Hegel on Infinity

8/1/2019 Hegel on Infinity

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HEGEL ON INFINITYQUENTIN LAUER

THERE IS SCARCELY ATERM IN HEGEL'S PHILOSOPHICAL ("speculative") vocabulary that he repeats with more bewildering frequency than the term "infinite"(unendlich) , usually, of course, accompanied by its opposite and correlativeterm, "finite" (endlich)-indicating at the very least that, if we are to understand either of these terms, as Hegel employs them, we must see them asmutually defining, implying, explicating each other. Since, in a paper of severelylimited scope, it would be clearly, if not impossible, at least counterproductiveto try to treat all the ways in which Hegel employs the term "infinite" (withits cognates), we can justifiably set limits to our consideration by approachingthe teml from the point of view of its at least initially religious use. In religiouslanguage-and here, for Hegel, the paradigm is Christian religious language(Christianity is "absolute religion")-there is only one infinite, and that is God,whether he be designated as "The Absolute," "absolute Spirit," "infiniteBeing," or "infinite Love, Truth, Goodness." All else is "finite," i.e., whatever can be multiplied, be they things, souls, spirits, thoughts-or the universe,as the sum-total of tinite reality-no conceivable accumulation of finite realitycould add up to infinite reality. That Christian religious language does speakthis way there can be no doubt; the problem for Hegel-and it occupied himfrom the beginning to the end of his career-was that of making rational senseout of what religious language proclaimed so glibly. One might, of course,claim, with both the philosophers and the religionists of his day, that we mustrest content with not making "rational" sense of such language; but Hegel willhave none of that. I f believing is not to be an offense to human dignity, wemust know what we are believing.

In Hegel's view this refusal to make rational sense of the Infinite, who isGod, although it could look like cognitive humility, is in reality a far cry fromhumility; it is the existential refusal to submit to the Infinite, the refusal torelinquish one's own finite particularity; it is the arbitrary decision to set upfinitude as the standard of human endeavor. It is as though one were to say,"M y heart, my emotions, my religious intuition can affirm an unintelligibleinfinite, but my mind knows that it can affirm only finite reality." This kind of"humility" Hegel can do without: "True humility, on the contrary, renounces

THOUGHT Vol. 56 No. 222 (September 1981)


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288 THOUGHTitself, renounces its claims as this particular to be the affirmative and recognizesonly the true, the Absolute, as the affirmative" (WA PR I, 182).1 The decisionto insist on the absoluteness of one's finitude is a strange humility indeed--tosay that ultimate truth cannot be known is equivalent to saying that ultimatelytruth cannot be known-"some, then, also ask whether the truth can be known,in order to justify their persistence in the pettiness of their finite aims. Humilityof this sort accomplishes little" (WA E 19, Zusatz 1).

There would seem to be in this sort of "humility" a kind of fear that byallowing infinite Spirit to be known by finite mind the Infinite thus becomesfinitized-not unlike the contention that to speak of God as related to finitespirit is to degrade God. Difficult as it may be to comprehend on the level ofreflective understanding, what Hegel consistently says is that, although the relation of finite to finite is itself part and parcel of the limitation of what is finite,the relation of finite to infinite is not of itself a limiting relationship. By thesame token, a relationship of infinite to finite is not a limiting relationship,precisely because the very reality of the finite is relation of the infinite to itself.The distinction of finite from infinite is a distinction which is no distinction,because as source of all distinctions the infinite is identical with itself in alldistinctions.

Infinity is identical with itself, because its distinctions are tautological; they are distinctions which are no distinctions. This self-identical being, therefore, is related onlyto itself; to itself, which is thus an other to which the relation is directed, and lherelationship to itself is rather duplication; in other words, precisely that self-identity isinternal distinction. What have been doubled are thus in and for themselves, each anopposite of another. In this way, to say the one is at the same time to say the other. Toput it another way, it is not a question of the opposite of another, rather only the pureopposite, and thus the one is in itself its own opposite (WA PG, 125).Such language, quite obviously, is completely unintelligible on the level of mere"understanding," all of whose forms are simply finite; what is only the objectof finite reflective thought is in fact finite (W A GP 49).2

As mentioned above, to speak in this way of finitude and infinity is to spelkthe language of religious consciousness, for which God is the unique" Infinite,"but it is also to try to make this language intelligible to "speculative thought"What Hegel is doing is taking seriously talk about God as unique, uncreated,eternal Creator, absolute Being, infinite Spirit, a subject of whom predicatessuch as "omnipotent," "omniscient," "omnipresent," "all good," "all loving" etc., can be said. At the same time, he is convinced that none of this canbe said in a way that is other than nonsensical, unless placed squarely in acontext of human knowing, which alone can make sense out of any language.This is not to say that the language of religion, of faith, of devotion, is non-

'At the risk of incurring the scorn of the erudite I shall refer to the Lectures on the Philosophyoj Religion, Lectures on the History oj Philosophy, and Lectures on the Philosophy oj History. inthe Suhrkamp edition (which corresponds to SW).

