The Arithmetic of Boethius

Arith. Boetij

For since the works of our mind and reason are to number, to weigh, and to measure, which are by no means activities suitable for beasts: these cannot be done without discretio discernment or distinction. All discernment, however, happens through the one. For if you take away the one, discernment perishes. For one is one once, and two is twice one, and three is thrice one, and so on. And that "one" is the minimum in every thing. As in numbers, it is the unitas unity or the unit; in weights, it is the minimum weight; and in other measures, it is the minimum measure. Furthermore, since the composite is posterior to the simple by nature, and the posterior is by no means the measure of the prior: it is certain that the composite does not measure that which is the minimum and simplest in each thing. For you would not make ten the measure of two, such that through ten you would understand that two are two. Indeed, that would seem no less ridiculous than wanting to discern the light of the sun by a torch. Hence, the imperfection of our knowledge suggests and betrays itself: for we wish to discern the divine things themselves, which are most simple, through creatures and sensible things, which are most composite. For such a mode of discerning is almost similar to that by which we wish to measure the center itself by lines or bodies. And by this very reason it happens that we apprehend those supreme things in a composite way, just as one apprehends a center compositely: who assigns various ratios to it through lines, according as he terminates these or those lines, or as it is the beginning of these and those. By a not dissimilar reason we apprehend God compositely through creatures: namely, to whom we assign various names when compared to creatures. Thus we call God great, good, wise, and just. And very often we accommodate the names of our own mind to Him: calling Him intellectus understanding and mens mind, when He is nevertheless above all understanding and mind. And certainly to believe that those supreme beings are discerned by sensible things is to believe that smaller and simpler numbers are reached by more composite ones. Hence the wisdom of this world, which is to know divine things through creatures: if compared to that divine and most true wisdom, it is foolishness. So much so that the ignorance of God is seen to be superior to all science. And the more we apprehend divine things as incomprehensible, the more perfectly we gaze upon them. By these things it is clear: the simple is not reached and discerned by the composite, but on the contrary the composite is reached by the simple. And that is simple: namely, that which underlies the ratio of its own precise discernment and measure. Wherefore every number is reached and discerned by unity, as its own and most simple measure. So weights are measured by the minimum of weights. So almost all measures are measured by that which is the minimum and simplest of its own kind. On the contrary, the minimum is touched by no number, no weight, and likewise no measure in its own dimension. You see that we are led through unity and the one in number, weight, and measure to this point: that we assert without doubt that the supreme unity of all things, which is most simple, is the meter and measure of all things. And that very thing is namely that in which, as in truth and exact measure, each thing is known. Without this, every dimension, and likewise every knowledge of things, is an altered dimension and a shadowed knowledge. Our recognition is found to bring us to an enigma in all its parts, upon which it depends that we sigh for that knowledge in the Word and in truth. There, every knowledge coincides: not differently than every number in unity. We assert moreover that that unity is reached by no creature: just as unity is not reached by number, light by brightness, nor a torch by splendor or shadow. And thus no name of creatures pertains to the divine unity. Wherefore it is the principle through which, in which, and from which all things are: but which is reached by none of such things. So it is the principle of all intellects: and that which is understood by none. So it is that through which every speakable thing exists, and whatever can be said or enunciated: and yet it remains ineffable. It is that by which each terminable thing, I might say, is terminated: but it flees every limit. It is the end of all things: but it is finitary by none, and can be hemmed in by no limits. And so you surely perceive that God is least definable, wherefore, his substance is incomprehensible: especially since definition is the way to the comprehension of substance. You see that He is innamable: therefore nothing can be ascribed or attributed to Him. For what could our finite mind attribute to that unity, seeing as it is infinite? For whatever our mind conceives is finite. And that is far less suitable to the infinite unity than the name of a plant or a beast is to a man. Led by these things: we can assert that God is so all things, that nothing of all things exists. Hence Plato rightly cried out, that in the One, both affirmations and negations lie at the same time: as those which ascribe what is not suitable to the same. So not only can nothing be affirmed of God: but neither can it be denied. For negation and affirmation are opposites. Opposites, however, must happen concerning the same thing. Wherefore in that which no affirmation has a place: neither does any negation have a place in the same. Add that when you say God is not a man: what you say is a speakable and finite thing. But the infinite is reached by no speakable thing, and by no speech, as every speech is finite. It remains therefore above all enunciation: above all affirmation and negation alike. But indeed when you consider God as the principle of all beings: nothing of that which has been originated original: "principiato"

