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Of Learned Ignorance
2nd edition, college text
202 pages, Paperback
First published January 1, 1440
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April 8, 2025
Nicholas of Cusa (1401-1464) has always been something of a curious figure, standing as he does at the threshold between the medieval and early modern periods. Although his lifetime coincides with the onset of the flourishing of what, in art history, we call the Italian Renaissance, his outlook is profoundly influenced by an earlier mindset, so it is apter to see in him the last great representative of the medieval German mystical tradition. For indeed, his foremost authorities are Pseudo-Dionysius (6th c.) and Meister Eckhart (14th c.). Yet, what to a contemporary reader is so attractive about Nicholas of Cusa is precisely the innovative use he makes of his sources, with respect to astronomy and mathematics (not to mention theology). Thus, he poses to us an engaging counterfactual question: could there not might well have been an alternate trajectory out of the middle ages into a modern civilization quite different from the one we know? Was the rupture with the past imposed by the Protestant Reformation, in religion, and later, in the natural sciences, by the anti-Aristotelianism of the pioneers of the seventeenth-century revolution necessary?
To get a handle on an answer to a query such as this, it will be well to look closely at the Cusan’s magnum opus, De docta ignorantia (Of learned ignorance, 1440) – not to be led astray by its slender size, for, stationed at the very start of his literary career, it encapsulates in nuce all the great themes he would go on to explore in his later works. The present Wipf and Stock edition, translated into English and outfitted with a twenty-page introduction by Germain Heron, is nothing short of excellent. Read it to set the context, both in Nicholas’ life itself as well as in the intellectual milieu in which he moves.
Since the work itself is so pregnant and concise, there is little call to paraphrase it. Rather, let us essay a few general comments so that the reader can know what to look for in Nicholas of Cusa’s initially strange-seeming system. What this recensionist finds so admirable in Nicholas of Cusa is his superlative ability to get conceptually inside the absolute which is reminiscent of the German idealists, for instance, in his discussion of eternal generation [pp. 20-21]. For him as for the church fathers as a whole, God comes decidedly first, unlike what is the case with modern theologians who are always concerned with what I get out of my relation to God. For Nicholas regales us with a kind of counterintuitive argument familiar from Peter Lombard but what’s missing in modern theologians who no longer strive to rise up to divine things, being more interested in self-affirmation and thereby confining themselves to the finite and undivinized (esp. typical of mainline liberals). Our author is not one to detain himself thus; the subject of God as he is in himself suffices to captivate his attention.
The first book treats of God as the absolute maximum, Nicholas’ preferred terminiology with which to elucidate the principles of theology – why so? It is descriptive of his line of thought, to start with something we can name – a creature, or better yet a mathematical construct, and to perform a limiting operation in order to abstract from our concept of it something absolute. His points are repeatedly illustrated with mathematical examples. The basic idea here is not hard to grasp; for example, if one takes the radius of a circle to infinity, the circle will degenerate into a straight line. But Nicholas wants to do more than just state a simple mathematical truth; for him, it is emblematic of how to envisage what pertains to the absolute. Thus, he educes from his mathematical illustrations a host of surprising and counterintuitive metaphysical conclusions, which he likes to declare in pithy and paradoxical terms. Yet, it is all very logical – recalling Parmenides, who also dares to elevate rational logic over the plain evidence of the senses.
It will suffice to quote a single specimen of this style:
Sacred ignorance has taught us that God is ineffable, because he is infinitely greater than anything that words can express. So true is this that it is by the process of elimination and the use of negative propositions that we come nearer the truth about him. For that reason the most noble Denis would not have called him Truth or Intellect or Light or any name that man can utter; and in this he was followed by Rabbi Salomon and all the wise. According to this negative theology, therefore, he is neither Father nor Son nor Holy Ghost; one word alone may be used of him: Infinite. Infinity, as such, does not engender, is not engendered and does not proceed, – which called from Hilary of Poitiers, whilst distinguishing the Persons, these subtle words: ‘In aeterno infinitas, species in imagine, usus in munere’. His meaning is that all we see in eternity is infinity; and, while it is true that infinity is eternity, yet infinity is a negative and for that reason it cannot be conceived as a principle of generation. Eternity, on the other hand, clearly can be so conceived, for eternity is an affirmation of infinite unity or of the infinite present, and is, therefore, a principle that does not proceed from any other. ‘Species in imagine’ expresses the principle that proceeds from a principle and ‘usus in munere’ signifies procession from both. [p. 60]
Compare Anaximander’s apeiron?
