Chapter 2 — Exposition of Chapter 2

Boethius has previously set forth the doctrine of the Catholic faith regarding the unity of the Trinity, and indicated the reason of this belief. Now he intends to proceed to an investigation of the aforesaid doctrine. Since, according to the opinion of the Philosopher in Metaphysics, 2, inquiry into the method of a science ought to precede science itself, he therefore divides this section into two parts. (Aristotle, Metaphysics, 2.5, 995a13–15.)

In the first place Boethius points out the method proper for this kind of inquiry, which is concerned with divine things.

In the second place he proceeds, according to the method he has indicated, to inquire into the proposition determined upon, where he says, which form, indeed.

The first part is again divided into two sections.

First, he indicates the necessity of making clear the method of investigation.

Second, he shows that the method of the present inquiry is suitable, saying: speculative science may be divided into three kinds.

Therefore he says: wherefore it is certain that this is the doctrine of the Catholic faith regarding the unity of the Trinity, and the nature of that unity without difference. Thereupon, he says by way of exhortation, let us now begin, that is, let us inquire more deeply, carrying our investigation to an examination of the intimate principle of things and of truth which is, as it were, veiled and hidden away from view. And that method which he deems fitting is indicated by the words: let us now begin a careful consideration of each several point, as far as it can be grasped and understood, that is, according to the mode by which understanding and apprehension are possible.

Moreover, he uses the two words (“grasped” and “understood”) because the method of any investigation ought to be in harmony both with things and with us. For if it is not suited to the matter, things will not be understood; and if it is not suited to us, we shall not be able to apprehend the matter;

for example, divine things are such by their very nature that they cannot be known except by intellect. Wherefore, if anyone wished to follow another way and to use imagination instead, he would not be able to understand anything of them as a result of his consideration, because truths, of this kind are not thus to be known.

But if, on the other hand, one wished to know divine things so as to see them in themselves, and to comprehend them with the same certitude with which sensible things or mathematical demonstrations are comprehended, this too would be impossible; even things which are, in themselves, understandable in this way cannot be perfectly grasped because of the weakness of our intellect.

He also shows that the mode of inquiry used must always correspond to the kind of investigation undertaken, by reference to the authority of the Philosopher in Ethics, 1, when he says: for it has been wisely said that it is a scholar’s duty to formulate his belief about anything according to its real nature. (Aristotle, Ethics, 1.3, 1094b23–25.) So, in regard to a doctrine of faith, the same principle must be applied: for in all cases, equal certitude and demonstrative evidence cannot be demanded. And these are the very words of the Philosopher in Ethics, 1: it is the duty of the scholar to demand as much certitude in his investigation of each thing as the nature of that thing permits.

In the second place, when he says: speculative science may be divided into three kinds, he inquires into the method of his own investigation, testing its congruousness by distinguishing it from the methods employed in other sciences; and, since method ought to correspond to the matter under investigation, he therefore divides this part of his consideration into two sections.

First, he distinguishes sciences according to the matter with which each is concerned.

Second, he indicates the methods suitable for each kind of matter, beginning, physics deals.

In regard to the first point, he does three things.

First, he shows what the objects of natural philosophy are.

Second, he indicates the objects of mathematics.

Third, he speaks of the truths with which divine science is concerned, when he says: theology does not.

Therefore he says: it has been wisely said that it is a scholar’s duty to formulate his belief about anything according to its real nature.

For, since there are three divisions of speculative science (or philosophy), and he calls it “speculative” to differentiate it from ethics, which is operative or practical; in each of these the method must be in conformity with the matter. The three divisions of speculative science indicated are physics or natural science, mathematics, and divine science or theology. While, I say, there are three divisions, natural philosophy, which is one of the, three, deals with motion and is not abstract, that is, it is concerned with things in motion and not abstracted from matter. This he proves by examples, as is evident in his treatise. When, however, he says: form takes on the movement of the particular thing to which it is annexed, his words should be understood as follows: that what is composite of matter and form, inasmuch as it is due the nature of a thing of this kind, has motion; or, in other words, a form existing in matter is the principle of motion. Therefore the consideration of things that are material and of things that are in motion is the same.

He then indicates the subject matter of mathematics, saying: mathematics does not deal with motion; that is, it involves no consideration of motion or of movable things, and on this point it differs from natural philosophy. Mathematics, moreover, is said to be not abstract; that is, it considers forms which according to their existence are not abstract from matter, and in this respect it is in agreement with natural philosophy.

