On the distinction of the arts. Philosophy is the love of wisdom, which, lacking nothing, is the living mind and the sole primeval reason of things. This definition pertains rather to the etymology of the name. For 'philos' in Greek is 'love' in Latin, 'sophia' is 'wisdom,' and thence philosophy is derived, that is, the love of wisdom. But that which is added—'which, lacking nothing, is the living mind and the sole primeval reason of things'—signifies the divine wisdom, which is said to lack nothing for this reason: that it contains nothing less, but at once and together beholds all things past, present, and to come. It is called the 'living mind' for this reason: that whatever has once been in the divine reason is never blotted out by any forgetting.
It is the primeval reason of things, because all things were formed after its likeness. Some say that that from which the arts proceed always abides. This, then, is what all the arts do, this is their aim: that the divine likeness may be restored in us—the likeness which is for us a form, but for God a nature; and the more we are conformed to it, the more we are wise. For then there begins to shine again in us what was always in His reason; and what in us passes away abides unchangeable with Him. Otherwise: Philosophy is the art of arts and the discipline of disciplines, that is, that to which all the arts and disciplines look. 'Art' can be said of a science that consists of the precepts and rules of an art, as in writing; 'discipline' of what is called full, as in doctrine.
Or 'art' can be said when something probable and a matter of opinion is treated; 'discipline' when, concerning those things which cannot be otherwise, something is discoursed by true demonstrations. This difference Plato and Aristotle wished to exist between art and discipline. Or 'art' can be said of what is done in an underlying material and is unfolded through operation, as architecture; but 'discipline' of what consists in contemplation and is unfolded through reasoning alone, as logic. Otherwise: Philosophy is the meditation of death, which is more fitting for Christians, who, having trampled upon the ambition of the world, live by a disciplined manner of conduct, in the likeness of the homeland to come. Otherwise:
Philosophy is the discipline investigating in a probable manner the reasons of all things divine and human. Thus the reason of all pursuits looks to philosophy. Not every administration is philosophical, and therefore philosophy is said in some way to pertain to all things. Philosophy is divided into the theoretical, the practical, the mechanical, and the logical. These four contain all knowledge. 'Theoretical' is interpreted as 'speculative'; 'practical' as 'active,' which by another name they call 'ethics,' that is, 'moral,' because morals consist in good action; 'mechanical' as 'adulterate,' because it is concerned with human works; 'logical' as 'verbal,' because it treats of words. The theoretical is divided into theology, mathematics, and physics.
This division Boethius makes in other words, dividing the theoretical into the intellectible, the intelligible, and the natural—by 'intellectible' signifying theology, by 'intelligible' mathematics, by 'natural' physics. Finally, he defines the intellectible thus. On theology. The intellectible is that which, being one and the same, abiding by itself always in its proper divinity, is grasped by no senses ever, but by the mind and intellect alone. This subject is composed for the contemplation of God and for the consideration of the incorporeality of the soul by the investigation of true philosophy—which, he says, the Greeks call theology.
Now it is called 'theology' as it were a discourse held concerning divine things, for 'theos' is interpreted 'God,' 'logos' 'discourse' or 'reason.' Theology, therefore, is when we discourse either of the ineffable nature of God, or of spiritual creatures, from some part of their most profound quality. On mathematics. Mathematics, moreover, is called the doctrinal science. For 'mathesis,' when it has the 't' without aspiration, is interpreted 'vanity,' and signifies the superstition of those who place the fates of men in the constellations—whence such men are called 'mathematici' (astrologers). But when it has the 't' aspirated, it means 'doctrine.' And this is that which considers abstract quantity.
For 'abstract quantity' is so called when, separating it in the intellect from matter, or from other accidents—such as the even, the odd, and the like—we treat of it in reasoning alone, which doctrine does, not nature.
This Boethius calls the 'intelligible,' which comprehends by thought and understanding the first part, the 'intellectible'—which things are of all the heavenly works of the supreme divinity, and whatever beneath the lunar globe has power by a more blessed mind and a purer substance, and lastly of human souls; all of which, since they had been of that prior intellectible substance, by the touch of bodies degenerated from the intellectibles to the intelligibles, so that they are no more understood than they understand, and are then the more blessed in purity of understanding the more often they apply themselves to the intellectibles. For the nature of spirits and souls, since it is incorporeal and simple, is a partaker of the intellectible substance.