The second book takes up the universe and how its existence reflects the indwelling presence of God. Here we encounter two more of Nicholas of Cusa’s core technical terms, contraction and the coincidence of opposites. For he reverses the commonly received procedure of proceeding from the creature to God. Instead, finite being is to be thought of as obtained from the absolute maximum by subtraction, or as he calls it, contraction. That is why the origin of plurality is in God [p. 77] and why opposites coincide originally in him. By and by, the principle of contraction begins to make sense, for it leads to a natural explication of how the universe, which is only a restricted form of maximum, can be a likeness of the absolute [p. 80], of how everything interpenetrates everything [pp. 83-86] and of how God’s design is displayed in the world [pp. 118-122]. Let us point out to the interested reader how Nicholas’ overtly theological perspective stimulates him to engage in innovative thought about the world, for instance, in his speculations on the nature of motion and the corollaries he draws therefrom which mix astronomy and theology in a characteristic fashion. He accepts without further ado that the earth must be in motion and therefore promotes the terrestrial realm to a kinship with the celestial – he sees the earth as merely another star! Thus:
In movement there is no absolute minimum, like a fixed center, since necessarily the minimum and the maximum are identical. Therefore the center and the circumference are identical. Now the world has no circumference. It would certainly have a circumference if it has a center, in which case it would contain within itself its own beginning and end; and that would mean that there was some other thing which imposed a limit to the world – another being existing in space outside the world. All of these conclusions are false. Since, then, the world cannot be enclosed within a material circumference and center, it is unintelligible without God as its center and circumference. It is not infinite, yet it cannot be conceived as finite, since there are no limits within which it is enclosed. The earth, which cannot be the center, must in some way be in motion; in fact, its movement even must be such that it could be infinitely less. Just as the earth is not the center of the world, so the circumference of the world is not the sphere of the fixed stars, despite the fact that by comparison the earth seems nearer the center and heaven nearer the circumference. The earth, then, is not the center of the eighth or any other sphere, and the appearance above the horizon of the six stars is no proof that the earth is at the center of the eighth sphere. If even at some distance from the center it were revolving on its axis through the poles, in such a way that one part would be facing upwards towards one pole and the other part facing downwards towards the other pole, then, it is evident, that to men as distant from the poles as the horizon only half of the sphere would be visible. Further, the center itself of the world is not more within than outside the earth; and this earth of ours has no center nor has any other sphere a center. Since the center is a point equidistant from the circumference, and since it is impossible to have a sphere or circle so perfect that a more perfect one could not be given, it clearly follows that a center could always be found that is truer and more exact than any given center. Only in God are we able to find a center which is with perfect precision equidistant from all points, for he alone is infinite equality. God, ever to be blessed, is, therefore, the center of the world: he it is who is center of the earth, of all spheres and of all things in the world; and at the same time he is the infinite circumference of all. [pp. 107-108]
The third book expounds Nicholas of Cusa’s Christology, which follows fairly logically from what has been set out in the first two books. For in the incarnation we have a coincidence of that which is unsurpassably maximal and at the same time constricted to finite being, a union of creator and the creature. Nicholas investigates why this solution is necessary to man’s salvation and the further mystery of the resurrection. In so doing, he recapitulates in his own terms the great patristic tradition, which sees in Christ a guarantee of man’s divinization: God became man so that man may become God (Athanasius). How paltry Luther’s imputed righteousness appears in comparison! But to this recensionist, the exposition in the third book appears a little too condensed, however exalted its theme. Nicholas stands in need of a fuller anthropology – admittedly, not really envisaged as part of the scope of this opusculum.
A concluding reflection on role of mathematics in theology: Nicholas (relying on the older tradition of Boethius and the anonymous book of the twenty-four philosophers) theologizes too quickly while modern mathematicians do not theologize at all. One wonders what he would he make of Cantor’s transfinitum? At the least, modern ideas in set theory would force him to refine his notion of the absolute maximum. Can his doctrine of the descent from eternal unity [p. 90] be likened to the transfer principle in non-standard analysis? If the reader should find his play with mathematical examples confusing, we could seek to allay his misgivings by suggesting that, in modern terms, what Nicholas is up to could be described as carrying out limiting procedures in a moduli space. Perhaps if he were conversant with modern idiom – say, the Schubert calculus – he might succeed in formulating his stark paradoxes in a fully rigorous garb!
