Descartes and the Horizon of Finitude

DESCARTES AND THE HORIZON OF FINITUDE

JEAN-LUC MARION, (SORBONNE)

Finitude in Question

The last words of the Meditationes de prima Philosophia shall serve as our point of departure: “… we must confess that the life of man is apt to commit errors regarding particular things, and we must acknowledge the infirmity of our nature” 1 (AT 7:90, 15-16). The second last words of the Principia Philosophiae had also concurred: “At the same time, recalling my insignificance, I affirm nothing…”2 (IV, §207, VIII-1, 329, 8-9). Do these consist of merely anecdotal protestations, indeed diplomatic, and of an entirely conventional modesty? On the contrary, we shall attempt to demonstrate that, beneath an appearance of rhetoric, Descartes here marks the final point of his slow conquest of a thought of finitude. Here we understand not a thought of finitude within the Cartesian philosophy, but rather of the finitude of the Cartesian philosophy itself. For, at least this shall be our hypothesis, philosophy consists, for Descartes, in more than a theory of science and of objecticity, it consists in more than a transcendental doctrine of the ego, indeed it consists only in the constitution of an onto-theo-logy, a test of finitude. And, by this decision that opposes him in advance to all his successors until Kant (not included), he anticipates at least one of the essential characteristics of contemporary philosophy. This conquest was not, however, either direct or easy. We shall attempt to reconstruct it by opposing two seemingly different experiences of finitude: one in the epistemological theory of the object constructed by the Regulae of 1627, and the other in the doctrine of the infinite discovered by the Meditationes of 1641.

Limits Without Limits (1627)

It seems not insignificant that the Regulae never employs the term finitus. In one sense, the finitude of the human spirit appears dismissed right from the start. 205 Chapter Eleven

In effect, when Regula I introduces, against the Aristotelian division of the sciences based on their respective disciplines, and therefore against their irreducible plurality, the central thesis of their unity through a common source —“… human intelligence, which always remains one and the same, however different the subjects to which it is applied”3 (X, 360, 8-9)—it suggests at the same time what we could name a consequence of infinitude: because human wisdom does not differentiate itself based on its objects any more than does the light of the sun based on that which it illuminates,4 therefore it does not vary, or change, and it follows that it must have an absence of limits: “…there is no need to impose any boundaries upon the mind”5 (360, 12)—the minds of men receive no limitation, which means that they can apply the same “knowing” to any discipline, insofar as they are all formally and structurally identical, irrespective of their objects of application. In a nutshell, because science always deploys the same operations, irrespective of its diverse objects, these last cannot themselves modify science, and therefore do not limit it either—the unity of “human knowing” also makes a “… universali[s] Sapientia” (360, 19-20). And the unity of the method, which ends with the Mathesis universalis, does not produce a similar limitlessness, just because it employs and emanates from the originary limitlessness of the bona mens. The employment of this infinitude, however, and its consequent epistemological non-finitude, raises a serious difficulty. In effect, after Regulae I-VII have given the first outline of the method and of the Mathesis universalis – the theory of order, the subversion of the Aristotelian categories, the institution of the series from the bases of epistemologically absolute terms in order to deduct knowledge of relative terms, etc.—Regula VIII undertakes to explicate when and where one must “stop, sistere” (392, 11=400, 7). And yet why now must we stop, immediately upon establishing that “… there is no need to impose any boundaries upon the mind—ullis limites cohibere”? An obvious answer immediately arises: because it is not an “… arduous or difficult [thing] to determine the limits of the mind, which we feel within ourselves—ejus, quod in nobis ipsis sentimus, ingenii limites cohibere” (398, 11-12); and yet, this assertion does not seem to clear up the problem and seems even to introduce a contradiction: ingenia would be free of all limits and nevertheless we should feel—and this easily—the limits of our own ingenium. But a great philosopher never contradicts himself, and certainly not when he proposes a paradox. It is this paradox that we shall here try to understand, in order to hear in it the first Cartesian acceptance of finitude—finitude in the theories of objecticity and of knowing. Why do ingenii limites appear? Precisely because the ingenium remains always one and the same in all of the sciences; for, although it receives no external limitation by dint of its objects, it submits itself to an at least double Descartes and the Horizon of Finitude 206 internal limitation: it can only know that which falls under the jurisdiction of the two “… acts of our intellect”6 (368, 9), perception or intuitus and deduction, which constructs series. What’s more, it is in fact quite easy to discover the questions which reveal themselves to these two functions: (a) The title of Regula VIII announces right away that it is necessary to “… stop, sistere” where “…our intellect is unable to intuit sufficiently well, satis intueri” (392, 11); for example, the search for the equation of the anaclastic. If one holds oneself entirely to mathematical principles, in fact to mathematics applied to