principiato

Lib. I

belongs to Him The text continues from the previous page: "nothing of that which has been originated belongs to Him". This is what Dionysius Referencing Pseudo-Dionysius the Areopagite, a Christian Neoplatonist philosopher. meant when saying: Since he is the cause for all things that they exist: he himself is not, as being superior to all essence. And he enunciates this of himself properly and expertly by negations. No one (he says) knows the father, except the son: nor the son, except the father. For all sciences are of subsisting things. Wherefore he who exceeds all substance: is likewise superior to all science. Thus the supersubstantial infinity and unity is superior to all sense and mind. And from there: the negative mode of philosophizing about God emanates. For thus you would deny every name of numbers concerning unity: namely, that which is prior to every number, and because every name of numbers carries a certain composition. For if you name the even and the odd: you imply parts. You do the same: if you name the perfect, the diminished, or the abundant. And far more so: if you name the multiple, the superparticular, or the superpartient. But most of all: if you name the corporeal, the pyramid, the cube, the superficial, the square, the oblong altera parte logiorem longer in one part, or the linear. It is certain therefore that unity is properly distinguished by no names of numbers. And that is the closest vestige of divine unity. Furthermore, each individual thing subsists more perfectly in God than in itself: which is not at all lost from unity itself. For every number is more distinguished by unity than by itself. So through unity itself: you apprehend the numerical quantity, and that exactly and perfectly; but not likewise by the number. For instance, you discern the duodenarium the number twelve most perfectly with unity, but not with the quaternario the number four or another number. I omit that he who is measured by number: is not without unity. Not differently, that which is discerned through the smallest magnitude, as by which you are certain how many inches there are: is more perfect than that which is measured through a greater magnitude, by which only the number of acres is known to you. Which if you proceed in this tenor in other things: you will see all things subsist more perfectly distinguished in the minimum measure than in themselves. Wherefore also in that supreme unity: each thing subsists more perfectly distinguished than in itself. For thus images are truer in truth than in their own subsistence. And that indeed will be deduced below. But nothing subsists in God: which is not God himself. Therefore all things are in a certain way God: and God is all things. And from here emerges the affirmative mode of speaking about God: which (as Dionysius wishes in Mystica Theologia Mystical Theology) beginning from the more perfect things, gradually progresses to the lowest and most abject things, being opposed to negative theology: as that which progresses gradually from the lowest things to the supreme. But since affirmation and negation (which are from a finite mind) are finite: they can by no means reach that which excels all that is finite, remaining in the shadows of its infinity, inaccessible to all light. Wherefore, it is above all affirmation and negation. And from here, emanates the theology of excellent negations: which neither asserts anything, nor denies anything concerning God. Whence divine theology is also found to be very brief. And to every interrogation about God, a single response is to be assigned: neither that he is, nor that he is not. And Dionysius indicates that the divine Bartholomew understood this wonderfully: as one who asserted theology to be both very much and very little, the Gospel wide and concise, since the good cause of all is expressed in very many words, as that which all things exist: just as unity is every number, namely in virtue and power. And it is brief: when only those things which excel are rightly attributed. So to unity itself: approved authors ascribe only the foremost and more perfect nomenclatures of numbers. For the first ,, trigonus triangular number, the first tetragonus square number, the first pyramis pyramidal number, the first cubus cube is said of them. But not ,, very commonly does one call unity oblong, even, abundant, or diminished. ,, Moreover, to no one: since it excels all enunciation, and is above every name. It gives nothing less to ,, all things than its own super-ineffable name. For each thing is said to be: from that ineffable being, ,, each thing is good: from that ineffable good. Of those who are purged: the supreme purity, infinite ,, brightness. Of those who are illuminated: the intimate splendor. Of those who are perfected: the supreme and exuberant perfection. Of those who become ,, divine-formed: the supreme divinity. Of the simple: true simplicity. Of those who are assumed into union: ,, unity. Of those following peace: peace. Of the living: life. Of the subsisting: substance. Of all life and substance: ,, the beginning and cause. By its ineffable goodness: producing and conserving all things so that they might be. Whose ,, providence all things admire. Spiritual things: intellectually. Rational things: knowingly. Sensible things: those which ,, have not experienced their senses. Plants: vitally. Substantially: those things which are, and the inanimate things themselves. And that is ,, found symbolically in unity. For unity: gives its name to all numbers. Since every ,, number: is considered to be and to be one from unity. Subtract unity: and there will be no number. You see that ,, on that part every creature asserts God to be: just as every number asserts unity, ,, for when you say the number exists: you likewise say unity exists. You see likewise that every question: ,, supposes Him. For what it is: supposes the quiddity. If it is: essence. Why it is and because of what: ,, it supposes the cause and the end. However, the supreme unity itself is: of which there is quiddity, essence, cause, and end. Wherefore when anything