problems of the infinite cusanus and descartes

8/12/2019 Problems of the Infinite Cusanus and Descartes

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Problems of the Infinite usanus and Descartesby Karsten Harries

Many contemporary philosophers are uneasy about what philosophy

has become and where it has led uso Their uneasiness mirrors widespreadconcern about the shape of modern culture. As more and more begin tosuspect that the road on which they have been travellingmay be a deadend, attempts are made to retrace steps already taken. A search beginsfor the missed turn and for those who may have misled uso

Among these Descartes would appear to deserve a special place. Hashis understanding ofproper method not helped found modern philosophy,science, and indeed modernity? The present essay is part of an attempt toexcavate what lies beneath this supposed foundation. It here takes theform ofa step back from the mathesis universalis ofDescartes to the doctaignorantia of Nicolaus Cusanus. That step invites a rethinking of tl le artesianproject.Not that Descartes writings call for such an excavation. DespiteMaurice de Gandillac s suggestive remarks on the many ways in whichCusanus s speculations look forward to Descartes,l the latter cannot havefound the cardinal s anything but clear and distinct prose much to hisliking. Descartes mentions Cusanus only once, in a letter to Chanut,where he points out thatthe Cardinal of usa andmany other Doctorshave supposed the world to be infinite without ever being censured by theChurch, and insists that his own opinion

is not as difficult to accept as theirs, because I do not say that theworld is infinite, but only that it is indefinitely great. There isIMaurice de Gandillac, Nikolaus von ues Studien zu seiner Philosophie undphilosophischen Weltanschauung (Dsseldorf: Schwann, 1953), substantially re-vised translation of philosophie de Nicolas de ues (Paris: Aubier, 1942) byKarl Fleischmann.


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90 AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLYquite a notable difference between the t ~ o for we cannot saythat something is infinite without an argument to prove thissuch as we can give only in the case ofGod himself; but we cansay that a thing is indefinitely large, provided that we have noargument to prove that it has bounds.2

Descartes returns to this distinction in the Principles of Philosophywhere he admonishes usthat we must never discuss the infinite, but must simplyconsider those things in which we notice n limits as indefinite:as, for instance, the extension of the world, the divisibility ofparts ofmatter, the number of stars, etc.

He explains thatThus we shall never be wearied by any debates concerning theinfinite. For of course, inasmuch as we are finite, it would beabsurd for us to attempt to determine anything concerning theinfinite, and thus attempt as it were to prescribe limits to it andcomprehend it. Therefore we shall not bother to respond to thosewho ask whether the half of a given infin.i.te line would also beinfinite; or whether infinite number is even or odd, and such:because surely only those who judge their own mind to beinfinite ought to think about such things.3

Descartes would have agreed with Cusanus t:hat it is self-evident thatthere is no comparative relation of the infinite to the finite. 4 utwhileCusanus concluded from this that a finite iIltellect cannot preciselyattain the truth about things; 5 Descartes denied that infinity is so2Letter to Chanut June 6, 1947, Descartes, Philosophical Letters tr. and ed.Anthony Kenny (Minneapolis: University of Minnesota Press, 1981), 221. Descartes had insisted on this distinction already in his Reply to Caterus. See Replyto Objections I Philosophical Works ofDescartes tr. E.S. Haldane and G.R.T. Ross(New York: Dover, 1955), vol. 11 p 17. Descartes goes on there to distinguishbetween the formal notion of the infinite and the thing which is infinite; theformer we understand only in a certain negative fashion, from the fact namelythat we perceive no limitation in the thing, but the thingwhich is infinite is itselfpositively understod. Descartes wants to claim both: that we have a positiveunderstanding ofGod, yet cannot comprehend his infinity. Ibid., 18.3Rene Descartes, Principles ofPhilosophy I, 26; tr. \lalentine Rodger Miller andReese P Miller (Dordrecht, Boston, Lancaster: Reidel, 1983), 13.4Nicolaus Cusanus, De docta ignorantia I 3, tr. JasperHopkins, Nicholas of uson Learned Ignorance A Translation nd n Appraisal ofDe Docta Ignorantia(Minneapolis: Banning, 1981), 52. e docta ignorantia I, 3; tr. p 52.


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WINTER 91constitutive of things that whenever we attempt to really understandthem we become entangled in what he would dismiss as wearying debatesconcerning the infinite. This dismissal covers up an abyss that liesbeneath the supposedly secure realm of truth.

Separated by two hundred years, Cusanus and Descartes have th is i ncommon: their thought is informed by a profound understanding of th esignificance ofperspective, which threatens to imprison th e finite humanknower in mere appearance. But while the young Descartes promises to

hand us with his Rules for the Direction ofthe indthe Ariadne s threadthat will lead us out of what Baroque writers liked to call the labyrinthof the world 6 an d th e mature Descartes attempts to demonstrate thatthis promise of an escape from what is but a Christian version ofPlato scave was no t idle, Cusanus would teach us to recognize and accept ourprofound ignorance. All ou r attempts to seize the truth must founder onthe reef of infinity.

Arguing for th e perspectival character of all knowledge, Cusanusresists the temptation to absolutize a particular mode ofknowledge an d tomake it the measure of reality. Ou r knowledge of reality is inescapablyconjectural. It is thus not surprising that later thinkers, such as Bodinan d Schookius consider Cusanus a leading Pyrrhonist.7 Such a conclusionis difficult to avoid once we agree with Descartes that we must reject allsuch merely probable knowledge and make it a rule to trust only what iscompletely known an d incapable of being doubted. 8

To be aware of perspectival appearance as such is to be aware not onlyofwhat is seen, but also ofthe conditions imposed on th e seen by our pointof view. Such awareness cannot be divorced from another: awareness ofwhat constitutes my point ofview carries with it some awareness ofotherpossible points of view. To recognize th e limits imposed by any particularperspective we have to be in some sense already beyond these limits,while failing to recognize them, we are likely to mistake appearance forreality. This mistake constitutes that ignorance about which Cusanuswould have us become learned.6See RuZes for the Direction ofthe Mind PhiZosophicaZ Works ofDescartes tr. E.S.Haldane and G.R.T. Ross, vol. I (New York: Dover, 1955), RuZe V p 14.7See Gnter Gawlich, Zur Nachwirkung Cusanischer Ideen im Siebzehnten un dAchtzehnten Jahrhundert in NicoZo Cusano agZi inizi deZ mondo moderno tt ideZ Congresso internazionaZe in occasione deZ V centenario della morte di NicoZoCusano (Firenze: Sanzoni, 1970): 227, n. 4 an d Richard H. Popkin, The History ofScepticism (New York; Harper, 1968), 84 an d 202.RuZe 11 tr. p 3


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AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLYAn example helps Cusanus to illustrate the key point: Cusanus asks usto imagine someone on a moving ship in the middle of a large body ofwater. Such aperson unable to see the shores and to find a point ofreference there, might think his ship the unnl0ving center of the world.