2The reference is to Einleitung in die Geschichte der Philosophie (Hamburg: Meiner, 1959).


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INFINITY 289sensical; it is to say that it is not faith by itself which can make sense of thislanguage, only faith informed by rational thinking. For Hegel, the very "concept" of the human is that it must be characterized by thought. Human beings,to be sure, do many things which are not characterized by thought, but it isprecisely these things which do not constitute the uniquely human in man. I f itcan be said, and it would seem that it must be, that science, morality, law,politics, art, religion, philosophy, are uniquely human accomplishments, thenthey are so only because all are characterized by thinking; take away the thinkingand they are empty, "sounding brass and tinkling cymbals." But a thinkingwhich is not a knowing-or, at least, oriented to knowing--is itself not athinking in any intelligible sense of the term.

If , then, we are to understand what Hegel means by saying that a humanthinking which stops short of the infinite and turns that over to "faith" or"intuition" is not really thinking at all, or that a human knowing which stopsshort of knowing God who is infinite is not really knowing at all, how are weto proceed? A necessary presupposition of any procedure, I think, is the rec-ognition that, for Hegel, the essential focus of all philosophical investigation ishuman thinking, both as that which essentially characterizes the human and asthat which delivers all that is susceptible of philosophical investigation.

SPIRIT ESSENTIALLY INFINITE

Here a caution is in order. There is a persistent temptation to see in the qualityof infinity, as applied to the human, either (a) the human infinitely multiplied(through time and space) which would, so to speak, exhaust and therefore "infinitize" the possibilities of the human, or (b) the human ideally expanded toinfinity, ala Feuerbach, such that the "universal" human spilit would constitutethe only "infinite" which can make sense. The first of these is too obviouslynonsensical to need comment: numerical infinity simply cannot be concretized,least of all in its application to concrete humanity; the number of humans whohave existed in this world is clearly finite, and multiplication through futuretime will not make that number infinite. The second kind of infinity simply fliesin the face of all that Hegel has said, both in terms of God as the paradigm ofinfinity, and of the individual human person as in some intelligible way "infi-nite" -because continuous with the essential infinity of spirit. We have but toconsult the Phiinomenoiogie des Geistes, the Vorlesungen iiber die Philosophieder Geschichte, the Vorlesungen iiber die Geschichte der Philosophie, the"Philosophy of Objective Spirit" in the Enzyklopiidie, the Grundlinien derPhiiosophie des Rechts-all are replete with statements regarding the infinity ofthe individual human person. We must concretely come to grips with a conceptof infinity which is paradigmatic ally said of God but also said authentically ofthe individual human subject, spirit, person, thought, will, rights, value, etc.

Here again we run into a difficulty created by the limitations of space: ideally,a study such as this should be genetic, tracing the development of Hegel's


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290 THOUGHTthought on "The Infinite" from his earliest published writings down throughthe third edition of the Encyclopedia of the Philosophical Sciences, but thatquite clearly would be to present Hegel's entire "system." Even to analyzeadequately the three most pertinent texts on "infinity" (WA L I, 125--46; PR,II, 205-13; E, 564-77) would require more space than is available. We shallhave to rest content, then, with a more selective approach: focusing on therelationship of human knowing (as spiritual activity) to infinite Being (absolutespiritual activity) as the absolutely necessary condition for the very possibilityof human knowing, of human spiritual activity.

