De docta ignorantia
Nicholas of Cusa (1401–1464)
De docta ignorantia (On Learned Ignorance, 1440), in three books: the absolute maximum (God), the contracted maximum (universe), and Jesus Christ. Latin text transcribed from the Rotta 1913 Bari edition.
Prologue
Liber primus
Capitulum I: Book One: How Knowing Is Being Ignorant.
Capitulum II: Book One: Preliminary Elucidation of What Follows.
Capitulum III: Book One: That Precise Truth Is Incomprehensible.
Capitulum IV: Book One: The Absolute Maximum Is Understood Incomprehensibly, with Which the Minimum Coincides.
Capitulum V: Book One: The Maximum Is One.
Capitulum VI: Book One: The Maximum Is Absolute Necessity.
Capitulum VII: Book One: On the Threefold and One Eternity.
Capitulum VIII: Book One: On the Eternal Generation.
Capitulum IX: Book One: On the Eternal Procession of the Connexion.
Capitulum X: Book One: How the Understanding of the Trinity in Unity Surpasses All Things.
Capitulum XI: Book One: That Mathematics Aids Us Greatly in the Apprehension of Diverse Divine Things.
Capitulum XII: Book One: How Mathematical Signs Are to Be Used in This Inquiry.
Capitulum XIII: Book One: On the Properties of the Maximal and Infinite Line.
Capitulum XIV: Book One: How the Infinite Line Is a Triangle.
Capitulum XV: Book One: That That Triangle Is a Circle and a Sphere.
Capitulum XVI: Book One: How the Maximum Stands Translatively to All Things, as the Greatest Line Stands to Lines.
Capitulum XVII: Book One: The Profoundest Doctrines from the Same Source.
Capitulum XVIII: Book One: How from the Same Source We Are Led by the Hand to the Understanding of the Participation of Beingness.
Capitulum XIX: Book One: The Transfer of the Triangle to the Greatest Trinity.
Capitulum XX: Book One: Still Concerning the Trinity, and That Quaternity and Beyond Are Not Possible in Divine Things.
Capitulum XXI: Book One: The Transfer of the Infinite Circle to Unity.
Capitulum XXII: Book One: How the Providence of God Unites Contradictories.
Capitulum XXIII: Book One: The Transfer of the Infinite Sphere to the Actual Existence of God.
Capitulum XXIV: Book One: On the Name of God and Affirmative Theology.
Capitulum XXV: Book One: The Gentiles Named God Variously in Respect of Creatures.
Capitulum XXVI: Book One: On Negative Theology.
Liber secundus
Book Two: Prologue
Capitulum I: Book Two: Preliminary Corollaries for Inferring the One Infinite Universe.
Capitulum II: Book Two: How the Being of the Creature Is Unintelligibly from the Being of the First.
Capitulum III: Book Two: How the Maximum Enfolds and Unfolds All Things Intellectually.
Capitulum IV: Book Two: How the Universe, the Contracted Maximum, Is Only a Likeness of the Absolute.
Capitulum V: Book Two: Each Thing in Each Thing.
Capitulum VI: Book Two: On the Enfolding and the Degrees of Contraction of the Universe.
Capitulum VII: Book Two: On the Trinity of the Universe.
Capitulum VIII: Book Two: On the Possibility or Matter of the Universe.
Capitulum IX: Book Two: On the Soul or Form of the Universe.
Capitulum X: Book Two: On the Spirit of Universals.
Capitulum XI: Book Two: Corollaries on Motion.
Capitulum XII: Book Two: On the Conditions of the Earth.
Capitulum XIII: Book Two: On the Admirable Divine Art in the Creation of the World and the Elements.
Liber tertius
Book Three: Prologue
Capitulum I: Book Three: That a Maximum Contracted to This or That, Than Which a Greater Cannot Be, Cannot Exist Without the Absolute.
In the first book it is shown that the one absolute maximum, incommunicable, immensurable, and incontrahible to this or that, persists in itself eternally, equally, and immovably the same itself. After this, in the second place the contraction of the universe is made manifest, since this and that exist in no other way than contractedly. The unity of the maximum, therefore, is absolute in itself; the unity of the universe is contracted in plurality. The many, however, in which the universe is actually contracted, can in no way agree in supreme equality; for then they would cease to be many. All things must therefore differ from one another either in genus, in species or number, in species and number, or in genus and number, so that each subsists in its own number, weight, and measure. Hence all things are distinguished from one another by degrees, so that none coincides with another. No contracted thing, therefore, can participate with precision in the degree of contraction of another, so that necessarily each exceeds or is exceeded by any other. All contracted things stand therefore between the maximum and the minimum, so that, any being given, a greater and a lesser degree of contraction can be given, without this process going on to infinity in act, because an infinity of degrees is impossible, since to say that infinite degrees exist in act is nothing other than to say that there is none, as we said of number in the first book. The ascent or descent among contracted things cannot therefore be unto the maximum or minimum absolutely. Hence just as the divine nature, which is absolutely maximal, cannot be diminished so as to pass into the finite and contracted, so neither can the contracted be diminished in contraction so as to become wholly absolute.