optics, one quickly realizes that the equation depends on the values of the angles of reflection and refraction; but, because these angles themselves depend upon the density of two media, one must pass in turn to their study, which is matter not for mathematics—sole domain of pure intuition –but rather for physics, where one must proceed so far as to determine the nature of light, and thus “… what a natural power is in general”7 (395, 2-3). However, we may reasonably doubt that, in the field of physics, at least as defined by Aristotle, as the changes to an irreducible “way”, we can attain to a true intuitus mentis (395, 4) and not be reduced to a simple experientia (394, 9). If this were the case—and we know that the debate over what the Dioptric of 1637 really conceded on this point has never really ceased—it would be necessary to renounce the search for the equation of the anaclastic. And thus, whatever the case with this precise question, it is clear that the shortcomings of the intuitus impose, by right, a limitation on the ingenium… Does this then consist in a finitude? Before examining this, let us consider the second operation of the intellect. (b) Nothing can be presented as evident, if it is not either an object absolute from all others for the intuitus, or deduced, by a relation or a combination of relations from such absolutes, and thus if it is not, by one or more degrees, a respectivum; this placing into series does not depend upon ontical determinations (the categories of being according to Aristotle), but follows rather from the naturae simplicissimae, the most simple natures, principally the “material” ones (extension, shape, movement, etc.) and the “common” ones (existence, unity, duration, etc.), privileged, what is more, from the a priori concepts of the understanding (in a way already close to the pure categories of the understanding that Kant will formulate). Thus, these most simple natures should hypothetically remain in a finite and perfectly known number; consequently, since it is only upon the basis of them that we can know, we can also know whether a question can be reduced in one way or another (if it can be formulated); but if it is not reducible, we therefore know that it can never be known: “… nothing can be so complex and scattered that, by means of the enumeration […] it cannot be circumscribed within definite limits and arranged under a certain number of headings”8 (398, 17-20). All questions have limits, that of the most simple natures; either it arises from the domain of 207 Chapter Eleven consciousness (experience in the Kantian sense) or it does not. And yet does this second limitation attest to a finitude? Precisely, no: it opens on the other hand the possibility of measuring the indefinite field of experience, already based on the principle that the conditions of possibility of objects coincides exactly with the conditions of possibility of experience itself—that is to say with the concepts and the intuitus of the human mind. Descartes does not hesitate, in effect, to support a proposition that would seem to be absurdly ambitious were it not to be understood in a transcendental way: “Nor is it an immense task to attempt to embrace in thought all the things contained in this universe”9 (398, 14-16). There is nothing impossible to measuring the whole universe of knowable things, because excluded from this universe, on the one hand, are those things which no intuitus may regard clearly and distinctly, and, on the other, those which do not enter into series confined by the certis limitibus of the most simple natures. We must therefore conclude the validity of the paradox: the human mind, while always limited by the two primitive epistemological operations, encounters no limits to its knowledge—because what it does not know finally and quite simply does not belong to the transcendental field of knowledge. The limits of “human wisdom” do not, therefore, contradict the continuation of the project of erecting a “universal wisdom,” but circumscribe only the universitas of the knowable. The limits of the mind do not therefore confer upon it any epistemic finitude. Many arguments confirm this foundational paradox of the Cartesian doctrine of science. Not only do the Regulae never employ, as we have seen, the term finitus (or any of its derivatives), any more than they suggest that finis could signify the frontier (and not only the goal); but above all they make use of infinitus (only six times) only to characterize a knowable object or an operator of knowledge. Thus the Mathesis universalis—well named, considering it pretends to a boundless knowledge of the universitas embraced by the cogitation—proceeds by placing in order and taking of measure, operations that most often, and quite naturally, do not offer any order or measurability; how then does it succeed? Initially because order can be established between any objects, by complicating the infinitus modis on the model of the complex warp and woof of weavers (404, 2). And then primarily because each “…subject extended in every sense”10 is by right endowed with infinitae dimensiones (453, 15), themselves of an infinitae diversae (448, 11-12) and above all, secondly, because we measure in this way not only the three obviously measurable dimensions of space, but also weight, speed, and an infinitude of other parameters (alia ejusmodi infinita, 447, 29) which offer at the same time no real extension; to the point that the infinita multitudo of the possible figures “suffices” to realize (in effect to encode in pure intelligibility) the specific characters of nothing less than “all sensible things, omnium rerum sensibililium” Descartes and the Horizon of Finitude 208

