The finite and the infinite are a single unity.Hegel, Science of Logic
How to begin discussing such a concept as the infinite from a philosophical viewpoint? The not-so-obvious answer is from the middle; that is, from a point where all points converge—the philosophical, historical, and cultural center. This is the locus and concept that philosophers as diverse as Kant, Hegel, and Schelling have encountered and thought of quite differently.
It is well known that in the mathematical field the infinite can be actual or potential. It is also well known that the infinite presents paradoxes not easily resolved. For instance, in the series of natural numbers 1, 2, 3, . . .n,… the whole is equivalent to the part. Even if one extracts all the even numbers (2, 4, 6, . . . 2n,…) resulting in a much smaller series the result is still infinite. Within the infinite there is no smaller or larger. But leaving aside mathematics and returning to philosophy we realize that the infinite is linked for more than one reason to the sublime. What, though, is their relationship? The sublime is usually considered as belonging to the realm of aesthetics, whereas the pedigree of the infinite goes back to the long tradition of the first philosophers, observers of nature, and founders of geometry.
A linguistic turn could be our first guide in this labyrinth, as it can help clarify the seemingly tenuous connection between the infinite and the sublime. I will stay within this tradition as it sheds light on both a philosophical and poetic worldview. It is, in fact, an approach that brings the infinite close to poetry. And I choose this approach not because it makes it easier to untangle the mathematical and logical paradoxes of the infinite but because the infinite marks the highest point of speculative thinking, just as the aesthetic category of the sublime is the highest peak that poetry can reach. Qua poetic, therefore, the infinite is admired, since it produces in us an awe that has no equivalent in beauty.
The infinite is given incompletely but it can also be considered a totality in its undetermined fullness. Similarly the sublime: The starry sky affords us the first glimpse of both the infinite and the sublime, which so resemble each other as to form one of the most captivating phenomena a human being can experience. The fullness of being, or pleroma—the true infinite—is so overpowering that it overshadows even language, while the sublime encompasses that other form of the infinite, language. Language develops into an infinite number of possible combinations, producing an overdetermination of analogies and of synonyms: The same word has multiple meanings, and different words can have similar or analogous meanings. Such is the case with “sky.” The sky we all see during the day and, in a very different guise, at night are semantically “two different things,” but both have mythical and poetical resonances. So much so that the sky, particularly the starry sky, has become a literary topos.
The infinite, poetically speaking, is sublimity and is so overwhelming that poets, like Giacomo Leopardi and Emily Dickinson, who venture into this topos ultimately recognize the vanity of any infinite search. Yet where opposites meet, where light and darkness meet in an explosion of meanings, the infinite gives no repose at the individual level. Only when speaking in the name of the universal does the infinite seem to overcome its paradoxical nature.
It is Hegel who theorized about the circularity of the infinite when he called “spurious” or “bad infinite” the mathematical infinite of natural numbers reiterating ad infinitum and never reaching the actual infinite, which springs from the totality of what is knowledgeable. The true infinite follows an analytic logic that reaches “in the end” the fullness of synthetic thinking. In his Science of Logic, specifically in the first part, the doctrine of “Being,” Hegel discusses infinity immediately after finitude. This indicates an important transition, since Hegel never abandoned his particular vision of the infinite that is imprinted in every determination of the logic and beyond.
Far from ignoring a conception of the infinite that passes from the finite to the infinite and from the infinite to the finite, Hegel reaches a point at which the finite is recognized as determinate being, as Dasein, a reality that perpetuates itself ad infinitum although it keeps the characteristic of what is limited. The finite is therefore contradictory, yet at the same time it is affirmative being whose other is the infinite; and the infinite is not “really free from limitation” in that it harbors within itself the finite.1 Hegel calls “spurious infinite” the infinite of the understanding, whereas to dialectical reason belongs the true infinite.
