never get a foothold and move forward. Thus it must have a foothold, a beginning moment which has none before it. The empirical view says that there is no temporal beginning to the world. If there were a beginning it would be a limit. But a limit makes a division. There must be something on the antecedent side of the limit. But it cannot be a moment different from the first moment, because then it would be a prior moment giving rise to the first one, making the first one no longer first. Rather, all moments before the first must be identical [with each other and with the first moment] so that there can be a unique moment when the world’s unfolding begins. However, if all moments before the first were identical, then there is nothing that needs to be resolved or changed, and thus there is no explanation for how the first moment arises. Kant has his own diagnosis of the cause of this irresolvable antinomy. In the first case of there being a beginning, each moment of time is conditioned by its prior, except the first one, which has no prior one to condition it, and thus the first moment is unconditioned. That means the unconditioned is a moment like all the rest, they are all the same thing, moments in time, and as appearings of the world they can be understood by the categories of our understanding. In the second theory where the world has no beginning, also each moment is conditioned by its prior one. However, the series as a whole is assumed to always have been and always will be there. This means that there is nothing outside it that conditions it, for if there were such an external condition, that it would be considered the whole series’ beginning. Thus the series as a whole is the unconditioned. But again, because we are considering the series as a whole the unconditioned, but it is made up solely of parts that are conditioned, then we again are placing the conditioned and the unconditioned on the same level and we are understanding both using the categories of the understanding. Kant says that this is the problem. Instead for him, the unconditioned is on the level of the thing-in-itself, the noumenal level and not the phenomenal, thus it cannot be understood using the categories of the understanding. One view thinks that the world’s temporality is finite, the other infinite. But there is a third option, which is that the thing-in-itself is neither finite nor infinite, just like if we say, ‘bodies have either a good or a bad smell,’ then add that there is a third option, that bodies do not have smells. So for Kant, we encounter the antinomies when we only use our understanding at the urging of our reason which seeks the unconditioned of the conditioned. Hegel, however, thinks that we can know more than just the categories for understanding things, we can also understand the categories of the thing-in-itself. He thinks there is a form of thinking, infinite thought, that is able to conceive of contraries that sublate to produce a new category. In his analysis of the calculus differential, Hegel notes how two non-finite values are in an oppositional relation that produces a finite value. They are non-finite because they are in the act of vanishing, which means they are straddling both a finite value and zero, or being and nothingness. They can only have a value when they are in a differential relation, so the differential relation as something infinite contains in it something finite. But that also means that the finite value of the differential relation is composed of infinite values. This genuine infinite is a sublation of the concepts of infinite and finite and of being and nothingness. Using merely a representational system of logic, like the one Kant bases his metaphysical deduction on when determining the categories of our understanding, leads us to not be able to see how finite and infinite can include one another, how such a contradiction can not only hold but also be generative of new categories. Hegel will say that Kant’s antimony really affirms this infinite thought. So first he notes that each argument in the antinomy is circular. The argument that there is a beginning says that if there were not, we could not have arrived at the present moment. But this present moment that we are taking for granted is a limit, a beginning all its own, because it is the beginning for all moments happening after it. The argument for the limitlessness of time says that the first moment must have an antecedent of some kind, that every moment must have an antecedent, but that is what they were trying to prove. For Hegel, both sides of the antinomy are the parts of an infinite thought of the concept of infinity, because the one side affirms there must be a limit and the other affirms it must always be overcome. For Hegel, the unconditioned is the dialectical sublation, which is found in both reality and thought, and thus for Hegel the conditioned and the unconditioned are the same sort of thing, they and are contradictory, but they can be thought together. In Deleuze’s analysis of the antinomies, he will also say like Kant that the conditioned and the unconditioned are different in kind, but unlike Kant and like Hegel, the unconditioned can be thought. However unlike Hegel, the unconditioned cannot be thought representationally, because its terms, as we saw with the differential’s terms, are subrepresentational. Yet even though they are subrepresentational, that does not mean they are indeterminate or unthinkable; for, like the calculus differentials, the terms are determinable, meaning that when they are related, they produce a determination of finite value, and also they are thinkable, but only either in terms of a virtual multiplicity or in terms of an actual determination that implies the virtual multiplicity that it expresses.
Summary
Previously we saw how for Deleuze, Hegel’s interpretation of the calculus involves representation, but Deleuze’s does not.
Now we turn to Kant’s antinomies. They lead Kant to recognize that “reason is subject to transcendental illusions that are endemic in both dogmatic and empiricist positions.” (179) Hegel sees the antimonies another way. For him they reveal an objective contradiction in the world. This contradiction, he thinks, can only be resolved by reconceiving reason. We can no longer define the mode of reason’s operation as extending a concept of the understanding beyond the empirical. “For Deleuze, like Kant, the antinomies | do not show the existence of objective contradiction, but instead create a rupture in the world of representation that can only be resolved through the incorporation of an element that escapes representation.” (179-180) Kant cannot specify what element escapes representation.
