THE CONVIVIO, BOOK 2 CHAPTER 13 BY DANTE ALIGHIERI
by Dante Alighieri
translated by Richard Lansing
To see what is meant by the third heaven we must first see what I mean by the word “heaven” itself; and then it will be seen how and why it was necessary to speak of this third heaven. I say that by heaven I mean “science” and by heavens “the sciences,” because of three kinds of similarity that the heavens have above all with the sciences, and by the order and number in which they seem to agree, as will be seen in speaking of the word “third.”
The first kind of similarity consists of the revolution of the one and the other around something that is motionless with respect to it. For each moving heaven turns on its center, which is not moved by the motion of the heaven; and likewise each science moves around its subject, without moving it, because no science demonstrates its own subject, but presupposes it.
The second similarity is the illuminating power of the one and the other; for each heaven illuminates visible things, and likewise each science illuminates things that are intelligible.
The third similarity consists of bringing about perfection in those things disposed thereto. Concerning the bringing about of perfection, insofar as the first perfection is concerned, namely substantial generation, all philosophers agree that the heavens are the cause, although they explain it differently, some imputing it to the movers, as do Plato, Avicenna, and Algazel; some to the stars themselves, especially in the case of human souls, as do Socrates and also Plato and Dionysius the Academician; and some to celestial virtue which is in the natural heat of the seed, as do Aristotle and the other Peripatetics. Similarly, the sciences are the cause in us of bringing about the second perfection, by the possession of which we are able to contemplate 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 as well as many other kinds of similarity, science may be called “heaven.”
Now it remains to be seen why “third” heaven is said. For this it is necessary to give consideration to a comparison that obtains between the order of the heavens and that of the sciences. As was stated above, then, the seven heavens nearest to us are those of the planets; next come two heavens above them, which are in motion, and one above them all, which is still. To the first seven correspond the seven sciences of the Trivium and the Quadrivium, namely Grammar, Dialectics, Rhetoric, Arithmetic, Music, Geometry, and Astrology. To the eighth sphere, namely the Starry Heaven, corresponds natural science, which is called Physics, and the first science, which is called Metaphysics; to the ninth sphere corresponds Moral Science; and to the still heaven corresponds Divine Science, which is called Theology. And the reason why this is so must be briefly considered.
I say that the heaven of the Moon resembles Grammar because it may be compared to it; for if the Moon is closely examined, two things will be seen peculiar to it which are not seen in the other stars: one is the shadow in it, which is nothing but the rarity of its substance in which the rays of the Sun cannot terminate and be reflected back as in its other parts; the other is the variation of its luminosity, which shines now on one side, now on the other, according as the Sun looks upon it.(36) These two properties Grammar possesses; for because of its infinitude the rays of reason are not terminated, especially in the particular of words; and it shines now on this side, now on that, insofar as certain words, certain declensions, and certain constructions are now in use which formerly were not, and many were formerly in use which will yet be in use again, as Horace says at the beginning of his Poetics, when he says: “Many words shall be born which have long since fallen out of use.”(37)
The heaven of Mercury may be compared to Dialectics because of two properties: for Mercury is the smallest star of heaven, because the magnitude of its diameter is not more than 232 miles, according to Alfraganus, who says it is 1/28th of the diameter of the earth, which is 6500 miles; the other property is that in its passage it is veiled by the rays of the sun more than any other star. These two properties are found in Dialectics, for Dialectics is less in substance than any other science, for it is entirely constituted by and contained within that text alone which is found in the Old Art and in the New; and its passage is veiled more than that of any science, in that it proceeds by a more sophistical and polemical mode of argument than any other.
The heaven of Venus may be compared to Rhetoric because of two properties: one is the brightness of its aspect, which is sweeter to look upon than that of any other star; the other is its appearance now in the morning, now in the evening. And these two properties are found in Rhetoric: for Rhetoric is sweeter than all of the other sciences, since this is what it principally aims at; and it appears in the morning when the rhetorician speaks before the face of his hearer, and it appears in the evening (that is, behind) when the rhetorician speaks through writing, from a distance.
The heaven of the Sun may be compared to Arithmetic because of two properties: one is that all the other stars are informed by its light; the other is that the eye cannot look at it. And these two properties are found in Arithmetic: for by its light all sciences are illuminated, because all their subjects are considered under some numerical aspect, and in considering them we always proceed by number. For example, in Natural Science, the subject is a body in motion, which body in motion has in itself the principle of continuity, and this has in itself the principle of infinite number; and its foremost consideration is to consider the principles of natural things, which are three–namely matter, privation, and form–in which we perceive this numerical aspect. Number exists not only in all of them together, but also, upon careful reflection, in each one individually; for this reason Pythagoras, as Aristotle says in the first book of the Physics, laid down even and odd as the principles of natural things, considering all things to have numerical aspect.(38) The other property of the Sun is also seen in number, of which Arithmetic is the science: the eye of the intellect cannot look upon it, because number insofar as it is considered in itself is infinite, and this we cannot comprehend.
