The True Infinity of the Living: The Hegelian Infrastructure of Hägglund's This Life

Abstract

Although the concept of ‘true infinity’ is undoubtedly central to Hegel's philosophy, the Anglophone rehabilitation of Hegel as a post-Kantian critical philosopher has avoided any sustained interpretive confrontation with the concept. In this paper, I provide a revisionary reconstruction of Hegelian true infinity by engaging with Martin Hägglund's argument in This Life (2019) for the centrality of finitude to Hegel's philosophy. For Hägglund, Hegel's philosophy effects a ‘secular reconciliation’ with finitude by demonstrating that our mortality is not a negative condition to be overcome; rather, mortality is constitutive of rational social agency or ‘spiritual life’. While Hägglund's interpretive emphasis on finitude prima facie occludes a consideration of the concept of true infinity, I show that Hägglund's understanding of spiritual life in terms of the dynamic of self-maintenance implicitly articulates a revisionary understanding of true infinity as instantiated in and through the activity of finite living rational beings. More specifically, I show that Hägglund's understanding of finitude as constitutive of spiritual life is grounded in three closely interrelated Hegelian meta-concepts, all of which Hegel derives in the second chapter of the Logic (‘Existence’): (a) the distinction between abstract and determinate negation; (b) the form of individuality as constituted through determinate negation; and (c) true infinity as the form of individuality understood in explicitly processual terms. I thus ground a deflationary interpretation of true infinity in Hegel's logical account of determinate individuality, and at the same time, contribute to This Life's ongoing critical reception by articulating its Hegelian logical infrastructure.

Introduction

The concept of ‘true’ or ‘genuine’ infinity is undoubtedly central to Hegel's philosophy. Hegel provocatively claims in the Logic that commitment to the true infinite characterizes philosophy as such: a philosophy that does not admit the category of true infinity and thus ‘attributes to finite existence […] true, ultimate, absolute being, does not deserve the name of philosophy’ (SL: 124/21.143).¹ And yet, the Anglophone rehabilitation of Hegel as a post-Kantian Critical philosopher—typically associated with Robert Pippin's work since his seminal Hegel's Idealism (1989) and the ‘Pittsburgh Hegelianism’ of John McDowell and Robert Brandom—has avoided any sustained interpretive confrontation with Hegelian infinity.² Indeed, Hegel's claim in the Phenomenology that infinity is the ‘soul of the world’ (¶162) seems just the kind of pre-critical metaphysics from which Hegel's deflationary interpreters have sought to rescue him. In this paper, I provide a revisionary reconstruction of the concept of true infinity by engaging with Martin Hägglund's argument in This Life (2019a) for the centrality of finitude to Hegel's philosophy. For Hägglund, Hegel's philosophy effects a ‘secular reconciliation’ with ‘our finitude’ by demonstrating that our mortality is not a negative condition to be overcome (2019a: 365); rather, mortality is constitutive of rational social agency, which Hägglund terms ‘spiritual life’ (following Hegel's own idiosyncratic usage of the term ‘Spirit’ (Geist)). While Hägglund's interpretive emphasis on finitude prima facie occludes a consideration of the concept of true infinity, I show that Hägglund's understanding of spiritual life in terms of the dynamic of self-maintenance implicitly articulates a revisionary understanding of true infinity as instantiated in and through the activity of finite living rational beings. True to Hegel's own understanding of true infinity as the ‘determinate unity of finite and infinite’ (SL: 124/21.143), Hägglund's grip on the logic of finitude serves to bring true infinity into relief. More specifically, I show that Hägglund's understanding of finitude as constitutive of spiritual life is grounded in three closely interrelated Hegelian meta-concepts, all of which Hegel derives in the second chapter of the Logic (‘Existence’): (a) the distinction between abstract and determinate negation; (b) the form of individuality as constituted through determinate negation; and (c) true infinity as the form of individuality understood in explicitly processual terms. I thus ground a deflationary interpretation of true infinity in Hegel's logical account of determinate individuality, and at the same time, contribute to This Life's ongoing critical reception by articulating its Hegelian logical infrastructure.³

In the remainder of this introduction, I set out the basic coordinates of Hägglund's Hegel interpretation in This Life, which draws together contemporary Hegel scholarship in English with arguments drawn from Jacques Derrida's work in productive—but prima facie interpretively problematic—ways.

Hägglund's revisionary orientation bears an unmistakable family resemblance to deflationary Hegelianism: like Pippin, Brandom and McDowell, the interpretation of Hegel in the Conclusion of This Life takes Kant's understanding of self-consciousness as its point of departure in explicating Hegel's account of spiritual life.⁴ Hägglund also freely uses the shared language of ‘undertaking’ and ‘revising’ ‘commitments’ in interpreting spiritual life as a model of rational agency (Pippin 2008; Brandom 1994, 2019). Nonetheless, Hägglund clearly intends This Life as a critical intervention. In a key footnote, Hägglund claims that his argument ‘transforms’ McDowell's Aristotelian interpretation of Hegel's Geist. McDowell argues that Geist is Hegel's word for ‘the formally distinctive way of being a living being that characterises human beings’, a form of life activity distinguishable from that of plants and non-human animals. Both McDowell and Hägglund attempt to articulate the relationship between living beings (what Hägglund calls ‘natural life’) and human beings as rational or self-conscious living beings (‘spiritual life’), without reducing the latter to the former, and without detaching rational capacities from living activity.⁵ The key difference, Hägglund argues, is that McDowell pays no attention to the finitude of living beings, to mortality. In contrast, ‘every level’ of This Life seeks to ‘spell out the implications of mortality as constitutive of any form of natural life as well as any form of spiritual life’ (2019a: 403). The attendance to mortality means that Hägglund recasts both natural and spiritual life as species of self-maintenance, the activity of maintaining one's integrity against the threat of dissolution and death, where ‘integrity’ ought to be read as including both ‘bodily integrity’ and the specifically moral integrity of one's ‘practical identity’, constituted through a suite of normative commitments.