How then to interpret this duality, which is not dualism? To be noted first is the fact that in the finite are concentrated all the previous determinations discussed and developed in Hegel’s Logic, and that means the determinations of being and nothing, of becoming, of determinate being, something and other, and limit. All these transitions go from the affirmative to the negative via the negation of the previous determination. Thus the concept of being, with which Hegel begins his Science of Logic, is potential and actual at the same time, being the source of all that follows in the realm of thought.
Hegel’s definition of the true infinite is the following: “The infinite is determinate being reflected into itself.”2 The nothing of the finite vis-à-vis the infinite passes over to the infinite, while the infinite cannot separate itself from the “burden” of the finite, which, having no limit, paves the way to the infinite. The latter emerges without having to differentiate itself from the finite. In Hegel’s words “the infinite . . . emerges in the finite and the finite in the infinite.”3 Or, in other words, the finite is, as such, a limit that is not a limit. The infinite is the result of determinations that form a scattered totality. The finite is the other of the infinite, but the progress from one moment to the following one limits the progression toward the true infinite.
Hegel explains that “Both the infinite and the finite are negated in the infinite progress; both are transcended in the same manner.” However, limit “arises again”4 so that the reiteration of the same—that is, limit qua movement—is such that it sublates both the finite and the infinite; and the geometrical straight line, unending in both directions, becomes, with the true infinite, the circle. The circle, having no beginning and no end, is the being that returns to itself; but qua real it has a concrete content. The infinite “concentrates” within itself all the determinations of being. If it were only potential, it would be like the first determination of the logic; that is, a being of which not much can be said. It would also be nothing. As there is an infinite progression that does not coincide with the endless finitude of the spurious infinite, the return to itself of the true infinite sublates all the possible contradictions between finite and infinite. As Hegel writes: “The finite and the infinite are a single unity”5; that is, they cannot be separated.
It is interesting to note that Hegel, while discussing the quantitative idea of infinity introduces a remark on the sublime. He has, however, no laudatory comment on linking the idea of the sublime and the infinite. He speaks in this context of “the hollowness of this exaltation,” of “the shallow astonishment” typical of the sublime.6 This is because the sublime is not a rational state of mind, and it is noteworthy that the sublime, as Hegel discusses it in the lectures on aesthetics, is not mentioned as involving the infinite.
What can be conjectured from all this? The infinite is negativity, which is why it is only a moment in the development of thinking. But it is a moment that keeps reiterating itself until the circularity that was “present from the beginning” becomes explicit. In sum, the infinite encompasses both the finite and the infinite. The spurious infinite, without disappearing into nothingness, becomes part of the true infinite. Does this mean that the spurious infinite is to be considered only potentia and not actual? Yes and no. Hegel does not speak of potentiality as Schelling does. The spurious infinite for Hegel is not actual, yet it is part of the Absolute in that, through it, negativity and sublation are attained. “One more,” says the spurious infinite, but it will never reach the full meaning, which, as such, is other than itself.
Paradoxical as it may seem, the circularity of the true infinite is the result of the notion of limit. However, we are beyond representational thinking, and therefore the metaphor of the circle has to be taken with caution. Let’s think of the horizon. Where does it end?7 There is no simple answer to this question unless we think of something indeterminate and given only potentially. But Hegel philosophizes via a transcendental dialectic whereby the finite of the understanding and the infinity of reason are reconciled in the negation of the negation. The very first determination of the Science of Logic is already the infinite “in disguise.” As Enzo Melandri writes: “In Hegel, the actual infinite explodes into the finite thus destroying beings and multiplicity itself.”8
Breaking the Hegelian circle, one finds another mode of the infinite—the infinite that has within itself not only all the determinations of logical development but also, by extension, nature, life, and Geist. What William Desmond calls Hegel’s “infinitism”9 can be translated into a life form inclusive of the arts. Language, in particular, harbors within itself a potentially infinite combination of signifiers and meanings, so that it is a matter of discovering what mode of language is closer to the logic of the infinite. To say that poetic language is first pure syntax and also syntactical inversions makes [MTG: brings?] poetic language close to a dialectical mode of thinking.
