4 Jan 2013

Pt2.Ch5.Sb8 Somers-Hall’s Hegel, Deleuze, and the Critique of Representation. ‘The Speculative Position’. summary

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. Also, proofreading is incomplete.]


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 8: The Speculative Position

Very Brief Summary:

For Hegel, we have understanding’s finite thought and reason’s infinite thought. Infinite thought can conceive the contradiction in such speculative propositions as God is being. Here there is not a subject and predicate, but a subject and another different subject being equated. For finite thought this is unthinkable. Because infinite thought thinks interpenetrated contraries, it does not fall to Bergson’s critique of spatialized thinking.



Brief Summary:

For Kant, thinking is finite. It cannot think infinitely, hence the sublime. Hegel distinguishes two kinds of infinite, bad and true infinity. Something is finite because it has limits, but that means it is codetermined by what lies outside limitation, infinity. The finite transcends its limits to infinity, but the infinite needs something finite to codetermine it. [Or consider if we imagine an infinitely large number. We might then say, what about something one greater than that? This makes the prior infinity finite, and creates a new infinity, and of course that process repeats.] This bad infinity is an infinite repetition, the good infinity incorporates both finitude and infinity together in the same concept. While our understanding cannot conceive the bad infinite, our reason can conceive the good infinite. This is because it can conceive of dialectical contradictions. It deals with speculative propositions. Consider God is being. Here being is not a predicate. It is another subject that dialectically throws back upon the first subject. It is a contradiction for there to be two equated different subjects, but infinite thought can conceive it.


Previously we saw how the oppositional mixture of identity and difference in Hegel’s dialectic allows for movement and change.

Now we turn to the infinite thought of speculative propositions. Recall how for Bergson, propositional thinking involves externally related atomic terms, and so it depends on a homogeneous medium that allows for one to be external to the other as if spatially. It is useful for scientific analyses, but it fails to describe the interpenetrative nature of relations. For this reason, Deleuze is critical of propositional thinking. Hegel we saw was critical of the subject-predicate structure of judgment in Kant, because it involves a divide between thought and content. But Hegel is not against language, because it gives determinacy to thought. We understand Hegel’s position better when we distinguish two types of thought and thus two types of language. This distinction relates to the reconciliation between the finite and the infinite.

We noted that Hegel is critical of the fact that for Kant thought is finite. (150d) At the beginning of the Science of Logic, we did not discuss thought in terms of finite and infinite, because at that beginning point we were not yet able to explain the nature of thought and also it came before the point where we would discuss finite and infinite. Kant thought he could assume thought was finite before deducing the categories, but Hegel does not share that assumption. Hegel will agree with Kant that finite thought belongs to appearances, but he will also argue that matters go beyond this terrain.

A determinate being is determined by having a certain quality. This determination both characterizes but also acts as its limit, “beyond which the thing would cease to be what it is.” (151) The limit is also a negative limit constraining the being’s internal positivity, and this generates an ‘ought’ for the being to go beyond its negative limitation.

On the one hand, it needs to capture the idea of what the thing should be, apart from the limitation (otherwise it would simply be indifferent to the limitation). On the other hand, it needs to capture the fact that finite being is determined as precisely limited in its present form (otherwise it would already be what it should be). (151)

So this relates the finite to the beyond. Because the beyond is opposed to limited finitude, this beyond is infinite. However, this infinity is also finite, because it is limited by the limit that defines the finite being. [If finite being were to become infinite, it would need some other finite being to determine it as infinite, or, consider if we think an infinite number, then think one more than that, this makes the prior infinity finite creating a new infinity to again become finite. so]

When we look more closely at this sequence, we see that the finite persists within the infinite, rather than dissolving into the infinite, as finite being only ceases to be on the condition that finite being comes to be. Thus we have a new form of infinite that is the infinite perpetuation of the finite. We can now see that not only is the infinite finite by its necessary contrast | with finitude, but the finite also becomes infinite through its perpetuation. (151-152)

So the infinite and the finite contain the other. There is a synthesis of the two that incorporates finitude into the whole. Out of this synthesis emerges a new infinity. First we had a bad infinity of infinite repetition [of finite transcending to infinite and producing another finite that will transcend to infinite?] and we have the infinite simple. “ 'Only the infinitely simple, or that unity-and-multiplicity, is one’ (JL, 36).” (152)

This genuine infinite is a contradiction [having both the determinate and indeterminate together].