The emphasis on mortality by which Hägglund differentiates his account of rational agency is drawn from his earlier systematic reconstruction of Derrida's philosophy in Radical Atheism (2008a). Despite Hägglund's claim in This Life to have learnt the ‘most profound lessons’ from Hegel's work (2019a: 35), those familiar with Radical Atheism will inevitably attribute much of This Life's argument to Hägglund's Derrida interpretation. Radical Atheism's central claim is that Derrida's ‘differance’ marks an ‘absolute’, ‘originary’, ‘unconditioned’ or ‘infinite’ temporal finitude that makes it impossible for any determinate identity to be ‘pure’, ‘self-present’, or ‘in itself’. At the same time, however, the infinite finitude that makes pure identity impossible is also constitutive of any identity at all, in so far as to have an identity just is to preserve, record or ‘trace’ that identity on a material support across temporal displacement, to maintain one's identity in the face of a future that may erase it. Hägglund often puts this point in Derrida's quasi-Kantian terms, as ‘conditions of possibility and impossibility’: ‘what makes it possible for anything to be at the same time makes it impossible for anything to be in itself’ (2008a: 81).⁶ In short, no being is immune or exempt from temporal finitude—from eventual destruction and death—for they are rather constituted by the necessity of maintaining their identity in and through that very finitude. Having systematized this Derridean conceptual architecture, Radical Atheism draws the implications for religious belief: the final overcoming of finitude in an eternal life is unintelligible; such a life would be unrecognizable and undesirable. Our finite life cannot be consistently conceived as a ‘fallen’ or tragic condition—a ‘negative predicament that we desire to overcome (2008a: 121)—but rather is to be affirmed as a constitutive condition of all that we value, as well as all that we fear and defer.

This Life continues and expands the arguments of Radical Atheism, sometimes retaining the Derridean formula: ‘the conditions of possibility for spiritual life are the conditions of the fragility of spiritual life’ (2019a: 196), where ‘fragility’ means the impossibility of any life exempt from finitude, and the necessity, again, of maintaining our bodily and moral integrity in face of death. Just as in Radical Atheism, This Life invites us to understand finitude not as a ‘negative predicament’, but as constitutive of meaningful activity: ‘Our finitude is not a chain from which we need to be released by an eternal Saviour but the condition of possibility for our freedom’ (2019a: 350). This time, however, Hägglund's claim for the constitutive function of irreducible finitude is attributed not to Derrida, but to Hegel:

The aim of Hegel's Phenomenology can thus be seen as a secular ‘reconciliation’ with our finitude, in the sense of grasping that our finitude is not a limitation that blocks us from attaining the absolute. Rather, grasping finitude as the condition of intelligibility for any form of spiritual life is what Hegel calls the ‘absolute knowing’ of ‘absolute spirit’. (2019a: 365)

However, Hägglund's articulation of Hegel's ‘absolute’ in terms of finitude generates a series of prima facie interpretive difficulties that This Life does not directly address, and which this essay seeks to resolve. Neither Hegel's discussion of ‘Absolute Knowing’ and ‘Absolute Spirit’ in the Phenomenology nor ‘Absolute Spirit’ in the Encyclopaedia proceed in terms of finitude, and Hegel identifies spiritual life not with finitude but with infinity: ‘At the mention of the infinite, soul and spirit light up, for in the infinite the spirit is at home, and not only abstractly; rather, it rises to itself, to the light of its thinking, its universality, its freedom’ (SL: 109/21.125). Hegel's derivation of the a priori concept (or ‘thought-determination’) of finitude is provided in the Science of Logic, in which Hegel seems to take issue with just the kind of ‘originary’ or ‘absolute’ finitude view worked out in Radical Atheism and continued into This Life. For Hegel, rendering finitude ‘imperishable and absolute’ is exemplary of the merely dualistic and so non-dialectical ‘Understanding’ (Verstand) (SL: 102/21.117). Such a non-dialectical view is only able to grasp a ‘bad’ or ‘spurious’ infinity (schlechte Unendlichkeit) opposed to and beyond the finite, which in turn gives rise to an understanding of infinity only as an ‘infinite progression’ (Progress ins Undendliche) of finite beings. In contrast, Hegel seeks to show that finitude, the bad infinite, and the infinite progression are ‘sublated’ by ‘true’, ‘genuine’, or ‘affirmative’ infinity (echte, affirmative Unendlichkeit). Hegel's argument on this point will be unpacked in some detail below. My point here is simply that This Life's continuation of Radical Atheism's commitment to an infinite finitude will initially sound, to Hegelian ears, like an endorsement of some version of the bad infinite and its corollary, the infinite progression.

Sure enough, Radical Atheism had in fact explicitly identified its model of infinite finitude with bad infinity, following Derrida's own critique of Hegel (2008: 93). Now, Derrida's ambivalent relationship to Hegel is routinely noted (Descombes 1980; Barnett 1998; Baugh 2003). On the one hand, Derrida and Hegel both oppose rigid philosophical dualisms (de Boer 2011). Paradigmatically, the early Derrida shows the subject's ostensible self-presence in speech to be contaminated by the delay and deferral classically associated with writing, while the Logic famously begins with the immediate collapse of the determinate difference between ‘pure Being’ and ‘pure Nothing’. For both Derrida and Hegel, no concept can be ‘pure’, because to be at all is to be in constitutive relationship to and thus ‘impurified’ by its contrary or ‘other’.⁷ For both, then, that there can be no pure identity inured from alterity cannot be conceived as a negative restriction, but rather a condition of possibility for there being identities or existents at all. That Hägglund is able in Radical Atheism and This Life to use Derrida and then Hegel to make much the same claim should not be surprising. On the other hand, however, Derrida and the Hägglund of Radical Atheism are sharply critical of Hegelian true infinity. Derrida in an interview collected in Positions appears to claim that Hegel undermines his own insight into constitutive impurity by attempting to ‘sublimate’ temporal deferral in an ‘anamnesic interiority […] interning difference in a self-presence’ (1981: 44).⁸ While Derrida does not in that interview single out the category of true infinity as effecting this internment, in ‘Violence and Metaphysics’ he claims that to ‘take issue’ with Hegel one must ‘undermine the idea of positive infinity’ (1978: 119). Radical Atheism directly quotes Derrida on this point: ‘the only effective position to take in order not to be enveloped by Hegel would seem to be […] to consider false-infinity[…] irreducible’ (Hägglund 2008a: 93). Derrida seemingly holds the category of true infinity to be a misguided attempt to reinstall the possibility of a fully self-present identity, exempt from finitude, which is to be resisted via a demonstration of finitude's insuperability.

