De docta ignorantia

By divine gift we discern that in all things there is a certain natural desire to exist in the better mode which the condition of each nature allows, and to work toward this end and to have suitable instruments, with which is inborn a judgment conformed to the purpose of knowing, lest the appetite be in vain and so that it may attain rest in the beloved weight of its own nature. But if perchance it happens otherwise, this must come about by accident, as when sickness seduces taste or opinion seduces reason. Wherefore we say that a sound free intellect knows the truth, which with insatiable inborn reasoning it desires to attain by surveying all things, once apprehended in a loving embrace, not doubting that that is most true to which no sound mind can dissent. All investigators, however, judge what is uncertain in proportionate comparison with a certain presupposed certitude. Every inquiry is therefore comparative, using proportion as its means, so that when the things inquired into can be compared with what is presupposed by a proximate proportional reduction, judgment of apprehension is easy, while when we need many means, difficulty and labor arise. As is well known in mathematics, where earlier propositions are more easily reduced to the first most-known principles and later ones with more difficulty, since only through the means of the earlier ones. Every inquiry, therefore, exists in comparative proportion, easy or difficult; hence the infinite as infinite, since it escapes all proportion, is unknown. Proportion, however, since it bespeaks agreement in some one thing together with otherness, cannot be understood without number. Number therefore includes all things proportionable. Nor is it only number in quantity that effects proportion, but in all things that can in any way agree substantially or accidentally and differ. Hence perhaps Pythagoras judged that all things are constituted and understood through the power of numbers. The precision of combinations in corporeal things, however, and the congruous fitting of the known to the unknown, surpass human reason, so that to Socrates it seemed that he knew nothing except that he was ignorant, wisest Solomon asserting that all things are difficult and inexpressible in speech. And another man of divine spirit says that wisdom is hidden and the place of understanding from the eyes of all the living. If therefore this is so, as even the profoundest Aristotle affirms in the first philosophy, that in the things most manifest by nature such difficulty befalls us as to one attempting like a night-owl to see the sun, then assuredly, since the appetite in us is not in vain, we desire to know that we are ignorant. If we can fully attain this, we shall attain learned ignorance. For nothing more perfect will come to a man even most studious in doctrine than to be found most learned in that very ignorance which is proper to him; and one will be the more learned the more one knows oneself to be ignorant. Toward this end I have taken up the labor of writing a few things on this learned ignorance itself.

Being about to treat of the highest doctrine of ignorance, I must take up the nature of maximality itself. By maximum I mean that than which nothing greater can be. Abundance, however, belongs to unity; unity therefore coincides with maximality, which is also entity. But if this unity is universally absolute from every respect and contraction, it is manifest that nothing is opposed to it, since it is absolute maximality. The absolute maximum is therefore one, which is all things, in which are all things, since it is the maximum. And since nothing is opposed to it, the minimum coincides with it at once, wherefore it is also in all things. And since it is absolute, it is then in act every possible being, contracting nothing from things, from which are all things. This maximum, which is also believed without doubt by the faith of all nations as God, I shall labor to investigate incomprehensibly above human reason in the first book, with him as guide who alone inhabits inaccessible light. In the second place, just as absolute maximality is absolute entity, through which all things are what they are, so too is the universal unity of being from that which is called the absolute maximum, and hence existing contractedly as the universe, whose unity is contracted in plurality, without which it cannot be. This maximum, although in its universal unity it embraces all things, so that all things which are from the absolute are in it and it is in all things, nevertheless has no subsistence outside the plurality in which it is, since it does not exist without the contraction from which it cannot be absolved. Of this maximum, namely the universe, I shall add certain things in the second book. In the third place the maximum of the third consideration will subsequently be made manifest. For since the universe has subsistence only contractedly in plurality, in those plural things themselves we shall investigate the one maximum in which the universe subsists in act maximally and most perfectly as in its end. And since such a one is united with the absolute, which is the universal term, because the most perfect end is above all our capacity, of that maximum, which is at once contracted and absolute, which we name Jesus ever blessed, I shall subjoin a few things, according as Jesus himself inspires. But the one willing to attain the sense must lift the intellect above the force of the words rather than insist on the properties of terms, which cannot be properly adapted to such great intellectual mysteries. One must also use exemplary manuductions transcendently, leaving sensible things behind, so that the reader may ascend readily to simple intellectuality, for seeking which way I have endeavored to open it to common minds as clearly as I could, avoiding all roughness of style, manifesting at once the root of learned ignorance, even in the inapprehensible precision of truth.