(413, 18-19).11 And so, the limitations of the “operations” of the human mind do not impose upon it any finitude, but submit it on the contrary to an infinitude of objects, that is, to infinity as a character of objecticity always receptive to further conquests. Another conclusion inevitably follows: if the theory of the limits of knowledge produces no real experience of finitude, it offers still less any experience of infinity. Or better: infinity does not intervene within the horizon of the constitution of objecticity, and thus neither can finitude itself.

Obstacle (1630) and Indetermination (1637)

The doctrine of science treats of limits, but, even for this, it ignores finitude and therefore infinity. With this result of the Regulae, however, Descartes did not say his last word, considering that he stigmatized as the “… chief defect” of one of his obscure rivals, J.-B. Morin (astrologist at the Collège de France) the fact “… that he treats of the infinite everywhere as if his mind were above it,” while he, Descartes, has “… never treated the infinite except to submit myself to it, and not in the least to determine what it is and what it is not.” 12 This criticism therefore excludes that one could think the infinite (and thus the finite) from “above,” to approach it from on high; moreover, as thinking from above means the same thing as thinking an object (because the object constitutes itself, measures itself and orders itself), it therefore excludes that one could think infinity as an object—as an object of the method. But can one know without knowing objects? We know that Descartes claimed so, when in 1630 he traced an irrevocable boundary between the truths of mathematics (and also the truths of logic and even ethics), supposed eternal by his principles at the time, and God, who created, instituted, and established them. This essential doctrine renounces the description of God on the basis of the most simple natures, at least those that are material, and certainly renounces “understanding” Him (I, 146,6,8; 150, 14), that is “…to embrace [Him] in thought” by deploying only the “touch…[of] our thought”13 (I, 152, 17-19).14 We must not, however, renounce the thought of God as an object only because we cannot imagine him “… as a finite thing,” in the way of the “vulgar” (146, 19)—those wise men that “… understand mathematical truths perfectly, and not the truth of the existence of God”15 (150, 14-15). To think God is to renounce his inscription in the space which governs objecticity, “… seeing as he would cease to be infinite, if we were able to comprehend him”16 (147, 4-5). It must be underlined here that infinity only becomes visible [visible], and therefore basically sightable [visable], from the moment when the constitution of the object is placed between brackets: infinity thus appears only where the model of comprehension ceases—literally, one 209 Chapter Eleven must see “… God as an infinite and incomprehensible being” 17 (150, 7), beyond comprehension, therefore ultimately infinite, for the proposition is analytic. With the suspension of the method employed in this way by a “human science” pretending to the status of a “universal science,” finitude is also released for the first time: “… we can know that God is infinite and all-powerful, but that our soul, being finite, cannot comprehend or conceive him”18 (152, 10-13). What is essential with the extraordinary doctrine of the eternal creation is not first of all —it must be underlined—due to the recognition of divine transcendence and its creative power, and therefore an ontical penetration, but rather it is an epistemological reversal: to know does not always mean the same thing as to constitute an object of the Mathesis universalis, nor to rely on the limits of “human wisdom” in order to infinitely expand knowledge of “… all the things contained in thought in this universe”19 (X, 398, 15), but rather it sometimes means to suspend comprehension. Infinity, and therefore also finitude, appears once the epistemological obstacle of a cogitatio restricted to objecticity has fallen. Infinity does not therefore appear by a growth in comprehension, but rather by its reduction—its demarcation or even suspension: to know the infinite is not to understand it, or, better, to not understand is therefore to begin to think it. Even if Descartes subsequently underlines the ontical positivity of infinity, he attains it only first by way of an epistemological de-negation (if not a negation). The emergence of this obstacle to infinity does not, however, suffice to avoid its indeterminacy. For the first explicit uses of infinity in the fourth part of the Discours de la méthode do not really take account of this operation. Infinity there at first takes on an ontical status, and even fulfills a function exclusive to rational theology. It defines without qualification “… a perfect and infinite being” (VI, 39, 4-5)20 and “… infinite perfections” 21 (VI, 43, 7-8): this simplistic juxtaposition passes over in silence the patent difficulty of an at least possible contradiction between perfection by definition remaining unachieved and infinity by logic always unachieved. Doubtless, a sequence allows one to perceive a more complex story: if I were “… alone and independent of everything else,” I could eventually imagine “… being myself infinite, eternal, unchanging, all-knowing, all-powerful; in short, to have all the perfections I could observe in God”22 (34,30-35, 6). Besides the fact that this hypothesis does not resist critique (I am precisely not “independent,” but in “dependence”, 35, 26), its validity depends only upon a simple ontical comparison of perfections, without any direct link being established between finitude and infinity. The principal question remains not only unresolved, but barely even posed: how, if I am imperfect, could the idea of a perfect and even infinite nature, be “… placed in me”23 (34, 20)? The argument always supposes an ascent from the finite (confused with the imperfect) to the infinite (assimilated to the perfect), but from the finite to the infinite the consequence is never good, because there is by Descartes and the Horizon of Finitude 210 definition no common measure between them (no “dimensions”)—how then could an epistemological transition be thinkable with the “incomprehensible”, and how could it be that only the idea of infinity could ontically reside within the finite? Moreover, does it follow that infinity—without limits, without comprehensible concepts, without definable essence—can directly designate an individuated essence, even that of God? In short, the succinct metaphysics sketched in 1637 by the Discours de la méthode leaves intact the principal problems of a thought of infinity that conforms exactly to finitude, worse, it barely indicates them. Let us formulate them: (a) How could infinity inhabit—affect, attain, enlighten, however we wish to say it—the finite? In a word, what finitude unites them? (b) Can infinity name the divine essence or else does it only open onto the indistinct horizon of the incomprehensible?