With this background in mind, it should be clear that any reconstruction of Hägglund's Hegel must explain why This Life's claim for finitude as a condition of spiritual life does not prima facie amount to his earlier Derridean endorsement of bad infinity. How might This Life's ostensibly Hegelian claim for finitude as the condition of intelligibility for any form of spiritual life be squared with Hegel's own identification of spirit with the infinite?

In this essay I show, contra Derrida and the earlier Hägglund, that Hegelian ‘true infinity’ is not the attempt to reinstall a ‘pure’ identity, but rather articulates for Hegel the minimally graspable logical form of living individuality as the activity of self-maintenance—and just as This Life so presents that activity. In my view, This Life is a book about true infinity, even if this Hegelian formula is never itself used.

This argument takes five steps. Firstly, I demonstrate that Hägglund's articulation of finitude as a necessary condition of spiritual life does not amount to an endorsement of ‘bad infinity’. For Hegel, ‘bad infinity’ arises from the conceptualization of the infinite as the ‘abstract negation’ of finitude—precisely the view that This Life opposes. Secondly, I reconstruct Hegel's account (in the Logic's chapter on Existence) of the determinacy of an existent individual—a ‘something’—as constituted via determinate negation or ‘the negation of the negation’. Thirdly, I reconstruct the Logic's account of true infinity as a further elaboration of the logic of individuality. Contra Derrida and the earlier Hägglund, true infinity is not an exception to finitude. Rather, it reflexively deepens finitude, in so far as it articulates the activity of self-relation in other-relatedness. Fourthly, I map Hegel's true infinity onto the structure of living self-maintenance advanced in This Life. Fifthly, I reconstruct Hägglund's account of rational agency—that is, the form of activity of self-conscious living beings—in explicitly Hegelian terms.

I. The unhappy understanding

Hägglund's extended discussion of Hegel in This Life occurs in Conclusion and centres on the figure of the ‘Unhappy Consciousness’ in the Phenomenology (PhG: §§206–30). While acknowledging that Unhappy Consciousness was understood by Hegel as a critique of a ‘certain understanding of Christianity’, Hägglund seeks to broaden its scope to all forms of ‘religious faith’ and their shared understanding of finitude:

[the Unhappy Consciousness] should also be understood more broadly as any standpoint that regards our finitude as a negative restriction, which prevents us from achieving the salvation we supposedly desire […]. This is the standpoint that Hegel seeks to overcome and help us leave behind. (2019a: 365)

The experience of the Unhappy Consciousness is organized around a distinction made within self-consciousness. On the one hand, there is the ‘changeable’, ‘inessential’, and ‘contingent’ consciousness of the ‘singular individual’. On the other hand, there is the ‘unchangeable’ and ‘universal’ consciousness that consciousness takes itself to essentially be. In more explicitly religious terms: I am not really my fragile body and ever-changing mind, and certainly not whatever social role I happen to play; I am in truth only my immortal soul. For our purposes, the key point is that the Unhappy Consciousness is unable to reconcile its changeable contents with the unchangeable universality it takes itself to truly be, in so far as its ‘elevation’ beyond the changeable would remain act of the singular individual (PhG: §209). As a result, the unchangeable and universal is represented as a ‘securely fixed […] otherworldly beyond’, and the singular individual's ‘hope of coming to be at one with it must remain a hope, which is to say, it must remain without fulfillment, without ever being present’ (PhG: §212). It is in this picture of an unchangeable beyond that the Unhappy Consciousness most clearly figures the religious longing for and faith in an eternal life exempt from change and loss.

While ‘finitude’ does not explicitly figure in Hegel's Phenomenology account of the Unhappy Consciousness, if we turn to ‘finitude’ in the Logic, we find it begins with an analogous structure to the Unhappy Consciousness—and with the same pathos. Finitude is the ‘most obstinate category of the understanding’ (SL: 101/21.117), and the understanding ‘persists in this sorrow of finitude’ (SL: 102/21.117). In Hegel's Logic and Encyclopaedia, the ‘Understanding’ (Verstand) is standardly opposed to ‘Reason’ (Vernunft), as differing accounts of conceptual content (EL: §§79–82). For the Understanding, concepts are independently intelligible and exclusive of their contraries, while for Reason—as we will see in more detail in Section II below—concepts are properly understood in terms of their dialectical interdefinability. As such, the Understanding's ‘official claim’—and the claim that generates its ‘sorrow’—is that finitude is to be opposed to an infinity it excludes, and with which it cannot be united: ‘the finite is incompatible with the infinite and cannot be united with it; that the finite is absolutely opposed to the infinite (SL: 102/21.117). So the Understanding at this moment in the Logic repeats the unhappy and estranged consciousness of the Phenomenology: on the one side, the ‘positive’ and essential; on the other, the ‘negative’ and inessential. On this picture, the finite and infinite constitute ‘two worlds’, the infinite emerging at the limit of the finite, and vice-versa (SL: 111/21.127). But because to be finite (endlich) on Hegel's definition is to be limited by an other and thus to come to an end in an other (SL: 101/21.116), the Understanding's conception of the infinite as limited by the finite is not truly or genuinely in-finite (un-endlich) at all, but rather only a ‘finite infinite’ (SL: 111/21.127), a ‘bad’ or ‘spurious’ (schlechte) infinite.