According to Hegel, then, one can say that, logically speaking, knowledgeof infinite being is prior to knowledge of finite beings-the former a logical precondition, so to speak, for the latter. Epistemologically speaking, on the otherhand, we must say that human knowing, finite as it is, must first come to gripswith the finite reality in which it is immersed, finding in the process that itsknowing is inadequate even to its finite object if it does not pass beyond (riseabove) the finite to the infinite pre-condition of both the being and the knowingof the finite. This is but another way of saying that, logically speaking, the velryconcept of being, with which thinking must begin, makes sense only if beingis infinite. What the system, taking its cue from logic, makes clear is that theonly conceivable concretely infinite being must be spirit. It is the Phenomen-ology of Spirit which attempts to make clear both that this is true and what itmeans for spirit to be infinite. The system in its totality, then, emerges out ofthe Logic and the Phenomenology operating, so to speak, in tandem. One mightsay, of course, as more than one contemporary author has tried to say (Kojeve,Findlay, Kaufmann, Schacht), that Hegel's "infinite being," "infinite spirit"need not be God--of course leaving it very unclear just what else it could be-but it is to be feared that one can do this only by making Hegel speak nonSenSI;!,a rather risky tactic. Why not take what Hegel says at face value? It is difficultto see how one can read Hegel's Science of Logic and not recognize that itsoverriding theme is that to know being at all is to know being as infinite (W AL, I, 31, 144; II, 159-60,441). It is equally difficult to see how one can say,without talking nonsense, that in affirming the infinity of being Hegel is notaffirming the being of God. Just what would an "infinite being" (Spirit) bewhich is not God? By the same token what would a "God" who is not infinitebeing (Spirit) be?

One might also want to say, very piously I am sure, that Hegel thinks heknows too much-not that the infinite Spirit of which he speaks is not God, butthat to claim to know the infinite Spirit who is God is to claim too much. Thisis tantamount to saying that the God whom faith acknowledges cannot beknown-a position that Hegel was clearly fighting. The difficulty here, it wouldseem, is that the disavowal of knowing God demands a context in which wespeak of the God we do not know. Might it not be better not to speak at all, ifwe know not that whereof we speak? Perhaps, with Kierkegaal'd we should notspeak of God at all, only speak to him. A tenable position, perhaps, but onewhich requires that we also do not speak of not knowing God. Faith may tell


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INFINITY 291us that God, infinite Spirit, is, but has faith told us anything, if we do not knowwhat it has told us? Are we to say that, philosophically speaking at least, theterms "God," "infinite being" (Spirit), are empty of meaning, or given ameaning by faith, which meaning is impervious to reason? Would that be"meaning" at all? What Hegel seems to be saying is that the term "infinite"has a meaning we cannot do without, that its meaning is discoverable by humanreason (indeed that reason will fail to be reasonable if it does not), and that theintelligibility of the term "infinite" is not confined to its application to theinfinite being who is God-although a failure to see God as the paradigm of alltalk of the' infinite" is to empty all such talk of meaning. If nothing else, Hegelshould shake those who think they know what they are saying when they say"infinite"-and shake even more those who think that the only paradigm fortalk of the infinite is the mathematical infinite. Our question, then, will bewhether Hegel successfully articulates a meaning of "infinite being," such thatit is both precise and detem1inate enough to be justifiably called knowledge, andnot simply feeling, aspiration, or religious conviction. In attempting to answerthis question we must first examine the manner in which he employs the tem1"infinite" as part of his philosophical (speculative) vocabulary. We must remember, too, that what Hegel does say can be understood only against thebackdrop of those contemporary opinions according to which the infinite couldbe the object only of faith, not of knowledge (Kant, Jacobi, Fichte)-withoutever explaining how even faith as human activity, could be capax infiniti-orof those according to which the infinite could indeed be known, but only immediately in intuition, not through a process of mediated rational thought(Schelling and the Romantics).What, then. does the term "infinite" mean for Hegel? I f the purport of thisquestion were taken to be "how does Hegel define the tem1 infinite," the question would, quite obviously, be self-defeating; the answer to it would necessarilybe a contradiction-to de-fine a term is to set identifiable limits to its meaning,so that language can legitimately perform its function of clarifying discourse.To define a term in a language is to express its meaning more clearly andprecisely in that same language and thus to set up boundaries beyond which thatmeaning does not go and within which that meaning is always the same. Thisis not to say, however, that the intelligibility of meaning need be confined todefinition. Plato taught us that lesson long ago: his Socrates was ever in searchof definitions which he never found, and yet he was ever shedding new andexpanding light on meanings. Plato it is who shows us that the intelligibility offorms cannot be confined to definitions and that the inexhaustibility (read: "infinity") of the forms of truth, beauty, goodness in no way militates against theirintelligibility.3 Nor is the inexhaustibility of intelligibility to be equated with the

3Perhaps what needs to be said here is that "defining" can be of two kinds: (a) putting limitationon a meaning in order to handle it conveniently; (b) permitting an object to define itself, and thisis the unfolding of its concept.