But because it does not descend uniformly through the instruments of the senses to the apprehending of sensible things, and draws their likeness to itself through imagination, in this it in some way forsakes its own simplicity, in that it takes on a mode of composition. For that cannot be called wholly simple which is like the composite. The same thing, therefore, in different respects is at once intellectible and intelligible: intellectible in that it is an incorporeal nature and can be grasped by no sense; but intelligible in that it is indeed a likeness of sensible things, yet not itself sensible. For the intellectible is that which is neither sensible nor a likeness of the sensible.
But the 'intelligible' is that which is itself indeed perceived by intellect alone, yet does not perceive by intellect alone, because it has imagination or sense, by which it grasps those things which are subject to the senses. By touching bodies, therefore, it degenerates, because, while it runs over the invisible forms of bodies through the passions of the senses, and draws them, once touched, into itself through imagination, it is split off from its simplicity as often as it is informed by some qualities of a contrary passion. But when, ascending from this distraction to pure understanding, it gathers itself into one, it becomes the more blessed by participation in the intellectible substance. On the quaternary of the soul. The reason of this progression and regression number itself also teaches. Say:
'Three times one makes three'; say: 'three times three makes nine'; say: 'three times nine makes twenty-seven'; say: 'three times twenty-seven makes eighty-one.' Behold, at the fourth step the first unity meets you, and you will see the same thing happen if you carry the multiplication on to infinity, so that always at the fourth step unity stands out. Now most rightly is the simple essence of the soul expressed by unity, which is itself also incorporeal. The ternary too, on account of the indissoluble bond of the middle unity, is fittingly referred to the soul; just as the quaternary, because it has two middle terms and is therefore dissoluble, pertains properly to the body.
The first progression of the soul, then, is that by which, from its simple essence (which is figured by the monad), it extends itself into the virtual ternary, where now it both desires one thing through concupiscence, despises another through anger, and discerns between the two through reason. And it is rightly said to flow forth from the monad into the triad, because every essence is naturally prior to its power. Again, that the same unity is found three times in the multiplying ternary signifies this: that the soul consists not by parts, but wholly in each of its single powers.
For we cannot call reason alone, or anger alone, or concupiscence alone a third part of the soul, since reason is neither other than the soul nor less in substance than the soul, nor is anger other or less than the soul, nor is concupiscence other or less than the soul; but one and the same substance, according to its diverse powers, obtains diverse names. Then, from the virtual ternary, by a second progression the soul descends to governing the music of the human body, which is composed by the novenary, because there are nine openings in the human body through which, according to the natural tempering, there flows in and flows out everything by which this same body is quickened and governed.
Here too there is an order, because the soul naturally has its powers before it is mingled with the body. But afterward, in the third progression, now poured out beyond itself through the senses, it is dissipated through countless actions toward these visible things, which are to be administered as figured by the number twenty-seven—which is a solid number and is extended in three dimensions after the likeness of a body.
But in the fourth progression, released from the body, it returns to the purity of its own simplicity; and therefore in the fourth multiplication, where three times twenty-seven has grown into eighty-one, the monad appears at the summit, so that it may plainly be clear that the soul, after the term of this life (which is designated by eighty), returns to the unity of its own simplicity, from which it had earlier departed when it descended to govern the human body. And that the limit of human life naturally stands at eighty, the prophet declares: 'If,' he says, 'in strength there be eighty years, and what is more of them is labor and sorrow.'
This quadruple progression some think to be that quaternary of the soul of which we spoke above, and that it is called the quaternary of the soul to distinguish it from the quaternary of the body. On the quaternary of the body. For to the body too they assign its own quaternary. Just as the monad befits the soul, so the dyad befits the body. Say: 'twice two makes four'; say: 'twice four makes eight'; say: 'twice eight makes sixteen'; say: 'twice sixteen makes thirty-two.' Here in the fourth place likewise the same number—that is, the binary, from which the multiplication took its beginning—meets you; and the same thing, if you proceed to infinity, will undoubtedly come about, that at the fourth step the binary always stands out.
