§ 1. Immense is the force and multitude of the things proposed to us for learning, but so great is our weakness that we scarcely possess perfectly one part of them all. For who, after the studies of many years, understands those great mysteries concerning God, angels, and souls? That mind, so swift, so active, so curious about all things, cannot determine what it itself is. Concerning points and lines, concerning the connection of corporeal things and συνέχεια (continuity), after so many thousands of volumes, we all carry ignorance to the grave. But it is foolish to lament these things, since clarity and knowledge are promised to us in the future life; nevertheless, to subdue pride, our darkness must often be impressed upon us.
A twofold order of the sciences must be established, one of method, the other of nature. In method they generally observe this order: that youth is first polished by grammar, poetry, eloquence, and history; that it is next exercised in the subtlety of logic, physics, mathematics, metaphysics, and moral philosophy; and that from here some pass to the profundity of most sacred theology, others to the studies of law and legislation, and others to those of medicine. I too approve and confirm this method of teaching, approved by almost all academies and neglected by a few not without public harm to youth. This order, indeed, was established according to the convenience of learners. The other is natural: following the summits of things, it distributes the sciences to us according to their division. If we consult it, it does not readily appear how one ought to call a science one and by what limits it ought to be defined.
The philosophers indeed establish that one science is so called from one formal aspect of its object; but what that formal aspect which conciliates unity may be is not yet clear. Cajetan holds that formal unity is taken from being knowable, not from the being of the species. Light and color, for example, are objects of sight not from their nature and essence, which are diverse, but from the fact that they are visible. But he entangles the matter with a greater difficulty. For if body is the object of physics according to knowable being, what is that one knowable thing which makes one science? For there are many bodies and therefore many knowable things; and if they constitute one science because all can be known, spirits and bodies will also be joined into one because they can be known. Being itself, which contains all things, is also knowable.
The common distinction of the sciences is by three abstractions, which almost all the logicians whom I have seen put up for sale. For physics abstracts from singular matter, but not from sensible matter; it considers the species of bodies and their affections, not singular bodies. Mathematics abstracts from singular and sensible matter, for it considers points, lines, surfaces, and depths abstractly in themselves, and not as they are in matter. Metaphysics, however, abstracts from singular, sensible, and intelligible matter, because it considers only the most general or spiritual things, things which have no position and location.
I admit that there is something I miss in this matter. Those abstractions do not apply to rational and moral science, although their dignity is distinguished. Next, if a special abstraction is assigned to quantity, it can also be assigned to quality; for both quantity and quality are sensible, and writers on perspective treat light, while professing themselves mathematicians. And certainly it can be considered without matter. Finally, if physics expounds body, quality, and quantity, surely few things will be left for metaphysics. Therefore, a distinction of sciences must be sought which has been established by nature and exists in the objects before our mind has known them. I judge as follows.
§ 2. There is one peculiar science of each class of things and one general science of all. When I have demonstrated that every triangle has three angles equal to two right angles, I possess knowledge; when I have learned several propositions of the same kind, I have attained one total science from the likeness of things related to one another. But since the whole universe of things and system of all beings agrees in being, in like manner one most general science will be so called which corresponds to that whole. And just as Being taken most broadly is divided into its parts, so science will be divided into its parts. For just as being taken generally is intelligible, so the faculty of understanding extends to being and all its parts; in the same manner, a habit—either one or consisting of many—will bring the capacity of the power of understanding to firmness.
Thus formerly Plato, Book 7 of the Republic; Proclus, Book 1, chapter 4, on Euclid; and Giles of Rome, preface to the Metaphysics, question 22. Accordingly, Antonio of Mirandola is not the author but the elucidator of that opinion in Book 3 of The Overthrow of the Singular Contest, sections 6 and 7. Those who attack this reasoning do not sufficiently observe that, when they call physics one science, they force very many and very widely separated things into one object and cannot give a law to others preventing them from adding still more. They extend metaphysics itself to every class of things. But now, following the nature of things, let us divide the sciences.
Science taken most broadly is divided into that which treats spiritual being and is properly speculative metaphysics—its primary object is the uncreated spirit, its secondary object the created spirit. On account of the difficulty of its object, the general doctrines of the other sciences have been added to it. The other is physics, which treats material being and contains many practical and speculative sciences. By the name of material being we understand not only bodies but also all accidents of bodies and whatever things possess some order toward bodies, such as the rational soul, intellect, and human will, because the former is the form of the body and the latter are properties of that form.
Physics taken in this manner is divided into physics strictly taken, whose object is natural body, which Aristotle explains in his books of the Physics; and mathematics, which considers quantity, a part which Euclid and his interpreters chiefly expound.
Physics is again twofold, for it treats either simple body or body compounded from simple bodies. If it treats simple body, it treats either incorruptible or corruptible body; if incorruptible, it is celestial; if corruptible, elemental. Aristotle explains these parts in his books On the Heavens and On Generation and Corruption. This celestial science, which is physical, differs from astronomy, which belongs to mathematics. For physics considers the quantity of the heavens in itself, its matter, form, and efficient cause; but astronomy considers the proportions of quantity and the magnitudes from the principles of mathematics. The object of the science of mixed body is
whatever is found in the whole universe besides the heavens and the elements. First, one science concerns imperfect mixtures, another perfect mixtures. Imperfect mixtures are snow, ice, mist, and the other things which Aristotle explains in the books of the Meteorology. The remaining mixtures are perfect, namely, those which possess a perfect tempering of the elements from which they are composed. Imperfect mixtures have one element so predominant that the powers of the others scarcely appear.