Somers-Hall explains:
The antinomy of reason deals with what Kant considers to be certain arguments which naturally develop from the use of reason to answer questions which go beyond direct experience. Whereas the paralogisms deal with concepts that are outside of the remit of empirical knowledge, such as the soul, the antinomies deal instead with the attempt to extend the application of the categories beyond their proper use by tracing back the conditions of an object to the point at which we arrive at the unconditioned. (180)
The antinomies are cosmological. So they do not deal with such things outside the world as God or the soul. Instead they refer to the world in its totality.
In order to accomplish this task, it is reason that takes up the categories of the understanding and attempts, by means of a regressive procedure that tries to move from the present, conditioned, to its conditions, to allow us to conceive of such a totality.(180)
Because there are two separate equally valid but mutually exclusive ways to specify the unconditioned through regressive analysis, we arrive at antinomy.
Reason requires that we obtain the unconditioned from the conditioned. This involves a regressive movement tracing back through a series of conditions until we arrive at the unconditioned. We can view the unconditioned in two ways. [1] as being a series of conditioned members, with the totality itself being unconditioned. This regression then is infinite. Or [2] the unconditioned is within the series, with the conditioned members being subordinate to it, and with no other members standing above it. For Kant, the first corresponds to empiricism, because it remains entirely within the world of appearances. The second is dogmatic, because by seeking the unconditioned at the beginning of the series, it presupposes intelligible beginnings. So is the unconditioned the first term or the totality of the series? Kant sees this in terms of the difference between Epicurus and Plato. We will concern ourselves with the first antinomy, which is concerned with space and time, which are the original quanta of all our intuition. The dogmatist thesis is that the world has a beginning in time and it is limited spatially. The empiricist antithesis is that the world has no temporal beginning and no spatial limits, so it is temporally and spatially infinite.
The argument for the world having a beginning is reducio ad absurdum. Assume the world has no beginning. That means it has existed already for an infinite amount of time. that means an infinite number of things must have happened. But an infinite series cannot be completed. [We can always imagine another event happening before a prior one. This means the past is continually under creation, and could not have passed away. Or, we could not have arrived at the present, if the past keeps going backwards and never hits a a starting place from which we can build forward to the present.] “An infinite series is by definition, however, a series that can never be completed, and hence, the past (as an infinite series) cannot have passed away.” (181) Thus the world must have a beginning. The empiricist antithesis first assumes that the world does have a beginning in time. But this implies that there was a time before that, which is an empty time where every moment is identical to every other. But in that case, nothing could have come into being in the first place [as there are no contraries to resolve] thus there can be no beginning to time. (181d)
The antinomies come from the natural application of reason that takes it beyond its proper domain. Reason wants to relate the conditioned to its condition. The mistake is to assume that the conditions are already really given.
This is the result of the understanding, which "represents things as they are, without considering whether and how we can obtain knowledge of them" (CPR, A498/B526-27). [182]
Somers-Hall continues.
Now, given the transcendental realist interpretations of the object given by the empiricist and dogmatist positions, we can see, as in the case of the representationalist systems that we discussed in earlier chapters, the object of the understanding is considered to be the thing in itself. (182)
So both the condition [the thing in itself?] and the conditioned [the object of the understanding?] exist on the same ontological plain, so they are both available to us. [I cannot explain what Somers-Hall writes here]
Therefore, transcendental realism lacks the ability to differentiate between the claim that it is reason's task to find the conditions for the conditioned and the availability of these conditions, meaning that it is unable to find a solution to the antinomies. Transcendental realism suffers from the transcendental illusion that the totality of conditions can be given. Transcendental idealism, however, while unable to remove the transcendental illusion, which derives from the analytic presupposition that the conditioned has conditions, is able to mitigate this illusion by showing that once we recognize that the world cannot be conceived of as a thing in itself, the arguments of both the dogmatists and the empiricists can be sustained without leading to contradiction. This fact further leads to Kant's claim that the antinomies provide the grounds for an indirect proof of transcendental idealism. (182)
Kant solves the antinomies by playing on the distinction that “transcendental idealism generates between the thing-in-itself and appearance”. (182) The transcendental realist perspective regards the totality of conditions to be available The means we arrive at an unconditioned conclusion, and this leads to a contradiction. The transcendental idealist, however, does not think we can reach the unconditioned through a “regressive application of the categories of the understanding, as these apply only to appearance, rather than to things-in-themselves.” (183) The categories only give us the conditions of the possibility of empirical experience, which means that they do not apply to the things in themselves. This mean that every part of the regressive series [as it is being understood through the categories] will be conditioned [by the categories.] (183) [Like we saw with Aristotle and Russell] “the attempt to represent a totality has resulted in a contradiction.” (183) Now consider if we say that all bodies have either a good or a bad smell. There is a third option that they have no smell at all. This means that both conflicting propositions, that all bodies have a good smell, that all bodies do not have a good smell, can both be false. “Likewise, the noumenal, falling outside of the constraints of the categories of magnitude, is neither finite nor infinite.” (183)
So “For Kant, the difficulty that transcendental realism suffers from is that it takes the totality of appearance to be totality in-itself, leading to the idea that the totality of appearances gives us the unconditioned, either immediately or mediately through the first cause.” (183) But this leads us to being unable to understand how we are acquainted with the world. [If we think that the totality of appearances gives us the unconditioned, we end up with the antinomies. This makes the world itself seem unknowable, because opposing manners of knowing it are equally valid. Either or both are wrong, but we have no way to know which when we think that the totality of appearances gives us the unconditioned.]