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292 THOUGHT"and-so-on" of endless repetition of the same--even though, as Hegel recognized so well, the intelligibility of this sort of mathematical infinity gives a hintof the intelligibility of a much more significant infinity (see W A E, 104, Zusatz2).

INFINITE BEING

The key text which will permit us at least to begin to understand Hegel'sconcern with infinity comes rather early in the first book (' 'The Doctrine ofBeing") in The Science of Logic. Hegel has already told us that the sciencewhich seeks to think thought-and all its implications-"must" begin with themost general and most unified object of thought, i.e., Being. This is but a wayof saying that to think at all is to say mentally of thought's object that it is,which is, quite obviously to say little or nothing. Only when thought saysdeterminate being does it say anything, but to say determinate being is to saydetermination as distinguishing. Thought is faced, however abstractly, with onebeing distinguished from another. With this introduction of otherness the seamless robe of unified being seems to have been rent; multiplicity has been insertedinto the very heart of unity; universality has surrendered to particularity-thatwhich is other is "something" other, and that which is something other bothlimits and is limited by its other. (See WA E 92)

Hegel's concern, then, becomes threefold: (1) can thought restore the i m p ( ~ r -iled unity of being; (2) can thought do this short of thinking a concretely infinitebeing which would embrace the totality of being; (3) can thought think infinitebeing, if thought itself is not in some sense infinite? In attempting to come togrips with Hegel's answers to these questions, we must bear in mind thatthroughout The Science of Logic Hegel is engaging in a not-too-thinly-veiledpolemic against all those who contended that human reason is essentially finiteand only finite; for him, to say that being makes sense only if there is infinitebeing involves saying that rational thought makes sense only if rational thoughtis infinite. What can it mean, then, to say that rational thought is infinite? Whatit cannot mean, in a purely negative way, is that human rational thinking is notthe activity of a finite being nor that it is simply not finite activity. There Clmbe no question that Hegel regards the human mind (spirit) as finite. This dOI!snot mean, however, that rational thought is essentially finite, nor that humanrational thinking is discontinuous with infinite rational thought. It means, rather,that human thinking, precisely as rational, is conceivable only as continuollswith infinite thought (see WA E 24). Thus, in saying that "reason observing"is seeking in what it observes "its own infinity" (WA PG 183). Hegel is quiteconsistently saying that only in infinity, where its "truth" is to be found, isrational thinking adequately rational (ibid., p. 184). By the same token, if Kantis right, and the content of rational thinking is to be found only in sensoryexperience, then rational thinking is not capable of coming to grips with theinfinite. "It is unquestionably correct to say that the infinite is not given in the


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INFINITY 293world, in sense-perception. . . . Spirit is for spirit alone" (W A GP, III, pp.352-53).

As Hegel approaches the task he has set himself he reminds one of the polevaulter distancing himself from the bar he is to clear in order to muster up forceand momentum and to plan carefully the sequence of steps which will take himto the bar-and over it. One could suppose, of course, that it is relatively simpleto say what one means by infinite; it is the opposite, the negative, of finite.What is limited is finite; what is unlimited is infinite. Such simplicity, however,labors under a number of difficulties. (1) It assumes that it is sufficient to lookfor a meaning without any concern as to whether what is meant is, to say whatthe infinite would be if it were. Heger s concern is to show that the infinite is,that apart from infinity there is no way to make sense of finitude. (2) The simplesolution presupposed too, that the intelligibility of the finite is primary and that,therefore, whatever intelligibility is to be found in the infinite is derived fromthat of which it is the negation. For Hegel it is the essential negativity of thefinite which makes it necessary to assert that the supremely affirn1ative is theinfinite. " I f in addition we say that the infinite is the not-finite, we have in factspoken quite truly, for, since the finite is itself the first negative, the not-finiteis the negative of the negation; it is the self-identical negative and thus at thesame time affirmation" (WA E 94, Zusatz). That, precisely, is finite which doesnot contain within itself all that it is to be what it is. (3) It presupposes, further,that the infinite differs from the finite in exactly the same way as one finiteentity differs from another or, worse still, as one thing differs from anotherthing; one is simply not the other. (4) Finally, the simple solution is based onthe assumption that finitude and detern1inacy are synonymous, with the resultthat infinity becomes synonymous with indeterminacy, indefiniteness, emptiness. For Hegel, on the contrary, it is the infinite which is supremely determinate, because it contains within itself all its own determinations; it is not determinate merely by its relation to others which thus limit it.