"Genuine infinity . . . is not a series that always has its completion in some other yet always has this other outside itself. Rather, the other is in the determinate itself; it is a contradiction" (JL, 35). When we looked at contradiction, we saw that each of the terms both stood opposed to the other, but also necessarily united with it in that the two terms could only be made determinate when in relation with one another. Thus, contradiction was an opposition that required no third to bring the terms into relation with one another. This same relation holds for the infinite: "The simple and infinity, or the absolute antithesis, make no antithesis save this very one that they are absolutely connected, and insofar as they are opposed, they are by the same token absolutely one" (JL, 36). This process is what Hegel calls "the absolute contradiction of the infinite" (JL, 38). [152]

For Kant, we could think of the infinite but our thought itself could not be infinite. Kant’s mathematical sublime is an infinite magnitude, and is Hegel’s bad infinite. The bad infinite has a bad contradiction. It is both infinite expansion and infinite aggregate. But the bad infinite does not allow for the integration of its contrary terms. The good infinite has a good contradiction because each term is within its opposite and are thereby united. (152d) But the bad infinite overcomes itself into the true infinite. [Because we can cognize finite, and because the infinite is contained in the finite…]

With the opposition between the finite and the infinite sublated, the possibility of a Kantian restriction of cognition to the finite collapses. The finite immanently overturns its own limitations, becoming infinite. Therefore, the infinite can be cognized by thought, and if this is the case, the Kantian restriction of the metaphysical deduction to a taxonomy of terms statically derived from the functions of judgment as well as the possibility of a separation of thought and being collapses. (153)


In Phenomenology of Spirit, Hegel distinguishes [1] the judgment of understanding and [2] the speculative proposition of reason. We understand a proposition by presupposes its subject being an objective fixed self. Hegel thinks Kant should have taken finite understanding to its limit. The understanding’s thinking is finite, but reason’s thinking is infinite. Then we can attach predicates to it. It is picture thinking, because the process takes as if it were in a sensuous manifold. (153) This is like how for Kant, the understanding’s concepts must be able to correspond to concepts given in intuition.  This makes the subject-predicate connection not necessary but the product of the judging subject. Consider on the contrary the speculative proposition of infinite reason. It relates categories to other categories and not subject to predicates. (154) For example, God is being. Here the second term is not a predicate. Rather, it is a subject. Were it a predicate, it would attach to the subject, but as another subject, it determines the first subject’s essence. This makes the subject no longer passive [passively receiving a static predication]. “Thus, we are "thrown back" (PS, 39) onto the original term as a subject, but as one which has been altered in the movement back and forth between the two terms.” (154) Note that both terms are subjects, with the second being thrown upon the first, and yet they are distinct terms. “What is important about the speculative proposition is first that it allows terms to be identified that remain different from one another”. (154) Also note that it involves a dialectical movement, (self-generating, going away from itself, returning to itself), and so it is in motion.

Finite understanding cannot grasp how two different subjects can be the same. If we want to preserve the primacy of finite understanding, we either say that in fact it is subject predicate or we say it is tautology. Or, we can give up picture thinking, which allows us to conceive such a contradiction. “By moving to an understanding grounded in infinite reason, the subject moves from a negative understanding of contradiction to a positive, contentful understanding”. (154d) The speculative proposition, because it is this throwing back on itself of the subject, is a transition from one term to the next. Thus movement becomes immanent to thinking. Thus Hegel is not using a spatial sense of language [discreteness of terms], so it does not succumb so easily to Bergsonian critique.

by moving to a conception of the proposition which by necessity cannot be captured in intuition, Hegel has kept open the possibility of a linguistic relation to the world which does not rely on a mechanistic, and atomistic, notion of space. (155)



Somers-Hall, Henry (2012) Hegel, Deleuze, and the Critique of Representation. Dialectics of Negation and Difference. Albany: SUNY.

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