‘Pairs’ and Other Patterns in Hegel’s Logic

Mark Randall James
University of Virginia

In his new book The Eclipse of Grace, Nick Adams argues that Hegel is most valuable to contemporary theologians not as a theologian himself, but as a logician. Logic is not a first-order discourse like science or theology, but second-order reflection on the grammar of these discourses. Adams finds in Hegel a triadic ‘logic of reconciliation’ that characteristically refuses reductive and exclusive relations between certain key terms. Adams coins the term ‘pair’ to express this relation: “a pair,” he says, “is two things, where each is what it is because of its relation to the other.”[1] For example, ‘individual’ and ‘community’ are a pair which are reconciled in the relation Hegel calls ‘spirit.’ ’Subject’ and ‘object’ are a pair which are reconciled in the relation Hegel calls ‘concept.’ Modernists characteristically take an exclusive opposition between paired terms as primary, and then struggle to show how traffic is possible between them. But when you grasp these terms as pairs, the philosophical task becomes that of articulating their interrelation as part of a single dynamic. One great merit of Adams’ book is to bring a basic pattern of non-binaristic logic to crystal clarity in his concept of a ‘pair’ and put it to use in reading Hegel.

Hegel’s own Science of Logic unfolds as a long developmental progression of pairs, or more precisely, of those elemental pairs the tradition called ‘categories.’ Being and nothing gradually unfold into something and other, finite and infinite, and on and on it goes. Hegel is particularly interested in the developmental relationship between categories: how and why one pair can lead to some other pair. To see the significance of this, one has to recall that for Hegel, logic should permit no distinction between form and content. To describe the activity of thought as it develops from one pair to another — i.e. ‘form’ — is at the same time to articulate the definition and analysis of these concepts — i.e. ‘content.’ To know the content of a category is, precisely, to grasp what one does in using it, which includes understanding how it relates to simpler and more complex concepts.

In this way, Hegel was able to address a familiar difficulty philosophers have faced in attempting to define them. If one thinks of definition, for example, in Aristotelian and Porphyrian terms, then the definition of a species is the conjunction of a genus and a specific difference. “Man is a rational animal.” But categories, as the highest thinkable genera, cannot be further analyzed, and because they are a priori, they cannot be defined in terms drawn from experience.

So Hegel instead defines the categories by displaying their development. Categories are not related to one another by way of subtraction and addition, as on the model of genus and species, but organically and synthetically, as way-stations or ‘moments’ in a developmental process. Though Hegel retains the word ‘abstract,’ he redefines it to refer to categories that occur earlier in this narrative progression, categories whose content is less determinate. The task of logic is thus rather like trying to explain how to build a house without using words or blueprints. One could only perform the building of a house and invite others to follow and work it out for themselves. Hegel’s logic is that kind of invitation.

Now Adams tends to downplay the developmental character of Hegel’s logic. This can give the impression that a ‘pair’ is just the sort of abstraction Hegel seeks to avoid; it can seem like a genus of logical relation. If one reads Adams and thus Hegel in this way, one is in danger of missing the rich content of the Logic, all of Hegel’s labor to define and analyze each particular category.

I believe this reading of Adams is not a necessary one. To show this requires us to locate the concept of a ‘pair’ itself within Hegel’s Logic as one of the categories. I argue that Hegel does indeed refer to pairs under the name of ‘Something and Other.’ If we accept this identification, we can then trace, with Hegel, the development of Adams’ own concept of ‘pair’ into increasingly more complex concepts. Development means that we do more than identify instances of pairs; rather, Hegel argues, our thinking must constantly stretch, reverse, or transform simpler concepts in order to articulate more complex ones. We must, as it were, constantly relearn what a ‘pair’ can be, constantly relearn how to say ‘pair’ in ever new contexts.

This essay aims to exhibit one occasion of this relearning: the transformation of the finite pair into the infinite. In this particular development, we come to learn how to use the pair to describe self-related or reflexive structures. It’s difficult to overstate the importance of this: Hegel was supremely a philosopher of the infinite. Because Adams’ concept of a pair remains focused on relations of opposition, his readers are liable to forget this all-important fact. I then try to exhibit how to use what we have learned in a particular empirical context: language. I suggest that the Hegelian infinite helps us to think through the character of linguistic systems by providing a powerful alternative to the binary logic of structuralism, which pervades a good deal of postmodern and post-structuralist thought. Structuralism models language as a closed system of signs, and meaning as a purely intra-systemic relation. By contrast, Hegel’s account of the infinite helps us to think of language as an open system, and thus to overcome the pernicious assumption that because something is within language, it cannot also be outside of it.[2] Language itself — including the language of scripture and tradition — can open us to the world and to others, rather than locking us into a particular conceptual scheme or discursive regime. One of the virtues of Scriptural Reasoning is to realize and display this possibility.

