The Banquet (Il Convito)

by Dante Alighieri

CHAPTER XIV.

In order to see what is meant by the "third Heaven," one has in the first place to perceive what I desire to express by this word Heaven alone: and then one will see how and why this third Heaven was needful to us. I say that by Heaven I mean Science, and by the Heavens "the Sciences," from three resemblances which the Heavens have with the Sciences, especially by the order and number in which they must appear; as will be seen by discussing that word Third. The first similitude is the revolution of the one and the other round one fixed centre. For each movable Heaven revolves round its centre, which, on account of its movement, moves not; and thus each Science moves round its subject, which itself moves not; for no Science demonstrates its own foundation, but presupposes that. The second similitude is the illumination of the one and the other. For each Heaven illuminates visible things; and thus each Science illuminates the things intelligible. And the third similitude is the inducing of perfection in the things so inclined. Of which induction, as to the first perfection, that is, of the substantial generation, all the philosophers agree that the Heavens are the cause, although they attribute this in different ways: some from the Movers, as Plato, Avicenna, and Algazel; some from the stars themselves, especially the human souls, as Socrates, and also Plato and Dionysius the Academician; and some from celestial virtue which is in the natural heat of the seed, as Aristotle and the other Peripatetics. Thus the Sciences are the cause in us of the induction of the second perfection; by the use of which we can speculate concerning the Truth, which is our ultimate perfection, as the Philosopher says in the sixth book of the Ethics, when he says that Truth is the good of the intellect. Because of these and many other resemblances, it is possible to call Science, Heaven.

Now it remains to see why it is called the third Heaven. Here it is requisite to reflect somewhat with regard to a comparison which exists between the order of the Heavens and that of the Sciences Wherefore, as has been previously described, the Seven Heavens next to us are those of the Planets; then there are two Heavens above these, the Mobile, and one above all, Quiet. To the Seven first correspond the Seven Sciences of the Trivium and of the Quadrivium, namely, Grammar, Logic, Rhetoric, Arithmetic, Music, Geometry, and Astrology. To the eighth Sphere, i.e., to the starry, correspond Natural Science, which is termed Physics, and the first Science, which is termed Metaphysics. To the ninth Sphere corresponds Moral Science; and to the Quiet Heaven corresponds Divine Science, which is designated Theology.

And the reason why this is, remains briefly to be seen. I say that the Heaven of the Moon is likened unto Grammar because it is possible to find a comparison to it. For if you look at the Moon well, two things are seen to be proper to it which are not seen in the other stars: the one is the shadow which is in it, which is no other than the rarity of its body, in which the rays of the Sun can find no end wherefrom to strike back again as in the other parts; the other is the variation of its brightness, which now shines on one side, and now on the other, according as the Sun sees it. And these two properties Grammar has: for, because of its infinity, the rays of reason can find no end in it in parts, especially of the words; and it shines now on this side, now on that, inasmuch as certain words, certain declensions, certain constructions, are in use which were not formerly, and many formerly were which again will be; as Horace says in the beginning of his book on the art of Poetry, when he says: "Many words will spring up again which have now fallen out of use."

And the Heaven of Mercury may be compared to Logic because of two properties: that Mercury is the smallest star in Heaven, that the amount of its diameter is no more than two hundred and thirty-two miles, according as Alfergano puts it, who says that it is one twenty-eighth part of the diameter of the Earth, which is six thousand five hundred miles; the other property is, that it is more concealed by the rays of the Sun than any other star. And these two properties are in Logic: for Logic is less in substance than any other Science, for it is perfectly compiled and terminated in so much text as is found in the old Art and the new; and it is more concealed than any other Science, inasmuch as it proceeds with more sophistical and probable arguments than any other.

And the Heaven of Venus may be compared to Rhetoric because of two properties: the one is the brightness of its aspect, which is most sweet to behold, far more than any other star; the other is its appearance, now in the morning, now in the evening. And these two properties are in Rhetoric: for Rhetoric is the sweetest of all Sciences, since it principally aims at sweetness. It appears in the morning, when the Rhetorician speaks before the face of the hearer; it appears in the evening, that is, afterwards, when it speaks by Letters in distant parts.