Does Nicholas of Cusa, by all means a representative of the conservative tradition at its best, have the resources to circumvent the forgetfulness of being ushered in, about a century ahead of his birth, by Duns Scotus and William of Ockham? To situate the question in its historical context, one could hardly do better than to refer to the major works of the distinguished German historian Hans Blumenberg, The Genesis of the Copernican World (German original, 1975, English translation, 1987) and The Legitimacy of the Modern Age (German original, 1966, English translation, 1983). The former, a sprawling historical study of the antecedents of the Copernican revolution as well as of its reception, refutes many a canard about what Copernicus intends and, throughout, recurs often to the thought of Nicholas of Cusa. But to assess the real significance of the early modern transition, one has to turn to the latter work. Here, Blumenberg defends the legitimacy of modernity against certain dark Romantic strains hinting that secularization has been an epochal mistake, by arguing that it constitutes an understandable reaction to the theological absolutism of late-medieval nominalism. Needless to say, the humanistic school associated with Nicholas of Cusa affords a constant reference point for Blumenberg, although ultimately he dismisses its solution as inadequate (preferring Giordano Bruno’s).
But we, though admittedly of exiguous learning in comparison with Blumenberg, may nevertheless dare to contest his interpretation of the Cusan, as it cannot escape an impartial observer that by focusing on the Cusan’s supposedly faulty anthropology of freedom to the neglect of his Neoplatonist transcendentalism, Blumenberg misses altogether the mystical élan that propels his spirituality. Certainly, Nicholas of Cusa stands for a hermeneutics of continuity and catholicity (ecumenism in the religious sphere), against the Protestant hankering after fissiparousness and alienation from the intellectual culture in which early Christianity took root. Thus, with due respect for Blumenberg’s immense labor of scholarship, we may suggest that Nicholas of Cusa is scarcely as resourceless as the modern-day German historian judges in retrospect, for, as Paul the apostle understands very well [2 Corinthians 5:17], in Christ all things have been made new and, hence, the man of grace is equipped to overcome every obstacle – but we can touch on an issue of such momentousness only tangentially here and accordingly will have to promise forthcoming reviews of Blumenberg’s two great works on intellectual history.
To get a handle on an answer to a query such as this, it will be well to look closely at the Cusan’s magnum opus, De docta ignorantia (Of learned ignorance, 1440) – not to be led astray by its slender size, for, stationed at the very start of his literary career, it encapsulates in nuce all the great themes he would go on to explore in his later works. The present Wipf and Stock edition, translated into English and outfitted with a twenty-page introduction by Germain Heron, is nothing short of excellent. Read it to set the context, both in Nicholas’ life itself as well as in the intellectual milieu in which he moves.
Since the work itself is so pregnant and concise, there is little call to paraphrase it. Rather, let us essay a few general comments so that the reader can know what to look for in Nicholas of Cusa’s initially strange-seeming system. What this recensionist finds so admirable in Nicholas of Cusa is his superlative ability to get conceptually inside the absolute which is reminiscent of the German idealists, for instance, in his discussion of eternal generation [pp. 20-21]. For him as for the church fathers as a whole, God comes decidedly first, unlike what is the case with modern theologians who are always concerned with what I get out of my relation to God. For Nicholas regales us with a kind of counterintuitive argument familiar from Peter Lombard but what’s missing in modern theologians who no longer strive to rise up to divine things, being more interested in self-affirmation and thereby confining themselves to the finite and undivinized (esp. typical of mainline liberals). Our author is not one to detain himself thus; the subject of God as he is in himself suffices to captivate his attention.
The first book treats of God as the absolute maximum, Nicholas’ preferred terminiology with which to elucidate the principles of theology – why so? It is descriptive of his line of thought, to start with something we can name – a creature, or better yet a mathematical construct, and to perform a limiting operation in order to abstract from our concept of it something absolute. His points are repeatedly illustrated with mathematical examples. The basic idea here is not hard to grasp; for example, if one takes the radius of a circle to infinity, the circle will degenerate into a straight line. But Nicholas wants to do more than just state a simple mathematical truth; for him, it is emblematic of how to envisage what pertains to the absolute. Thus, he educes from his mathematical illustrations a host of surprising and counterintuitive metaphysical conclusions, which he likes to declare in pithy and paradoxical terms. Yet, it is all very logical – recalling Parmenides, who also dares to elevate rational logic over the plain evidence of the senses.
