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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 2: Responses to Representation
Chapter 5: Infinite Thought
Subdivision 2: Kant and Hegel
Very Brief Summary:
Hegel will derive the categories of thought through his dialectic.
Brief Summary:
Hegel wants to derive the categories of thought like Kant does in the metaphysical deduction. However, Hegel will not use Kant’s assumptions. So Hegel will not regard the categories in terms of formal logic. He will not regard thought as finite, because it need not always apply to finite sensible content. Instead, the categories of thought will emerge from the dialectical process beginning with thought thinking itself. Here, determinate content can be negated and still produce new determinate content, unlike negation in formal logic.
Summary
We saw how Deleuze is situated in the Kantian tradition and yet moves beyond the limitations of transcendental idealism with his transcendental empiricism. Hegel also tries to overcome these problems. For Kant, the subject-predicate structure of judgment is mirrored in the subject-predicate nature of concepts and the subject-property nature of intuitions.
Kant argues in the metaphysical deduction that "the same function which gives unity to the various representations in a judgement also gives unity to the mere synthesis of various representations in an intuition; and this unity, in its most general expression, we entitle the pure concept of the understanding" (CPR B104-05). [126]
Empirical objects are conditioned by the transcendental categories, which makes them isomorphic to our concepts. So Kant is going beyond both mere empiricism [as the categories condition the intuitions] and naïve metaphysics [as there are no cognitions without both concepts and intuitions]. In this chapter we will focus on Hegel’s criticism of Kant’s metaphysical deduction, which establishes “an isomorphism between the functions of the understanding and the categories, as shown in the tables of functions and categories.” (16)
Rather than focusing on the finite determinations of the categories that Kant's deduction tries to uncover, Hegel wants instead to introduce movement into the process of the deduction of the categories by a renewed understanding of the role of reason in philosophy. (126)
Hegel will categorize Kant’s assumptions into two types and remove them. The first kind are assumptions regarding the type of thing that cognition is. The second kind are assumptions regarding “the nature of the possible types of cognition” (127a).
We are concerned here with the first sort of assumptions. They
invalidate Kant's metaphysical deduction as they show neither the immanent development nor the necessity needed to provide a ground for the kind of transcendental logic Kant requires. (126)
Assumption 1: Judgment is the only way the understanding can use concepts.
Thus all categories’ forms are analogous to judgment’s.
Assumption 2: Kant reverts to classical logic to derive the categories.
Assumption 3: All thinking requires a connection to a sensible manifold.
Kant uses the subject-predicate structure in his analysis of the fundamental categories of thought. Deleuze’s problem with this is that the transcendental merely repeats the empirical’s structure rather than being something generative of the object. “Deleuze instead conceived of the transcendental as composed of reciprocally determining entities that when brought together generated both form and content.” (127d) Hegel has a problem with Kant’s use of formal logic. Because the elements that are judged [the predicates thought to be subsumed under a subject] are inert, “judgment has a tendency to be reduced to the simple activity of classifying particulars under preestablished universals, the kind of activity permitted by the taxonomic system of Aristotle.” (128a) The other problem is that the subject predicate form of judgments does not show how the predicate is essential to the subject, only that it is so. “These limitations can present difficulties when judgment is taken as the paradigm of thought within a philosophical system, though the use of judgment in this way is not itself objectionable.” (128) Key to the structure of judgment and formal logic is dicursivity, which means that judgments and all propositions in formal logic are about something. (128) Because judgments are about something, they are related to peformed elements, and this aboutness for Kant is essential to the connection between concepts and intuitions. Allison writes that there are three fundamental assumptions in Kant’s project. [1] Cognition requires that an object be given. [2] Our mind is finite, thus it is receptive, and intuition is sensible and is based on objects’ affections. “That since the finite mind like ours is receptive rather than creative, its intuition must be sensible, resting on an affection by objects.” (128) [3] Sensible intuition alone is not enough for cognizing objects; for this it needs the coperation of the understanding’s spontaneity. Hegel is more concerned with the problems of the first two assumptions. These assumptions tie the structure of the transcendental with that of the object. The second one is especially the problem. It makes two assumptions: [1] the mind is finite, and [2] because of this, intuition must be sensible. The categories can only be legitimately applied to the spatio-temporal. But if the categories are only applied to our spatio-temporal experiences [which are always finite] we can never present infinite concepts. This is the case in the sublime when we are no longer able to represent the magnitude of what we perceive because it is too great. In this case, we do not really represent infinity conceptually but rather only grasp it in terms of the limitations of our imagination, and thus we do not have a sensible intuition of it. “Combining the necessity of the possibility of the presentation of concepts within space and time with the | impossibility of presenting the infinite within space and time gives us the following result: if thought is related to sensible intuition, it must be finite.” (129-130) But this is circular, because the reasoning goes like this, we are finite because we can only have intuitions of the finite, and we can only have intuitions that are finite because we are finite beings. “The necessary relation to a spatiotemporal manifold is justified by the finitude of the subject, but the finitude of the subject is in tum grounded in its relation to the manifold.” (130)
We see that the ground of Kant’s argument is the finitude of the subject require spati0-temporal intuitions and not that there is a connection between judgment and categories. [For, judgments are only possible on the bases of finite intuitions and not the other way around.] Also, we see that this assumption is circular. For Kant, intellectual intuitions, because they must have an aboutness, must also have the limitations of finitude. (130)’
Hegel opposes the arbitrary nature of Kant’s procedure. Kant' derives the categories from logic, but Hegel has them generated from thought thinking itself. But for Kant, judgment relates concepts rather than concepts implying relations to things outside themselves. For Kant, thought is finite and related to intuitive content. [There is a finite range of what it can conceive]. For Hegel, Kant can only produce an arbitrary deduction of the categories [since thought itself is not generating them, we must generate them arbitrarily.] “This difficulty is particularly evident if we look at Strawson's study of Kant's Critique of Pure Reason, as he shows here not only that modem logic presents a different set of categories to those assumed by Kant but also that, in modern logic itself, the specific categories that are taken as fundamental are necessarily arbitrary, as each can be defined in terms of the others.” (131) Recall Hegel’s analysis of Parmenides and Zeno. Parmenides argument required the acceptance of arbitrarily selected assumptions, but Zeno proves the same thing by showing how the idea brings about its own dissolution. Hence Hegel does not like Kant’s method.