For Deleuze, the difficulty with representation is that it takes the totality of actual states of affairs to be totality in-itself. This leads ultimately to the inability to understand any concept of difference that is not purely actualized as negation (as actuality is equated with reality). "Forms of the negative do indeed appear in actual terms and real relations, but only in so far as they are cut off from the virtuality which they actualise, and from the movement of their actualisation" (DR, 207).
So to resolve the antinomies, Kant introduces something that is neither finite nor infinite, and he thinks it is not determinable. Deleuze disagrees with this. Note how
Kant writes: "If the world is a whole existence in itself, it is either finite or infinite. But both alternatives are false (as shown in the proofs of the antithesis and thesis respectively). It is therefore also false that the world (the sum of all appearances) is a whole existing in itself. From this it then follows that appearances in general are nothing outside our representations-which is just what is meant by their transcendental ideality" (CPR, A506-07/B534-35). [184]
But for Deleuze, the totality of appearances can be understood in subrepresentational terms, so there is an alternative way to solve the antinomies.
Hegel values Kant’s antinomies, but for his own reasons. “For Kant, the difficulty was not with the categories themselves, but rather with their extension beyond their proper field of application by reason.” (184d) Kant thinks that reason does not generate any concept. The most reason can do is to free the understanding’s concepts from possible experience’s inevitable limitations. But reason’s function is negative. It generates the antinomies. Yet for Hegel, the antinomies that reason leads to are productive of the categories.
Hegel's approach to the Kantian antinomies is therefore to show that they represent the emergence of infinite thought, as reason provides a genetic deduction of the categories through exposing the one-sidedness of them taken individually. (184)
For Kant, the antinomies indicate that we need a noumenal [because assuming that the unconditioned is given with the conditioned leads to the antinomies.] Deleuze thinks that they show us we need the subrepresentational [to make the unconditioned given to our senses and the understanding, but only in an implicit subrepresentational form, so the unconditioned and the conditioned are on different ontological levels and so they are not to be both considered representable, meaning that they will not come into logical contradiction with each other.] Hegel instead sees contradiction as inherent to the genesis of the world [contradiction seems to be the unconditioned, so it is inherent to the conditioned, but it is only understandable with infinite thought, not finite thought, which leads to the irresolvability of the antinomies.]
Hegel will show the dialectical nature of the antinomies. He will do so by first showing that both arguments use circular reasoning. or “the fallacy of petitio principii, by affirming in the premises what they hope to prove in the conclusion.” (185) The first argument wants to say that the world has a temporal beginning. By doing so, it assumes a beginning or temporal limit with the form of the now. It is the point in time before which an eternity has elapsed. [It begins by assuming that there is a now before which there was an eternity, but that now has the form of a temporal beginning, so the argument’s conclusion is assumed in its premises.] The other argument wants to say that there is no temporal beginning to the world. But it assumes that the world has a coming-into-being, before which was still time.
In assuming the world comes to be in time, "this proof presupposes that this existence comes into being and that the coming-to-be has an antecedent condition which is in time" (SL, 236) . The idea that existence always requires such an antecedent condition is, however, the content of the antithesis. Taken together, the thesis and antithesis really assert two things: "that a limit is, and that the limit is equally only a sublated one" (SL, 237). The thesis contributes the notion of a limit, the antithesis, in the form of antecedent conditions, its overcoming. (184)
[The antithesis affirms that there is a limit in time, and the antithesis affirms that the limit is always being surpassed, hence together they express the sublation of the finite and the infinite, the true infinity.]
Whereas Kant keeps these determinations separate, for Hegel they are conjoined to form the immediate determination of the infinite, as "the beyond of the finite" (SL, 143). When these determinations are taken | up positively by reason, the antinomy generates a new category, where both determinations are united through their self-relation. By recognizing the place of contradiction within the world, therefore, and giving it a positive value, Hegel dissolves the negative implications that transcendental realism finds in the antinomy while staying within representation, albeit an infinitized form of representation. (184-185)
We see then that the sublation of the antinomies matches Hegel’s approach to the calculus, because it sublates finite and infinite, and thus also they “take place through the reconciliation in contradiction of the opposing determinations of being and nothingness.” (185)
Somers-Hall, Henry (2012) Hegel, Deleuze, and the Critique of Representation. Dialectics of Negation and Difference. Albany: SUNY.
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