Every contracted thing, therefore, since it can be less and more contracted, attains the limit of neither the universe, nor the genus, nor the species. For the first general contraction of the universe is through the plurality of genera, which must differ gradually. But genera do not subsist except as contracted in species, nor species except in individuals, which alone exist in act. Just as, therefore, no individual can be given according to the nature of contracted things except within the limit of its species, so too every individual cannot attain the limit of the genus and the universe. For among the several individuals of the same species a diversity of degrees of perfection must fall, hence according to the given species none will be most perfect, than which a more perfect cannot be given; nor can one so imperfect be given, than which a more imperfect cannot be given. No one attains the limit of the species, therefore.
There is therefore but one limit of species, of genera, and of the universe, which is the center, circumference, and connection of all; and the universe does not exhaust the infinite absolutely maximal power of God itself, as though it were simply the maximum terminating the power of God. The universe does not attain, therefore, the limit of absolute maximality, nor do genera attain the limit, nor species the limit of genera, nor individuals the limit of species, so that all things are what they are in the better way within the maximum and the minimum, and God is the beginning, middle, and end of the universe and of singulars, so that all things, whether they ascend or descend or tend unto the middle, approach God. But the connection of all things is through him, so that all things, though different, are also connected. Hence among the genera contracting the one universe there is such a connection of lower and higher that they coincide in the middle, and among the diverse species there is such an order of combination that the highest species of one genus coincides with the lowest of the immediately higher, so that there is one perfect continuous universe.
But every connection is gradual, and one does not arrive at the maximal, because that is God. Diverse species of a lower and a higher genus are not connected, therefore, in some indivisible admitting no more and less, but in a third species, whose individuals are gradually different so that none participates equally in both, as though composed of them, but it contracts in its own degree one nature of its own species, which, referred to the others, seems composed of the lower and the higher, yet not equally of them, since no composite can be precisely of equals, and, falling in the middle between those species, it necessarily prevails according to one, higher or lower namely, as examples of this are found in the books of the philosophers, in oysters and sea-shells and others.
No species descends, therefore, so as to be the least of any genus, since before it arrives at the least, it is changed into another before it is least. In the genus of animality the human species, while striving to attain a higher degree among sensible things, is rapt into a mixture with the intellectual nature; the lower part prevails, however, according to which it is called animal. Perhaps there are other spirits, of which in the end of the books of conjectures, and these indeed are loosely said to be of the genus of animality on account of a certain sensible nature, but since in them the intellectual nature prevails over the other, they are called spirits rather than animals, although the Platonists believe them to be intellectual animals. Hence it is concluded that species proceed in order after the likeness of number, which is necessarily finite, so that there is order, harmony, and proportion in diversity, as we showed in the first book, and one must arrive at the lowest species of the lowest genus, than which actually there is no lesser, and the highest of the highest, than which likewise actually there is no greater and higher, to which nevertheless a lesser and a greater could be given without process to infinity; so that whether we count upward or downward, we take our beginning from the absolute unity, which is God, as from the principle of all, so that species proceed as if to the encounter of number, from the least which is the maximum, and from the maximum to which the minimum is not opposed; so that there is nothing in the universe which does not rejoice in a certain singularity, which is found in no other, so that none surpasses all things in all respects or diverse things equally, just as with none can it at any time be equal in anything, even if at one time it was less than it and at another greater, it makes this passage in a certain singularity, so that it never attains precise equality, just as the square inscribed in the circle passes unto the magnitude of the circumscribed, from the square which is less than the circle unto the square greater than the circle, without ever arriving at one equal to itself, and the angle of incidence from less than right unto greater ascends without the mean of equality, and more such things effectively in the book of conjectures.
For the individuating principles cannot concur in one individual in such harmonious proportion as in another, so that each is one through itself and perfect in the way it can be. And although in any species, e.g. the human, at a given time some are found more perfect than others and more excellent in certain respects, as Solomon surpassed in wisdom, Absalom in beauty, Samson in strength, and those who surpassed others more in the intellective part deserved to be honored above the rest. Yet because diversity of opinions according to the diversity of religions and sects and regions makes diverse judgments of comparisons, so that what is praiseworthy according to one is blameworthy according to another, and those dispersed through the world are unknown to us, we do not know who is more excellent than the rest of the world, since we cannot know even one of them all perfectly. And this indeed was done by God, that each be content in himself, though admiring others, and in his own homeland, so that the native soil seems sweeter both in the customs of the kingdom and in language and the rest, so that there is unity and peace without envy, as much as this can be possible, since it cannot be altogether, except with those reigning with him, who is our peace surpassing all sense.