He then explains how this is. Mathematics considers forms which are without matter and hence without motion, because wherever there is matter there is motion, as is proved in Metaphysics, 10. (Aristotle, Metaphysics, 9.9, 1050b20–22.) For according as things have matter there will also be motion, and thus the speculations of a mathematician are without matter and without motion, although these forms, namely, those about which the mathematician speculates, being connected with matter, cannot really be separated from bodies, according to their being [real existence]; but according to speculation, they can be considered as separable.

Then he indicates the objects of divine science, calling it, theology, that is, the third division of speculative science, which is termed divine, or metaphysics, or first philosophy; and it deals with objects apart from motion, in which it agrees with mathematics and differs from natural philosophy. It also is abstract, namely, from matter, and inseparable; and because of these two facts it differs from mathematics.

For the objects of divine science are of themselves abstract from matter and motion, but those of mathematics are not thus naturally abstract, but separable in thought. The objects of divine science, however, are called “inseparable” because a thing is not separable unless there is some conjunction with matter. Hence the objects of divine science are not separable from matter by thought, but are abstract according to their very being; while the converse is true in the case of the objects of mathematics. This he proves by the fact that the substance with which divine science is principally concerned is that of God, and on this account it is called “divine.”

In the next place, when he says, in physics, then, we are bound to use scientific concepts, in mathematics systematic concepts, in theology intellectual concepts, he points out the methods that correspond to the aforesaid divisions. Here he treats of two things.

First, he draws conclusions about the methods appropriate for each of the divisions named, and the disposition of this section is left open for discussion.

Second, he describes the last mode, which is that proper to the present investigation, and indicates a twofold procedure.

First, by the removal of that which is an impediment to speculation saying, in theology we will not let ourselves be diverted to play with imaginations (that is, in such a way that in formulating judgments we follow the judgment of the imagination).

Second, he indicates the method which is the proper one when he says: but will consider simply form (apart from motion and matter), the nature of which he consequently explains in beginning his treatment of the proposed question.

There are two questions here.

The first concerns the division of speculative science which the text proposes.

The second concerns the methods it attributes to the parts of speculative science.

Question 5

The division of speculative science

With regard to the first question there are four points of inquiry.

1. Is speculative science appropriately divided into these three parts: natural, mathematical, and divine?

2. Does natural philosophy treat of what exists in motion and matter?

3. Does mathematics treat, without motion and matter, of what exists in matter?

4. Does divine science treat of what exists without matter and motion?

Article 1

Is speculative science appropriately divided into these three parts: natural, mathematical, and divine?

Obj. 1: We proceed as follows to the first article: it seems that speculative science is not appropriately divided into these three parts, for: the parts of speculative science are the habits that perfect the contemplative part of the soul. But the Philosopher says in the Ethics that the scientific part of the soul, which is its contemplative part, is perfected by three habits, namely, wisdom, science, and understanding. (Aristotle, Ethics, 6.1, 1139a12; 3, 1139b15–17; 5–6, 1140b31–1141b8.) Therefore these are the three divisions of speculative science, not those proposed in the text.

Obj. 2: Again, Augustine says that rational philosophy, or logic, is included under contemplative or speculative philosophy. (Augustine, City of God, 8.4 (PL 41:228; CCL 47:219–20; CSEL 40.1:359).) Consequently, since no mention is made of it, it seems the division is inadequate.

Obj. 3: Again, philosophy is commonly divided into seven liberal arts, which include neither natural nor divine science, but only rational and mathematical science. Hence natural and divine should not be called parts of speculative science.

Obj. 4: Again, medicine seems to be the most practical science, and yet it is said to contain a speculative part and a practical part. By the same token, therefore, all the other practical sciences have a speculative part. Consequently, even though it is a practical science, ethics or moral science should be mentioned in this division because of its speculative part.

Obj. 5: Again, the science of medicine is a branch of physics, and similarly certain other arts called “mechanical,” like the science of agriculture, alchemy, and others of the same sort. Therefore, since these sciences are practical, it seems that natural science should not be included without qualification under speculative science.

Obj. 6: Again, a whole should not be contra-distinguished from its part. But divine science seems to be a whole in relation to physics mathematics, since their subjects are parts of its subject of divine science or first philosophy is being; and changeable substance, which the natural scientist considers, and also quantity, which the mathematician considers, are parts of being. This is clear in the Metaphysics. (Aristotle, Metaphysics, 3.6, 997a26–30.) Therefore, divine science should not be contra-distinguished from natural science and mathematics.

Obj. 7: Again, as it is said in the De anima, sciences are divided in the same manner as things. (Aristotle, De anima, 3.7, 431b24.) But philosophy concerns being, for it is knowledge of being, as Dionysius says. (Dionysius, Letter to Polycarp, n. 2 (PG 3:1080B).) Now being is primarily divided into potency and act, one and many, substance and accident. So it seems that the parts of philosophy ought to be distinguished by such divisions of being.