Finitude Approached Negatively (1641)

Only the Meditationes de prima Philosophia confronts these questions, though initially only in an indirect manner and by negation. In effect, no occurrence of the “finite/infinite” couplet appears in the text before the great caesura of Meditatio III, where “cause” and “substance” emerge for the first time.24 During their time of latency, however, finitude is nevertheless put into place; by finitude, we understand here this articulation by the finite of the infinite, which alone permits conception of finitude itself, rather than substituting for it a (limited) transcendental theory of (limitless) universal science. And so finitude is discovered despite (or perhaps by virtue of) its latency in two operations, doubt and the existence of the ego: (a) In Meditatio I, doubt rests on the hypothesis that I can deceive myself (and certainly not, as it is too often simplified, to be deceived by a supposed “great deceiver”, which Descartes never mentions with this title)—fallor. Could this self-deception be understood as an experience of finitude? Certainly, but based on at least two interpretations. (i) The consciousness of fallibility, more than that of certain knowledge, means recognition of an imperfection; nevertheless, if we are to believe an objection to Descartes by Burman, it does not follow that imperfection means in its turn recognition of the infinite, and therefore knowledge of the finite, because, according to the order of arguments, doubt precedes any experience of the infinite: “… dubitationem non esse argumentum tantae perfectionis quam cognitionem. Ergo id cognovit [Descartes in the Discours de la méthode] sine relatione ad ens perfectum, et non cognovit prius Deum quam se”. To which Descartes responds that, at least in the Meditationes, one must distinguish the explicit from the implicit. For, if “… explicite possumu prius cognoscere nostrum imperfectionem, quam Dei perfectionem, quia 211 Chapter Eleven possumus prius ad nos attendere quam ad Deum, et prius concludere nostrum finitatem, quam illius infinitatem” (and the doubt of Meditatio I proceeds explicitly so), nevertheless “… implicite semper praecedere debet cognition Dei et ejus perfectionum, quam nostri et nostrarum imperfectionum.”25 We must understand, therefore, that we can exercise (and establish) doubt explicitly, without reference to the infinite, and therefore without its interpretation as finitude (literally finites), but that implicitly its finitude cannot be denied. Following this authorized commentary, it must be concluded that from doubt to the infinite, at least through the intermediary of imperfection and finitude, the continuity does not admit of a solution. Nevertheless, this first interpretation remains unsatisfying because, even placed under the authority of Descartes, it restricts itself to affirming what it should demonstrate—that doubt does consist of a finitude and that this already implicitly supposes the infinite—and what doubt precisely does not show. (ii) It would therefore appear legitimate to interpret the continuity from doubt to infinity otherwise. The final hyperbole of doubt rests on the opinion “… that there exists a God who is able to do anything —Deum esse qui poteste omnia”26 (VII, 21, 2): two consequences immediately follow. First, the all-powerful, by right of this hypothetical title, necessarily relates to infinity, right from the Discours evoking the “… perfect being […] infinite, eternal, unchanging, all-knowing, all-powerful…”27 (VI, 35, 2-5), and confirmed in Meditatio III in the definition of God as “… infinitum, omniscium, omnipotentem…” (VI, 40, 16-17). Above all, the all-powerful implies incomprehensibility, no longer directly as in 1630, but by the bias of my error, which prohibits me from understanding even the truths of mathematics; because divine omnipotence, by disqualifying objective knowledge through doubt, reproduces the bracketing of the doctrine of science by the “incomprehensible power” of God, creator of eternal truths. The Mediatio I consequently discovers, in the directing thread of the all-powerful, if not expressly the infinite, the basically epistemic position of the infinity of 1630. The second interpretation attains finitude more closely, therefore, than does the first. But (b) should Meditatio II not mask finitude, as soon as it resists doubt (which had opened to finitude) in assuring itself of the existence of the ego? Better, how could this res cogitans better recognize the finitude to which the Regulae could not attain, having already established that “…nothing can be known before the intellect”28 (X, 395, 23)? In short, how could a “pronouncement… necessarily true”29 (VII, 25, 12-13) or a “… first principle…” (VI, 32, 23), in unwavering certitude (“… certain and unshaken,”30 VII, 24, 12-13), attest to finitude? Here again, we may interpret this in two ways. (i) First, it does not necessarily follow that the certitude of the existence of the ego prohibits access to its finitude, because Descartes obtain its certainty not just from the cogitatio, neutral and supposed active, but also from doubt, Descartes and the Horizon of Finitude 212 and therefore from its imperfection and passivity: “… verum etiam est te, qui dubitas, esse. […] si non essem, non possem dubitare”.31 And, in fact, it is really beneath the figure of its own doubt that the cogitatio performs its existence, and therefore in effect through finitude. (ii) But we can demonstrate more directly the finitude of the res cogitans, because the ego performs its unconditioned existence only temporally—namely “each time—quoties” (VII, 25, 12; 36, 12) and “for as long as—quamdiu” (25, 9; 27, 10; 36, 16), it thinks, “…we already perceive that we think”32 adds Principia, I, §8. The ego does not know its own existence once and for all by assertion, or even by intuitus, it must perform it by a temporalized act, an act that therefore must be repeated ceaselessly, as an event; and, concomitantly, “… if I were to cease all thinking I would then utterly cease to exist”33 (27, 11-12). My existence remains, of course, absolutely certain, but during the time and at the same time that it performs this thought, and, thus, only for a time. This does not consist of an anticipation of the more banal thesis of the discontinuity of time (49, 12-20; 53, 15), but rather it heralds the Kantian determination of finitude—by the temporality of thought (as much as by its sensibility). And so the first two Meditationes deal at least indirectly with finitude, first by repeating the incomprehensibility of that which bypasses the science of objecticity, and then by temporalizing the cogitatio. These openings still do not, however, ever mention the finite (“finitus”) or the infinite (“infinitus”)—and still less do they articulate the space between them. It remains for Meditatio III to confront these difficulties.