In Schelling one finds a different conception of the infinite. Schelling begins with an indeterminate indifference that is absolute from the start. Whereas Hegel’s spurious infinite is nebulous, not so Schelling’s vision of an infinite Absolute, which is given potentially and which develops into a chain of dynamical potencies that become actual, thanks to intuition. In Bruce Matthews’ words: “The violent surplus of power released by the unconditioned being of the actual infinite characterizes the awe-inspiring force of nature.”10 Through intuition, the unconditional (the infinite) and the finite (the conditioned) become one. This explanation turns out to be ontologically productive. Schelling refutes Hegel by positing the two potencies of the real and the ideal, derived from the initial indifference that is, still undifferentiated, Absolute. In this way Schelling concretizes nature and the arts—literature and poetry belonging to the potency of the ideal. More specifically, sublime poesy is the “informing of the infinite into the finite,”11 whereas beauty is the informing of the finite into the infinite. From the Absolute, Schelling derives all the artistic forms that have the infinite within themselves, making them actual to the highest degree. The transition from the potential to the actual, which comes about because of the dynamic character of the potential, signals the “creation” of art and nature. We are, therefore, within the realm of an infinite reality.
What is the specific criticism that Schelling addresses to Hegel? Hegel’s infinite is abstract, pure thinking without ever coming close to the real. Unlike Hegel’s conceptual philosophy, which is ultimately subjective, Schelling’s beginning is a potentiality wherein—once it is actualized—life makes its appearance. Life is not, like Hegel’s, “a cold metaphor” of conceptual thinking where even nature is “artificially made objective.”12 Since for Hegel only the concept is real, actuality remains barren.
For Schelling, the Absolute—and therefore the infinite—is potential that exists so that nature is from the start real. On the contrary, Hegel’s Idea, which ends the Science of Logic, cannot progress, since it is limited by the Concept. For Hegel, nature “in general is . . . nothing but the agony of the concept.”13 Such strong language indicates that the two different conceptions of the Absolute lead to different consequences. For Schelling, Hegel remains prisoner of the concept; and the Idea, being complete in itself, does not allow any progression. Instead, for Schelling, nature exists. It is not something totally other as it is for Hegel. Nothing new is ever possible within Hegel’s system: his conception of the infinite is barren, since life does not emanate from logical categories. Hegel reduces even the infinity of nature to a lifeless concept.
In an early work, System of Transcendental Idealism (1800), Schelling speaks of two infinites deriving from activity: The first is the activity of the Self, generating a positive infinity; the second activity is that of a negative, limiting, infinite matter. If the positive infinite, that of the Self, does not encounter opposition it becomes “an infinite expansive force.”14 But the infinite is intuited and thus it must encounter limitation, yet it is productive intuition that makes us aware of the infinite in the finite. Schelling writes: “Imagination is . . . a wavering between finitude and infinity; or, what comes to the same, an activity mediating the theoretical and the practical.”15 It is a productive power torn between infinity and finitude whereby the ideal Self is open to infinity: “But [the Self] cannot make infinity an object to itself without delimiting it; conversely, infinity cannot be limited absolutely, but only for the purposes of action.”16 Freedom stems from the interaction between finitude and infinity, and it is in this capacity that the Self embraces imagination and, consequently, art. As opposed to Hegel, who thought of art as the most problematic and transitory form of Geist, Schelling embraces art as the organon of philosophy.
Symbolizing Hegel’s true infinite—that is, the circle of logical determinations—we become close to the sublime. But the sublime is not yet the true form. It is, in fact, measureless.17 Hegel does not mention the infinite in his two volumes of the Lectures on Aesthetics. Nevertheless, in art, determinations are expressive; that is, artistically beautiful or sublime.