Butwith what right? And where is the point ofreference that would allowus to claim that the earth is at rest in the middle of the cosmos?

Because of the fact that it would always seem to each person(whether he were on the earth the sun, or another star) that hewas the immovable center, so to speak, arld that all other thingswere moved: it would assuredly be the case that ifhe were on thesun, he would fix a set of poles in relation to himself; if on theearth another set; on the moon another; on Mars, another, andso on. IO

Human beings have a natural tendency to t k ~ e whatever place they justhappen to occupy for a center. But as we recognize that all supposedlynaturally given centers are precariously established by human knowersand bound to their finite condition, rest and rn.otion, too, become relativeconcepts, for we apprehend motion only through a certain comparisonwith something fixed. ll By questioning the very idea ofa naturally givencenter the perspectivism ofCusanus s thought experiment thus turns notonly against the geocentric cosmology of Aristotle and Ptolemy, but alsoagainst the not yet born heliocentric cosmology of Copernicus, Kepler,and Galileo.12While reflection on the phenomenon of perspective may suffice to callinto question particular centrist illusions, it is insufficient to show thatthe very idea of a natural center should be rejected. Cusanus does so,because he finds the conception of a center of the cosmos unintelligible: Dedocta ignorantia 11 12; tr. p. 117: For exan1ple, if someone did not know thata body of water was flowing and did not see the shore while he was on a ship inthe middle ofthe water, how would he recognize that the ship was being moved?Invoking the authority of Virgil s eneid Copernicus uses essentially the sameimage to introduce his De Revolutionibus r b i u r r ~ Coelestium and Descartesadopts the Copernican example: Just as a man in ealm weather and looking atseveral other fairly distant vessels, which seem to hirn to be changing position, isfrequently unable to say whether the change is caused by the movement of thevessel on which he is or by that of the other vessels; when from our situation, weobserve the course of the planets and their positions, even careful observationdoes not always bring sufficient understanding to enable us to determine to whichbodies we ought properly to attribute these changes Principles 111 15; tr. p 89.lODe docta ignorantia 11 12; tr. p. 117.llIbid., 11 12; tr. p. 117.l2Given his perspectivism, it is no surprise that the eardinal should have gone onto write De Pace Fidei which pleads for religious tolerance in a way that looksforward to Lessing sNathan derWeise In the sphere ofreligion, too, what we taketo be central depends on our point of view.


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For if it had a [fixed] center, it would also have a [fixed]circumference; and hence it would have its own beginnlg andend within itself, and it would be bounded in relation tosomething else, and beyond the world there would be bothsomething else and space loeus . But all these [consequences]are false. Therefore, since it is not possible for the world to beenclosed between a physical center and a [physical] circumference, the world ofwhich God is the center and circumference-is not understood. 3

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The apparent dome of the firmament is itselfbut a perspectival illusion.Challenging Aristotle, Cusanus insists that the cosmos can only bethought as infinite, where, very much like Descartes, who in the citedletter to Chanut does not prove hirnself a careful reader of De doetaignorantia, Cusanus, too, is careful to distinguish it s infinity from that ofGod: the cosmos is infinite in that it lacks limits in which it can beenclosed, while true infinity precludes all indeterminacy.14

Our inability to think a boundary or limit of the universe is just acorollary of our more general inability to think an absolute maximum.Take the case of counting. To ask for the greatest number is to ask for animpossibility. Were we to frame what Descartes is right to insist is theunreasonable thought of the numerical maximum and ask the equallyunreasonable question whether we move closer to that maximum whenwe multiply, say, 100 by 10, we should have to answer that despite suchmultiplication we have gotten no closer, but remain equally, i.e., infinitelydistant from it. When referred to the unreasonable limit of the greatestnumber, the number line becomes a circle and that limit its center, itselfno longer a number. But with this transformation greater and smallerlose their meaning. With it the plurality ofnumber vanishes. Left is theessence ofnumber itselfno longer a number. The same holds when we toattempt to refer numbers to the numerical minimum, which Cusanusunderstands as oneness; which is the essence ofevery number. Were weto ask whether this minimum is contained more times in 1000 than in100, we should have to say once again that oneness is equally containedin both, just insofar as they are nUITlbers Le that both are equallydistant from it. 5Once again the number line turns into a circle with the De docta ignorantia, 11 11; tr. p. 114.14Ibid., tr. p. 90: Therefore, only the absolutely Maximum is negativelyinfinite. Hence, it alone is whatever can at all possibly be. But since the universeencompasses all the things which are not God, it cannot be negatively infinite,although it is unbounded and thus privatively infinite. And in this respect it isneither finite nor infinite. Cf Descartes, Principles Philosophy, I, 27; tr. p 14.5De docta ignorantia I, 5; tr. pp. 54-55.


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94 AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLYlimit provided by the minimum at its center. Nor can we finally distinguish these two centers, which fall equally outside the number sequence.The minimum merges with the maximum. For the [unqualifiedly]minimum must coincide with the [unqualifiedly] maximum, therefore thecenter of the world coincides with the circumference. 16

The source of Cusanus s famous description of the universe as aninfinite sphere which has its center everywflere and its circumferencenowhere,17 is Meister Eckhart,18 who in turn found the formulation in theBook ofthe 24 Philosophers. Cusanus, however, transfers what is first ofall a metaphor for God to the cosmos. Not that it thereby loses itstheological aura: The endless universe is understood by Cusanus as anepiphany of the one and infinite God.Although Cusanus s understanding of the cosmos in the image of theinfinite sphere is linked to his conception ofthe infinite power ofGod, thepersuasive force of his cosmology does not depend on its theologicalorigins. Speculation will be led to such metapllors, whenever it attemptsto bound the boundless. We may, to be want to heed Descartesadmonition that such speculation surpasses the infinite human intellect.

But the very ease with which we are drawn into it suggests that thehuman intellect is more involved with the infinite than its supposedfinitude would seem to allow.