What would for Hegel count as a self-consistent conception of infinity will be outlined in Section III of this essay. My point here is simply that Hägglund's counsel against the Unhappy Consciousness—that we should not understand finitude as a ‘negative restriction’ that holds us back from our desire—indicates at the same time opposition to the Understanding's account of the relation between finite and infinite, an account that generates the ‘sorrow’ of the bad infinite. As such, This Life's reading of finitude as constitutive of spiritual life cannot be said—despite initial appearances—to be an endorsement of the bad infinite, but rather arraigns itself against the Understanding's approach to contrary conceptual contents that generates the bad infinite. It also means—and as the remainder of this essay bears out—that This Life cannot follow Derrida in taking true infinity to be an exemption from finitude and the reinstallation of unadulterated self-presence, because such an exemption would simply reassert the Understanding's incoherent account of the finitude-infinity relation.

So Hägglund follows Hegel in arguing that finitude ought not to be understood as a mere restriction. But how exactly is Hegelian dialectical Reason, in Hägglund's words above, to help us ‘leave behind’ this sorrow of the Understanding? To elucidate Hägglund's answer to this question in explicitly Hegelian terms, we need to reconstruct the way in which, for Hegel, individuality—and further, the relation between finitude and infinity—cannot be understood with the resources of the Understanding alone.

II. Negation and the individual

Hegel's meta-conceptual distinction between the Understanding and Reason broadly maps onto the distinction in the Logic between ‘abstract negativity’ or the ‘first negation’ and ‘absolute negativity’ or the ‘negation of negation’. Following the Phenomenology's usage, commentary often terms the two modes of negation ‘abstract’ and ‘determinate’ (PhG: §59). For the Understanding, a given content is not its contrary. Reason ‘negates’ this ‘first’ negation as necessary but insufficient for a coherent grip on the determinacy of conceptual contents. This picture will of course be familiar to readers of Hegel. I nonetheless take the time to reconstruct the derivation of determinate negation in the Existence chapter in some detail, in order to show that determinate negation is bound up with Hegel's attempt to think the minimal logical form of individuality, and later in the same chapter, of infinity. While this material is extremely abstract, it is ultimately indispensable to a proper grasp of This Life's account of living individuals: living beings are, of course, not dead, but this merely abstract negation is insufficient to render living activity as self-maintenance intelligible. I am also motivated by Pippin's recent account of the Logic in Realm of Shadows (2019a), which, however indispensable, does not pick out the dependence of individuality on determinate negation.⁹

At the start of the Existence chapter, negation constitutes what Hegel takes to be the minimally intelligible form of qualitative difference, i.e., being real rather than being negative, where the latter means not being real. This first negation is the ‘not’ that renders the quality of ‘being real’ qualitatively distinct from ‘being negative’. Hegel here emphasizes the way in which the first negation results in two qualities mutually excluding one another: ‘reality only has, therefore, the value of something positive from which negating, restriction, lack, are excluded’ (SL: 85/21.99). Negation is thus immediately understood in the Logic as material incompatibility.¹⁰ However, negation at this point in the Logic only grounds a distinction between ‘ways of being determinate’ (being real, being negative); it does not of itself account for the qualitative determinateness of an individual ‘something’, i.e., something being itself and not another something (Houlgate 2006: 313). The logical form of the latter is more complex, and results from Hegel's diagnosis of the ‘one-sidedness’ or incomplete intelligibility of negation as it is immediately conceived, i.e., in terms of mutual exclusion.

Hegel thinks negation understood as the mutual exclusion of contrary terms is a partial or incomplete model of determinacy for the following reason. While the first or most immediate negation figures reality and negation as mutually exclusive, it at the same time implicitly indicates their mutual imbrication, in the sense that their respective determinacy is dependent on their relation to one another. To borrow the language of the Phenomenology, what is meant or intended (gemeint) here is not what is actually said (PhG: §97). We mean to say that reality excludes negation, but what we actually say—what is legible in such a claim—is that reality ‘includes’ negation in the sense that it necessarily has reference (Beziehung) to negation in order to be qualitatively distinguishable from it, and negation similarly ‘includes’ reality.¹¹ So we might say that the first negation is termed ‘abstract’ because it abstracts from the mutual dependence of reality and negation that it nonetheless makes legible. Once we come to see this, we have followed Hegel in ‘negating’ negation understood as mutual exclusion. Importantly, this does not mean dismissing our immediate understanding of negation as simply false, but—to use Hegel's famous term of art—to sublate (aufheben) that understanding, embedding it as a logical moment of a more robust account of determinacy: contents are determinate by not being—and through that negation necessarily referring to—their contraries. To dismiss abstract negation as simply false would be only to repeat its one-sidedness: we would figure abstract negation and determinate negation as mutually exclusive, assigning truth value to the latter only.