Pair’ as ‘Something and Other

First, what Adams calls a “pair,” Hegel refers to as “Something and Other.” Recall Adams’ definition: “A pair is two things, where each is what it is because of its relation to the other,’ and again, ‘A pair is two things, where each is distinct from the other, but each cannot be adequately described independently of its relation to the other” (33). Paired terms are neither separable from one another nor reducible to one another, because each term is what it is by virtue of its relation to the other.

Although Adams’ formulation is quite general, it does presuppose certain even more basic concepts: that of a ‘thing’ and its relation to its ‘other.’ If we then examine Hegel’s account of precisely these elemental concepts — Something and Other — we find that his account closely parallels Adams’. Hegel wants to show that attempting to think through the abstract opposition between Something and Other requires us to articulate a more complex interrelation between the two: Something is determined by its relation to another, a ‘being-for-other,’ but Something remains distinct from and opposed to the other, a ‘being-in-itself.’ The key text reads:

Being-for-other and being-in-itself constitute the two moments of the something. There are present two pairs of determinations: 1. Something and other, 2. Being-for-other and being-in-itself. The former contain the unrelatedness of their determinateness; something and other fall apart. But their truth is their relation; being-for-other and being-in-itself are, therefore, the above determinations posited as moments of one and the same something…[3]

Stephen Houlgate says, in commenting on this passage, that Something is necessarily ‘other-related’ or ‘other-directed,’ yet without undermining its “identity quite separate from that of any other.”[4] This is, it seems to me, more or less Adams’ concept of a pair. (Fittingly, this passage is the only place in the Logic that Hegel uses the word “pair” in a speculative context). And since this concept is sublated without ever being absolutely abandoned in the course of Hegel’s Logic, we can say that for Hegel — though not perhaps for Adams — all subsequent categories will be terms within pairs, at least in a certain sense.

Transforming Pairs

Let us now consider how the pair (i.e. Something and Other) undergoes development in the course of Hegel’s Logic. Hegel thinks of conceptual development in organic terms. In an organic process, a simple structure can evolve continuously into something vastly more complex which, if not absolutely other than the initial structure, may nevertheless be almost unrecognizably different. In this way, Hegel routinely pushes concepts to their breaking point, stretching them almost beyond recognition. As an analogy, consider the evolution of a bat’s wing from the front paws of some early mammal. A simple glance at the hand-like skeletal structure of a bat’s wing shows that it remains structurally homologous to the paws of a rodent. Yet evolution has stretched the “finger” bones of a bat far out of their usual proportion and expanded the tissue between them. Without becoming entirely other, rodent paws evolved into something with extraordinary new capacities: wings.

The transition from finitude to the infinite is similar. Hegel unfolds a series of concepts, from Something and Other through finitude itself, that are all characterized by some form of binary opposition. For this reason, Hegel argues, these categories apply most straightforwardly to the finite things that populate our ordinary, common sense experience, the realm of the Kantian ‘understanding.’ Now without tracing every step, what happens in the transition to the infinite is basically this. The concept of finitude includes a negative relation to its other, and one can deploy this negative relation reflexively upon finitude itself. We can, in other words, articulate the concept of the not-finite, the infinite. The infinite thus emerges out of the finite both as its other and as its self-relation. Insofar as the infinite is only determined negatively, as excluding the finite, even the infinite remains finite, limited by an other: Hegel calls this the ‘spurious infinite.’ The true infinite, rather, is a self-related process that includes rather than excludes the finite. Hegel calls this “the self-sublation of the infinite and of the finite as a single process.”[5]  The finite and the infinite are plainly what Adams would call a pair. They are different from one another and yet inseparable and dynamically related. Adams’ analysis is spot-on here.