But why this need to bound the boundless? Is it perhaps because wecannot understand ourselves except as parts of the universe? To reallyunderstand ourselves as such parts, we need to grasp the universe as auni verse, i.e., as a whole, even ifthis attempt ,viII inevitably outstrip theunderstanding and involve us in mythopoeic construction.To think the universe as a whole, we have to think its boundaries. Butjust this we appear unable to do for we are unable to think the boundaryofspace, i.e., the spatial maximum. This means also that we cannot makesense of an absolute center of space. With tllis loss of the center thesupposed truth of key propositions in astronom.y also becomes difficult tomaintain How can we assert the absolute truth of say, the Copernicanhypothesis, if we are unable to make sense of a center of space and thusto understand the cosmos as a whole? Once the infinity of space has beenrecognized, the attempt to think such a center no longer makes sense.16Ibid., 11; tr. p 114.17Ibid., I, 23 and 11 11, 12. See Dietrich Mahnke, Unendliche Sphre unAllmittelpunkt (Halle: Niemeyer, 1937). and Karsten Harries, The InfiniteSphere: Comments on the History of a e t a p h o r ~ 1 he Journal ofthe History ofPhilosophy 13, (1975): 5 1518See Mahnke, pp. 76-106, 144-158, 169-176 and Herbert Wackerzapp, DerEinfluss Meister Eckharts uf die ersten philosophischen Schriften des Nikolausvon Kues 1440-1450 (Mnster: Aschendorff, 1962).


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WINTER 95When we nevertheless attempt to seize that center, we end with theimpossible thought ofthe coincidence ofopposites, which denies absolutetruth to the human understanding and teaches us about our ignorance. 9

Given Cusanus s understanding ofthe infinity ofthe cosmos, it is to beexpected that he should have rejected the traditional distinction, sofamiliar to Aristotelians, between the sublunar and the superlunarworld. Ockham s critique ofthe heterogeneity ofthe cosmos had preparedfor this. But when the heterogeneity of the cosmos is challenged, soinevitably is Aristotle s physics. It, too, is shown to rest on anthropocen-

tric prejudice. That hierarchical conception of the cosmos we think socharacteristic of the Middle Ages had been undermined speculativelylong before it was overthrown by the new science, by Tycho de Brahe sobservation of a new star in the superlunar realm, by Galileo s andScheiner s discovery ofchanging spots on the supposedly immaculate faceofthe sun, and by the theories ofCopernicus and Kepler.2

Like Cusanus, Descartes, too, argues from the infinity of space for thehomogeneity ofthe cosmos.2 From the perceived identity ofthe ideas ofextension and corporeal substance he deduces that the matter of theheaven does not differ from that of the earth; and that even if there werecountless worlds in all it would be impossible for them not to all be ofone19Cusanus impossible speculation on the coincidence of opposites and theinfinite sphere throws an interesting light on Nietzsche s elusive doctrine of theeternal recurrence. Since we can map the number line onto the time line, thereference to the infinite which closes the number sequence to a ring would appearto hold also for time. Time, too, will not be bounded. Any attempt to think anabsolute beginning oftime leads to thoughts ofthat time before time began. Butif the infinity of time is assumed, the impossible thoughts of a beginning and anend of time have to coincide and referred to this Alpha and Omega of time, timecloses into a ring. Georges Poulet, in the introduction to his The Metamorphoseso the Circle (BaItimore: Johns Hopkins, 1966), cites a number of passages bymedieval writers, including Bonaventure, Aquinas, and Dante, that show thatthe temporal implications of the metaphor of the infinite sphere were weBrecognized. Hans Blumenberg speaks of a Sprengmetapher a metaphor thatexplodes a world view, and, pursuing a hint provided by a diary fragment byGeorg Simmel, relates it to Nietzsche s doctrine of the eternal recurrence. SeeSchiffbruch m t Zuschauer Paradigma einer Daseinsmetapher (Frankfurt:Suhrkamp, 1979), 84.2For an iBuminating account of the incon1patibility of God s omnipotence andomnipresence with Aristotelian physics see Hans Blumenberg, Die Genesis derkopernikanischen Welt (Frankfurt: Suhrkamp, 1975). Blumenberg places specialemphasis on Bishop Tempier s Condemnation of 1277, which helps bring intofocus the specifically Christian character of the prehistory ofmodern science.21Principles 21; tr. p 49.


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96 AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLYand the same [kind of] matter. 22 Where Descartes differs from Cusanusis in the confidence with which he asserts that our inability to imagine alimit of space allows us to say that in reality space has no limit.Cusanus would have questioned the presupposed commensurability ofour imagination and reality and insisted tllat the boundless cosmosopened up by reflection is itselfbut a human eonjecture. We shall neverknow as God knows. Absolute truth belongs only to God. When weattempt to seize it we inevitably end up in arltinomies and paradox. Tosail past these pillars of Hercules is to lose all bearings. All we knowbears the imprint of our human measure. We escape the prison of oneperspective only to find ourselves bound by allother.

IVDescartes too recognizes how our supposedly clear and distinct perception of extension entangles us in the infi.llite. But on this reef ourresolution to accept only that as true which is completely known andincapable of being doubted has to founder. D1escartes is thus forced toconclude his Principles Philosophy with the admission that in naturalscience absolute certainty is not to be had that we have to settle for whatis morally certain that is certain to a degree which suffices for the

needs ofeveryday life; although ifcompared to the absolute power ofGodthey are uncertain. 23 We must take Descartes by his word when heinsists that the works ofGod cannot be thought too great and that wemust beware lest in thinking too highly ofourselves we suppose that weunderstand for what ends God created the worJld. 24 This must mean alsothat we have no reason to assume that God created the world so that wemight gain an adequate understanding of it. i \l l the physicist can do isconstruct mechanical models ofwhat he observes and use these to predictwhat is going to happen. Such abili ty to prediet need not mean that thereal causes have been understood; indeed givell the infinite divisibility ofmatter it is very unlikely that our finite models will ever allow us toduplicate nature s processes.

For just as the same artisan can make two clocks which indicatethe hours equally weIl and are exactly similar extemally butare internally composed ofan entirely dissimilar combination ofsmall wheels; so there is no doubt that the greatest artificer ofthings could have made all those things ~ h i h we see in manydiverse ways. And indeed most willingly concede this to be

Principles 11 22; tr. pp. 49-50. 3principles IV 205 tr. p. 287. 4principles 111 1 and 2; tr. p. 84.