Since it is manifest of itself that there is no proportion of the infinite to the finite, it is also most clear from this that where exceeding and exceeded are found, one does not arrive at the maximum simply, since things exceeding and exceeded are finite, while such a maximum is necessarily infinite. Given therefore anything whatever that is not the maximum simply itself, it is manifest that a greater can be given. And since we find equality to be gradual, so that one thing is more equal to one thing than to another according to generic, specific, local, influential, and temporal agreement and difference, with the like: it is plain that neither two nor more things can be found so similar and equal but that still more similar ones could be in infinitum. Hence measure and measured, however equal, will always remain different. The finite intellect therefore cannot precisely understand the truth of things through likeness. For truth is neither more nor less, consisting in a certain indivisible point, which everything existing that is not the true itself cannot precisely measure; just as what is not a circle cannot measure the circle, whose being consists in a certain indivisible point. The intellect, therefore, which is not the truth, never comprehends the truth so precisely that it could not be comprehended more precisely to infinity, standing to the truth as a polygon to a circle, which, the more angles it has inscribed, is the more like the circle, yet never becomes equal, even if it multiplies its angles to infinity, unless it resolves itself into identity with the circle. It is plain, therefore, that of the true we know nothing other than that we know it to be precisely incomprehensible as it is, truth standing as the most absolute necessity, which can be neither more nor less than it is, and our intellect as possibility. The quiddity of things, therefore, which is the truth of beings, is in its purity unattainable, investigated by all philosophers but found by none as it is; and the more profoundly learned we shall have been in this ignorance, the more we shall draw near to truth itself.

The maximum, than which there cannot be a greater, simply and absolutely, since it is greater than can be comprehended by us, because it is infinite truth, we attain in no other way than incomprehensibly. For since it is not of the nature of those things which admit exceeding and exceeded, it is above all that can be conceived by us; for all things whatever that are apprehended by sense, reason, or intellect differ within themselves and from one another in such a way that there is no precise equality among them. The maximal equality, therefore, which is other or diverse from nothing, exceeds every intellect; wherefore the absolute maximum, since it is all that is or can be, is wholly in act, and just as there cannot be a greater, by the same reason neither can there be a less, since it is all that can be.

But the minimum is that than which there cannot be a less. And since the maximum is of this sort, it is manifest that the minimum coincides with the maximum. And this will be clearer to you if you contract the maximum and the minimum to quantity. For the maximal quantity is maximally great; the minimal quantity is maximally small.

Absolve, therefore, the maximum and the minimum from quantity by mentally subtracting the great and the small, and you clearly discern that the maximum and the minimum coincide. For thus the maximum is a superlative just as the minimum is a superlative. Absolute quantity, therefore, is no more maximal than minimal, since in it the minimum and the maximum coincide.

Oppositions, therefore, admit only exceeding and excess in these things, and belong to them differently, but in no way to the absolute maximum, since it is above all opposition.

Since, therefore, the absolute maximum is absolutely in act all things that can be, in such a way without any opposition that in the maximum the minimum coincides, then it is above every affirmation alike and negation. And everything that is conceived to be, is no more than is not. And everything that is conceived not to be, is no more not than is.

But thus it is this which is all things, and thus all things so that it is none, and thus maximally this so that it is minimally itself. For to say otherwise: God, who is absolute maximality itself, is light, than: God is maximally light, who is minimally light. For otherwise absolute maximality would not be all possibles in act, if it were not infinite and the term of all things and terminable by none of all things, as we shall explain afterwards in what follows, by the loving-kindness of God himself.

This, however, transcends all our intellect, which cannot combine contradictories in its principle by way of reason, since we walk by those things which are manifest to us from nature itself, which, falling far short of this infinite power, cannot connect contradictories at once, distant from each other by infinity. Above every discourse of reason, therefore, we see the absolute maximality incomprehensibly to be infinite, to which nothing is opposed, with which the minimum coincides.

But the maximum and the minimum, as they are taken in this little book, exist as transcendent terms of absolute signification, so that above every contraction to quantity of mass or of power they embrace all things in their absolute simplicity.