I f this is what Hegel means by infinity, then there should be no doubt inanyone's mind that the paradigm of infinity for him should be God, the Absolute,absolute Spirit, the absolute totality of reality, the lnbegriff aller Realitiiten.That God is the paradigm of infinity, however, does not mean that every timeHegel employs the terms infinity, the infinite, or simply infinite, as an adjective,he is referring--directly at least-to God. He also, for example, speaks of theworld, the soul, the concept, thought, freedom, the value of the human individual as "infinite." It is nevertheless necessary to say that the true concept ofunqualifiedly infinite is realized in God alone and, thus, that other uses of theterm are derivative. Wherever, then, reality can be said to be infinite (or infinitysaid to be real), it will be (a) determinate, not an undifferentiated abstraction,(b) self-determining, not needing what is other than itself for its determination.which would be limitation, (c) having predicates which, although in a finitemode they might be contradictory, do not contradict or limit each other and yetare not simply indifferent to each other, and (d) self-contained, complete initself.


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294 THOUGHTWhether or not one likes the language Hegel speaks, there can be no question

that the overriding theme of his Science ofLogic is that to know being at all isto know being as infinite (as we have already seen). This, however, can makesense for Hegel only if to know being as infinite is to know what it is for beingto be infinite, and short of knowing God as he is (the paradigm of concrete,determinate infinity) knowing being as infinite does not make sense. This, intum, is but another way of saying that to know being as finite without knowingbeing as infinite is not even to know being as finite-"finite being" withoutreference to "infinite being" is a meaningless formula (" finite" and "infinite"are, as we have seen, mutually implicative-but only infinite is explicative offinite (see WA L, I, 41,80, 109,117,126, 128, 143, 145; E 36,112).

The difficulty that we all experience in coming to grips with (begreifen)infinity in our thinking, according to Hegel, is that we have the seeminglyinescapable tendency (Kant would call it essential to human thinking) to coupleconceptual thought with sensible or imaginative representations, while it is thevery nature of the infinite that it cannot be represented, either sensibly or im-aginatively; it is the object of thought alone, or it is no object at all.

We might put it this way. It could scarcely occur to anyone that what isinfinite-if there be such-could possibly be the object of the senses or ofimagination. There is simply no way that the senses or imagination could rep-resent infinity. Nor could the understanding (Verstand), if its task is to representabstractly what the senses or imagination have presented sensibly or imagina-tively, represent infinity-the mathematical infinite is its last ditch attempt todo this. Infinity, then, can be the object of thought and thought alone-as Hegelputs it, of pure rational thought (Vernunjt). The question then arises, whetherthe converse of this will not also be true: that, whatever is the object of thoughtonly and in no way of the senses and imagination, e.g., unity, universality (tbeunity of multiplicity), value, truth, beauty, goodness, etc., in short, the idealas such, is infinite in some intelligible sense of that term. At the very least itshould be said that such objects of thought are not finite in the way objects ofsense and imagination are. I f this is true, however, then infinity is inseparablefrom ideality-' 'ideality is the quality of infinity"- the infinite is ideal; no::,however, in the s e ~ s e that it is not real but rather in the sense that the ideal isthe truly real (TO OVTW


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INFINITY 295sense (logically, ontologically?) antecedent to its finite exemplifications in isolated individuals, such that the concept of the human serves as the criterion forthe reality of the humanity of each individual, then as the foundation of thereality of the humanity in each isolated individual, the inexhaustible, infinite,concept has to bespeak more reality than the particular exemplifications it unitesin a totality which only mind can grasp. The universal "man" is the concrete,determinate totality of the human. When the manufacturers of Coca-Cola, forquite unphilosophical reasons, to be sure, insist that "Coke is the real thing,"they are not saying that each individual bottle of Coca-Cola is more real than"coke." They are saying that there is a very real concept of "real thing,"against which the reality of the individual drink can be evaluated. The illustrationis trivial, but it points up an important fact of life; we simply do not look to thefinite individual human being for the total reality of what it is to be truly human-or else, what is striving all about. "Be an authentic human being" means"strive to embody in yourself what it is to be really, truly human." The modelof the "really, truly human" is to be found in the inexhaustible concept of thehuman-or, perhaps, in the "true idea of humanity," a goal. not afac! (Objektvs. Gegenstand).