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WINTER true, and will think that I have achieved enough ifthose thingswhich I have written are only such that they correspond accurately to all phenomena of nature.

Descartes compares the scientist to someonewho attempts to read a letterin code:

Thus, for example, if someone wishes to read a message writtenin Latin letters, to which however their true meaning has notbeen given and if, upon conjecturing that wherever there is an Ain the message, a B must be read, and a C wherever there is a B,and that for each letter, the following must be substituted; hefinds that by this means certain Latinwords are formed by theseletters: he will not doubt that the true meaning of that messageis contained in these words, even if he knows this solely byconjecture, and even though it may perhaps be the case that theperson who wrote the message did not put the immediatelyfollowing letters but some others in place of the t rue ones, andthus concealed some different meaning in the message.6

Ifwe accept that God s power is infinite or just the infinite divisibility ofmatter, there is no way for science to take the measure of natureMeasured by his own conception ofabsolute truth all Descartes can claimfor science are well-founded conjectures. Descartes, to be sure, modifiesthis admission when he claims that there are even among naturalthings, some which we judge to be absolutely and more than morallycertain. He mentions mathematical demonstrations, knowledge thatmaterial things exist, and indeed all evident demonstrations which aremade concerning material things. He goes on to suggest that despite hisdisclaimers These reasonings ofourswill perhaps be included among thenumber ofthese absolutely certain things by those who consider how theyhave been deduced in a continuous series from the first and simplestprinciples of human knowledge. 27 But where in the Principles do evidence and deduction leave off and conjectures begin?Ifthe endless divisibility ofspace suggests the artificiality ofDescartesreconstruction of nature by means of mechanical models, i ts limitlessextension makes it impossible to assert either absolute motion or rest.Descartes thus follows Cusanus with his relativistic conception ofmotion:Movement, properly understood, concerns only the bodies contiguous to

25Principles V 204; tr. p. 286.26Principles IV, 204; tr. p. 287. Cf. Hans Blumenberg, Die Genesis der koperni-kanischen Welt 368 70.27principles V 206; tr. p. 287.


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98 AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLYthe body which is moving. 28 In this sense sorneone who rests on a deckchair on a moving ocean liner can properly say that he is notmoving. Andin the same sense Descartes can agree with Copernicus and yet say thatproperly speaking the earth does not move si]tlce on his conception of afluid heaven, it is carried along by its vortex.Descartes knew that his insistence that the earth does not properlymove, but is carried around the sun was not likely to satisfy those criticsof the Copernican system who not long aga had attempted to silenceGalileo. As he himself points out, besides its own proper movement, abody can also participate in innumerable other movements, in as muchas it is apart of other bodies which have other movements. 29 He asks usto imagine a sailor wearing a watch. Although each ofthe watch s wheelswill have its own proper movement relative to the watch case, it alsoparticipates in the movements ofthe sailor, the ship, the ocean, the earthand, we can continue, the solar system, and the galaxy. Is there a final, allencompassing whole that would allow us to speak ofthe absolute motionof each wheel? Given Descartes clear and distinct conception of exten-sion, that question is as meaningless as the question whether the infinitenumber is odd or even. This means also that someone who wants to holdon to his conviction that the earth is at rest cannot be refuted byastronomy.

Since the nature of our intellect is such that it perceives nolimits to the universe and since, consequently, anyone who takescareful notice of the greatness of God and the weakness of otITperception willjudge that i t is much more appropriate to believethat perhaps, beyond all the fixed Stars w]tlich we see, there areother bodies in relation to which we would have to say that theEarth is at rest and all the Stars move together, than to supposethat none such could exist.3

No doubt, the Church s condemnation of Copernicus s De Revolutioni-bus and its subsequent ruling against those who continued to teach thecondemned doctrine played an important part in Descartes refusal tosimply proclaim the truth ofthe Copernican system. But he also could nothave reconciled such a proclamation with the infinity of the cosmos hethought implied by the clear and distinct perception of extended sub-stance.

VCusanus, as we have seen, derives the infinity of the cosmos from themore general principle thatwe cannot think an absolute maximum. Ifthe

28principles 28; tr. p. 52.29Principles 31; tr. p. 54.3 Principles 29; tr. p. 96.


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WINTER 99boundlessness of the cosmos is thus not grasped, it nevertheless showsitselfin the knowledge that in thought at least we are free to pass beyondany boundary. Such, knowledge, however, presupposes that we possess afaculty that reaches up to what will always exceed our grasp. While ourability to comprehend is finite, the freedom of thought is infinite.Descartes, too, recognizes that by its very essence human being, no lessthan extension, is entangled in the infinite.

For to take an example, if I consider the faculty of comprehension which I possess, I find that it is of very small extent andextremely limited, and at the same time I find the idea ofanother faculty much more ample and even infinite, and seeingthat I can form the idea ofit I recognize from this very fact thatit pertains to the nature of Od

Indeed, ifwe could not measure the reach ofour faculty ofcomprehension by a much more ample and even infinite faculty, we could notrecognize its finitude. In this case, too, the principle applies that tounderstand a perspective as such is already to be beyond it, at least inthought: to think the reach ofour faculty ofcomprehension as essentiallyfinite we have to in some sense transcend ourselves as finite knowers.Regardless ofwhether God exists, our ability to form some idea of God sinfinite nature presupposes that the power of human self-transcendencereaches up to the infinite. Descartes points in this connection to the will:

It is free-will alone or liberty ofchoice which I find to be so greatin me that I can conceive no other idea to be more great. It isindeed the case that it is for the most part this will that causesme to know that in some manner I bear the image and similitude of God. For although the power of will is incomparablygreater in God than in me, both by reason ofthe knowledge andthe power, which conjoined with it, render it stronger and moreefficacious, and by reason of its object, inasmuch as in God itextends to a great many things; it nevertheless does not seem tome greater if I consider it formally and precisely in itself.

As will, thought transcends the finite understanding towards infinityAndjust as the fact that I have a clear and distinct understanding ofGoddoes not mean that I comprehend hirn, or the fact that I have a clear anddistinct idea ofextension does not mean that I comprehend it, so the factthat I have a clear and distinct idea ofmyself as thinking substance doesnot mean that I comprehend myself. The self transcends its own understanding. Every free action manifests human self-transcendence. Allhuman behavior remains finally incomprehensible.31Descartes, Meditation IV; tr. p. 174. Meditation IV; tr. 175.