Finitude Approached Positively (1641)

In Meditatio III, or, more precisely, in the “… alia quaedam adhuc via…” which opens its second part (VII, 40, 5sq.) appear for the first time, at the risk of a rupture or of a suture in the order of reasons, the principle of causality (40, 21sq.) as well as the term “substance”. What is more, it is precisely with the first occurrence of this last term (40, 12) that infinity is explicitly introduced for the first time—“…summum aliquem Deum, […] infinitum…” (40, 16-17) -, and the finite—“… finitae substantiae…” (40, 20). Thus, the alternative of finite and infinite imposes itself and its metaphysical radicality only in conjunction with the term which is the metaphysical acceptation of the being par excellence; and, for the first time, Descartes breaks with a simple epistemic (and therefore implicit) determination of the terms of finitude. In a stroke, the “substantia incompleta” (222, 15) or “something incomplete and dependent upon another”34 (51, 24-25; 53, 10) restricts itself (strictly speaking defines itself) in relation to God, considered as substantia infinita (45, 11, 21, 22, 27), in accord with a paradigmatic couplet opposing the “…idea of an infinite substance” to the “idea 213 Chapter Eleven of a finite substance”35 (166, 1-2), the “…infinite and independent substance” to the “… finite and dependent thing”36 (185, 26-27). But as this opposition passes from the epistemic to the ontic, from science to realitas, its centre of gravity passes from the finite (the first and implicitly finite thought in terms of doubting) to the infinite, first in terms of the only absolutely independent substance: “… I clearly understand that there is more reality in an infinite substance than there is in a finite one. Thus the perception of the infinite is somehow prior in me to the perception of the finite, that is, my perception of God is prior to my perception of myself”37 (45, 26-29). This reversal of priorities relieves in several ways—in fact, irrevocably—the ego of its anteriority, which had rested only on its function as first in knowledge, but which evaporates as soon as the first is considered as a substance, as a being. Not only does the finite submit itself here, and for the first time, to the infinite (thus conforming to the recommendation made to Morin, but not yet followed by the Regulae or by the Discours), but significantly it deploys, under the aegis of substantiality, the crease of finitude—the finite, ontically dependent on the ordinary support of God, deduces and conceives itself only on the basis of the infinite, as an act of the divine and sole independent being. Or, to speak as does the Principia, “… God, the creator of all things, is [ontically] infinite and we are altogether finite”38 (I, §24). Of course, priority reversed towards God, and then ontically transposed, must always be epistemically translated as the incomprehensibility of God (as an object of the method): “… our minds are to be regarded as finite, while God is to be regarded as incomprehensible and infinite”39 (VII, 9, 15-17). This does not consist, however, of a conquered reversal of position faced with the finitude of the cogitatio, but rather of the definition of the infinite itself, as such and based on its epistemic properties: “… the nature of the infinite is such that it is not comprehended by a being such as I, who am finite”40 (46, 21-23), “…idea enim infiniti, ut sit vera, nullo modo debet comprehendi, quoniam ipsa incomprehensibilitas in ratione formali infiniti continetur” (368, 2-4), “…the nature of the infinite is such that we, being finite, cannot comprehend them”41 (Principia, I, §19).42 And so incomprehensibility does not so much impose a limit on the human mind, so much as it declares the nature of the infinite positively; and it succeeds at this because it exposes this nature using the ontical terminology of “substance”. There remains nothing less than a justification of how a finite substance might accede to an infinite substance; that is to say, because this finite substance thinks, how it might contain this idea. It is not sufficient to affirm that, even without comprehension of the divine perfection, “… our mind can well have several ideas—quocunque modo attingere cogatione possum…” (IX-1, 41, 27- 28 = VII, 52, 5), it remains to be explained how this modus could articulate two incommensurable terms. Further, declaring that the ideas of the finite and of the Descartes and the Horizon of Finitude 214 infinite are equally innate (51, 13-14) does not suffice to render them compatible, let alone commensurable. Or, what amounts to the same, it does not suffice to enroll the biblical theme of man created ad imaginem et similitudinem of God, to indicate just where and in which way (quodammodo, 51, 20) one could bridge the abyss separating them.43 It remains still to think what Lévinas has called, “… the arrival or the descent or the contradiction of the infinite in a finite thought…”44. It is why Meditatio III risks taking two extra steps. (i) It suggests that the image and likeness of God that I hold amounts to his idea, and therefore to the idea of the infinite, which becomes in this way an idea without limit, beyond restrictions, because it exists still less within me than it is me myself—“… in the same way, in which the idea of God is contained…”45 (51,21). (ii) It then unites this unique idea (of the infinite) to the idea which the ego has of itself in one and the same faculty, left, moreover, without any other name: “… by means of the same faculty by which I perceive myself” 46 (51, 21- 22). The crease of finitude could, therefore, succeed in being unfolded by means of the operation of a single faculty, that would perceive “simul etiam—also at the same time” (51, 27 = IX-1, 41, 18) the two sides, finite and infinite. How can this be conceived? In principle like so: when I regard “me ipsum”, I see double—not one being, but two; on one side me, therefore an imperfect thing aspiring to perfection (finite, therefore desiring its progress “indefinitely”, without end), and on the other side the infinite—these same perfections, but “infinite” and no longer “indefinite” (51, 24, 26, 28 and 29). The infinite is perceived at the same time and by the same gaze as the finite: this vindication has only one acceptable meaning—that the finite can discharge itself within its limits only if we can trace them clearly and distinctly, and so therefore only if the infinite surrounds these limits and renders them visible. Contrary to Wittgenstein, who, admitting, “… to trace a limit to thought, we would have to be able to think the two sides of this limit,” concluded immediately, “… we would have to then think that which does not let itself be thought,” 47 and therefore renounced delimiting the finite as such, Descartes intends to think it fundamentally and therefore to see its limits clearly and distinctly—he therefore assumes the necessity of thinking the other side of the finite, and thus he postulates that one can accede to the infinite. The infinite (God) is not added to the finite (the ego), it does not even intensify or double it up, but comes along with it, as the condition of its own arrival on the scene. The ego can assure its own finitude only in recognizing its limits; but it cannot test them without testing their resistance, and therefore in ceaselessly pushing them back and attempting (though always in vain) to overstep them—“…aspiring indefinitely for greater and greater […] things”48 (51, 26); this movement, which remains, in the final analysis, immobile, advances without end into the excess of the infinite over the finite. And so Descartes rediscovers to the letter St. Anselm’s negative 215 Chapter Eleven determination of God, when he evokes in passing, “… this power that I am to understand that there is always something greater to conceive, in the greatest numbers, that I could never conceive—… vim concipiendi majorem numerum esse cogitabilem quam a me unquam posit cogitari”—and returns this to a being more perfect than me, “… alio ente a me perfectiore” (IX-1, 110, 4-8 = VII, 139, 19-22). This endless advance into the beyond of the already known, into the always greater cogitable than that which has already been cogitated, has two characters; first, that it never attains the infinite, because the infinite in actuality excludes all progress; but it presupposed that nothing cogitated can exhaust the cogitatable, and thus it admits an excess without any always already given limits, in short, it requires the infinite. The undeniable “vis argumenti” (VII, 51, 30) rests on the fact that the finite, to be conceived simply as finite, implies both sides of the crease of finitude, and thus the infinite as its own condition of possibility. The finite claims [réclame] always more than itself in order to be said—it proclaims [clame] therefore the infinite. This conclusion raises a difficulty at the same point at which it convinces; because the infinite, insofar as the finite implies it as its condition of possibility, must now take on a transcendental function49; for the term “transcendental” never qualifies an object or a phenomenon given in experience, but always and only that which renders experience possible. If, therefore, Descartes claims to have attained the idea of infinity in the form of a transcendental condition of the experience of the ego sum—and this is indeed the case, because they are but two sides of one and the same faculty, sight, and not two distinct forms of knowledge—then the infinite cannot designate a being distinct from the ego, nor can it name God, because it renders possible experience, yet inscribes within it nothing substantive. Between employing the infinite in a transcendental mode or receiving therein the idea of God, a decision must be made. Did Descartes choose? Did he even see the aporia?