INFINITY AND CONCEPT

It is thus that we can begin to understand how the finite particular, the objectof particular experience, is real only as the realization of the infinite realitywhich is its concept. We can also begin to understand how the infinite universalconcept is but an empty abstraction apart from its realization in finite particulars.Of course, the universal is the object of thought alone, not of sensation orimagination, but it is also the product of thought alone; it is not produced inthought by something other than thought. This is not to say that thought cansimply dispense with sense or imagination; it is to say that in the activity ofthinking, of bringing forth (conceiving) its object it is self-contained, gives itselfa content, does not receive it from what is other than thought. None of this, ofcourse, would make sense, if thought were no more than the finite activity ofparticular finite minds--or even or the accumulated totality of all finite mindsif one could make sense of the latter at all! "All" and "every" are not synonymous; "all" bespeaks essence and, therefore, infinity; "every" bespeaksaccumulation and, therefore, finitude. Nevertheless, it is still true to say thatfinitude is intelligible only in relation to infinity, and infinity is intelligible onlyin relation to finitude; each contains the other in its concept, i.e., each is amovement toward, a passing over into the other. Thus, infinity must be somehowsaid of the finite (only if the finite is idealized, i.e. infinitized, is anything beingsaid), and finitude must be said of the infinite (only if the infinite expressesitself finitely is it actual), if either is to be intelligible.

To ordinary thinking it can well seem patently contradictory and, therefore,absurd to speak of an infinite which is also finite or a finite which is also infinite;


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296 THOUGHTthe terms (concepts) are mutually exclusive-what is infinite is not-finite, andwhat is finite is not infinite, and that is all there is to it. And so it is, Hegelassures us, for a thinking which fragments the universe of reality and is, thus,constrained by mathematical or formal-logical rules. Such a thinking is abstract,compelled to "represent" a reality presumably over-against itself by Vorstel-lungen which it constructs, keeping its distance from a reality which is notpresent in it but only represented by it. This, Hegel goes on to say, is not athinking which comes to grips with (begreift) reality, precisely because it leavesreality "out there," never bridging the gap between thinking and the realitythought-the "thing-in-itself" mentality--contracting thought by abstractlyfragmenting reality, thus enabling it to manipulate reality, perhaps even satisfactorily, but comprehending reality only partially because statically. Beyondthis, Hegel tells us, there is a thinking which expands in Begriffe, seeking 10reproduce in itself the conceptual movement of dynamic reality, recognizing inthis very reality a thought which is its source, not its outcome.If, then, we look in another way at the thought which Hegel describes,

wherein finitude and infinity arc inseparably linked conceptually (see WA E 60),we may find that the contradiction which "ordinary thinking" shies away fromresolves itself (i.e., its resolution is not due to the efforts of abstract thinking'l.Just what meaning could we assign to (find in) an infinite reality which wouldbe so cut off from finite reality, so opposed to it, that the very reality of thefinite would be inimical to it? By the same token, what could it mean to speakof a finite reality whose only claim to reality would be its not being infinite (onthe assumption, of course, that finite is eo ipso more determinate than is infinite)? Either each would exclude the very possibility of the other, or each wouldbe limited in its reality by the reality of the other which it itself is not; the realityof the infinite would conflict with the reality of the finite, and the reality of th,;:finite would conflict with the reality of the infinite. "All well and good," onemight say, "let us drop the terminology altogether"-other than in mathematicalabstraction, "finite" and "infinite" are empty terms which lead only to confusion of thought. Still, dropping terminology will not make the problem disappear: unity and diversity are going to remain with us, whether we talk aboutthem or not or, no matter what terminology we employ in talking about them.The unity which the mind cannot but find in reality (totality) hespeaks infinity(the self-containedness of totality); the diversity of reality (plurality) which themind cannot think away bespeaks finitude, Neither militates against the other,but only the decision to throw up our hands in the presence of reality can promptus to ignore the problem of concretely reconciling diversity and unity, finitudeand infinity. What Hegel is trying to show, then, is not merely that they do notmilitate against each other but that neither is conceivable without the other.What further needs to be shown, perhaps, is that it is not nonsensical to speakof unity in terms of infinity and of diversity in terms of finitude.

Here it is, then, that we can, in one sense, see all of this as an attempt toclarify language about infinity by reference to an infinite which is not God-e.g., thought (concept, idea), truth, value, spirit. freedom, the universe-the


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INFINITY 297elaboration of which will enable us better to understand the concept of infinityin a thinking which has God (Der Inbegriff alter Realitdten) as its object. Byspeaking of a qualified infinite which is nevertheless intelligible precisely asinfinite, we can move on to the intelligibility of an unqualified infinite whichexhausts the very concept of infinity, seeing in God the very foundation for thepossibility of unifying the totality of reality in conceptual thinking--provided,of course, one does not prefer to remain on the fringe of reality, seeing only achaotic manifold, upon which a finite thinking is satisfied to impose order, sincethat works-up to a point.