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100 AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLYDescartes touches on this difficulty in he j ~ s s o n s of the Soul where

he suggests that the machine of the body is so formed that from thesimple fact that this [the pineal] gland is diversely moved by the soul, orby such other cause, whatever it is, it thrusts the spirits which surroundit towards the pores of the brain, which condulct them by the nerves intothe muscles by which means it causes them to move the limbs. 33 Thisraises the question that already troubled Gassendi, how that union andapparent intermingling, or confusion, can be found in you, if you areincorporeal and indivisible. 34 How, given Descartes distinction betweenres cogitans and res extensa can the soul be said to be the efficient causeof bodily actions? What could cause mean here?

But perhaps we are given a hint of how to approach this problem byDescartes answer to Arnauld s question what the former might possiblymean when he calls God his own efficient eause. Descartes answerdepends on the mathematical symbolism Cusanus had advanced in docta ignorantia:

But in order to reply expressly to this, let Ine say that think wemust show that intermediate between ef{icient cause in theproper sense, and no cause there is sOInething else, viZe thepositive essence ofa thing to which the cOIlcept of efficient causecan be extended in the way in which in geometry we are wont toextend the concept ofa circular line that is as long as possible tothat of a straight line; or the concept of a rectilinear polygonwith an infinite number of sides to that of a circle.3

When Descartes calls God his own efficient cause, efficient cause isnot to be understood literally, but in an extended sense that presupposesa willingness to follow Cusanus in his infinite ascent to the coincidentiaoppositorum

would like to suggest that if we are to understand Descartes claimthat the soul is the cause of bodily actions, cause must be given asimilarly extended meaning, which involves a movement to the infinite.Note the scale change when in his reconstruction ofthe machine ofthebody Descartes turns to the animal spirits, w hich name a certain verysubtle air or wind that courses through the nerves and the brain ofwhich only the most subtle enter the cavities of the brain.7 These33Descartes, The Passions of the Soul I, 34; tr. Phil080phical Works vol. I, p. 347.340bjections V; tr. Philosophical Works vol. p. 201. Cf. Anthony Kenny,Descartes A tudy of his Philosophy (New York: Random House, 1968), 224-26.350bjections IV; tr. p. 89.36Reply to Obj IV; tr. p. 110.37The Passions ofthe Soul 1 7 and 10; tr. pp. 334 and 335.


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WINTER 101animal spirits are nothing but material bodies and their one peculiarityis that they are bodies of extreme minuteness. 38 The soul is said toexercise its functions immediately only in a certain very small glandwhich is so situatedthat the slightest movements which take place in it may altervery greatly the course ofthese spirits; and reciprocally that thesmallest changes which occur in the course ofthe spirits may domuch to change the movements ofthis gland.9Descartes mechanics of the body proves incapable of giving an adequateaccount of human action. To do so it would have to model what isindefinitely small and thus must remain indeterminate. This indeterminacy opens up the space that. allows what Gassendi considered theconfusion of body and soul. Perhaps it would be better to speak of theircoincidence.

VIAccording to Descartes, the perception of the understanding is extended to those few things which are presented to it, and is always veryfinite. 40 Cusanus would have agreed that our understanding, if not ourintellect, is limited by its inescapably finite perspective. Convinced ofthe

perspectival nature of all human knowledge Cusanus was led to defendProtagoras and his thesis that man is the measure of all things againstthe criticism ofAristotle.4 I suspect that his interest in Protagoras wassparked by the slightly younger Leon Battista Alberti, who made passingreferences to Protagoras in book two of the Libri della famiglia and in hisDe pictura As Cusanus was to do a few years later, first in De doctaignorantia Alberti insists that all things are known by comparison.4Alberti, too, is convinced that neither objective space nor it s subjectiveappearance, which alone is the proper concern ofthe painter, allows us to38Ibid., I 10; tr. p 336.39Ibid., I 31; tr. pp. 345-346.4Principles I 35; tr. p. 17.41See De beryllo chs. 5 and 36; tr. Karl Fleischmann, ber den Beryll (Leipzig;Meiner, 1938), 69 and 125. Cusanus could find a discussion ofProtagoras s dictumin Aristotle, Metaphysics 1002b8-23, 1009a6-13, 1009bl-6 1047a4-7, 1053a3536, 1062bI2-13. Ficino translated Plato s Protagoras and Theaetetus only in the1460 s. See Charles Trinkaus, Protagoras in the Renaissance: An Exploration;in Philosophy n Humanism: Essays in the Honor ofPaul Oscar Kristeller (NewYork: Columbia University Press, 1976), 190-213, especially 194.42Trinkaus, Protagoras, 195-196.43Leon Battista Alberti, On Painting tr. and int. John R Spencer (New Haven:Yale University Press, 1966). 55. See also Nicholas of Cusa, On Learned Igno-rance I, 1; tr. p. 50.


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102 AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLYspeak of the true size of things. This would presuppose that somewherethere is a true measure. Where is such a measure to be found? Measuresmay indeed suggest themselves quite naturally, as the body provides thehuman being, and especially the painter, wit:h a natural measuring rod,but this measure depends on an accident 1 natllre. His own artisticpractice must have suggested to Alberti that Protagoras, notwithstanding all his critics, got hold of something very important: By saying thatman is the mode and measure of all things [he] meant that all theaccidents ofthings are known through the accidents ofman. 44 And whatcould it mean to grasp things as they really are? Presumably Alberti ssensate wisdom would have dismissed this question as useless to thepractical task he had set himself, just as he dismissed as quite useless forhis purpose the dispute whether the visual rays issue from the eye orfrom whatever is seen.45 Alberti s practice-oriented relativism invites hisreaders to renounce the claim to absolute trutll. We can leave such truthto God. But such an invitation does not imply anything like resignation.Quite the opposite: Alberti s refusal to engage in what he considers idlespeculation concerning the way things really are is but the other. side ofa proud confidence that relying only on himself the artist is able to somaster appearance, that anotller god; 46 he is able to create anotherworld. In this respect his treatise on painting is a forerunner ofDescartespractical philosophy.