It will suffice to quote a single specimen of this style:
Sacred ignorance has taught us that God is ineffable, because he is infinitely greater than anything that words can express. So true is this that it is by the process of elimination and the use of negative propositions that we come nearer the truth about him. For that reason the most noble Denis would not have called him Truth or Intellect or Light or any name that man can utter; and in this he was followed by Rabbi Salomon and all the wise. According to this negative theology, therefore, he is neither Father nor Son nor Holy Ghost; one word alone may be used of him: Infinite. Infinity, as such, does not engender, is not engendered and does not proceed, – which called from Hilary of Poitiers, whilst distinguishing the Persons, these subtle words: ‘In aeterno infinitas, species in imagine, usus in munere’. His meaning is that all we see in eternity is infinity; and, while it is true that infinity is eternity, yet infinity is a negative and for that reason it cannot be conceived as a principle of generation. Eternity, on the other hand, clearly can be so conceived, for eternity is an affirmation of infinite unity or of the infinite present, and is, therefore, a principle that does not proceed from any other. ‘Species in imagine’ expresses the principle that proceeds from a principle and ‘usus in munere’ signifies procession from both. [p. 60]
Compare Anaximander’s apeiron?
The second book takes up the universe and how its existence reflects the indwelling presence of God. Here we encounter two more of Nicholas of Cusa’s core technical terms, contraction and the coincidence of opposites. For he reverses the commonly received procedure of proceeding from the creature to God. Instead, finite being is to be thought of as obtained from the absolute maximum by subtraction, or as he calls it, contraction. That is why the origin of plurality is in God [p. 77] and why opposites coincide originally in him. By and by, the principle of contraction begins to make sense, for it leads to a natural explication of how the universe, which is only a restricted form of maximum, can be a likeness of the absolute [p. 80], of how everything interpenetrates everything [pp. 83-86] and of how God’s design is displayed in the world [pp. 118-122]. Let us point out to the interested reader how Nicholas’ overtly theological perspective stimulates him to engage in innovative thought about the world, for instance, in his speculations on the nature of motion and the corollaries he draws therefrom which mix astronomy and theology in a characteristic fashion. He accepts without further ado that the earth must be in motion and therefore promotes the terrestrial realm to a kinship with the celestial – he sees the earth as merely another star! Thus:
In movement there is no absolute minimum, like a fixed center, since necessarily the minimum and the maximum are identical. Therefore the center and the circumference are identical. Now the world has no circumference. It would certainly have a circumference if it has a center, in which case it would contain within itself its own beginning and end; and that would mean that there was some other thing which imposed a limit to the world – another being existing in space outside the world. All of these conclusions are false. Since, then, the world cannot be enclosed within a material circumference and center, it is unintelligible without God as its center and circumference. It is not infinite, yet it cannot be conceived as finite, since there are no limits within which it is enclosed. The earth, which cannot be the center, must in some way be in motion; in fact, its movement even must be such that it could be infinitely less. Just as the earth is not the center of the world, so the circumference of the world is not the sphere of the fixed stars, despite the fact that by comparison the earth seems nearer the center and heaven nearer the circumference. The earth, then, is not the center of the eighth or any other sphere, and the appearance above the horizon of the six stars is no proof that the earth is at the center of the eighth sphere. If even at some distance from the center it were revolving on its axis through the poles, in such a way that one part would be facing upwards towards one pole and the other part facing downwards towards the other pole, then, it is evident, that to men as distant from the poles as the horizon only half of the sphere would be visible. Further, the center itself of the world is not more within than outside the earth; and this earth of ours has no center nor has any other sphere a center. Since the center is a point equidistant from the circumference, and since it is impossible to have a sphere or circle so perfect that a more perfect one could not be given, it clearly follows that a center could always be found that is truer and more exact than any given center. Only in God are we able to find a center which is with perfect precision equidistant from all points, for he alone is infinite equality. God, ever to be blessed, is, therefore, the center of the world: he it is who is center of the earth, of all spheres and of all things in the world; and at the same time he is the infinite circumference of all. [pp. 107-108]
The third book expounds Nicholas of Cusa’s Christology, which follows fairly logically from what has been set out in the first two books. For in the incarnation we have a coincidence of that which is unsurpassably maximal and at the same time constricted to finite being, a union of creator and the creature. Nicholas investigates why this solution is necessary to man’s salvation and the further mystery of the resurrection. In so doing, he recapitulates in his own terms the great patristic tradition, which sees in Christ a guarantee of man’s divinization: God became man so that man may become God (Athanasius). How paltry Luther’s imputed righteousness appears in comparison! But to this recensionist, the exposition in the third book appears a little too condensed, however exalted its theme. Nicholas stands in need of a fuller anthropology – admittedly, not really envisaged as part of the scope of this opusculum.