Of perfect mixtures, however, some are animate and others inanimate. Aristotle also treats mixtures in general in the two books On Generation and Corruption, and animate things in the three books On the Soul, the Short Natural Works, and On the Generation of Animals. The science of inanimate things has two principal parts, gemology and metallurgy, concerning which Aristotle says little, but Pliny, the alchemists, and Cardano say much in the books On the Variety of Things and On Subtlety.
The science that concerns animate things is held either concerning sentient things or those without sense. The latter is threefold: arboriculture, shrub-lore, and herb-lore; for root-lore, which others add, is common to all these. Aristotle treats these matters first in On Plants, as do Dioscorides, Theophrastus, and his interpreter Julius Scaliger. There are three species of sentient things, which both Aristotle and Gesner—above all a diligent investigator of natures—treat.
But since man is as it were a little world, there are several sciences concerning him as species of anthropology.
For if we consider the body, either its nature and parts are considered, and this is a species of the science of animate things—Vesalius treats it with the greatest accuracy—or the body is considered insofar as it is capable of being healed. This science is subordinate to the former, namely medicine, which they divide into active and contemplative medicine. The latter they again divide into physiology, which investigates the natures of things so that it may use their powers for health; this part they divide again into the physiology of elements, humors, temperaments, powers, and members; into etiology, which investigates the causes of all diseases and symptoms; and, third, into semiomantics, which infers from signs either past, present, or future things. All these matters were treated by Hippocrates of Cos and his interpreter Galen, and thereafter by Avicenna and others.
The science which treats the human mind can be called noetics and is threefold. First is that which explains the actions of the mind as such; this is customarily called animastics by the Latins. Two sciences are, as it were, subordinated to this: the first directs the operations of the intellect toward truth, namely logic; the other directs those of the will toward the good or honorable, and is moral philosophy. Moral philosophy is again twofold, principal and ministering. The ministering is called oratory and is divided into dialectic, rhetoric, and poetics; for those sciences were invented to incite the will toward the honorable. The principal is called ethics, or moral philosophy properly so called; its object is human actions insofar as they are good or evil. They divide this very variously, concerning which matters in their own proper place. Aristotle treated it in the Nicomachean Ethics, the Great Ethics, and the Politics. Jurisprudence can be referred here; one part of it is positive, the other epideictic or demonstrative. Its parts are various.
The science which treats quantity deals either with continuous or with discrete quantity. That which treats continuous quantity is generally called geometry by one name. It is divided in two: one part treats lines and surfaces and does not have a proper name but claims the general name for itself and is called geometry; the other treats solid body and is called stereometry, as though “measurement of solids.”
They further divide geometry in another manner: into that which discusses quantity as it exists by itself and contains the parts just named; and into that which treats quantity as joined with matter and subject to the senses. This, from its primary part, is called astronomy; others call it impure mathematics because it does not treat quantity considered in isolation. It is again divided into astrology, geodesy, perspective, and mechanics.
Astrology is that which discusses the motions of the world, the magnitude, figure, illumination, and distance of the heavenly bodies. It has three parts. The first is gnomonics, which measures time by the position of the gnomon or style. The second is meteoroscopy, which examines differences of elevations and the other theorems. The third is dioptrics, which investigates the distances of the planets and other stars with dioptric instruments.
Perspective is that which uses visual rays in the manner of lines and the angles constituted from those lines. This again is threefold. First is perspective properly so called, which gives the causes of those appearances in which things seem to us to be otherwise than they are, whether because of distances, position, or medium. The second is the science of mirrors, which is occupied with various refractions. The third is sciography, namely the delineator of shadows, which gives an account of various appearances arising from shadows.
Geodesy is the science which measures various things—such as fields, heaps, wells, and towers—by visible lines. If it treats the entire earth and sea, it is customarily called geography; if some one region, chorography; if some one place, topography.
Mechanics embraces various arts and therefore has almost the same definition as art, although properly those arts which leave no work behind them, such as the art of dancing, are not mechanical. Its parts are architecture, which constructs every kind of building; organopoetics, which constructs various machines and instruments; and, third, thaumaturgy, which effects certain wonders by air, weights, sinews, and fires. To this they refer the art which they call natural magic, which uses no magical deceptions but, on account of a hidden knowledge of things, produces effects of such a kind that they seem incapable of being accomplished naturally, but only by the aid of demons—as when Archimedes draws a ship by himself.
Arithmetic is occupied with discrete quantity. They call one kind speculative and another practical. Music is subordinated to the latter, which they likewise divide into speculative and practical. Both practical and speculative music are divided into melic, harmonic, and rhythm. Melic contains oratorical and poetical feet; and so, with respect to this part, poetry and rhetoric were subordinated to music. Harmonic is the account of acute and grave sounds, by whose proportion all songs are completed. Rhythm is the artful motion of the body according to harmony. A dance is constituted from harmony and rhythm.
It has been granted to us to know many things concerning uncreated being—God, the Best and Greatest—and concerning the holy angels, especially concerning God, who can in some manner be known from created things.
The sciences that I have named possess many parts under themselves, and in every single part difficulties which only those who have devoted themselves to them for a very long time and with the greatest diligence know to exist, but which they have never thoroughly penetrated. All these things must be taught in the state, and to excel in one part of them is
glorious. But as one who treats on behalf of the state, my purpose is to follow the method and the ordinary manner of transmitting the sciences themselves. For confusion in learning prevents more people from attaining wisdom than does weakness of ability or the will to advance.