Given the overlapping biographies and interests ofAlberti and Cusanus, find it inconceivable that these two seminal figures of the Renaissance should not have met.47 And given Cusanus s interest in painting44Alberti, n Painting45Ibid., p 46.46Ibid., p 64.47See Joan Gadol, Leon Battista Alberti. Universal Man o the Renaissance(Chicago and London: The University ofChicago Press, 1969), 196, n. 66: Thereis no direct evidence that Alberti ever knew Cusa personally, although both wereclose friends of Toscanelli. Cusa studied at the university of Padua from 1417-1423, when he received his doctorate in law, and Toseanelli was as the Universityas a student during these years. There the two became friends and remained sothroughout their lives. Alberti left Padua in 1421. He may have known Cusa andToscanelli there, but there is no evidence that he actually did. There were severaloccasions at which Alberti and Cusa could have met after that During theCouncil of Florence-Ferrara, Alberti was at Ferrara with Eugenius IV as wasCusawho received his appointment there as apostolie visitor to Germany. In 1540,Alberti was residing in Rome when Cusa was made a cardinal by Nicholas Vanother mutual friend. In the late 1450 s, Cusa s ho:me in Rome was a gatheringplace for men of science like Peurbach, Regiomontanus, and Toscanelli; Albertimust have been a member of that group. CitingG Mancini s Vita di LeonBattista Alberti Paul O Kristeller points out that Cusanus owned Alberti sElementae picturae A Latin Tanslation of Gemlistos Plethon s De Fato by


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WINTER 103and the problem of perspective, he must have read Alberti s De picturawith interest. What Alberti had to say there about Protagoras and thegodlike creativity of the artist must have seemed especially suggestive.Cusanus, at any rate followed Alberti in finding in the saying ofProtagoras hints of a deeper understanding of the nature of knowledgethan his critic Aristotle possessed. On first consideration it is difficult notto agree with Aristotle; for if, as Plato teIls us in the TheaetetusProtagoras held that all things are becoming and we cannot rightly callanything by any name, such as large and small, heavy or light, for givena different point of view, a different perspective, the great will be judgedsmall and the heavy light,48 what is discourse, what are agreement anddisagreement finally about? Once more recalling Alberti, Cusanus, too,ties the thesis that man is the measure ofall things to another, the thesisthat man is a second god, although the cardinal invokes the authority ofthe mythical Hermes Trismegistus.The language Cusanus used to develop his understanding ofthe humanbeing s godlike creativity, which can of course invoke the Biblical understanding of man as created in God s image, remains quite traditional.Following Thomas Aquinas and supported by a false etymology, Cusanusrelates mens (mind) to mensura (measure).5 The mind s proper activity ismensurare (to measure).51 And again, like Thomas and Aristotle, Cusanus takes counting to be the paradigm of all measuring. ut inkeepingwith Alberti s understanding ofthe Protagorean dictum, Cusanus gives avery different meaning to such seemingly traditional formulations.According to Thomas the human being is really the measure only ofthosethings it i tself creates. The things of nature measure us more than wemeasure them. Cusanus, on the other hand, understands the humanknower rather like an Albertian artist who creates conceptual, andespecially mathematical forms with which he structures what presentsitself to hirn in his own image. Cusanus knows that things presentthemselves to us as they do because we have always already taken theirmeasure. Constitutive of appearance is our way of understanding it.Following Plato and the Platonic tradition, Cusanus, too, understandsthe activity of the mens as a search for unity. This search expresses itselfin unending attempts to subject the world to unity, to reduce what isJohannes Sophianos Dedieated to Nieholas ofCusa, in Nicolo Cusano agli inizideI mondo moderno 184-185. See also Pauline Moffitt Watts, Nicholas CusanusA Fifteenth Century Vision ofMan (Leiden: BrilI, 1982), 150.48Plato, Theaetetus 152d.49Nieolaus Cusanus, De beryIo ehs. 5 and 36; tr. pp. 69, 125, 129.50ST I. 11. 2; 1 11. 91. 3ad2. See also Aristotle, Metaphysics X 1 1053 a35-b4.51Nieholas Cusanus, Idiota de mente eh. 2.


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104 AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLYmany to one. But although unity is our most filndamental measure it ismuch too empty and formal to be directly applicable to what is given.Measures with content are necessary to meditate between what is givento our senses and this abstract one. This is to say, if there is to be anyknowledge at all, the human knower must hirnself first provide themeasures by which he is to know. He does not simply see them with theeye of the mind, as Descartes insists. Knowledge rests on creativity andhuman invention. It is fundamentally artistic or poetic.o call knowledge poetic is not to argue that the knower creates the

known x nihilo Not even the Albertian artist creates his fictions xnihilo but draws his material from what he observes. He only creates themeasures he applies towhat he sees. Thus measuring the human knowerknows hirnselfsurpassed by the reality he is trying to measure. Considera rose. o see what I see before me as a rose, I must already be inpossession of the concept rose. This measure applies not only to theflower now before me, but to countless sinlilar actual and possible roses.All our linguistic measures are in principle inadequate to whateverconcrete reality we encounter. o be sure, it is a rose I see, but how muchdoes this say? It does distinguish it from an arlimal or a tree, but rosestill says much too little, although given what JDescartes calls the needsofeveryday life, such a descriptionmay be adequate enough. Still, it failsto capture this particular, concrete reality. o be sure, I can refine mymeasures point out the rose s color or give it a fancy name. And I can goon and find ever richer descriptions, descriptions definite enough to singleout this rose. And yet, no matter how rich my description, I can alwaysimagine a still indefinitely large number ofpossible roses besides the onewhich I am now seeing that this description would fit. Just as space andhuman freedom are boundless, so is every individual thing. Whatever wegrasp of reality is shadowed by what has eseaped the activity of ourunderstanding shadowed by transcendence. This transcendence an-nounces itself in th 3 failure of our attempts to describe adequately orgrasp conceptually what we are given. What remains unmastered re-minds us that what we have arrived at is only a conjecture concerningreality and that it is in principle always possible to improve on thatconjecture.Openness to transcendence is part of our encounter with reality. Thereis always a beyond, a horizon that forces us to ac]{nowledge that limits areset to our understanding. Our descriptions will r ever be full enough. Thislack of closure prevents our understanding from ever arriving at adefinition that will not in some way fall short of what it defines, thatwould coincide with the defined. Once again we are faced with theincommensurability of the finite and the infinite, here in the form of theincommensurability of our concepts or words arid reality.