And this is the quaternary of the body, in which it is given to understand that everything which receives its composition from dissoluble things is itself also dissoluble. You now see clearly enough, as I think, how souls degenerate from the intellectibles to the intelligibles, when, from the purity of simple understanding—which is darkened by no image of bodies—they descend to the imagination of visible things; and again become more blessed when, gathering themselves from this distraction to the simple fountain of their own nature, they are composed as though stamped by the imprint of some excellent figure. There is, then, that I may speak more plainly, in us the intellectible, which is understanding, but the intelligible, which is imagination.
But understanding (intelligentia) is the pure and certain cognition concerning the first principles of things alone—that is, God, the ideas, and matter (hyle)—and concerning incorporeal substances. Imagination is the memory of the senses arising from the remnants of bodies adhering to the mind, a principle of cognition having nothing certain in itself. Sense is a passion of the soul in the body, arising from qualities accidentally present from without. On the quadrivium. Since, then, as was said above, it properly pertains to mathematics to attend to abstract quantity, in the parts of quantity its species must be sought. Abstract quantity is nothing else than a visible form, according to linear dimension, impressed upon the mind, which consists in imagination, of which there are two parts:
one continuous, as a tree or a stone, which is called magnitude; the other discrete, as a flock or a people, which is called multitude. Again, of multitude some things are per se, as three, four, or any other number; others are relative to something, as the double, the half, the sesquialteral (3:2), the sesquitertial (4:3), or any such ratio. But of magnitude some things are movable, as the sphere of the world; others immovable, as the earth. Multitude, therefore, which is per se, arithmetic considers; but that which is relative to something, music. Geometry promises knowledge of immovable magnitude; but of movable magnitude the expertise of the astronomical discipline claims the science. Mathematics, then, is divided into arithmetic, music, geometry, and astronomy. On arithmetic.
'Ares' in Greek is interpreted 'virtue' (power) in Latin, 'rithmus' 'number'; whence arithmetic is called the power of number. And the power of number is that after its likeness all things were formed. On music. Music took its name from water (aqua), because no euphony—that is, good sonority—can come to be without moisture. On geometry. Geometry is interpreted 'the measure of the earth,' because this discipline was first discovered by the Egyptians, who, when the Nile by its flooding covered their boundaries with mud and confounded their landmarks, began to measure the earth with rods and ropes. Then by wise men it was also brought and extended to measuring the spaces of the sea, the sky, the air, and of any bodies whatever. On astronomy.
Astronomy and astrology seem to differ in this, that astronomy takes its name from the 'law of the stars' (lex astrorum), while astrology is so called as it were 'a discourse discoursing about the stars'; for 'nomia' is interpreted 'law' and 'logos' 'discourse.' Thus astronomy seems to be that which discourses concerning the law of the stars and the revolution of the heaven, investigating the regions, the circles, the courses, the risings and settings of the stars, and why each is so named. But astrology is that which considers the stars according to the observance of nativity and death and of any other events whatever—which in part is natural, in part superstitious;
the natural in the complexions of bodies, which vary according to the tempering of the higher things, such as health, sickness, storm, fair weather, fertility, and barrenness; the superstitious in contingent things and in those which are subject to free will, which part the 'mathematici' (astrologers) treat. On arithmetic. Arithmetic has for its matter the even and the odd number. Of the even number, one is evenly even, another evenly odd, another oddly even. The odd number too has three species: the first is prime and incomposite; the second is secondary and composite; the third is per se secondary and composite, but compared to others prime and incomposite. On music. There are three kinds of music: mundane, human, and instrumental.
Worldly music is found partly in the elements, partly in the planets, partly in the seasons of time. In the elements, it lies partly in weight, partly in number, partly in measure. In the planets, partly in position, partly in motion, partly in nature. In the seasons, partly in days, through the alternation of light and night; partly in months, through the waxings and wanings of the moon; partly in years, through the changing of spring, summer, autumn, and winter. Human music is found partly in the body, partly in the soul, partly in the bond joining both.