The structure of Hegel’s Science of Logic has two fundamental difference to Zeno’s paradoxes. Zeno begins by assuming his interlocutors assumptions [or conclusion?] But because the deduction of the categories is about thought, and because we cannot make any philosophical assumptions about thought [I don’t know why], there are no assumptions for Hegel to begin with in this case. Also, Zeno merely dissolves the interlocutor’s position, but Hegel needs to generate the categories. In order to begin without assumptions, Hegel begins by with a concept stripped of all determinations, pure being.
Once we have discarded the supposition that the understanding is responsible for the connections between concepts, it now becomes possible for the concepts to explicate the connections between them themselves. As we proceed from the indeterminate concept of being through more and more determinate concepts, we will find that each concept immanently shows itself to be unsustainable without some kind of reference to another concept (131)
There is an important difference between logic and Hegel’s dialectic. In logic, the unsustainability of a concept leads to its negation and not to a new concept altogether. A concept’s negation is not another determinate entity. When we say the rose is not red, we are not saying it has some determinate color. So for Hegel, logic provides a theory of indeterminate negation, because negation of a concept negates it without determining it. Such a negation is possible in a system where content is separated from form [because we can negate the (determinate) content while keeping the form intact]. But this means that the material that our inferences relate to [the contents] are separated from the movement of the inference [which is able to operate on a proposition without touching its content.] “This is because inference is reduced to a purely mechanical operation that is performed on the content”. (132) [But if content is not what is part of the movement of inference, “it is impossible for the content itself to add anything productive to the movement of thought.” (132) This is a finite limitation of thought. [It cannot see how the negation of something can lead to its transformation or further determination.] “If we do not accept this limitation, however, thought becomes free to recognize in negating the object the specific movement of the object itself and thus to move beyond a purely mechanical external conception of inference. This means that a contradiction such as Zeno's can indeed produce positive content. […]. while contradiction is necessary, as long as it is not understood in purely formal terms, it contains the possibility of a movement that is productively determinate.” (132)
For Hegel, Kant is unable to properly overcome the limitations of skepticism, because he uses a formalist conception of the understanding. Kant thought that reason could not operate without intuitions. Later we will examine this quotation by Hegel
"The so called 'principle of contradiction' is thus so far | from possessing even formal truth for Reason, that on the contrary every proposition of Reason must in respect of concepts contain a violation of it. To say that a proposition is merely formal, means for Reason, that it is posited alone and on its own account, without equal affirmation of the contradictory that is opposed to it; and for that reason is false" (RSP, 325). [132-133]
So for Hegel, the content determines the dialectic’s process of movement. But there is a problem. Since the content motivates the transitions between categories, can we uncover a method (in that procedure)? But no, our means for determining the necessity of its movement is not transcendent to the content [so we cannot determine a methodology that would be applied to content.] However, we might say it is methodical because we let the content produce its own determinations. “In this sense, dialectic claims to be more methodical than the procedures of mathematics and classical logic, within which the movement from term to term is arbitrary, in the sense that while each deduction may be negatively constrained by the laws of inference, these laws do not determinately specify which term follows from the preceding one in the deduction.” (133)
So we see that Hegel is trying to accomplish Kant’s task in the metaphysical deduction, to derive the fundamental categories of thought, without using Kant’s assumptions. Two important assumptions are that the subject’s understanding in finite and it thought is separated from content. They are related: thought is finite because it is conditioned to the sensuous manifold and is thus distinct from it. We now see how far Hegel moves beyond Kant’s metaphysical deduction. (134)
Somers-Hall, Henry (2012) Hegel, Deleuze, and the Critique of Representation. Dialectics of Negation and Difference. Albany: SUNY.
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