In another sense, however, we might approach Hegel's endeavor from anotherpoint of view, seeing it as an attempt to move in the other direction a l sosomehow Hegel's thought always does-beginning with God as the paradigmof infinite reality and, thus, making it possible to understand Hegel when hespeaks of an intelligible infinity which, although not unqualified, characterizesreality in the order of idea, where it is most authentically present to mind. If itcan be said that it is impossible to make sense of the concept of being (foundational for all logical thinking), unless being ultimately reveals itself as bothinfinite and determinate (the task of logic, as Hegel sees it), then it is only inrecognizing that any idea, precisely qua idea, is infinite-reality must reveal itscharacteristic infinity-that we can come to terms with it in its truth, which,Hegel tells us, is the goal and purpose of logic (see WA E 213, 214).

I f we are to understand what Hegel is saying when he speaks of " infinity,"of the close link he sees between the infinity of God, the unique concretelyinfinite Being, and the infinity characteristic of the ideal order which unifies thediversity of the finite, the time has come to examine what he has to say offinitude, of the negativity which is inseparable from the finite, which negativitythe infinite negates in affirming its own reality, affirming its own determinacyin negating the unsatisfactory detemlinacy of the finite (see W A L, I, p. 143).Actually, however, Hegel has little to say about the finite by itself, preciselybecause, as he sees it, there is little to say of the finite by itse(f, since by itselfit is nothing; its reality is its relation to thought, to the infinity of idea: "theproposition which states that the finite is ideal (ideel!) constitutes idealism. Theidealism of philosophy consists in nothing else but the recognition that the finiteis not a true being" (W A L, I, 145). More than that. reality without ideality isnot truly real, because it is merely finite (ibid., 146). He goes so far as to saythat both "finite being" and "finite thinking" are of themselves contradictoryand that their contradictoriness can be both recognized and resolved only in"infinite thought" (WA BZ, 408-09; see ibid., 79-80). This is not to say thatfinitude is not significant, but that what can be said of it is significant only aspointing to infinity; merely finite being can neither be nor be thought (see W AE 92, Zusatz).

To further understand what has just been said we must grasp the close parallelwhich Hegel draws between finitude-which characterizes "things" (Etwas)and "immediacy"-which characterizes the given (to sense or imagination)independently of the mediation of thought. If Hegel says, then, that the "im-


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298 THOUGHTmediate" is not true, because the mediation of thought is absent from it, he isbut saying the same in asserting that the "finite" is not true, because its reality(Dasein) is that which characterizes "things" (Etwas) without reference tothought in the fullest sense. The mind can give no account (logic) of "things,"only of thought conceptualizing things in the unity of idea. It is not too difficultto see that thinking cannot deal with "things" by themselves, but only with thethought of things. What may be difficult is to see that thinking is dealing withreality at all when it is dealing only with thought. What can it mean to say thatthings are true only when mediated by thought? What it does not mean, according to Hegel, is that the very being of what is other than thought is thesubjective thinking of it, esse is not percipi. What, at the very least, it doesmean is that thought enters into the constitution of the object of thought; thelatter is not simply there, to be reproduced or mirrored in thought. More thanthat, it means that thought-in its fullest sense-is indispensable to the constitution of reality. Here it is that Hegel distinguishes between subjective thinking,which is finite, and objective thought, which is infinite, and whose paradigm isdivine thought which is productive of not only the objectivity but also the reali,:yof its object.

In regard to the relationship already mentioned of the three stages of the logical idea.this relationship presents itself thus in concrete and real form: God, who is the truth, isknown by us in his truth, i.e. as absolute Spirit, only to the extent that we at the sametime recognize as untrue the world created by God-nature and finite spirit-if separawdfrom God (WA E 83, Zusatz).Infinite Being, which can only be absolute Spirit, thinks, and its thinking iscreative of finite reality, and this, since thought can think only itself, is, so tospeak, the finitizing of the infinite. This is not to say that infinite thought existsin sovereign independence and then decides to think and, thus, create finitereality. Rather it is to say that infinite thought in thinking itself both engendersits infinite trinitarian Other, the Son, and creates its finite other, the world offinite reality, a self-finitizing othering. "The answer to the question, how theinfinite becomes finite, therefore, is this: that there is no infinite which is firstof all infinite and then, in order simply (erse) to become finite needs to go outof itself into finitude. Rather, in its very being for itself it is already just asmuch finite as infinite" (WA L, I, 143); "The absolute, then, is that which inone unity is both finite and infinite" (W A GP, II, 79). Hard to swallow, indeed,if we take Hegel to be saying by "is" that "infinite" and "finite" are beingpredicated of God in exactly the same way. If, however, we take the Hegelian"is" as descriptive of a movement which is inseparable from the very being ofthe infinite-"this inseparability is the concept of the infinite" (ibid., 144), wecan see him saying that all thought-even infinite thought-is movement, andthat infinite thought is a creative movement toward finitude (see WA E 441,Zusatz).