And the Heaven of the Sun may be compared to Arithmetic because of two properties: the one is, that with his light all the other stars are informed; the other is that the eye cannot gaze at it. And these two properties are in Arithmetic, which with its light illuminates all its Sciences: for their subjects are all considered under some Number, and with Number one always proceeds in the consideration of these; as in Natural Science the movable body is the subject, which movable body has in itself three reasons of continuity, and this has in itself reason of infinite number. And of Natural Science its first and chiefest consideration is to consider the principles of natural objects, which are three, that is, matter, privation, and form; in which this Number is seen, and not only in all together, but again in each one, as he who considers subtly may perceive. Wherefore, Pythagoras, according to what Aristotle says in the first book of the Physics, established as the principles of natural things, the equal and the unequal; considering all things to be Number. The other property of the Sun is again seen in Number, of which Number is the Science of Arithmetic, that the eye of the intellect cannot gaze at it. For Number, inasmuch as it is considered in itself, is infinite; and this we cannot, understand.

And the Heaven of Mars may be compared to Music because of two properties. One is its most beautiful relative position; for, when enumerating the movable Heavens, from which one soever you may begin, either from the lowest or from the highest, this Heaven of Mars is the fifth; it is the central one of all, that is, of the first, of the second, of the third, and of the fourth. The other is, that this Mars dries up and burns things, because his heat is like to that of fire; and this is why it appears flaming in colour, sometimes more and sometimes less, according to the density and rarity of the vapours which follow it, which of themselves are often kindled, as is determined in the first book on Meteors. And, therefore, Albumassar says that the kindling of these vapours signifies the death of Kings and the change of Kingdoms; for they are the effects of the dominion of Mars. And, therefore, Seneca says that, on the death of Augustus, he beheld on high a ball of fire. And in Florence, at the beginning of its destruction, there was seen in the air, in the form of a cross, a great quantity of these vapours following the planet Mars. And these two properties are in Music, which is all relative, as is seen in harmonized words and in songs, from which the sweeter harmony results in proportion as the relation is more beautiful, which in this Science is especially beautiful, because there is in it a special harmony. Again, Music attracts to itself human spirits, which are as it were chiefly vapours from the heart, so that they almost cease from all labour; so is the whole soul when it hears it, and the power of all those spirits flies as it were to the spirit of sense, which receives the sound.

And the Heaven of Jupiter can be compared to Geometry because of two properties. The one is, that it moves between two Heavens, repugnant to its good tempering, namely, that of Mars and that of Saturn. Hence Ptolemy says, in the book alluded to, that Jupiter is a star of a temperate complexion, midway between the cold of Saturn and the heat of Mars. The other is, that amongst all the stars it appears white, as if silvered. And these things are in the Science of Geometry. Geometry moves between two things antagonistic to it; as between the point and the circle, and I term circle freely anything that is round, either a body or superfices; for, as Euclid says, the point is the beginning of Geometry, and, according to what he says, the circle is the most perfect figure in it, which must therefore have reason for its end; so that between the point and the circle, as between the beginning and the end, Geometry moves. And these two are antagonistic to its certainty; for the point by its indivisibility is immeasurable, and the circle, on account of its arc, it is impossible to square perfectly, and therefore it is impossible to measure precisely. And again, Geometry is most white, inasmuch as it is without spot of error, and it is most certain in itself, and by its handmaid, called Perspective.

And the Heaven of Saturn has two properties because of which it can be compared to Astrology. One is the slowness of its movement through the twelve signs; for twenty-nine years and more, according to the writings of the Astrologers, is the time that it requires in its orbit. The other is, that above all the other planets it is highest. And these two properties are in Astrology, for in completing its circle, as in the acquirement of this Science, the greatest space of time is revolved, because its demonstrations are more than any other of the aforementioned Sciences, and long experience is requisite to those who would acquire good judgment in it. And again, it is the highest of all the others, because, as Aristotle says in the commencement of his book on the Soul, the Science is high, because of its nobility, and because of the nobleness of its subject and its certainty. And this Science more than any other of those mentioned above is noble and high, for noble and high is its subject, which is the movement of the Heavens; and high and noble, because of its certainty, which is without any defect, even as that which springs from the most perfect and most regular principle. And if any one believe that there is defect in it, it is not on the part of the Science, but, as Ptolemy says, it is through our negligence, and to that it must be imputed.