From these considerations it is most clearly established that the absolute maximum is unintelligibly intelligible and unnameably nameable, as we shall set forth below a fuller teaching on this point. There is nothing nameable than which a greater or a smaller could not be given, since the names attributed to such things belong to the motion of reason, which admits of exceeding and being exceeded. And since all things are in the best mode in which they can be, without number there can be no plurality of beings; for with number removed, the distinction, order, proportion, and harmony of things, and even the very plurality of beings, cease. But if number itself were infinite, since it would then be the maximum in act, with which the minimum would coincide, all the aforesaid would likewise cease. For it comes to the same thing whether number is infinite or least.

If, then, by ascending among numbers one arrives in act at a maximum, since number is finite, one still does not arrive at a maximum than which a greater cannot be, since that is infinite.

Hence it is manifest that the ascent of number is finite in act, and that it will be in potency toward another, and number would behave likewise in descent, so that, given any small number whatever in act, a smaller would always be obtainable by subtraction, just as in ascent a greater by addition; and it would still be the same; for no distinction of things, nor order, nor plurality, nor exceeding and exceeded would be found in numbers — indeed, there would be no number.

Therefore it is necessary to arrive in number at a minimum than which there cannot be less, as unity is. And since there cannot be less than unity, unity will be the minimum simply, which coincides with the maximum through what was just shown.

But unity cannot be a number, since number, admitting of exceeding, can in no way be the minimum simply nor the maximum simply; but it is the beginning of all number, because the minimum, and the end of all number, because the maximum.

Absolute unity, therefore, to which nothing is opposed, is absolute maximality itself, which is blessed God.

This unity, since it is maximal, is not multipliable, since it is everything that can be.

It cannot, therefore, itself become number. See how we have been led through number to this: to understand that absolute unity befits the unnameable God more closely, and that God is so one as to be in act everything that is possible. Therefore this unity admits neither more nor less, nor is it multipliable. The Godhead, then, is infinite unity. He who said: 'Hear, O Israel, your God is one; and one is your master and father in heaven,' could have said nothing truer; whoever would say that there are several gods would most falsely affirm that neither God nor anything at all of the universe exists, as will be shown in what follows. For just as number, which is a being of reason fashioned by our comparative power of distinction, necessarily presupposes unity as the principle of such number, so that without it number cannot be: so the pluralities of things, descending from this infinite unity, stand to it in such a way that without it they cannot be; for how would they be without being? Absolute unity, moreover, is entity itself, as we shall see later.

It has been shown in what precedes that all things besides the one maximum simply are finite and terminated in respect of it. But the finite and terminated has that from which it begins and that to which it is terminated; and since it cannot be said that the one is greater than the given finite and the finite greater in proceeding always to infinity, since in things exceeding and exceeded progression to infinity cannot come about in act, therefore the maximum would be of the nature of finite things, therefore it is necessarily the maximum in act, the principle and end of all finite things. Moreover nothing could be, if the maximum simply did not exist; for since everything that is not the maximum is finite, it is also principiated; but it will be necessary that it be from another, otherwise, if it had been from itself, when it had not been, nor is it possible in principles and causes to go to infinity, as is plain from the rule.

The maximum simply will therefore be, without which nothing can be.

Moreover let us contract the maximum to being and say: nothing is opposed to maximal being, wherefore neither being nor minimal being. How then can it be understood that the maximum can not be, since to be minimally is to be maximally?

Nor can anything be understood to be without being. But absolute being cannot be other than the absolute maximum.

Nothing therefore can be understood to be without the maximum.

Moreover maximal truth is the absolute maximum. It is therefore maximally true that the maximum simply itself is or is not, or is and is not, or neither is nor is not; and more things can neither be said nor thought. Whichever of these you say, I hold the maximally true as my resolve. For I hold the maximal truth, which is the maximum simply.

Whence, although it be manifest through what was premised that this name being or any other name whatever is not the precise name of the maximum, which is above all nameable being, yet being, maximally and unnameably, through the name maximum above all nameable being, must belong to it.

By such reasonings indeed, and by infinite like ones, learned ignorance sees from what is above most openly that the maximum simply necessarily is, so that it is absolute necessity. But it has been shown that there can be but one maximum simply, wherefore that the one maximum is, is most true.