Hegel’s conception of the infinite finds a confirmation in his systematic approach to philosophy. But within this approach art does not have a key role to play, since the infinite is the sum total of beings. Although imbued with negativity, it is inclusive of the sublime. One could even go so far as saying that the whole system of Hegel’s philosophy is sublime.
Looking at poetry, and specifically at lyric poetry, we discover in the works of Emily Dickinson a dialectic of finitude and infinite that takes the shape of life itself. In her case, life is not to be squandered in frivolous comportment. Life, although finite at the individual level, dwells in the infinite of possibility. Dickinson writes: “I dwell in Possibility — .”18 What is most interesting in the present context is the close link Dickinson establishes between silence and infinity in her poem, number 1251:19
Silence is all we dread.
There’s Ransom in a Voice –
But Silence is Infinity.
Himself have not a face.
Here infinity is not linked to life per se, rather it indicates the distance of the poet from the mundane word, and the distance is such that the faceless silence and infinity become one. Infinity, then, seems to transcend the human world … and humanity itself. However, in another of Dickinson’s poems, number 1695, we read:20
There is a solitude of space
A solitude of sea
A solitude of death, but these
Society will be
Compared with that profounder site
That polar privacy
A soul admitted to itself –
Given that infinity has so much reality, it is not surprising that it has been the object of scientific studies21 and a preferred topos for poets. Emily Dickinson has not been shy in evoking infinity, even though it is thought of as being limited by the finite. Dickinson’s poems, especially her late poems, dwell on the infinite and the finite, giving shape to finitude itself, which in turn is close to solitude and silence. The space of interiority is, naturally, what captivates the poet, especially a lyric poet like Dickinson, who absolutizes solitude and interiority. Silence encompasses the cosmos that has not lost the music of the spheres, but this music is non human and cannot be heard by humans—it dwells in the language of the poet who makes it resonant in the unity of the infinite and the finite.
What are we to make of Dickinson’s juxtaposition of eternity and finitude? In its most revealing moments her poetry touches almost palpably the way she sees life—not as mundane but rather as encompassing the divine and the human. The poem, number 1695, that begins “There is a solitude of space,” evokes the finite and infinity in the last line. Space belongs to a solitary, empty, and yet meaningful universe. Even if, on the contrary, space were not empty, this view would not contradict Dickinson’s grand images. Life appears like a soul that confers movement to the poet’s inner state. Caught between inner and outer, whose intermingling determines the movement not only of the soul but also of the cosmos, the word emerges, silent as sublimity itself demands. The poet appropriates both solitude and infinity in a dialectic that has nothing static since it derives from language itself, the world, the words. Now the question raised is whether this is a weak dialectic, by which is meant a dialectic that rests neither on life nor on an inner sentiment. Or alternatively: is it a compelling dialectic resting on the will of the poet, who knows how to transfigure both the inner and the outer, space and time, finitude and infinity? It is certainly a dialectic that responds to the demands of a language that is in itself lively, animated, destined to endure. In her poem, number 765, Dickinson addresses the most philosophical of themes:22
You constituted Time –
I deemed Eternity
A Revelation of Yourself –
’Twas therefore Deity
The Absolute – removed
The Relative away –
That I unto Himself adjust
My slow idolatry –
Here Dickinson while using philosophical language seems to disparage it. She denies the eternity and the infinite of which she speaks. In her words is born a vision that negates both the Absolute and the Relative. What is thus emphasized is the contrast between finite and infinite by means of a language that is both somber and witty. This is how she approaches philosophical themes—in a way that Schelling would have admired for its depth.
The Absolute and the Relative of Dickinson’s poem 765 have no ontological permanence; what remains is her “slow idolatry” that touches every chord of her being. If Eternity is deemed and Time is thought of as being other, then the Absolute and the Relative disappear into a finitude that denies every permanent infinity. However, thinking and poetizing is actualized thanks to the potential infinity of a language that takes into itself the infinity of the sky, of the heavens, of a universe that becomes one with the spoken and written word, even though in poetry the infinite does not recede, nor can it be internalized. It is, rather, an object of awe.