One way we might understand the relation between first and second negations—and the crucial importance of this difference for Hägglund's account of living beings—is by distinguishing Hegel from Meister Eckhart, who first coined the formula, ‘negation of negation’, and whom Hägglund criticizes in Radical Atheism. For Eckhart, the created world is characterized by negation: finite beings will, sooner or later, not be what they are—they change into others, they come to an end. Through contemplation, we detach ourselves from desire for any changeable, perishable being, so as to be ‘as little moved by joy and sorrow, honour and disgrace, as a broad mountain by a gentle breeze’ (cited in Hägglund 2008a: 117). We thus approach God's nature, defined by Eckhart as the ‘negation of the negation’ (negatio negationis; Versagen des Versagenes), the ‘Indistinct Being’ who is ‘free and empty’ (McGinn 2021: 3). Hegel's understanding of the ‘negation of the negation’ formula is crucially different. While not specifically targeting Eckhart, the Logic criticizes theology that understands God, as in the ontological proof, ‘as something affirmative that contains no negation’ (SL: 86/21.99-100). Such a God would be the pure Being Hegel has shown to be indistinguishable from pure Nothing, an ‘empty absolute, void of determination and content, in which all is one’ (SL: 86/21.99–100). Such a theology would only mean God while in fact saying nothing. Importantly, although Radical Atheism does not refer to Hegel in critiquing Eckhart, that critique is already Hegelian: since to be free from negation is to be free from any determinacy, Eckhart's ‘God is Nothing, since everything that is finite (which is to say everything) must be eliminated in God’ (2008a: 118). While those sympathetic to Eckhart will point out that God's Nothingness is the very point of an apophatic theology, Hägglund's basic claim is that the identification of spirituality and freedom with emptiness and passivity is deeply misguided; for Hägglund, our commitment to freedom in collective, ‘spiritual’ life is constituted through the activity of individual living beings. It is indicative that Hegel's God is identified not with perfection, purity, and impassibility, but with ‘activity, creation, power’ (SL: 62/21.72).¹² For Hegel, the negation of negation does not cancel or remove negation, necessary as it is for determinate difference. Rather, as we will see in the remainder of this section and the next, the Hegelian negation of negation brings the logical form of individuality—and infinity as the minimal logical form of living activity—into view.

The logical transition from negation to the negation of negation is simultaneously the derivation of a qualitatively distinct, self-identical individual. Unfortunately, Hegel himself puts this movement extremely rapidly:

Therefore, what is de facto at hand is this: existence in general, distinction in it, and the sublation of this distinction; the existence, not void of distinctions as at the beginning; but again self-equal through the sublation of the distinction […] this state of sublation of the distinction is existence's own determinateness; existence is thus being-in-itself; it is existent, something. (SL: 89/21.103)

Hegel here presents the ‘sublation’ of the first negation that constitutes the logical structure of an ‘existent’ or ‘something’ via contrast with the ‘pure Being’ ‘void of distinctions’ that famously begins the Logic. ‘Pure Being’ was said to be ‘self-equal only to itself’, but that self-equality proved radically indeterminate in so far as it immediately proved to be indistinguishable from its contrary, i.e., pure Nothing. It is through the distinction between the qualitative determinacies of reality and negation—and the mutual reference implicitly entailed in that distinction—that the Logic can for the first time articulate a stable form of self-equality. Unlike pure Being, something possesses a self-equality and self-standing that does not collapse into its contrary only in so far as it contains in itself the reference to its other, or, more specifically, its necessary relation to negation is a moment of its own self. Hegel will call this ‘negative unity with oneself’, being what one is by referring in what one is to what one is not.

At this point in the Logic, Hegel's account of negativity as determinative of self-identity is extremely thin. But the logical form of individuality so derived is essential to the entire progress of the Logic and the Realphilosophie, and especially for any account of the logical form of the living and thinking subject. Hegel immediately highlights this importance:

Something is the first negation of negation [Negation der Negation], as simple existent self-reference. Existence, life, thought, and so forth, essentially take on the determination of an existent being, a living thing, a thinking mind (‘I’), and so forth […]. As something, the negative of the negative is only the beginning of the subject […]. It determines itself further on […] until it finally obtains in the concept the intensity of the subject. At the base of all these determinations there lies the negative unity with itself. (SL: 89/21.103)

So if we wish to conceptually grasp the activity that constitutes living and thinking individuals (‘a living thing, a thinking mind’), what is required is determinate negation, i.e., the ‘negative unity with oneself’ that lies “at the base” of all the Logic's further determinations of subjectivity.

As Hegel's own connection of determinate negation to life should indicate, the above elaboration of the distinction between abstract and determinate above provides the resources to articulate Hägglund's account of living activity in Hegelian logical terms. Abstractly speaking, life and death are mutually exclusive in the sense that when one is alive one is not dead. But this abstract negation is insufficient to render intelligible the activity of living individuals: to live just is to actively and continually oppose oneself to one's negation in death, to ‘stave off’ death. This relation to death as the negation of life belongs to the description of any living being: one lives through negating the negation of one's death. But this processual understanding of the individual as coming to itself through what it is not is only articulated in the last stage of the Logic's Existence chapter, in ‘true infinity’.

III. True infinity in the finite

As we have seen above, infinity is for Hegel a qualitative distinction between that which is limited and so finite (endlich) and that which is without limit (un-endlich). Again, the Understanding—availing itself of the resources of abstract negation alone—is only able to articulate a spurious infinity: in taking infinity and finitude as mutually exclusive, it sets a limit on infinity, rendering qualitatively identical what it had hoped to distinguish. To resolve this, Hegel's true infinity further concretizes of the logic of determinate negation and individuality rehearsed above, understanding infinity to ‘include’ the finite as a necessary moment of itself.

Before continuing, it is important to note that the categories of finitude and infinity are themselves derived from the self-standing character of the something. Hegel seeks to demonstrate that the negative self-unity characteristic of the existent something entails opposition to and mutual limitation by an ‘other’ such something. While something and other are initially ‘indifferent’ (gleichgültig)—in the sense of qualitatively indistinguishable from one another—Hegel accounts for the qualitative distinguishability of existents by further articulating something and other as co-constitutive through their shared limit. In the sense that its limitation by an other belongs to the definition of the something, something is by definition finite (endlich), in so far as its limit or end is not contingent but belongs to its constitution.¹³ Infinity then immediately presents itself to the Understanding as the abstract negation of the finite, opposed and excluding it.

