On learned ignorance

Chapter One: How it is that knowing is not-knowing

We see that by the gift of God there is present in all things a natural desire to exist in the best manner in which the condition of each thing's nature permits this. And [we see that all things] act toward this end and have instruments adapted thereto. They have an innate sense of judgment which serves the purpose of knowing. [They have this] in order that their desire not be in vain but be able to attain rest in that [respective] object which is desired by the propensity of each thing's own nature. But if perchance affairs turn out otherwise, this [outcome] must happen by accident-as when sickness misleads taste or an opinion misleads reason. Wherefore, we say that a sound, free intellect knows to be true that which is apprehended by its affection ate embrace. (The intellect insatiably desires to attain unto the true through scrutinizing all things by means of its innate faculty of inference.) Now, that from which no sound mind can withhold assent is, we have no doubt, most true. However, all those who make an investigation judge the uncertain proportionally, by means of a comparison with what is taken to be certain.

Therefore, every inquiry is comparative and uses the means of comparative relation. Now, when, the things investigated are able to be compared by means of a close proportional tracing back to what is taken to be [certain], our judgment apprehends easily; but when we need many intermediate steps, difficulty arises and hard work is required. These points are recognized in mathematics, where the earlier propositions are quite easily traced back to the first and most evident principles but where later propositions [are traced back] with more difficulty because [they are traced back] only through the mediation of the earlier ones. Therefore, every inquiry proceeds by means of a comparative relation, whether an easy or a difficult one. Hence, the infinite, qua infinite, is unknown; for it escapes all comparative relation. But since comparative relation indicates an agreement in some one respect and, at the same time, indicates an otherness, it cannot be understood independently of number. Accordingly, number encompasses all things related comparatively. Therefore, number, which is a necessary condition of comparative relation, is present not only in quantity but also in all things which in any manner whatsoever can agree or differ either substantially or accidentally. Perhaps for this reason Pythagoras deemed all things to be constituted and understood through the power of numbers.

Both the precise combinations in corporeal things and the congruent relating of known to unknown surpass human reason-to such an extent that Socrates seemed to himself to know nothing except that he did not know. And the very wise Solomon maintained that all things are difficult and unexplainable in words. And a certain other man of divine spirit says that wisdom and the seat of understanding are hid den from the eyes of all the living. Even the very profound Aristotle, in his First Philosophy, asserts that in things most obvious by nature such difficulty occurs for us as for a night owl which is trying to look at the sun. Therefore, if the foregoing points are true, then since the desire in us is not in vain, assuredly we desire to know that we do not know. If we can fully attain unto this [knowledge of our ignorance], we will attain unto learned ignorance. For a man—even one very well versed in learning—will attain unto nothing more perfect than to be found to be most learned in the ignorance which is distinctively his. The more he knows that he is unknowing, the more learned he will be. Unto this end I have undertaken the task of writing a few things about learned ignorance.

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Chapter Three: The precise truth is incomprehensible

It is self-evident that there is no comparative relation of the infinite to the finite. Therefore, it is most clear that where we find comparative degrees of greatness, we do not arrive at the unqualifiedly Maximum; for things which are comparatively greater and lesser are finite; but, necessarily, such a Maximum is infinite. Therefore, if anything is posited which is not the unqualifiedly Maximum, it is evident that something greater can be posited. And since we find degrees of equality (so that one thing is more equal to a second thing than to a third, in accordance with generic, specific, spatial, causal, and temporal agreement and difference among similar things), obviously we cannot find two or more things which are so similar and equal that they could not be progressively more similar ad infinitum. Hence, the measure and the measured—however equal they are—will always remain different.

Therefore, it is not the case that by means of likenesses a finite intellect can precisely attain the truth about things. For truth is not something more or something less but is something indivisible. Whatever is not truth cannot measure truth precisely. (By comparison, a non-circle [cannot measure] a circle, whose being is something indivisible.) Hence, the intellect, which is not truth, never comprehends truth so precisely that truth cannot be comprehended infinitely more precisely. For the intellect is to truth as [an inscribed] polygon is to [the inscribing] circle. The more angles the inscribed polygon has the more similar it is to the circle. However, even if the number of its angles is increased ad infinitum, the polygon never becomes equal [to the circle] unless it is resolved into an identity with the circle. Hence, regarding truth, it is evident that we do not know anything other than the following: viz., that we know truth not to be precisely comprehensible as it is. For truth may be likened unto the most absolute necessity (which cannot be either something more or something less than it is), and our intellect may be likened unto possibility. Therefore, the quiddity of things, which is the truth of beings, is unattainable in its purity; though it is sought by all philosophers, it is found by no one as it is. And the more deeply we are instructed in this ignorance, the closer we approach to truth.

Chapter Four: The Absolute Maximum, with which the Minimum coincides, is understood incomprehensibly

Since the unqualifiedly and absolutely Maximum (than which there cannot be a greater) is greater than we can comprehend (because it is Infinite Truth), we attain unto it in no other way than incomprehensibly. For since it is not of the nature of those things which can be comparatively greater and lesser, it is beyond all that we can conceive. For whatsoever things are apprehended by the senses, by reason, or by intellect differ both within themselves and in relation to one another— [differ] in such way that there is no precise equality among them. Therefore, Maximum Equality, which is neither other than nor different from anything, surpasses all understanding. Hence, since the absolutely Maximum is all that which can be, it is altogether actual. And just as there cannot be a greater, so for the same reason there cannot be a lesser, since it is all that which can be. But the Minimum is that than which there cannot be a lesser. And since the Maximum is also such, it is evident that the Minimum coincides with the Maximum. The foregoing [point] will become clearer to you if you contract maximum and minimum to quantity. For maximum quantity is maximally large; and minimum quantity is maximally small. Therefore, if you free maximum and minimum from quantity—by mentally removing large and small—you will see clearly that maximum and minimum coincide. For maximum is a superlative just as minimum is a superlative. Therefore, it is not the case that absolute quantity is maximum quantity rather than minimum quantity; for in it the minimum is the maximum coincidingly.

Therefore, opposing features belong only to those things which can be comparatively greater and lesser; they befit these things in different ways; [but they do] not at all [befit] the absolutely Maximum, since it is beyond all opposition. Therefore, because the absolutely Maximum is absolutely and actually all things which can be (and is so free of all opposition that the Minimum coincides with it), it is beyond both all affirmation and all negation. And it is not, as well as is, all that which is conceived to be; and it is, as well as is not, all that which is conceived not to be. But it is a given thing in such way that it is all things; and it is all things in such way that it is no thing; and it is maximally a given thing in such way that it is it minimally. For example, to say “God, who is Absolute Maximality, is light” is [to say] no other than “God is maximally light in such way that He is minimally light.” For Absolute Maximality could not be actually all possible things unless it were infinite and were the boundary of all things and were unable to be bounded by any of these things—as, by the graciousness of God, I will explain in subsequent sections. However, the [absolutely Maximum] transcends all our understanding. For our intellect cannot, by means of reasoning, combine contradictories in their Beginning, since we proceed by means of what nature makes evident to us. Our reason falls far short of this infinite power and is unable to connect contradictories, which are infinitely distant. Therefore, we see incomprehensibly, beyond all rational inference, that Absolute Maximality (to which nothing is opposed and with which the Minimum coincides) is infinite. But “maximum” and “minimum,” as used in this [first] book, are transcendent terms of absolute signification, so that in their absolute simplicity they encompass—beyond all con traction to quantity of mass or quantity of power—all things.

Tr. Jasper Hopkins

At the Haas Collection

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