And yet something more has happened, which requires us to relearn the very meaning of ‘pair’ in the new context of the infinite. Because the infinite is a self-related concept, Hegel has to articulate a curious reflexive grammar for its use. The infinite, he says, is one of its own moments: “the infinite…has the double meaning of being one of these two moments — as such it is the spurious infinite — and also the [true] infinite in which both, the infinite and its other, are only moments…”[6] The same grammar recurs again in what Hegel calls being-for-self, which is simply sublated infinity, or roughly, the concept of a system. Here again, Hegel says, “Being-for-self is the simple unity of itself and its [other] moment.”[7] So even when the infinite or a being-for-self is related to its other, Hegel infers, it is always “related in its other only to its own self.”[8]

In the context of infinite relations, then, we have pairs, but pairs in which one term — the infinite or being-for-self — is both an element of the pair and the name for the whole relation between the two elements. This means that while the finite term remains other, it is no longer distinct from the infinite — and distinctness, you will recall, was part of Adams’ definition of a pair. This is what I mean that the infinite stretches the concept of a pair to its breaking point. We express this in the distinctive reflexive grammar proper to infinite systems: the infinite, in relation to its other, is relating only to its own self, yet without reducing that other to its self.

Language as a System

Now the payoff of wading through these Hegelian abstractions is that we have learned to think ‘pairs’ in the quite particular context of systems. Thinking about systems remains a very difficult task for modern thinkers. I want to end with a few remarks on the system of language; but before doing so, it will be helpful to examine the analogous system of consciousness, which Hegel discusses explicitly. If one assumes, as Descartes did, that what is within consciousness cannot also be outside it, then the so-called mind-body problem becomes a pressing one: from our standpoint ‘within’ consciousness, how do we show that psychic entities are in touch with something ‘outside’ consciousness? How is there traffic from one total system to another, from consciousness to the material world?

As Adams would read him, Hegel’s answer is to articulate a different logic. There is no necessary contradiction between something being within the totality of consciousness and outside it at the same time. (We now recognize this, after Brentano and Husserl, as the logic of intentionality.) On the one hand, Hegel says:

Consciousness [is a] being-for-self in that it represents to itself an object which it senses, or intuits, and so forth; that is, it has within it the content of the object, which in this manner has an ‘ideal’ being; in its very intuiting and, in general, in its entanglement…with its other, consciousness is still only in the presence of its own self.

Yet this does not entail solipsism or Berkleyan idealism, for:

along with this return of consciousness into itself and the ideality of the object, the reality of the object is also still preserved, in that it is at the same time known as an external existence.[9]

The object of consciousness may be both ideally within consciousness and really without it. Consciousness can include its other within itself without reducing its other to itself. In short, a system like consciousness can be total without being totalizing. (To be sure, actual systems may be totalizing; a totalizing system is what Hegel calls a spurious infinite. Hegel’s argument only permits us to deny the a priori claim that systems must always be totalizing. This is worth highlighting: logic opens conceptual possibilities, but it cannot determine particular judgments).

Similar difficulties arise in the analysis of language,[10] and these difficulties have knock-on effects for contemporary theologians, who must deal with linguistic objects like Scripture and who tend to figure key phenomena in linguistic terms: we speak of theological ‘grammar,’ of traditions as ‘language games,’ etc. Like consciousness, language is a kind of system. But if one assumes a binary logic in which what is within language cannot also be without, one must try to account for language as a total and closed system, separate from the external world, what Saussure called langue. The elements of such a system are, on Saussure’s account, arbitrary and conventional, as they must be if they are, by definition, abstracted from the processes of the natural world. The actualization of language in the world (parole) is, on this account, quite distinct. Within this structuralist logic, linguistic reference becomes particularly puzzling, since reference is supposed to be the mechanism by which language relates to its other, the world. Either reference must be treated as a kind of leap outside of language that somehow nevertheless guarantees correspondence between linguistic signs and things; or reference must itself be reducible to relations between signs within the system of language.

This latter view is an article of faith for many post-modern thinkers: “There is nothing outside of the text.”[11] And in one form or another, a denial of reference has become the conventional wisdom among contemporary theologians of various stripes. For example, feminist Foucauldian theologian Mary McClintock Fulkerson says, “One cannot get behind the signifying to some reality in itself.”[12] So too the Reformed theologian James K. A. Smith: “The locus of meaning is not the line that connects the dots of a word to a thing; rather, the locus of meaning is an entire web of communal practice and conventions.”[13] Despite their very different theologies (and politics), both theologians treat language as a (perhaps unstable) conventional system and deny that meaning involves any relation to the external world. Given this assumption, a host of familiar post-modern anxieties about how traffic is possible between language and world become pressing. How can our languages or traditions be responsive to empirical facts? How can we avoid reducing language to power relations? How can members of one language-game or tradition talk to those of another?