There was never any nation which did not worship God and did not believe him to be the absolute maximum. We find Minar to have noted in the books of Antiquities that the Sissenni most worshipped unity. Pythagoras, however, a man most illustrious in his age by irrefragable authority, asserted that unity to be threefold. Investigating the truth of this, lifting our mind higher, let us say according to what was premised. That no one doubts which precedes all otherness is eternal: for otherness is the same as mutability, but everything which naturally precedes mutability is immutable, wherefore eternal. But otherness consists of one and another, wherefore otherness, like number, is posterior to unity. Unity is therefore by nature prior to otherness, and since it naturally precedes it, unity is eternal.

Further, all inequality is from the equal and the exceeding. Inequality is therefore posterior in nature to equality, which can be most firmly proved by resolution. For all inequality is resolved into equality: for the equal is between the greater and the less. If therefore you take away that by which the greater is greater, it will be equal; but if the less be in question, take from the remainder that by which the greater is greater, and it will become equal. And this you can also do until by taking away you come to simples. It is plain therefore that all inequality, by taking away, is reduced to equality. Equality therefore naturally precedes inequality, and inequality and otherness are simultaneous in nature: for where there is inequality, there is necessarily otherness, and conversely. For between at least two there will be otherness. But that will make doubleness with respect to one of those two, wherefore there will be inequality. Otherness and inequality, therefore, will be simultaneous in nature, especially since the binary is the first otherness and the first inequality; but it has been proved that equality precedes inequality in nature, wherefore also otherness: equality is therefore eternal.

Further, if there be two causes, one of which is prior to the other, the effect of the prior will be prior in nature to that of the posterior. But unity either is connexion or is the cause of connexion. For things are called connected from this, that they are united together. The binary also either is division or is the cause of division. For the binary is the first division. If therefore unity is the cause of connexion, but the binary the cause of division; then, just as unity is prior in nature to the binary, so also connexion is prior in nature to division.

But division and otherness are simultaneous in nature, wherefore also connexion, just as unity is eternal, since it is prior to otherness.

It has been proved, therefore, that since unity itself is eternal and equality is eternal, likewise connexion is eternal. But there cannot be several eternals. For if there were several eternals, then since unity would precede all plurality, something would be prior in nature to eternity, which is impossible. Moreover, if there were several eternals, one would be lacking to the other, and therefore none of them would be perfect, and thus there would be something eternal which would not be eternal, because it would not be perfect; which, since it is not possible, hence several eternals cannot be. But since unity is eternal, equality is eternal, likewise also connexion: hence unity, equality, and connexion are one. And this is that threefold unity which Pythagoras, the first of all philosophers, the glory of Italy and Greece, taught to be adored. But let us yet subjoin some things more expressly on the generation of equality from unity.

Let us now show most briefly that from unity is begotten the equality of unity, but that connexion proceeds from unity and from the equality of unity.

Unity is so called as it were oneness from the Greek word ov, which in Latin is called being, and unity is entity. For God is the very entity of things, for he is the form of being, wherefore also entity. But the equality of unity is as it were the equality of entity, that is, equality of being or of existing. But equality of being is that in a thing there is neither more nor less, nothing beyond, nothing below.

For if in a thing there is more being, it is monstrous; if less, it is not: the generation of equality from unity, which is clearly discerned when one attends to what generation is; for generation is the repetition of unity, or the multiplication of the same nature proceeding from the father into the son.

And this generation is indeed found only in perishable things: but the generation of unity from unity is one repetition of unity, that is, unity once; for if it multiplied unity twice, or thrice, or successively, unity would already procreate another from itself, as the binary, or ternary, or another number; but unity repeated once only begets the equality of unity, which cannot be understood as anything other than that unity begets unity, and this generation is indeed eternal.

Just as the generation of unity from unity is one repetition of unity, so the procession from both is the repetition of that repetition of unity, or if you prefer to say it, the uniting of unity itself and of the equality of unity. But procession is so called as it were a certain extension from one into another, just as, when two things are equal, then a certain equality extends as it were from one into the other, which in some way joins and connects them.

Rightly, therefore, is connexion said to proceed from unity and from the equality of unity: for connexion is not of one only, but unity proceeds from unity into the equality, and from the equality of unity into unity. Rightly therefore is it said to proceed from both, because it extends as it were from one into the other.