The Name and the Horizon

It appears at least certain that he attempted both directions, the infinite as the name of God (in the tradition inaugurated by Duns Scot), as much as the infinite as a transcendental condition of experience for a finite being and in its Mathesis universalis. Infinity thus gives itself first as a determination of the essence of God, as his first metaphysical name. The equivalencies here are explicit: (i) “… perceptionem infinitii, hoc est Dei…” (45, 28-29); (ii) Deus infinitus (9, 16-17; 40, 17 and 47, 190; (iii) natura or substantia infinita (55, 21 and 45, 11sq.); what is more, this determination was being sketched out right from the Discours, although not without some confusion: “… a perfect and infinite Descartes and the Horizon of Finitude 216 being…” (VI, 39, 4). This consists not only of a determination of the divine essence on the basis of the infinite, but more significantly of a determination of the infinite as a region, as a region of the being; and, in fact, Descartes indeed also names it an ens infinitum (46, 12). The ens, first object of metaphysics, and which becomes with Clauberg the first object of the ontologia, admits several Cartesian divisions; besides the properly onto-theo-logical difference between the being as cogitatum/cogitans and as causatum/causa, there is another, ontical difference traced between the finite and the infinite. It matters little that Descartes here borrows from Duns Scot and especially from Suarez (whose Disputationes Metaphysicae xxx remain especially evident in the background),50 what must above all be underlined is the restriction of the thematization of finitude engendered by this ontical and regional interpretation of infinity; for the ego seems to define itself as a res incompleta et dependens (53, 10-11), a res limitata (84, 6) or a natura infirma et limitata (55, 19-20), simply by opposing itself, in the ontical region of the finite, to the unique being of the region of the infinite; its ontical dependence thus appears curiously intelligible on the basis of itself alone, with an epistemological independence contradicting its ontical dependence; for the infinite remains here exterior, indeed opposed, to the finite, whose existence asserts itself wholly within the limits of one of the two regions, without intrinsic relation to the other; and therefore finitude, which supposes an access to the other side of its limit, remains to it as extrinsic. Reciprocally, in confiscating and exhausting the infinite for Himself alone, God restricts Himself to only one of the two ontic regions—his natura immense […], infinita (55, 20- 21) limits itself moreover to the infinite and excludes itself from the finite, and thus, from an even ontical point of view, contradicts Himself in limiting himself in fact. To think the relation of the finite to the infinite in strictly ontical terms, as though there were two different and opposed regions, just as to reduce the infinitum to a being, even were it supremely perfect, abuts at a irreconcilable series of aporias: (i) the finite defines itself independently of the infinite, which remains for it extrinsic, and so therefore loses its finitude (contradiction between its ontical status and its epistemological status); (ii) the infinite restricts itself to one region and therefore avers itself finite yet without intrinsic function in the definition of the finite; (iii) finally, as was strongly objected by Caterus, the infinite sinks into the unknown: “Somebody […] will ask: “Do you clearly and distinctly know the infinite? What then does this common verdict mean, known by one and all [tritum illum et vulgo notum]: infinitum, qua infinitum, est ignotum”?” (IX-1, 77, 18-21 = VII, 96, 12-13)51. The infinite, as infinite, stuck within the limits of the ontical region which it defines and which defines it, remains epistemologically finite and inaccessible, just as the finite, established in an ontical region it has itself defined, lacks its finitude, because it presupposes epistemologically a certain knowledge of the infinite. It is 217 Chapter Eleven necessary to envisage another path in order to escape from the traps of this impasse: to know the infinite, no longer as the infinite and nothing else (as the metaphysical name of God), but rather as it defines (and this for us) the finitude of the finite, and thus the infinite as transcendental operator of finitude. We must also return to the inclusion of the infinite within the finite, as outlined by the eadem facultas (51, 22), which, at the end of Meditatio III, was attempting to think it in its strictly transcendental function—the finite thinks itself in its finitude only insofar as it thinks itself from the basis of its own transcendental condition of possibility—the infinite. Immediately, the infinite passes from the status of metaphysical name of God to that of the horizon of the ego. Here we understand ‘horizon’ in its Husserlian usage: when a phenomenon appears, “… there is necessarily a seizable nub of ‘effective presentation,’ surrounded by a horizon of improper ‘concomitant givens’” in short “… a horizon of determined indeterminacy.”52 And it is this horizon that it remains for Meditatio IV to trace. It succeeds by introducing the crease of finitude, that is to say the reciprocal articulation of the finite and of the infinite, in the midst of the res cogitans itself; which, from this point of view, no longer plays the role of one ontical region faced with another, but rather establishes itself in the centre of an immanent scene containing the intrinsic intrigue between the finite an the infinite. The res cogitans, while a substantia finita, admits of two principal modes. On the one hand, a facultas intelligendi valde finita (57, 4), to wit an intellectus finitus (60, 14, 15), belonging to the region of the ens finita (61, 11) and producing only a cognition finite (61, 11). On the other hand, a will that I test containing nullis limitibus (56, 26), contained non intra […] limites (58, 22), so that contrary to the understanding, which can and must always aspire to a surplus of concepts and struggle in its progress, it does not leave any space for anything greater: “”… I experience to be so great in me that I cannot grasp the idea of a greater faculty”53 (57, 12-13); even God’s formal power of decision “… non […] major videtur” (57, 20-21). We have already remarked that this text never directly qualifies the will with infinita;54 but we find nevertheless a text that, after having initially negatively defined the privilege, after the fashion of Meditatio IV, (“… God gave us a will without limits”), accords it this title: “it is principally because of this infinite will that is within us, that we can say that he created us in his image.”55 We would not, either, be able to disqualify this infinitude of and in the res cogitans by arguing that it is only formally exercised, in a faculty of choice itself entirely empty. First, because this formal emptiness constitutes, for Descartes, precisely the condition of its own infinity, and not an obstacle: because it does not consist in willing the infinite as content (would this even make any sense?), but of willing to infinity, of deciding infinitely; thus deciding, for Descartes, always amounts to deciding infinitely, whereas deciding in a finite manner amounts to not deciding anything at all; the will does not Descartes and the Horizon of Finitude 218 exercise itself other than formally, and thus its infinitude cannot be other than formal. And, secondly, because “… we have ideas not only of all that is in our intellect, but even of all that is in our will”56; immediately, we a have a true idea of infinity by the simple fact that we will infinitely. The infinite, be it merely formal and bearing an empty appearance, will from now situate itself in the will, and therefore no longer beyond the res cogitans interpreted as a finite ontical region, but rather in its very heart—“…mihi innata” (51, 13), “…in me” (57, 1,12). Infinity characterizes the will, but the will belongs, inasmuch as does the intellectus finitus, to the created res cogitans: it must therefore be concluded that the will has the rank of a created infinity. We need not be surprised by this conclusion. Its apparent “contradiction” (Lévinas) results from the fact that by it we are exposing in metaphysical language that which might be more adequately enunciated in critical or phenomenological terms.We could first say that the res cogitans only achieves a clear knowledge of its finitude by testing its limits, and therefore by testing the resistance of the infinite, which prohibits their overstepping. The infinite plays “…in me” the role of a transcendental condition of perception of my character as a res incompleta, and therefore of my finitude; just as the ideas of reason mark the finitude of my sensible knowledge by being really ideas, but without ever by the same token enumerating the phenomena of objects, the idea of the infinite is innate to me and belongs to the created being which I am, without ever enumerating all of the ideas of objects, but by exercising a strictly transcendental function. We could then say that the infinite traces, around each idea of an object or of a finite phenomenon, a halo, forever irreducible, but always presupposed from the as yet unknown, indeed of the irreducible unknown, and that it arranges in this way an horizon, such that its ineffectiveness itself permits a limitless, and yet essentially finite, unfolding of possible experience. We can, therefore, very likely interpret the paradox of the infinite innate to the finite res cogitans not through following an ontical acceptation, but rather through a transcendental, indeed phenomenological, interpretation of the infinite, taken as a condition or as an horizon. This conclusion calls for several remarks: (a) Descartes, by privileging the transcendental or phenomenological use of the infinite rather than its exclusively ontical use, compromises henceforth its status as first definition of the divine essence; by which he anticipates more of Pascal than he follows in the line of Suarez. Further, even Malebranche and Fénelon, who are the last to maintain the privilege of the infinite amongst the other metaphysical names of God, will nevertheless also have to impose upon this ontical infinity a universal function, as is evident in the patently ambiguous phrase “universal Being”57; often employed in order to maintain an essential ambiguity, it assures in effect nothing less than the onto-theo-logical coherence of all classical metaphysics: in 219 Chapter Eleven the capacity of infinite being, God also exercises the transcendental and phenomenal functions of the universal. The contradiction that Descartes hoped to construct and to resolve in the finite ego—finite res cogitans, endowed with an infinite faculty—is now displaced onto God—infinite being, who serves as the empty horizon and the formal condition for experience in general. (b) When Descartes assumes, not without detours and hesitations, the paradox of a finite res cogitans endowed with an infinite faculty, he achieves a veritable determination of finitude, for he names and unfolds both planes, the infinite as well as the finite—for finitude cannot be thought of otherwise than as such a paradox, and it engenders still others. Thus, the ego keeps its role as “first principle of the philosophy I was seeking” (VI, 32, 23), while remaining an “… intellectus creatus ut sit finites” (VII, 60, 15); thus the principle of a certain science remains finite; or, better: in order to construct an absolutely certain science, it is not requisite to pretend to an absolute knowledge. The certitude of science (and this we owe also to Descartes alone) is deployed perfectly in the finitude of its foundation and implies no infinite knowledge. In fact, only finitude as conceived by Descartes, and which opposes him in advance to all metaphysical pretensions to absolute knowledge (from Spinoza to Hegel) permits one to describe the ontical and epistemic situation in which we find ourselves today: certain finitude, but a certitude without absolutes, an absolutely certified science, but without any wisdom or absolute knowledge. (c) Descartes thus posed, more clearly than most metaphysicians, the principle that there is no subjectivity other than the finite. Because, even more essential to the res cogitans than its ontical status, than its cogitative performance or its rational qualification, is the finitude in it. Before and yet like Kant and Heidegger, Descartes thought the ego that we ourselves are, whatever the case may be, as finite. But better than they, who opposed to the finite only an “inevitable appearance” or the being devoid of all ontological difference, he discharged this finitude upon the horizon of an infinity always and already positively given. Even that which makes us flawed remains, as lacking, given. And this generosity of the infinite, in these times of nihilism, is lacking. Descartes can therefore instruct us, he for whom it did not lack at all. 1 In the original French version of this paper, the author quoted Descartes in the original languages. This translation has provided translations for all the texts using Roger Ariew’s translations found in René Descartes Philosophical essays and Correspondence (Indianapolis: Hackett, 2000), refered to throughout as Ariew,. The original text is provided in the footnotes; all other footnotes are from the original text. Ariew, 141. “… fatendum est humanam vitam circa res particulares saepe erroribus esse obnoxiam, et naturae nostrae infirmitas est agnoscenda.” 2 Ariew, 272. “At nihilominus, memor meae tenuitatis, nihil affirmo…”. 3 Ariew, 2. “… humana sapentia, quae semper una et eadem manet, quantumvis differentibus subjectis applicata”. 4 This could, moreover, be disputed: in effect, the light of the sun receives a differentiation from each of the objects that it illuminates, since their surface modifies on each occasion the wave length so that, for the sensing eye, this modification of wave length makes it appear not white, but coloured. 