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WINTER 105This incommensurability has its foundation in the very nature of

thought and language, which determine what something is by assigningit a place in a humanly established conceptual or linguistic space, thusmeasuring it with a measure that is not its own. Language-and this isnot a fault but its very point-is finally incommensurable with reality.We can know adequately only what we can create. Thus we can havecertain knowledge in mathematics, which according to Cusanus, whohere disagrees with Plato, is simply the unfolding of the mind and of theunity which is its measure. The world of mathematics is so transparentbecause we constitute that world without having to engage reality. Thisexplains why science should turn to mathematics to find its form ofdescription. Compare our understanding ofa rosewith our understandingof a circle of a given radius: to know the definition of a circle is to knowhow to construct one.

This makes it difficult to dismiss Descartes suggestion that we under-stand nature precisely to the extent that we can reconstruct her workswith our mathematical models. Descartes promise of a practical philos-ophy that will render us the masters and possessors of nature can berealized ifhe is right with the suggestion that this new philosophy wouldteach us to know the forces of nature as distinctly as we know thedifferent crafts of our artisans. 52 If we are to reconstruct the works ofnature we have to understand its mode of production in the image ofhuman production. Such a practical philosophywill notwant to hear anymore ofmy elusive concrete rose than Alberti wanted to hear of the truebeing ofthe visual ray. And given their practical sufficiency, what sensedoes it make to speak of the essential inadequacy of all our descriptionsofwhatever is real or ofthe essential absence ofreality from whatever wehave grasped clearly and distinctly, i.e., able to reconstruct out ofDescartes simple natures?There is an obvious difficulty with this artistic view: how are we todistinguish knowledge from arbitrary construction? How are we to savethe truth? Even if, as Cusanus holds, the finite and the infinite areseparated by a gulf reason cannot bridge, this separation cannot be socomplete as to destroy all connection. Something is obviously right aboutthe traditional view that reality provides our thoughts with a measure.When I recognize the essential inadequacy of all description, this cannotmean that all descriptions are therefore equally good. Some must bejudged better than others. What then allows us to grade descriptions inthis manner? Observation provides an obvious answer. But perceptiondoes not allow us to step outside language. Perceiving, too, can finally not52Descartes iscourse on the Method VI; tr p. 119.


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106 AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLYbe divorced from naming. Whatever we see has always already beensubjected to a human measure.And yet, ifwe are to make sense ofmore or less adequate descriptions,these must have their measure in some ideal description. Such a description, usanuspoints out, cannot be other thall the thing described. Inthe fully adequate description, description and thing described are oneand the same thing. Here to describe means to create. This, of course, isthe traditional understanding of God s creative Word. Like knowing,seeing has its measure in the creative knowledge ofGod. Sight is hauntedby absence, and yet that absence is present as iVhat provides sight with ameasure. usanusgoes on to suggest that it is this DivineWord Plato hadin mind when he spoke of the forms. By forIn, usanus argues, Platomeant that principle which accounts for everything being just what it isand nothing else. To see something as nothing other thanjustwhat it is,is to see beyond appearance the form, the DivineWord. For Plato s eidos usanussubstitutes the non aliud the not other. The eidos of the rose isthus not other than the rose itself. To this eidos only an infinitelycomplicated description could do justice, a description which would be notother than the rose itself. While inaccessible to discursive reason, thisdescription furnishes all our descriptions with a measure.Why is the earth the earth? Cusanus asks, and answers: Because itis not other than the earth. 54 What is the point of such seeminglytautological statements? The question asks: WblY is the earthjust what itis and not something different? Indeed why is there such a thing as theearth at all? To ask: why is the earth the earth is thus to see it assomething that only happens to be what is, that could be other than it isor not at all. Such questions presuppose what vre can perhaps call a viewof the world sub specie possibilitatis a view that is inseparable from theway our understanding presupposes a conceptllal space that by its verynature has room not only for this world, but for an indefinite number ofother possible worlds.This awareness that ourworld is only an infi:nitesimally small island inan ocean of endless possibilities parallels that other awareness that ourearth is only another star swimming in an endless ocean of stars. Boththoughts have their foundation in a movement that leads reflection fromwhat is initially given to other possibilities. JBoth threaten to rob theearth of its special place and significance. Tlle later Middle Ages aremarked by this frightening discovery of the eontingency of the world.53Nieholas ofCusa, n God s N ot Other a Translation nd n Appraisal ofDe non liud by Jasper Hopkins, 3rd ed. (Minneapolis: :Banning, 1987), eh. 1, tr. pp.31-33. De non aliud 21; tr. p 141.


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WINTER 7Why did God create this world? The voluntarism of Ockham and hisfollowers insisted that speculation could throw no light on this question.God s will is inscrutable. As far as philosophy is concerned, we might asweIl speak ofa cosmic accident. For essentially the same reason Descartesinsists that the philosopher should not look for final causes.

As long as we view the world sub species possibilitatis there can be nofinal answer to the question: why are things the way they are? Suppose Iwere to answer the question: why is the earth the earth? by pointing to anefficient cause, say some cosmic event that caused the earth to come intobeing, or to some supposed form of earthness. Again we could repeat ourquestion with respect to this process or form. Such questioning wouldhave to continue until we arrived at a principle which is causa sui whichis what it is because it is not other than what it iso utgiven the ratio andits mode of operation I cannot grasp the meaning of causa sui Whateverfalls into the spaced defined by my language is thereby understood assomething which could also not be. As Descartes critics recognized, inthat space there is no room for a causa sui no place for God. And evenDescartes recognized that to think the causa in causa sui required anextension of the meaning of cause infinitum

Ifwe are to use our language to name God, wemust do so in a way thatcalls into question the very conditions under which language operates.Language must be used in a such a way that i t turns back on and againstitself, putting itselfinto question, casting us beyond its limits, beyond theratio to the intellectus Rightly understood, the phrase causa sui does this. ut so does Cusanus s formulation: the ear th is earth because it is notother than the earth. This is not so much an answer as it is rejection ofthequestion, pointing to another way of viewing the world, not sub speciepossibilitatis but sub specie necessitatis

As long as I understand the earth as falling into the space defined byreason I see it as something accidental. To understand transcendence asthe non liu is to admit that the question: why is the world the way it is?ultimately receives no answer. As long as the world is seen in the mode ofthe liu or the other, it cannot but seem accidental to us and itssignificance must escape uso God cannot show hirnself in the worldunderstood this way. If that world is understood as the world, thenNietzche is right and God is dead. ut in the experience of the world, orany particular object, as not other than what it is, we escape frompossibility. Now the why no longer arises. Rephrasing Kierkegaard sdictum, we can say: purity of heart is to see one thing. It follows fromthis conception of the non aliud which Cusanus takes to be his best55Principles I, 28 and 2, 3; tr. pp. 14 and 84-85.