A concluding reflection on role of mathematics in theology: Nicholas (relying on the older tradition of Boethius and the anonymous book of the twenty-four philosophers) theologizes too quickly while modern mathematicians do not theologize at all. One wonders what he would he make of Cantor’s transfinitum? At the least, modern ideas in set theory would force him to refine his notion of the absolute maximum. Can his doctrine of the descent from eternal unity [p. 90] be likened to the transfer principle in non-standard analysis? If the reader should find his play with mathematical examples confusing, we could seek to allay his misgivings by suggesting that, in modern terms, what Nicholas is up to could be described as carrying out limiting procedures in a moduli space. Perhaps if he were conversant with modern idiom – say, the Schubert calculus – he might succeed in formulating his stark paradoxes in a fully rigorous garb!
Does Nicholas of Cusa, by all means a representative of the conservative tradition at its best, have the resources to circumvent the forgetfulness of being ushered in, about a century ahead of his birth, by Duns Scotus and William of Ockham? To situate the question in its historical context, one could hardly do better than to refer to the major works of the distinguished German historian Hans Blumenberg, The Genesis of the Copernican World (German original, 1975, English translation, 1987) and The Legitimacy of the Modern Age (German original, 1966, English translation, 1983). The former, a sprawling historical study of the antecedents of the Copernican revolution as well as of its reception, refutes many a canard about what Copernicus intends and, throughout, recurs often to the thought of Nicholas of Cusa. But to assess the real significance of the early modern transition, one has to turn to the latter work. Here, Blumenberg defends the legitimacy of modernity against certain dark Romantic strains hinting that secularization has been an epochal mistake, by arguing that it constitutes an understandable reaction to the theological absolutism of late-medieval nominalism. Needless to say, the humanistic school associated with Nicholas of Cusa affords a constant reference point for Blumenberg, although ultimately he dismisses its solution as inadequate (preferring Giordano Bruno’s).
But we, though admittedly of exiguous learning in comparison with Blumenberg, may nevertheless dare to contest his interpretation of the Cusan, as it cannot escape an impartial observer that by focusing on the Cusan’s supposedly faulty anthropology of freedom to the neglect of his Neoplatonist transcendentalism, Blumenberg misses altogether the mystical élan that propels his spirituality. Certainly, Nicholas of Cusa stands for a hermeneutics of continuity and catholicity (ecumenism in the religious sphere), against the Protestant hankering after fissiparousness and alienation from the intellectual culture in which early Christianity took root. Thus, with due respect for Blumenberg’s immense labor of scholarship, we may suggest that Nicholas of Cusa is scarcely as resourceless as the modern-day German historian judges in retrospect, for, as Paul the apostle understands very well [2 Corinthians 5:17], in Christ all things have been made new and, hence, the man of grace is equipped to overcome every obstacle – but we can touch on an issue of such momentousness only tangentially here and accordingly will have to promise forthcoming reviews of Blumenberg’s two great works on intellectual history.
September 2, 2020
One of the most complex and mesmerizing medieval books about the existence of God. Cusa makes use of theoretical geometry (understandable even for those who hate Math, like me) to discuss our inability of grasping God’s existence (negative theology) and, thereof, believes to undoubtedly prove it. Leave the Scholastic authors behind!
August 28, 2009
Since my release from the Facility I have been at work on Nicholas of Cusa's 'De Docta Ignorantia,' both in the Latin of the Heidelberger Akademie der Wissenschaften and in Felix Melner Verlag's Philosophische Bibliothek's fine Latin-German edition.
But what in the name of Heaven does Nicholas mean by contractum/contractio?
It bedevils me!
Jasper Hopkins has it that:
"..the universe is a contracted maximum in that it is that maximum which is ever a oneness-in-plurality because it is a differentiated oneness, in which contradictories cannot coincide. But when we read that “the universe is contracted in each actually existing thing” or that a universal is contracted in a particular, the sense is rather the following: the universe (or some given universal) exists in a restricted way—which Nicholas will have to explain—in each actually existing thing (or in the designated particular)."
but still it sticks in my craw...
O aethereal epithelia, O hard granus of stuff,
give us our nacred quire, our opusculus!
July 4, 2024
En märklig text. Den kan både förstås ironiskt, som ett förlöjligande av de som tror att man kan förklara numen; som en genomgång av kristen mystik; och som en genomgång av Pythagoras sifferlära och dess filosofiska konsekvenser på religion och etik. Jag är fascinerad mer än frälst.
September 30, 2023
I read a different translation. Cusa combines a searing intellect with a thoroughgoing love for his Savior and constructs a philosophical system at once terse and all-encompassing. We must all discover 'learned ignorance', if we are to come any closer to truth.
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