Understanding the finite and infinite as mutually exclusive gives rise to the ‘infinite progression’ or ‘alternating determination [Wechselbestimmung] of finite and infinite’ in which the finite makes necessary the thought of the infinite, and the infinite in turn that of the finite. The finite points beyond itself into the infinite in so far as limited (endlich) it has reference to its other or contrary. In reaching its limit at the infinite, it proves, however, to have only ‘arrived at itself [bei sich angekommen]’ or ‘in its beyond has only found itself again [sich in seinem Jenseits wiedergefunden]’ (SL: 117/21.134), in so far as the infinite it refers to is itself finite in being limited by the finite. At the same time, because as the finite ‘finds itself’ beyond its limit in the infinite, it is equally unending—infinite (unendlich)—being.¹⁴ So just as the finite re-joins itself in the infinite, so the infinite finds itself in the movement in which the limit between finite and infinite is transcended. Once this activity of finding itself in the other is made explicit, the form of true infinity as a further determination of the ‘negation of the negation’ has been derived:

Thus the finite and the infinite are both this movement of each returning to itself through its negation; they are only as implicit mediation, and the affirmative of each contains the negative of each, and is the negation of the negation. (SL: 117/21.135)

This derivation of true infinity is analogous to the derivation of the something: as we saw, first reality and negation were opposed, but then negation came to be understood as the moment of determinateness in any reality. To think a self-standing individual all that was required was to make explicit this dependency: the something stood on its own only in so far as it was the ‘negation of the negation’, not only not its other, but itself constituted by its relation to it. Here, true or genuine infinity is no longer understood as the limit and ‘beyond’ of the finite, but is rather the process by which finite existence maintains itself as what it is in the relationship to what it is not. To quote Houlgate's recent Hegel on Being, true infinity is ‘the movement or process of returning to, or continuing to be, itself in and through its other’ (2022: 243).

As above, were the first negation to be itself simply excluded by the operation of a further negation, the finite and infinite would be rendered immediately identical or indistinguishable—there would be no ‘not’ to distinguish finite and infinite. In this way, Hegel criticizes the characterization of infinity as the ‘unity of finite and infinite’ that would lack distinction between its moments: such ‘unity is abstract, motionless self-sameness […] the infinite is rather essentially only as becoming’ (SL: 118). Hegel's words here serve to highlight Derrida's misreading: the true infinite is not the reinstallation of pure self-presence (‘self-sameness’) but identity only in relation to another, and so because it is a movement, process, or activity (a ‘becoming’). As Hegel says, clearly foreshadowing his account of the characteristic formal activity (Formtätigkeit) of living beings in the Logic's third book, ‘the affirmative truth’—that is, affirmative infinity—is ‘internally self-moving unity’ (SL: 122/21.139). The infinite is reconceived as a process constituted in and by the finite, such that the finite and infinite can no longer be conceived as other than one another (Houlgate 2006: 424). Derrida's critique misses the deflationary character of Hegel's dialectical reinterpretation of the concept of infinity. To exhibit the form of true infinity is not to be other than—exempt from—the finite; this would be the infinite incoherently conceived as an unreachable beyond. The true infinite rather names the minimal logical form of the activity of maintaining oneself in one's finitude in relation to one's finite others: the activity or process of being what one is by establishing a relation to what one is not.

IV. Infinity as natural life

All of this may sound like an unwarranted imposition of Hägglund's themes of ‘living activity’ and ‘self-maintenance’ language onto Hegel's text, but the link between true infinity and life—and indeed spiritual life—is a deep-seated one in Hegel's thought. For example, the Phenomenology presents infinity immediately before its discussion of living activity and self-consciousness: ‘This simple infinity, or the absolute concept, is to be called the simple essence of life, the soul of the world, the universal bloodstream’ (PhG: §162). Infinity is here understood as a ‘self-equality’ in and through difference (PhG: §163), just as it is in the Logic, where, as above, true infinity names the form of self-relation in the activity of other-relatedness. Unlike the Phenomenology's brief and difficult discussion of life (PhG: §§168–73), the ‘Life’ chapter of the third book of the Logic elaborates the form of living beings, explicitly identifying living form with the true infinite: ‘Living natures […] are an actuality of infinite power [eine Wirklichkeit von der unendlichen Kraft] […] in their otherness [Anderssein] they preserve themselves’ (SL: 684/12.188). Although Hegel himself does not consistently articulate the form of life in terms of true infinity,¹⁵ it is clear that life exhibits the form of true infinity in three interrelated ways, following Hegel's own tripartite schema for the Life chapter: as (a) the ‘living individual’; (b) the ‘life process’; and (c) the ‘genus process’. I restrict my discussion to the first two moments as most directly relevant to Hägglund's text.

(a) Living individuals are infinite on account of the self-identity they exhibit in and through their different parts. As above, to be truly infinite is to be a process composed of finite moments that, as moments of that process, are what they are only in relation to those others. When occupying its proper place within the self-relating whole of the living individual, a hand, for example, is not limited by other organs but is able to fulfil its own function through its relation to them. But, as Aristotle famously remarks, the hand severed from the body is a hand in name only. Hegel at the beginning of the Life chapter rehearses this Aristotelian line of thinking in terms of the contrast between spatiotemporal externality and the unity of the living individual. While the parts of a living body can be conceived ‘as a mutual externality of entirely diverse and atomistic matters’ (SL: 678/12.182), in so far as its organs are outside one another occupying different places in space, this is not to consider the body as living, but rather as dead (SL: 680/12.183). As living, the individual is not the externality of its parts but has unity in and through that externality: the living individual is to be ‘distinguished from its externality but, in thus distinguishing itself from it, pervading it thoroughly and self-identical’ (SL: 681/12.184). This form of self-identity through difference, of differences conceived as moments of a process rather than in opposition, is first articulated in the category of true infinity.

In this way, true infinity is the minimal conceptual determination of the internal purposiveness that for Hegel characterizes living beings: the member organs of the organism do not serve as means to some end external to the life of the organism (‘external purposiveness’) but each organ is both means and end (‘internal purposiveness’). That is, each organ serves to sustain the living individual as a whole, and in so far as each organ is required for the living individual to sustain itself, the continued integrity of each organ is also the purpose of the organism as a whole. In Hegel's words, it is the ‘impulse’ (Trieb) of each organ ‘to produce itself […] but no less to sublate itself and make itself a means for the other’ (SL: 681/12.184). Internal teleology is thus a further determination of true infinity as, again, the Logic's first articulation of the process of self-relation through difference.