In the body, one kind lies in growth, by which that which is common to all living things increases; another lies in the humours, from whose combination the human body subsists, which is common to all sentient creatures; another lies in operations, which belongs especially to rational beings, over which the mechanical arts preside. These operations, if they do not exceed due measure, are good, so that desire may not be nourished from the very source by which weakness ought to be sustained — as Lucan reports in praise of Cato: 「For him a feast was to have conquered hunger, and his great household gods to have driven off the cold beneath a roof; and a precious garment was to have drawn over his shaggy limbs, after the manner of a Roman citizen, the toga.」
The music in the soul lies partly in the virtues, such as justice, piety, and temperance; partly in the powers, such as reason, anger, and desire. The music between body and soul is that natural friendship by which the soul is bound to the body, not by bodily chains but by certain affections, so as to move and give sensation to the body itself; and according to this friendship 「no one ever hated his own flesh.」 This is the music, that the flesh be loved, yet the spirit more; that the body be cherished, yet virtue not be destroyed. Instrumental music is found partly in percussion, as with drums and strings; partly in wind, as with flutes and organs; partly in the voice, as in songs and melodies. There are also three kinds of musicians:
one who composes songs; another who performs by instruments; and a third who judges both the work of the instruments and the song. Concerning geometry. Geometry has three parts: planimetry, altimetry, and cosmimetry. Planimetry measures the plane, that is, length and breadth, and extends forward and backward, to the right and to the left. Altimetry measures height and extends upward and downward; for the sea too is called 「high,」 that is, deep, and a tree is called 「high,」 that is, lofty. 「Cosmos」 is interpreted as 「world,」 and hence the name cosmimetry, that is, the measure of the world.
This measures spherical things, that is, globular and round things, such as a ball and an egg; whence cosmimetry is also so named from the sphere of the world on account of its excellence — not because it deals only with the measure of the world, but because the sphere of the world is more worthy than all other spherical things. Concerning astronomy. Nor is it contradictory that above we attributed immovable magnitude to geometry and movable magnitude to astronomy, for this was said according to the original invention, by which geometry too is called 「the measure of the earth.」 Or we may say that what geometry considers in the sphere of the world — namely, the dimension of regions and of the celestial circles — is immovable, insofar as it pertains to geometrical consideration.
For geometry considers not motion but space; whereas what astronomy contemplates is movable, namely the courses of the stars and the intervals of times. And so we shall say universally that immovable magnitude is the subject of geometry, and movable magnitude the subject of astronomy; for although both deal with the same thing, yet the one contemplates that which remains, the other contemplates that which passes. The definition of the quadrivium. Arithmetic, then, is the science of numbers. Music is the division of sounds and the variety of tones; or otherwise, music or harmony is the concord of many unlike things brought together into one. Geometry is the discipline of immovable magnitude and the contemplative description of forms, through which the boundaries of each thing are wont to be declared.
Or otherwise, geometry is the source of the senses and the origin of utterances. Astronomy is the discipline investigating the spaces, motions, and returns of the celestial bodies at fixed times. Concerning physics. Physics considers the causes of things in their effects, and the effects from their causes, by investigation: 「Whence comes the trembling of the earth, by what force the deep seas swell, the powers of herbs, the spirits and rages of wild beasts, every kind of shrub, and of stones too, and of creeping things.」 「Physis」 is interpreted as 「nature」; whence also, in the division of theory given above, Boethius named physics the natural science. This is also called physiology, that is, discourse treating of natures, which pertains to the same matter.
Physics is sometimes taken broadly as equivalent to theory; and according to this acceptance some divide philosophy into three parts, namely physics, ethics, and logic — in which division the mechanical is not included, but philosophy is restricted to physics, ethics, and logic. What is proper to each art. But although all the arts tend toward one and the same goal of philosophy, yet they do not all run by one road; rather, each has certain considerations of its own by which they differ from one another. Logical consideration is in things, attending to the understanding of things, whether through intellection — as that these things neither exist nor are likenesses of things; or through reason — as that they do not exist, yet are likenesses of things.
Logic therefore considers the species and genera of things. But it is proper to mathematics to attend by reason, in an unconfused way, to things that are confused. For example, in the actuality of things, no line is found without surface and solidity; for no body is so merely long as to lack breadth or height, but in every body these three are together. Yet reason attends to the line purely in itself, without surface and thickness — which is the mathematical — not because in reality it either is so or could be so, but because reason often considers the actualities of things, not as they are, but as they could be: not in themselves, but as far as concerns reason itself, that is, as reason would allow them to be.