The heaven of Mars may be compared to music because of two properties: one is its most beautiful relation, for in counting the moving heavens, from whichever we begin, whether from the lowest or the highest, this heaven of Mars is the fifth and the middlemost of them all, that is, of the first, second, third, and fourth pairs. The other, as Ptolemy says in the Quadripartitus, is that Mars dries things out and incinerates them because its heat is like that of fire;(39) and this is why it appears fiery in color, sometimes more and sometimes less, according to the density or rarity of the vapors which accompany it, which often ignite by themselves, as is established in the first book of Meteorics.(40) For this reason Albumassar says that the ignition of these vapors signifies the death of kings and the changing of kingdoms, because they are effects of the lordship of Mars, and this is why Seneca says that at the death of the Emperor Augustus he saw on high a ball of fire. This is also why in Florence, at the beginning of its ruin, there was seen in the sky in the shape of a cross a great quantity of these vapors which accompany the star of Mars. And these two properties are found in Music, which consists entirely of relations, as we see in harmonized words and in songs, whose harmony is so much the sweeter the more the relation is beautiful, which relation is the principal beauty in this science, because it is its principal aim. Moreover, Music attracts to itself the human spirits, which are, as it were, principally vapors of the heart, so that they almost completely cease their activity; this happens likewise to the entire soul when it hears music, and the virtue of all of them, as it were, runs to the spirit of sense which receives the sound.
The heaven of Jupiter may be compared to Geometry because of two properties: one is that it moves between two heavens that are antithetical to its fine temperance, namely that of Mars and that of Saturn; consequently Ptolemy says, in the book referred to, that Jupiter is a star of temperate constitution between the cold of Saturn and the heat of Mars; the other is that among all the stars it appears white, almost silvery. And these things are found in the science of Geometry. Geometry moves between two things antithetical to it, namely the point and the circle–and I mean “circle” in the broad sense of anything round, whether a solid body or a surface; for, as Euclid says, the point is its beginning, and, as he says, the circle is its most perfect figure, which must therefore be conceived as its end. Therefore Geometry moves between the point and the circle as between its beginning and end, and these two are antithetical to its certainty; for the point cannot be measured because of its indivisibility, and it is impossible to square the circle perfectly because of its arc, and so it cannot be measured exactly.(41) Geometry is furthermore most white insofar as it is without taint of error and most certain both in itself and in its handmaid, which is called Optics.
The heaven of Saturn has two properties by which it may be compared to Astrology: one is the slowness of its movement through the 12 signs, for according to the writings of the astrologers, a time of more than 29 years is required for its revolution; the other is that it is high above all the other planets.(42) And these two properties are found in Astrology: for in completing its circle (that is to say, to master this science) a very great span of time passes, both because of its handmaids, which are more numerous than those of any of the above-mentioned sciences, and because of the experience required in it for making proper judgments. Furthermore, it is far higher than all the others, since, as Aristotle says at the beginning of On the Soul, a science is high in nobility by virtue of the nobility of its subject and by virtue of its certainty; and this one, more than any of those mentioned above, is high and noble because of its high and noble subject, which regards the movement of the heaven, and high and noble because of its certainty, which is flawless, as coming from a most perfect and regular principle. And if anyone believes that there is a flaw in it, it does not pertain to the science, but as Ptolemy says, it results from our negligence, and so must be attributed to that.(43)
36. the rarity of its substance The theory that the spots on the moon were the result of the varying density of lunar material from place to place, later rejected by Dante in Par. II, 61 ff. as false, derives from Averroes.
37. as Horace says Ars poetica, 70-71. 38. as Aristotle says in the first book of the Physics Dante is referring to the commentary on the Physics by St. Thomas, I, 10.
39. as Ptolemy says in the Quadripartitus A treatise on astronomy by Claudius of Tolomea (Egypt) written in the third century A.D.
40. in the first book of Meteorics A work by Albert the Great; the reference is to Book I, 4, 9.
41. it is impossible to square the circle perfectly The last simile of the Divine Comedy embraces this concept; see Par. XXXIII, 133 ff.
42. the 12 signs The signs of the Zodiac.
43. it results from our negligence The reference is to the Quadripartitus I, 1, 2. It is likely that “negligence” signifies indolence. Dante uses the same root word to describe Belacqua’s moral condition (Purg. IV, 110-111).