So somehow, in spite of feeling I’ve been doing very little other than writing and talking about Hegel off the blog recently, I’ve nevertheless fallen hopelessly behind in blogging Hegel’s Science of Logic. The in-person reading group has continued to meet, with a brief break around the Hegel conference a couple weeks back, which all of us attended. We’re moving slowly, but we have won our way through to this week’s selection – the opening chapter of the section on Quantity. Meanwhile, I’ve been blogging only on stray paragraphs here and there, without tackling any decent sections of what we have been discussing.
There’s a great deal I would like to go back and write about. Just to get back in the rhythm, though, I think tonight I’ll just write something on today’s selection. Perhaps some of the other reading group folks, either in person or online, can fill in some of the gaps, or perhaps I’ll be able to backtrack in a quieter moment. For today, I just wanted to draw attention to some of the points Hegel makes in the second remark on the section Pure Quantity – an extended reflection on Kant’s importance (and limitation) for critical philosophy.
This remark further develops some of the concerns I’ve written on previously: Hegel starts by recognising Kant’s importance for dissolving an older metaphysics, and thus opening the path to a new philosophy. This recognition is promptly tempered by Hegel’s observation that Kant’s approach is “imperfect” in both its methods and its results. Hegel treats Kant’s antinomies as possessing a rational core that needs to be extracted from its form of presentation. His concern, as always with Kant, is that the approach is intrinsically dogmatic – that it presupposes that cognition possesses characteristics that have not been established (and, specifically, that it presupposes what it claims to prove) – and that the approach restricts reason, predeciding that it “should not soar beyond sensuous perception and should take the world of appearance, the phenomenal world, as it is” (407, 428). In the process of demonstrating these arguments, this remark also casts some light on Hegel understands his own method.
Hegel begins by suggesting that Kant has inappropriately exceptionalised his four cosmological antinomies, not recognising that such antinomies can be found at the heart of any Notion. Hegel argues “as many antinomies could be constructed as there are Notions” (408). Kant compounds this mistake by not locating the antinomies he does identify in the Notions themselves, but rather in a concrete, “applied” form in which such antinomies cannot be explored in their purity, but rather become intrinsically caught up in other determinations extrinsic to the Notion (409). Further, although Kant on one level recognises that these antinomies are not simply illusions, but contradictions that reason necessarily confronts, his attempt to resolve these contradictions contravenes this insight by treating the contradiction as fundamentally something subjective, something residing in the “transcendental ideality of the world of perception” (410).
These problems can only be overcome, Hegel argues, by grasping the antinomies as “two opposed determinations which belong necessarily to one and the same Notion” (410). Such an approach recognises the validity of each determination – but only as sublated within their Notion. By contrast, Kant’s approach is one-sided – it attempts to take up each determination in isolation from the other – to assert the validity of each dogmatically. Hegel’s description of Kant’s method here is not kind:
…this simple categorical, or strictly speaking assertoric statement is wrapped up in a false, twisted scaffolding of reasoning which is intended to produce a semblance of proof and to conceal and disguise the merely assertoric character of the statement… (411)
Hegel proceeds to illustrate his point by examining how the antinomy of continuity and discreteness arises in Kant’s argument relating to the infinite divisibility of matter. Much of the subsequent discussion consists of an argument that the way in which Kant frames his discussion of this problem, already assumes what it sets out to prove, and is therefore a tautological statement, rather than the proof it purports to be. Hegel wields an interesting and somewhat expansive concept of tautology here.
Hegel begins with Kant’s statement that every composite substance in the world is comprised of the simple (the atom) (412). Hegel notes that, by substance in the world, Kant intends substances as sensuously perceived, and that this substance is taken to be indifferent to the existence of the antinomy itself. Hegel argues that the very definition of a composite is that of something externally put together from things other than itself. The “other” of the composite, however, is the simple. Therefore it is tautological to say the composite consists of the simple – we know nothing more by this statement, than we already knew by simply examining the term “composite” (413). In Hegel’s (sarcastic) words:
To ask of what something consists is to ask for an indication of something else, the compounding of which constitutes the said something. If ink is said to consist simply of ink, the meaning of the inquiry after the something else of which it consists has been missed and the question is not answered but only repeated. (413)
Hegel then suggests that satisfaction provided by a tautological response to this question may derive from the tendency in ordinary thinking to presuppose some particular simple, out of which some specific composite has been formed. This intuition of ordinary thinking is, however, inadequate for the present question, which concerns not some specific composite, but rather the composite as such (413).