According to this consideration it has been said that continuous quantity decreases to infinity, and discrete quantity increases to infinity. For such is the liveliness of reason that it divides every length into lengths, every breadth into breadths, and so on, and that to reason itself nothing lacking an interval generates an interval. But it is proper to physics to attend, in an unmixed way, to the actualities of things that are mixed. For the actualities of the bodies of the world are not pure, but composed from the actualities of pure things; and physics, although these are not found by themselves, nevertheless considers them purely and by themselves — namely the pure actuality of fire, or of earth, or of air, or of water — and from the nature of each considered by itself it judges concerning the composition and efficacy of the whole.
This too must not be passed over: that physics alone properly deals with things, while all the others deal with the understandings of things. Logic treats of these understandings according to their predicamental constitution; mathematics, however, according to their integral composition. And therefore logic sometimes uses pure intelligence, but mathematics is never without imagination, and so it has nothing truly simple.
For since logic and mathematics are prior in the order of learning to physics, and in a certain way serve it in the role of instruments by which one must first be trained in each before devoting effort to physical contemplation, it was necessary that they place their consideration not in the actualities of things — where experience is deceptive — but in reason alone, where unshaken truth abides; and then, with reason itself going before, descend to the experience of things. Therefore, after we have shown how the division of theory which Boethius sets forth agrees with the one above, we now briefly review both, so that we may compare the individual terms of each division with one another. A comparison of the foregoing.
Theory is divided into theology, mathematics, and physics; or otherwise, theory is divided into the intellectible, the intelligible, and the natural; or otherwise, theory is divided into the divine, the doctrinal, and philology. The same, then, is theology, the intellectible, and the divine; the same is mathematics, the intelligible, and the doctrinal; and the same is physics, philology, and the natural. There are those who think these three parts of theory are signified mystically by a certain name of Pallas, who is feigned to be the goddess of wisdom. For she is called 「Tritona,」 as if 「tritoona,」 that is, threefold knowledge — namely of God, which we have called intellectible; of souls, which we have called intelligible; and of bodies, which we have called natural.
And rightly does wisdom take its name from these three alone; for although we might fittingly refer the other three — namely ethics, the mechanical, and logic — to wisdom, yet more expressly we call logic, on account of the eloquence of speech, and the mechanical and ethics, on account of the circumspection of morals and of works, by the name of prudence or knowledge. But theory alone, on account of the contemplation of the truth of things, we name wisdom. Again. The practical is divided into the solitary, the private, and the public; or otherwise, into the ethical, the economic, and the political; or otherwise, into the moral, the dispensative, and the civil. One and the same is the solitary, the ethical, and the moral; one again is the private, the economic, and the dispensative.
And likewise the public, the political, and the civil are the same. 「Oeconomus」 is interpreted as 「steward」; hence economics is called the dispensative. 「Polis」 in Greek is called 「city」 in Latin; hence it is named political, that is, civil. When we make the ethical part a part of the practical, ethics is to be taken strictly as concerned with the morals of each individual person, and is the same as the solitary. The solitary, then, is that which, taking care of itself, raises itself above all things, adorns and increases itself with virtues, admitting nothing into life in which it cannot rejoice, doing nothing to be repented of. The private is that which, arranging the duty of the household with moderate management, distributes it.
The public is that which, taking up the care of the commonwealth, heals the welfare of all by the diligence of its providence, the balance of justice, the stability of fortitude, and the patience of temperance. The solitary, then, befits individuals; the private, heads of households; the political, the rulers of cities. The practical is called 「actual,」 because it works out by its operations the matters proposed. It is called 「moral,」 because through it an honourable manner of living is sought, and habits tending toward virtue are prepared. It is called 「dispensative,」 when the order of household affairs is wisely arranged. It is called 「civil,」 because through it the welfare of the whole city is administered. The division of the mechanical into seven. The mechanical contains seven sciences:
the working of wool, armament, navigation, agriculture, hunting, medicine, and the theatrical. Of these, three pertain to the outward clothing of nature, by which nature protects itself from discomforts; four pertain to the inward, by which it nourishes itself by feeding and cherishing — in likeness indeed to the trivium and quadrivium, since the trivium treats of the words which are outward, and the quadrivium of the understandings which are conceived inwardly. These are the seven handmaids which Mercury received from Philology as a dowry; for surely every human action serves eloquence, to which wisdom is joined, as Tully says in his book of Rhetoric concerning the pursuit of eloquence: