De docta ignorantia

It will profit the doctrine of learned ignorance greatly to premise preliminary corollaries from our principle. For they will afford a certain facility for eliciting infinite similar points by the same art, and will make what is to be said clearer. We held at the root of what was said that in exceeds and exceedings there is no arriving at the maximum in being and in power. Hence in the earlier chapters we showed that precise equality befits God alone; from which it follows that all givables besides him differ. One motion, therefore, cannot be equal to another, nor can one be the measure of another, since a measure necessarily differs from the measured.

These points, though they serve you unto infinity, yet if you transfer them to astronomy, you grasp that the calculator's art lacks precision, since it presupposes that the motion of all the other planets can be measured by the motion of the sun. The disposition of the heaven too, as regards any place whatever, whether the risings and settings of the signs or the elevation of the pole, and what concerns this, is not precisely knowable. And since no two places agree precisely in time and situation, it is manifest that the indications of the stars are far from precision in their particularity.

If consequently you adapt this rule to mathematics in geometrical figures, you see equality in act to be impossible, and that no thing can agree precisely with another in figure or in magnitude. And although the rules given in their formal character for describing an equal to a given figure are true, yet in act equality among diverse things is impossible. From this you ascend to how truth abstracted from material things sees equality in its concept, which it is altogether impossible to experience in things, since there it exists only with defect.

Come now: in music there is no precision from rule. No thing therefore agrees with another in weight, nor in length, nor in thickness; nor is it possible for harmonic proportions among the various voices of pipes, bells, men and other instruments to be found precisely, but a more precise one can always be given, nor is the same degree of truth of proportion in diverse instruments, as neither in diverse men; but in all there is necessary diversity according to place, time, temperament and other things. Precise proportion therefore is seen only in its concept; and we cannot find the sweetest harmony in sensible things without defect, for it is not there. Ascend here to how the most precise maximal harmony is proportion in equality, which no living man can hear in the flesh, since it would draw to itself the reason of our soul, since it is all reason, as infinite light draws all light; so that the soul, freed from sensibles, would not hear that supremely concordant harmony with the ear of the intellect without rapture. Some great sweetness of contemplation could be drawn here, both concerning the immortality of our intellectual and rational spirit, which bears incorruptible reason in its nature, through which it attains from itself concordant and discordant likeness in musical things, and concerning the eternal joy into which the blessed, freed from worldly things, are transferred. But of this elsewhere.

Further, if we apply our rule to arithmetic, we see that no two things in number can agree; since for the truth of number, composition, temperament, proportion, harmony, motion and all things are varied by extending to infinity. From this we understand that we are ignorant, since no one is like another in anything whatever, neither in sense, nor imagination, nor intellect, nor in operation or writing or painting or art, even if for a thousand years one strove to imitate another, and yet in anything whatever would never attain precision, although the sensible difference is sometimes not perceived. — Art too imitates nature as much as it can, but can never arrive at its precision. Medicine, alchemy, magic and the other arts of transmutation therefore lack the precision of truth, although one be truer in comparison with another, as medicine is truer than the arts of transmutation, as is evident of itself.

Still eliciting from the same foundation, let us say: since in opposites we find exceeding and exceeded, as in simple and composite, abstract and concrete, formal and material, corruptible and incorruptible and the rest, hence there is no arriving at either pure opposite, or at that in which they concur precisely equally. All things therefore are from opposites in diversity of degree, having more of one, less of the other, taking on the nature of one of the opposites through the victory of one over the other. From this the knowledge of things is rationally investigated, that we may know how composition in one thing exists in a certain simplicity, and in another enfolded in composition — as corruptibility in incorruptibility in one, the contrary in another — as of the rest, as we shall show in the book of Conjectures, where this will be treated more widely. Let these few points suffice for showing the marvelous power of learned ignorance.

Further, descending more to the point, I say that ascent to the maximum and descent to the minimum simply is not possible, lest there be transit to infinity, as is established in number and in the division of the continuum. Then it is clear that, given any finite thing whatever, a greater and a lesser is necessarily givable, whether in quantity or power or perfection, and in other respects, since a maximum or minimum simply is not givable in things, nor is there process to infinity, as was just shown. For since every part of the infinite is infinite, it implies contradiction that more and less be found where infinity would be reached, since more and less can no more befit the infinite than they have any proportion whatever to the infinite, since it is itself necessarily infinite too. For two would not be less than a hundred in infinite number, if by ascent to it one could arrive in act, just as an infinite line of infinite two-foot lines would not be less than an infinite line of infinite four-foot lines. There is therefore nothing givable that would terminate the divine power; hence for everything given a greater and a lesser is givable through it, unless the given were the absolute maximum, as will be deduced in the third little book. Only the absolute maximum therefore is negatively infinite; hence only it is that which can be by all power. The universe, however, since it embraces all things that are not God, cannot be negatively infinite, although it be without limit and thus privatively infinite; and in this consideration it is neither finite nor infinite. For it cannot be greater than it is: this indeed happens from defect; for possibility, or matter, does not extend beyond itself. For to say the universe can always be actually greater is nothing other than to say possibility can pass into actually infinite being, which is impossible, since the actuality of the infinite, which is absolute eternity, cannot arise from possibility, which is all possibility of being. Hence although in respect of the infinite power of God, which is interminable, the universe could be greater, yet, with the possibility of being, or matter, resisting, which is not actually extensible to infinity, the universe cannot be greater, and is thus unterminated, since nothing actually greater than it is givable at which it would be terminated, and it is privatively infinite. It, however, exists in act only contractedly, in the better way indeed which the condition of its nature allows. For it is a creature, which of necessity is, from the simply absolute divine being, as we shall show consequently in learned ignorance as clearly and simply as can be, as briefly as possible.