From here, Hegel dives into Kant’s proofs, to which Hegel objects in whole and in most parts… He thinks Kant could be more brief and more direct (when Hegel says this about your writing, etc…), and that much of the argument is tautological, smuggling in through the back door what it claims to prove. A characteristic example:
It is clear that the apagogical detour could be omitted and the thesis, ‘composite substance consists of simple parts’, could be directly followed by the reason: because composition is merely a contingent relation of substances, and is therefore external to them and does not concern the substances themselves. If the composition is in fact contingent then, of course, substances are essentially simple. But this contingency which is the sole point at issue is not proved but straightway assumed, and casually, too, in a parenthesis – as something self-evident and of secondary importance. (416)
(As a side point, while Hegel is opposed to presupposing anything that you want to prove, he is absolutely incensed by Kant’s parenthesis – it comes up several times in this passage. It offends Hegel deeply. If you are going to presuppose something, don’t do it parenthetically…)
The upshot of Hegel’s argument is that Kant’s conclusion essentially points back to the externality and contingency of composition – the very assumption smuggled in as a starting point for the proof, such that, in Hegel’s tones of rising sarcasm:
its laboured, tortuous complexity serves no other purpose than to produce the merely outward semblance of a proof and partially to obscure the quite transparent fact that what was supposed to emerge as a consequence is, parenthetically, that on which the proof hinges; that there is no proof at all, but only an assumption. (419)
Hegel next moves to Kant’s antithesis, which he treats with similar scorn – “This proof can be called a whole nest (to use an expression elsewhere employed by Kant) of faulty procedure” (419). Here, Hegel complains again about the mixing of metaphors from everyday experience and ordinary thinking – in this case, the assumption that whatever is substantial is spatial – in the construction of the argument. For Hegel, Kant’s assumptions pile up, insights are achieved and then perversely discarded in the movement of the argument, and the argument fails to comprehend its object by grasping it in its Notion. (419-422)
This extended close critique of Kant leads Hegel to a larger objection to Kant’s method – its self-restriction to appearances or phenomena, to what can be sensuously perceived. Contemplating objects as sensuously perceived, for Hegel, is never sufficient to grasp objects in their Notion. Kant’s conclusions are therefore restricted to what is available to sensuous perception – yet Kant extrapolates his conclusions to reason as a whole. Hegel argues that this amounts to an argumentative leap from:
all our visual, tactile and other experience shows us only what is composite; even the best microscopes and the keenest knives have not enabled us to come across anything simple (424)
to:
Then neither should reason expect to come across anything simple. (424)
Close examination of Kant’s method, however, demonstrates a tacit dogmatism – assumptions smuggled in without proof, that composition (rather than continuity) is the mode of relation of substances, and that substances are therefore absolute and are related contingently. From the point of view of Hegel’s argument about quantity, Kant’s approach amounts to a separation of the two moments of quantity, that fixes each moment as absolutely separate. This approach results from treating substance, matter, space, time and similar categories as absolutely distinct and divided from one another – taking these categories as continuous, sublates this division. In Hegel’s words:
Since each of the two opposed sides contains the other within itself and neither can be thought without the other, it follows that neither of these determinations, taken alone, has truth; this belongs only to their unity. This is the true dialectical consideration of them and also the true result. (425)
Hegel’s move here is extremely interesting: this sublation in the category of the continuous, contains division – but as potential, as possibility (425). Hegel will develop from this an interesting critique of non-dialectical positions for confusing abstractions that grasp such potentials, with concrete or really existing entities. Hegel argues:
What is abstract has only an implicit or potential being; it only is as a moment of something real.
And:
Such intellect commits the error of holding such mental fictions, such abstractions, as an infinite number of parts, to be something true and actual; but this sensuous consciousness does not let itself be brought beyond the empirical element to thought. (427)
I’d like to explore the implications of this a bit further, but the reading group is about to assemble (contingently?), so I’ll leave things with this summary for the moment. Since I’ve stolen time to write this in a small slice of time before the reading group, apologies if this is unclear or poorly expressed…
Rough Theory 