In thinking out the implications of thought, then, it is inevitable that thethinking of being should come up against a being which is special, which is notonly a thought being but also a thinking being-thinking thinks itself, is self-


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INFINITY 299conscious; there is self-conscious being (Selbstbewusst-sein). It is in this category that the perfection of being will be found--or else it will not be found atall (or there will not be any finding at all). Such a being, even though "posited"(gesetzt) by thought as its own object, is "complete" (vollbracht) in itself,depending on nothing outside itself for being what it is (WA L, I, 148) and is,thus, "the parade example (das niichste Beispiel) of the presence of infinity"(ibid.), of which it is characteristic to become other while remaining the same(see WA E 95). The being in question is the being an object has for the onewho thinks it, but the object and the one who thinks it are one and the same."The ideal is necessarily for one, but it is not for another [one]; the one forwhich it is only itself" (WA L, I, 149). This is true of the "I" (who thinks);it is true of "spirit" (which is active source of thinking); it is, above all, trueof "God" (the active source of all reality): "God, therefore, is for-self, in thesense that (insofern) he is himself that which is for him." The being, then,which the I, spirit, God have is "ideal," but not merely ideal in the sense of"not-real" (Ibid., 150). The infinity which must be said of this ideal being isnot the vague, undifferentiated infinity of Parmenides' "being," nor yet that ofSpinoza's "substance"; rather it is the self-differentiating being, whose determinations are its own activities, differences which do not limit each other (Ibid.,151--52).

CONCLUSION

From this painfully but necessarily brief and sketchy summary of Hegel'sthought on infinity, then, we can conclude that, as he sees it, mere finitude byitself contains within itself insuperable contradictions. Only a thought whichintegrates the multiplicity of the finite into the unity (totality) of the infinite canresolve the contradictions of finitude. The essential relativity of multiple finitebeings can be unified only in the absoluteness of infinite Being. It might wellseem that, as this thought unfolds, the distinction between finite and infinite isgradually becoming blurred; the finite is infinite and the infinite is finite; whathas happened to the distinction? No, the distinction is not being denied; to dothat would be to affirm "the dark night in which all the cows are black." It isbeing affirmed, but as a dialectical distinction of dynamic relationship, wherefinite and infinite are only in the passage from one to the other (WA L, L 125).To say that the "I" is infinite or that God is finite is not to employ the propositional "is," which could result only in contradiction; it is to affirm "activity,vitality, and spirituality" of both the ' ' I ' ' and God (WA LPR 1192). Hegel willlater say that the created world is the finitizing of the infinite (WA LPR II 236);God himself cannot create an infinite world. Here he says that the infinite divineactivity of creation both posits (puts into being) the world and lifts it to infinityin the human spirit (ibid.). In the present context religion is the lifting-up inquestion--not the finite activity of a finite subject, but the infinite activity ofthe infinite in the finite (WA LPR I 198), the presence of the divine in thehuman, which is what "revelation," "lifting-up" (Erhebung) means (WA LPRII 220). The divine spirit present in human self-consciousness (WA LPR II 305)


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300 THOUGHTis the very "eternity of spirit" (WA LPR II 330). Thus, to say that "infinite"is the "ideal quality of thought" is to say that spirit which is characterized bythought, is the only being of which it makes sense to say' infinite. " Althoughit is Hegel's contention that only with the advent of Christianity-the "absolute" religion-is God recognized as spirit and only spirit, he nevertheless seeseven in the most primitive "religion of nature" a passage beyond the finitenatural object of worship to the infinite divine object (W A LPR II 308). Thisis, however vaguely, to see the being of the finite in the infinite, to rise to Godas more than an abstract infinity (the sort of infinity which the mind as mere"understanding" cannot but think of) (WA LPR I 311-12).

Fordham University

Hegel on Infinity

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