Importantly, in his discussion of living individuality, Hegel seeks to show that the self-relation and indeed ‘totality’ characteristic of the living individual—the simple oneness of the living individual in and through its different parts—entails a relation to an ‘indifferent’ world standing over against it (SL: 678/12.181). As glossed in Section II above, the negative self-unity characteristic of the existent something entails opposition to and mutual limitation by an ‘indifferent’ other and in this regard the something is finite. That structure is clearly recalled by Hegel here: in so far as the ‘indifferent’ world stands at the limit of the totality of the living being and opposes it, the living being in its infinite self-relation nonetheless remains finite. It is in this respect that Hegel's favoured image for the true infinite—‘the circle, the line that has reached itself, closed and wholly present, without beginning and end’ (SL: 119/12.136)—is only one half of the full Hegelian picture: the circle drawn by the living individual in negative self-unity sets itself against the world in a relationship of opposition that entails its finitude. Thus, that living natures have ‘infinite power’ does not mean, as it would seem on Derrida's reading of Hegelian infinity, that they possess a self-identity inoculated against difference and otherness. Rather, for Hegel, the living individual remains finite in two interrelated ways. Firstly, the spatiotemporal ‘externality’ of its parts means that organic unity can always ‘break down’, so to speak, into finite components. Secondly, the self-identity of the living individual entails a relationship to the world as other to and limiting of that individual. These two interrelated senses of finitude motivate Hegel's account of the ‘Life Process’ and Hägglund's reading of it.

(b) To be alive is to maintain one's self-organization—to hold oneself together—through relationship to the world standing indifferently over against one, maintaining one's bodily integrity through the establishing of the right kind of relations with that world. The Logic treats this process explicitly in terms of determinate negation, and This Life footnotes the crucial passage:

From pain begin the need and the impulse that constitute the transition by which the individual, in being for itself the negation of itself, also becomes for itself identity—an identity which only is as the negation of that negation. (SL: 685/12.188)

This is a highly abstract claim, but Hegel has in mind here the prosaic act of eating when hungry. Hunger pangs announce the threat of death to the living being: were the hunger to go unaddressed, the living being would be negated in death. But of course, the living being is not simply or immediately negated by the painful experience of hunger, but rather constitutes and maintains itself by overcoming that need through its living activity. In the same way that in (a) the true infinity of the living individual was bound up with finitude, so the life process exhibits the necessary presence of finitude in the true infinite. In the process of eating, both the finite and infinite moments of the true infinite are demonstrated: when we eat we bring another living thing to an end, demonstrating its finitude; at the same time, we demonstrate the infinite power of living beings, maintaining ourselves as the beings we are through that other we consume.

It is in its treatment of self-maintenance that the Hegelian logical infrastructure of This Life is on full display. In the pain of bodily need, Hägglund notes, ‘a living being is not simply negated but maintains itself in the negative experience of suffering’ (2019a: 186), and emphasizes in his footnote to the Logic that Hegel's ‘negation of the negation’ formula does ‘not mean that a living being can overcome its negative relation to pain, loss, and death’. Rather it simply indicates that ‘relation to the negative […] belongs to its positive constitution’ (2019a: 403). So just as any individual ‘something’ has negation as a moment of its own self-standing determinacy, and just as infinity is self-relation sustained only through relation to finitude, the living being is constituted not by the simple exclusion of pain and need, but ‘includes’ pain and need as a necessary moment of itself. As Hägglund repeatedly stresses, our finitude as living beings—the necessary possibility of bodily breakdown, the task of maintaining ourselves in a relation to a world immediately indifferent to our needs—cannot be coherently conceived as a merely negative restriction, which we might hope to transcend in an eternal life. To transcend our finitude would be to ‘transcend’ life—that is, to no longer be living.

V. Infinity as spiritual life

Hegel claims in that ‘self-consciousness is the nearest example of the presence of infinity’ (SL: 127/21.145), and thus a more consummate expression of infinity than what he describes as the ‘infinite power’ of living beings as such.¹⁶ Hägglund also wants to distinguish between natural and spiritual life, while nonetheless grounding the latter in the former. For Hägglund, for living and rational beings, death not only constitutes the sense of their self-maintenance as living; it is also a necessary condition for the maintaining of any rationally articulable normative commitment. In line with this, a central claim of This Life is that the practical identities we sustain through the management of a suite of normative commitments and the self-maintenance of our bodily life are distinguishable but inseparable (Hägglund 2019a: 222).

We can demonstrate the Hegelian character of Hägglund's thinking here by considering the concepts of risk and sacrifice. As Hägglund puts it, the ‘motivational force’ of our commitments is traceable to the finitude and so ‘precariousness’ of those commitments and their objects: ‘There has to be a prospective risk of loss for anything to be at stake in sustaining a form of life’ (2019a: 50).¹⁷ That we can go further than merely risking and in fact sacrifice bodily life for our normative commitments indicates the distinguishability of our normatively constituted identity and our bodily life. However, the first moment of the Phenomenology's Lord and Bondsman dialectic—the famous ‘struggle to the death’—demonstrates that this distinguishability is only formal in so far as the spiritual life of our normative commitments is materially dependent on natural life. Those who would sacrifice their bodily life before abandoning their self-conception do not, as they might have supposed, realize that self-conception. The Phenomenology importantly puts this point in terms of the distinction between abstract and determinate negation: the combatant's ‘deed’—their bodily sacrifice in the name of a commitment to a conception of themselves as independent of others—‘is abstract negation, not the negation of consciousness, which sublates so that it preserves and maintains what has been sublated and which thereby survives its having become sublated’ (PhG: §188). Consciousness in sacrificing its ‘natural location’ in the living body simply comes to its end and does not sustain its identity in otherness. That is, it neither maintains its bodily life through and against its other (death), nor has its self-conception assessed and recognized by an other self-conscious agent (I say more about these two senses of ‘other’ below). Thus the articulation of a normative identity, while formally distinguishable from bodily self-maintenance, is nonetheless materially inseparable from it.