The philosophers of the infinite, Hegel and Schelling, admired lyric poetry, considering it a subjective self-expression of feelings. For Schelling, poetry is an end in itself, whose life is intrinsic to our being since it speaks of an inescapable and dynamic view of the universe. The result of an absolute act of knowledge, poesy has a cognitive value. Moreover, Schelling sees in lyric art the “inner limitlessness of poesy.”23 According to him, in creating and connecting together the ideal potency and the infinite one reaches the essence of lyric poetry. He writes: “The essential nature of all lyric poesy is the portrayal of the infinite within the finite . . . contrast between the infinite and the finite thereby emerges as a kind of inner principle of life and movement.”24
Subjectivity prevails in lyric poetry, but it is a subjectivity that finds itself face to face with the infinite. Dickinson is a poet who is not shy about exploring the limitedness and infinity of nature. Her determination as a poet situates her among the rare poets who contend with eternity and the infinite by assigning to them an unforgettable space and dimension. Dickinson’s language knows what is higher and radiant, and what is impermeable to baseness. In her poem 370 we read:25
Heaven is so far of the Mind
That were the Mind dissolved –
The Site – of it –by Architect
Could not again be proved –
’Tis vast – as our Capacity –
As Fair – as our idea –
To him of adequate desire
No further ’tis, than Here –
Such poetry goes beyond the intimate, inner feelings of the individual poet to become a celebration of the infinite from which human existence achieves its own artistic and living momentum.
- Hegel’s Science of Logic, trans. A.V. Miller (London, New York: Humanities Press), p.137.
- Ibid., p. 138.
- Ibid., p.141.
- Ibid., p. 146.
- Ibid., p. 151.
- Ibid., pp. 229-230.
- Enzo Melandri, “I paradossi dell’infinito nell’orizzonte fenomenologico,” Omaggio a Husserl (Milan: Il Saggiatore, 1959), p. 83.
- Ibid. p. 85.
- William Desmond, “Between Finitude and Infinity,” in Hegel and the Infinite ed. by Slavoj Zizek, Clayton Crockett, Creston Davis (New York: Columbia University Press, 2011), pp. 115-140.
- Bruce Matthews, Schelling’s Organic Form of Philosophy-Life as the Schema of Freedom (Albany: State University of New York, 2011), p. 147 and p. 149.
- F.W.J. Schelling, The Philosophy of Art, trans. Douglas W. Stott (Minneapolis: University of Minnesota Press, 1989), p. 85.
- Schelling, On the History of Modern Philosophy, trans. Andrew Bowie, New York, Cambridge University Press, 1994), p. 143 and p. 145.
- Ibid. p 153.
- Schelling, System of Transcendental Idealism (1800), trans. Peter Heath (Charlottesville: University Press of Virginia, 1981), pp. 80-83.
- Ibid p. 176.
- Ibid p. 177.
- Hegel, Aesthetics-Lectures ob Fine Art, trans. T.M.Knox (Oxford at the Clarendon Press. 1975), vol. I, p. 303.
- Emily Dickinson, The Complete Poems, edit. Thomas H. Johnson (New York: Back Bay Books, Little, Brown, 1976), poem 657, p. 327.
- Ibid., poem 1251, p. 548.
- Ibid., poem 1695, p. 691.
- Michael Heller and W. Hugh Woodin, eds. Infinity-New Research Frontiers (Cambridge, New York: Cambridge University Press, 2011).
- Dickinson, poem 765, p. 374.
- Schelling, The Philosophy of Art, p. 203.
- Ibid., p. 208.
- Dickinson, poem 370, p. 176.
Apeiron Centre, 2012