One might try to solve these problems from within this broadly structuralist framework, but in light of Adams’ account of pairs, we have to consider another hypothesis: perhaps these problems stem from an errant logic. Language and world might be a pair, so that each is what it is by virtue of its relation to the other. We cannot simply assume that because something is within language, it cannot also be outside it.

But we can gain further insight into this alternative by reflecting on Hegel’s quite particular analysis of the infinite. If language is a genuinely infinite system in Hegel’s sense, then, as we have seen, it both develops out of the finite and is a process that includes the finite without reduction. Now one of the most finite of real relations is causality, in which one thing directly impinges upon another. So Hegel’s analysis of the infinite suggests a research program: to investigate whether language is better understood not as a static system but as a dynamic process that emerges within the world of causal relations, and whose activity includes causal relations along with structural ones. Causality need not only impinge on language from the ‘outside,’ but may instead be part of how language itself produces meaning.

On such a picture, language would not be purely conventional, but rather a process integrated with the natural world about which we speak. Causality is integral to meaning: think of the shout or gesture by which I seize your attention, or the pain a child suffers when she ignores her parents’ warning, or the feeling of surprise when someone hears something quite unexpected. These and other causal relations are part of how language opens us to the world rather than closing us off from it. Which is to say, as Hegel would surely want to, that language can mediate the real world rather than leaving some world-in-itself behind language as a residue.[14]

This, anyway, is one way of conceiving what it might mean for language and world to be an infinite pair. As a coda, let me suggest that SR also helps display this openness of language by creating opportunities for interruption. Interruption is another causal relation, which SR helps foster by sharply narrowing our focus on short texts and putting us into relation with people who are different from ourselves. Without leaving language, through the wholly linguistic activity of talking, we nevertheless find ourselves often surprised or disturbed, and in response, putting new things into words. In short, SR points towards a non-conventionalist theory of language that requires something like Adams’ logic of pairs and Hegel’s logic of the infinite. And this, I should think, is yet another reason for you to go read Adams’ book!

Notes

[1] Nicholas Adams, Eclipse of Grace: Divine and Human Action in Hegel (Malden: Wiley-Blackwell, 2013), 9.
[2] The close relation between Hegelian logic and language was one of the great themes of Jean Hyppolite. His account of language is close to mine: “Language is not only a system of signs alien to the signified, it is also the existing universe of sense, and this universe is the interiorization of the world as well as the exteriorization of the ‘I.’ Language is a double movement that must be understood in its unity” (Jean Hyppolite, Logic and Existence, trans. Leonard Lawlor and Amit Sen (Albany: SUNY Press, 1997), 24).
[3 G. W.. F. Hegel, Hegel’s Science of Logic, trans. A. V. Miller (London: Allen & Unwin, 1969): 119.
[4] Ibid., 334.
[5] Ibid., 137.
[6] Ibid., 148.
[7] Ibid., 163.
[8] Ibid., 159.
[9] Ibid., 158.
[10] See Hegel’s brief but suggestive comments on the rationality intrinsic to grammar in the introduction to the Science of Logic, 57.
[11] Jacques Derrida, Of Grammatology, trans. Gayatri Chakravorty Spivak (Baltimore: John Hopkins University Press, 1997): 158.
[12] Mary McClintock-Fulkerson, Changing the Subject: Women’s Discourses and Feminist Theology (Minneapolis: Fortress Press, 1994): 72.
[13] James K. A. Smith, Who’s Afraid of Relativism? (Grand Rapids: Baker Academic, 2014). He frames this as a reading of Wittgenstein; in this he is, I believe, badly mistaken.
[14] This is suggested by Paul Ricoeur, who borrows the logic of intentionality in speaking of linguistic reference: ‘the reference expresses the movement in which language transcends itself’ (Paul Ricoeur, Interpretation Theory: Discourse and the Surplus of Meaning (Fort Worth: Texas Christian University Press, 1976): 20).

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