This Life initially develops this intimate relation between bodily vulnerability and rational agency in Heideggerian terms: the ‘horizon of my death’ or ‘anxiety before death’ is the non-psychological ‘condition of intelligibility’ for the activity of undertaking and revising commitments. I lead a life in so far as normative determinations—decisions about what I ought to do—matter to me, and they matter in so far as my time is finite (Hägglund 2019a: 201). This Life brings this Heideggerian line of thought into dialogue with Hegel by quoting from §32 of the Phenomenology's preface, which serves here to bring into focus the Hegelian infrastructure of Hägglund's model of rational agency:

the life of spirit is not a life that is fearing death and austerely saving itself from ruin; rather, it bears death calmly, and in death, it sustains itself […] spirit is this power only by looking the negative in the face and lingering […] with it. This lingering is the magical power that converts it into being.—This power is the same as what in the preceding was called the subject […] which does not have mediation external to itself but is itself this mediation. (PhG: §32)

Hegel here equates ‘death’ with the logically ‘negative’ and the ‘life of spirit’ with the logically ‘positive’. With this equivalence in view, the above passage maps directly onto the logical structure of the negation of the negation and the constitution of individuality (a ‘something’) in the Logic covered above. What converts spirit into ‘being’, what gives it a determinacy distinct from the indeterminacy of pure Being, is its relation to the negative. This relation to or mediation with what it is not cannot be understood to be ‘external’ to spirit but rather belongs to its self-description, ‘is itself this mediation’. Spirit ‘sustains itself’ in relation to death, just as living individuals in general maintain themselves in and against the threat of death. And true to the Logic's claim that the ‘something’ as negation of the negation constitutes the basic logical form of living and thinking individuality (‘a living thing, a thinking mind’), the above passage from the Phenomenology identifies spirit in its constitutive relation to death-as-negation with ‘the subject’.

Put in this way, however, the spiritual life of self-conscious creatures is conceived on the model of the natural life of the individual discussed in section IV above: self-conscious beings are confronted with a world set indifferently over against them in which they must determine their normative identity, an identity only intelligible against the backdrop of finitude. In other words, the relevant other for self-conscious beings on the account rehearsed above is death, just as it was for living beings in general. As such, Hägglund's account of spiritual life as I have reconstructed it to this point inadequately captures the distinguishability of natural and spiritual life, i.e., true infinity as it is expressed more fully and concretely by self-conscious creatures.

One obvious way of distinguishing life and self-conscious life is that, above and beyond self-maintenance in and against the threat of death, the latter implicitly or otherwise takes up other self-conscious beings as moments of their normative identity. Self-conscious living beings constitute their normative identity through mutually recognitive relations with other self-conscious, norm-bearing agents, and can come to understand that identity not as limited by the existence of other self-conscious beings, but come to self-consciously apprehend their identity as not only dependent on but indeed enriched by the other. In the paradigmatic example of love, the individual ‘continues’ into their other in so far as the individual is dependent for a moment of their normative identity on that other (being ‘a good partner’) and comes to see that other's identity as a moment of their own.¹⁸ While both natural and spiritual life are instances of true infinity, the latter is the ‘nearest example’ of true infinity because the structure of self-constitution through otherness is not, as it is for non-rational animals, implicit or ‘blind’, but is rather made explicit and self-consciously affirmed as normative for rational beings. In this way, the true infinity of spiritual life takes in the individuality of rational individuals developing unique practical identities, participating in it by undertaking and collectively revisable norms.

Now, none of this of itself constitutes a criticism of Hägglund. This Life draws on Brandom's and Pippin's respective accounts of mutually recognitive relations as constitutive of normativity, and Hägglund is at pains to point out that the mutually recognitive structure of spiritual life transforms our natural lives in so far as how we ought to meet the constitutive demand of self-maintenance is a question for us. But it is to say that there is a danger in beginning and ending one's account of rational agency from the individual confrontation with death, in so far as it threatens to over-emphasize the inseparability between natural and spiritual life, at the cost of their distinguishability.

Conclusion

We have seen that the logic of self-maintenance central to Hägglund's This Life is organized by the form of true infinity, even if that term is not itself explicitly deployed. Contra Derrida and the earlier Hägglund, true infinity is not an exception to finitude but is rather the logical form of self-relation within finitude, a form which Hegel takes to characterize living and self-conscious living beings. Indeed the critical movement of This Life as a whole—from religious faith to ‘secular faith’ as a self-conscious comprehension of the logic of self-maintenance—itself follows the movement from the bad infinite to true infinity, from abstract negation to the negation of the negation, from dualistic Understanding to dialectical Reason: religious faith places its hope in a beyond of the finite, but on closer inspection that faith presupposes ‘secular faith’ in living on in this life—just as the infinite beyond the finite proved on closer inspection to be a movement within the finite itself. In these interrelated ways, Hägglund's book serves to clarify the status and significance of true infinity in Hegel, at the same time bringing that concept to bear on social life in the present.

In the introduction I quoted Hegel: ‘at the mention of the infinite, spirit lights up’. But the quality of that light depends on the way in which the infinite is understood, that is, whether the infinite is conceived by the Understanding or by Reason. The Understanding might light up in hope as a flame does only to burn out in disappointment when the infinite it desired proves inaccessible to it. Or we might, as Rational beings, ‘light up’ in the sense of becoming enlightened: the form of true infinity clarifies what was always present but only dimly sensed in our living activity. Through the explication of that form, we come to consciousness of ourselves. As Hegel says, spirit lights up at the mention of infinity because in the ‘infinite the spirit is at home’—not because its home is somewhere beyond this finite life, but because the infinite is the form of life itself, and in thinking it we think what has always belonged most intimately to us. But of course, as we saw above in the reconstruction of the movement from abstract to determinate negation, the latter Rational conception must contain the Understanding's position: there is no light without heat, and the illumination cast by the true infinite as the form of the living must be maintained by philosophical work at its clarification.