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108 AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLYconjecture concerning God, that anything can become an epiphany oftheDivine when seen in a certain way: a tree, a cloud, an old roof, Eckhart sdung-heap, or that rose ofAngelus Silesius, which blooms without a why.

VIII have insisted that to think a perspective as a perspective is to be insome sense already beyond it. Thus to think subjective perspectival spaceis already to have some understanding of objective space: to think of

language as providing a perspective is already to have some understanding of what transcends language, i.e., of the essential transcendence ofreality; and similarily, to think, as Cusanus would have us do, of logic asa perspectival phenomenon, is to have already some understanding ofthetrans-Iogical, i.e., of the coincidentia oppositorum.

To make this last point somewhat clearer le t me return once more toProtagoras and to his thesis that man is the measure of all things. This,it would seem, makes the law of non-contrad:ilction constitutive, not ofreality per se but only of reality as it presents itself in our finiteperspective. This is how Cusanus understands the implications of theProtagorean dictum. Aristotle s logic, on his view, is only a logic of finiteappearance.56 The self-transcending move froIn the perspectival to thetransperspectival becomes, once logic is understood as constitutive of theratio s perspective, the move from the ratio to the intellectus which isnecessarily also a move beyond the law of non-contradiction to thecoincidentia oppositorum.

That the law of non-contradiction is tied to the finite is clear fromAristotle s formulation:For a principle which every one must have who knows anythingabout being, is not a hypothesis; and that ~ h i h everyone mustknow who knows anything, he must already have when hecomes to a special study. Evidently then stIch a principle is themost certain of all; which principle this is, we proceed to say. Itis, that the same attribute cannot at the same time belong andnot belong to the same subject and in the same respect;. . . Forit is impossible for anyone to believe the same thing to be andnot to be, as some think Heraclitus says;

To understand this formulation, we must know what we mean when wesay same - same attribute, same subject, same respect. The law ofnon-contradiction depends on our ability to identify and hold on to the56Ernst Cassirer, The Individual n the Cosmos in Renaissance Philosophy tr.Mario Domandi (New York and Evanston: Harper, 1963), 1257Aristotle, Metaphysics IV l005bl4-26;tr. W D Ross.


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WINTER 9same. Such identification requires a criterion or measure. Is this the samerose I saw yesterday? Is there only one obviously correct answer to thisquestion?

The law of non-contradiction cannot be divorced from definition. Tosubject reality to the law of non-contradiction is to claim that reality isessentially definite. Both Plato and Aristotle recognize this and justbecause of this they are critical of Heraclitus and Protagoras who makebeing too evanescent and indefinite to be grasped and held fast and thusmake it impossible to distinguish error from truth To save this distinction they introduce definition into the very essence of being. Descartesdoes the same when he insists on the commensurability of our understanding and reality. utradical doubt calls such commensurability intoquestion. Does it not subject r ea li ty to our abili ty to comprehend? Thefinite r tio is ma de the foundation of being. Can this be reconciled withthe infinite being ofGod? The evil genius Descartes introduces to lead hisreader to doubt is but a mask ofGod whose infinity demands that we seekhirn beyond the law of non-contradiction.We do not have to turn to God to give some plausibility to the ide a of acoincidenti oppositorum Consider once more the coincidence of thecurved and the straight of the circumference of a circle and its tangents

as we increase the circle s radius to infinity. Or of the attempt to gra sppersons or things in al l their concreteness: again the attempt to seize theinfinite lets us glimpse a coincidence of opposites: the coincidence ofthought or language and the thing itself.

When we s peak of the infinity of space or the infinity of the individualwe speak ofinfinity in a restricted sense. In such cases the coincidence ofopposites is not a coincidence of all opposites. It is thus possible to opposeinfinite space to infinite time one individual to another. As opposed tothese restricted infinites God is thought by Cusanus as the infinitebeyond all restriction and opposition. Given our finite perspective we cansay: God is the utterly transcendent the beyond in which all that is finitehas both its ground and measure. This transcendence of God shows itselfin the inevitable failure of all our attempts to think the absolute. Yet aslong as we think God as transcendent we still tl1ink God from our finiteperspective and remain caught in its oppositions. To think God we mustthink hirn beyond the coincidence of immanence and transcendence.

VIIII have tried to show how perspective and infinity are joined in thethought of Cusanus and Descartes. Depending on the different meaninggiven to perspective we ar ri ved at different interpretations of theinfinite: thus from the ordinary spatial meaning ofperspective we arrived


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110 AMERICAN CATHOLIC PHILOSOPHICAL QUARTERLYat the idea of an infinite homogeneous space; from an understanding ofthe perspectival nature oflanguage we moved to an understanding oftheinfinite richness of each individual; from an lInderstanding of the perspectival nature ofthe principle ofnon-contradiction to an understandingofthe coincidentia oppositorum. In each case th e problem ofthinking theinfinite is analogous. In each case discursive reason suffers shipwreck andthis shipwreck frees an intuition ofthe infinite. This analogy allows us tounderstand why the attempt to square the c:ircle should have come tofigure the attempt to understand God.I would like to conclude with the suggestion that the attempt by artistsof the Renaissance to capture the infinity of space may be understood asa similar symbolic activity. Andwhat is true ofthe infinity ofspace is alsotrue ofthe infinity ofeach individual person or thing. The boundlessnessof space, the boundlessness of reality, and the boundlessness of theindividual are all experienced as epiphanies ofthe infinite God. Thus it ishardly surprising that on the first page ofDe Visione Dei Cusanus shouldcall his almost exact contemporary Rogier van derWeyden the greatest ofall painters. In their different ways, cardinal and painter revealed theinfinite depth of a reality which Cartesian science was going to concealwith its insistence on the clear and distinct, even as Descartes himselfhad to recognize that every attempt to render the human being themaster and possessor ofnature finally has to suffer shipwreck on the reefof the infinite.Yale Uniuersity

ew Hauen Connecticut

58Cusanus calls Rogiervan der Weyden 1400-1464) maximus pictor. De VisioneDei ; tr. Jasper Hopkins, Nicholas ofCusa s Dialectical Mysticism Text Trans-lation and Interpretive tudy ofDe Visione Dei 2nd ed. Minneapolis: Banning,1988), 113.

problems of the infinite cusanus and descartes

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