5 Ariew, 2. “… non opus est ingenia limitibus ullis cohibere” 6 Ariew, 6. “… intellectus nostri actions” 7 Ariew, 17 “… quid sit generaliter potentia naturalis” 8 Ariew, 19. “…nihl enim tam multiplex esse potest aut dispersum, quod per illam […] enumerationem certis limitibus circumscribe atque in aliquot capita disponi non posit”. 9 Ariew, 19. “Neque immensum est opus, res omnes in hac universitate contentas cogitatione velle complecti” 10 my translation: “…subjectum omnimode extensum” 11 One finds comparable phrases in the Discours de la methode: “une infinite d’artifices” (VI, 62, 9), “une infinite d’autre [formes ou espèces] (64, 18) “…ne infinité d’espériences” (75,3). 12 Ariew, 95. “… principal défaut […] qu’il trait partout de l’Infini, come si son esprit était au-dessus […] jamais traité de l’Infini que pour [se] soumetre à lui, et non point pour determiner ce qu’il est, ou ce qu’il n’est pas.” A Mersenne, January 28, 1641, AT 3, 20-27. Allusion to Quod Deus sit Mundusque ab ipos creatus fuerit in tempore…., Paris 1635. 13 Ariew, 30. “…l’embracer de la pensée”… “… le toucher de la pensée” 14 Moreover, the Meditationes confirm this distinction: “Deus […] habens omnes perfections. Quas ego non comprehendo, sed quocumque modo attingere cogitatione possum” (VII, 52, 2-6), going even to the point of withdrawing before such a contact: “…nec comprehendere, nec forte etiam attingere cogitatione, ullo modo possum” (VII, 46, 20-21). 15 Ariew, 29. “… ainsi qu’une chose finie”… “vulgaire”…. “... qui comprennent parfaitement les vérités mathématiques, et non pas celle de l’existence de Dieu” 16 My translation: “… vu qu’il cesserait d’être infini, si nous le pouvions comprendre” 17 Ariew, 29. “... Dieu comme en être infini et incompréhensible” 18 Ariew, 30. “… on peut savoir que Dieu est infini et tout-puissant, encore que notre âme étant finie ne le puisse comprendre, ni concevoir” 19 Modified Ariew, 19: “…toutes les choses continues par la pensée dans toute l’universitas” 20 My translation. “… un être parfait et infini” 21 My translation «… perfections infinies” 22 Modified Ariew, 62. “… seul et indépendant de tout autre”... “... être moi-même infini, éternel, immuable, tout connaissant, tout- puissant, et enfin avoir toutes les perfections que je pouvais remarquer être en Dieu” 23 Ariew, 61. “… être mise en moi” 24 On this decisive caesura, see our analysis in Sur le prisme métaphysique de Descartes, Paris, 1986, c.II. 25 Entretien of 16 avril 1648, AT 5, 153, 22-30 26 Ariew, 106. 27 Ariew, 62. “… l’être parfait […] infini, éternel, immuable, tout connaissant, tout-puissant…” 28 Ariew, 18. “…nihil prius cognosci posse quam intellectum” 29 Ariew, 108. “pronuntiatum […] necessario […] verum” 30 Ariew, 108. “… certum […] et inconcussum” 31 Recherche de la vérité, AT X, 515, 17 et 20. But… 32 Ariew, 232. “… eo temporare quo cogitat” 33 Ariew, 109. “… si cessarem ab omni cogitatione, […] illico totus esse desinerem - … je cesserais en même temps d’être ou d’exister” 34 Ariew, 121. “res incompleta et ab alio dependentem” 35 Ariew,165. “”… ideia [substantiae] infinitae”,.. “idea [substantiae] finitae” 36 modified Ariew, 174. “… substantiae infinita et independens”…”… res finita et depndens” 37 Ariew, 118.”… nam contra manifeste intelligo plus realitatis esse in substantia infinitia quam in finita, ac proinde quodammodo in me esse perceptionem infiniti quam finiti, hoc est Dei quam mei ipsius” 38 Ariew, 237 “… Deum authorem rerum esse infinitum [ontically], et nos omnino finites” 39 Ariew, 101. “… mentes nostras considerandas esse ut finitas, Deum autem ut incomprehensibilem et infinitum…” 40 Ariew, 119. “… est enim infiniti, ut a me, qui sum finitus, non comprehendatur” 946, 21-23) 41 Ariew, 236. “… est de natura infiniti, ut a nobis, qui summus finiti, non comprehendatur…” 42 See A Mersenne. January 21, 1641, AT 3, 284, 5-8; and A Clersier sur les Cinquièmes Objections, January 12, 1646: “Car, à cause que le mot de comprendre signifie quelque limitation, un esprit fini ne saurait comprendre Dieu qui est infini” (AT 9-1, 210, 10-12). 43 See our study “L’image de la liberté” in R. Brague (éd.), Saint Bernard et la philosophie, Paris, PUF, 1992 (suivi de “Réponse à J.- L. Viellard-Baron à propos d”une hypothèse sur saint Bernard et l’image de Dieu”, Philosophie, 42, 1994). 44 E. Lévinas, “Sur l’idée d’infini en nous”, en N. Grimaldi/J.-L. Marion (éd.), La passion de la raison, Paris, 1983, repris dans Entre-nous. Essais sur la penser-à-l’autre, Paris, 1991, p. 245. Where: “l’affection du fini par l’infini […], par dela la ure contradiction qui les opposerait et les sépareraient…” (ibid.). 45 modified Ariew, 121. “… similitudinem, in qua Dei idea continentur…” 46 Ariew, 121. “… a me percipi per eandem facultatem, per quam ego ipse a me percipior” 47 L. Wittgenstein, Tractatus logico-philosophicus, Préface, Scnhriften, I, Francfort s/m., 1980, p.9. But does not philosophy consists, in the end, in thinking what remains above all and most of the time to think, as phenomenology consists in seeking to show the phenomena which first and most often remain concealed? 48 Ariew, 122. “… ad majora et majora […] indefinite aspirantem” 49 We must agree with this judgment by N. Grimaldi: “L’infini peut donc être reconnu comme l”horizon transcendental de notre volonté” (Six etudes sur la volonté et la liberté chez Descartes, Paris, Vrin, 1988, p.34), or also, “L’infini est l”horizon transcendantal de toute representation comme de toute volonté” (Études cartésiennes. Dieu, le temps, la liberté”, Paris, Vrin, 1996, p.140). 50 Suarez and Scotus 51 “Quelqu’un demandera: “Connaissez-vous clairement et distinctement l’être infini? Que veut donc dire cette commune sentence, laquelle est connue d’un chacun [tritum illud et vulgo notum]: infinitum, qua infinitum, est ignotum”?” my translation. 52E. Husserl, Ideen I, §44, Hua. III, p. 100 and 101. 53Ariew, 124. “… tantam in me experior, ut nullam majoris ideam apprehendam” 54 N. Grimaldi, Six etudes, p.25 55 A Mersenne, 25 décembre 1639, AT 2, 628, 6-9. – Moreover Meditatio IV recognizes perfection in the will, the perfection proper even to God: “ …vis volendi […] amplissa et in suo genere perfecta” (VII, 58, 14-17). At the same time oner finds at the end this intial hypothesis refuted: “ …facultas verum judicandi […] infinita”(54, 29-30). 56 A Mersenne, 28 january 1641, AT 3, 295, 22-24. See Passions de l’âme, §19, AT 11, xx, xx. ET 30. Ariew, 95. 57 “…Être universel, sans restrictions particulière, être en général” (Recherche de la Vérité, III, 2,8,§1.O.C., t.I., p.4556, see pp. 449 and 473). Does Malebranche not expose himself to accusations of Spinozism (see t.XIX, p.849 and 898)? This difficulty, which Malebranch will never succeed in dissipating, finds itself in effect dissimulated by another decision: “The Being without restriction” tends little by little to cede the primary role to the “… vast and immense idea of the infinitely perfect Being” (Éclaircissement I, §18, t. III, p.168 and Traité de la Nature et de la Grâce, I, §11,t.V.p.26). See Questions cartésiennes II, c.XX, Paris, 1996.