But we do not say that connexion is begotten either from unity or from the equality of unity, since it comes about neither from unity by repetition nor by multiplication; and although the equality of unity is begotten from unity and connexion proceeds from both, yet unity and the equality of unity and the connexion proceeding from both are one and the same, just as if of the same thing it were said: 'this, it, the same'. The 'it' itself that is said is referred to the first; but what is said, 'the same', connects and joins the referred to the first.

If therefore from this pronoun, which is it, there were formed this noun, which is itness, so that we could thus say: unity, itness, identity, itness would indeed make a relation to unity, but identity would designate the connexion of itness and unity, they would agree closely enough with the Trinity.

But that our most holy doctors called unity the Father, equality the Son, connexion the Holy Spirit, they did this on account of a certain likeness to these perishable things.

For in father and son there is a certain community of nature, which is one, so that the nature itself is equal in son and father. 'For there is nothing more or less of humanity in the son than in the father, and between them there is a certain connexion.'

For natural love connects one with the other, and this on account of the likeness of the same nature which is in them, which descends from the father into the son; and for this very reason he loves the son more than another agreeing with him in humanity.

From such a likeness indeed, and a most distant one, the father has been called unity, the son equality, but connexion the Holy Spirit, only in respect of creatures, as we shall also show below in its place. And this is in my judgment, according to the Pythagorean investigation of the Trinity in unity and of unity in Trinity ever to be adored, the most manifest investigation.

Let us now inquire what Martianus means when he says that philosophy, wishing to ascend to the knowledge of this Trinity, vomited forth circles and spheres. It has been shown in what precedes the one most simple maximum; and that it is itself neither the most perfect corporeal figure, as is the sphere, nor the superficial, as is the circle, nor the rectilinear, as is the triangle, nor of simple straightness, as is the line. But it is itself above all those, so that those things which are attained either by sense, or imagination, or reason with natural appendages, must necessarily be vomited forth, that we may arrive at the most simple and most abstract understanding, where all things are one, where the line is the triangle, where the circle is the sphere, where unity is trinity and conversely, where accident is substance, where body is spirit, motion is rest, and the like, then it is understood, when anything whatever is understood in the one itself, the one and the one itself all things and consequently anything whatever in it all things. And you have not rightly vomited forth the sphere, the circle, and the like, unless you understand that the maximal unity itself is necessarily threefold; for the maximum can in no way be rightly understood unless it is understood to be threefold, as we may use fitting examples for this.

We see that the unity of the intellect is nothing other than the intelligent, the intelligible, and understanding.

If therefore from that which is intelligent you wish to transfer yourself to the maximum and to say that the maximum is maximally intelligent, and do not add that it is itself also maximally intelligible and maximal understanding, you do not rightly conceive of the maximal and most perfect unity. For if unity is the maximal and most perfect intellection, which without these three correlations can be neither intellection nor most perfect intellection, he does not rightly conceive unity who does not attain the trinity of unity itself.

For unity is nothing but trinity, for it bespeaks indivision, discretion, and connexion. Indivision indeed is from unity, likewise discretion, likewise also union or connexion. The maximal unity, therefore, is nothing other than indivision, discretion, and connexion; and since it is indivision, then it is eternity or without beginning, just as the eternal is divided from none; since it is discretion, it is from immutable eternity; and since it is connexion or union, it proceeds from both. Further, when I say: unity is maximal, I say trinity. For when I say: unity, I say a beginning without beginning; when maximal, a beginning from a beginning; when by the verb is there is copulation and union, I say procession from both.

If therefore it has been most manifestly proved from what is above that the one is the maximum, since the minimum, the maximum, and the connexion are one, so that unity itself is both minimal and maximal and one: hence it is established how philosophy must vomit forth all imaginable and reason-able things, which would comprehend the maximal unity, not but threefold, with the most simple intellection.

But you wonder at these things which we have said, how one wishing to apprehend the maximum with simple intellection must leap over the differences and diversities of things and all mathematical figures, since we have said that in the maximum the line is the surface and the circle and the sphere.

Whence, that the intellect may be sharpened, I shall endeavor to transfer you thither more easily by indubitable manuduction, that you may see these things to be necessary and most true, which will lead you, not unfittingly, if from the sign you elevate yourself to the truth, understanding the words transumptively, into wondrous sweetness; since in learned ignorance you will profit in this way, so that, as far as is granted to one studious, elevated according to the powers of human genius, you may see the one maximal incomprehensible itself, God one and threefold ever blessed.