Obj. 8: Again, there are many other divisions of beings studied by sciences more essential than the divisions into mobile and immobile and into abstract and non-abstract; for example, the divisions into corporeal and incorporeal and into living and non-living, and the like. Therefore differences of this sort should be the basis for the division of the parts of philosophy rather than those mentioned here.

Obj. 9: Again, that science on which others depend must be prior to them. Now all the other sciences depend on divine science because it is its business to prove their principles. Therefore Boethius should have placed divine science before the others.

Obj. 10: Again, mathematics should be studied before natural science, for the young can easily learn mathematics, but only the more advanced natural science, as is said in the Ethics. (Aristotle, Ethics, 6.7, 1142a11–20.) This is why the ancients are said to have observed the following order in learning the sciences: first logic, then mathematics, then natural science, after that moral science, and finally men studied divine science. Therefore, Boethius should have placed mathematics before natural science. And so it seems that this division is unsuitable.

On the contrary, the Philosopher proves the appropriateness of this division in the Metaphysics, where he says, there will be three philosophical and theoretical sciences, mathematics, physics, and theology. (Aristotle, Metaphysics, 6.1, 1026a18.)

Moreover, in the Physics three methods of the sciences are proposed which indeed seem to belong to these three. (Aristotle, Physics, 2.11, 198a29–31.)

Moreover, Ptolemy also uses this division in the beginning of his Almagest. (Ptolemy, Almagest, I c.1 (ed. Heiberg p. 5).)

I answer that the theoretical or speculative intellect is properly distinguished from the operative or practical intellect by the fact that the speculative intellect has for its end the truth that it contemplates, while the practical intellect directs the truth under consideration to activity as to an end. So the Philosopher says in the De Anima that they differ from each other by their ends; (Aristotle, De anima, 3.9, 433a15.) and in the Metaphysics he states that the end of speculative knowledge is truth, but the end of practical knowledge is action. (Aristotle, Metaphysics, 2.2, 993b20.) Now, since matter must be proportionate to the end, the subject-matter of the practical sciences must be things that can be made or done by us, so that we can direct the knowledge of them to activity as to an end.

On the other hand, the subject-matter of the speculative sciences must be things that cannot be made or done by us, so that our knowledge of them cannot be directed to activity as to an end. And the speculative sciences must differ according to the distinctions among these things.

Now we must realize that when habits or powers are differentiated by their objects they do not differ according to just any distinction among these objects, but according to the distinctions that are essential to the objects as objects.

For example, it is incidental to a sense object as such whether it be an animal or a plant. Accordingly, the distinction between the senses is not based upon this difference but rather upon the difference between color and sound. So the speculative sciences must be divided according to differences between objects of speculation, considered precisely as such.

Now an object of this kind—namely, an object of a speculative power—derives one characteristic from the side of the power of intellect and another from the side of the habit of science that perfects the intellect.

From the side of the intellect it has the fact that it is immaterial, because the intellect itself is immaterial. From the side of habit of science it has the fact that it is necessary, for science treats of necessary matters, as is shown in the Posterior Analytics. (Aristotle, Posterior Analytics, 1.13, 74b9–75a17.) Now everything that is necessary is, as such, immobile, because everything changeable is, as such, able to be or not to be, either absolutely or in a certain respect, as is said in the Metaphysics. (Aristotle, Metaphysics, 9.9, 1050b11–15.)

Consequently, separation from matter and motion, or connection with them, essentially belongs to an object of speculation, which is the object of speculative science. As a result, the speculative sciences are differentiated according to their degree of separation from matter and motion.

Now there are some objects of speculation that depend on matter for their being, for they can exist only in matter. And these are subdivided. Some depend on matter both for their being and for their being understood, as do those things whose definition contains sensible matter and which, as a consequence, cannot be understood without sensible matter. For example, it is necessary to include flesh and bones in the definition of man. It is things of this sort that physics or natural science studies.

On the other hand, there are some things that, although dependent upon matter for their being, do not depend upon it for their being understood, because sensible matter is not included in their definitions. This is the case with lines and numbers—the kind of objects with which mathematics deals.

There are still other objects of speculative knowledge that do not depend upon matter for their being, because they can exist without matter; either they never exist in matter, as in the case of God and the angels, or they exist in matter in some instances and not in others, as in the case of substance, quality, being, potency, act, one and many, and the like. The science that treats of all these is theology or divine science, which is so called because its principal object is God. By another name it is called metaphysics; that is to say, “beyond physics,” because it ought to be learned by us after physics; for we have to proceed from sensible things to those that are non-sensible. It is also called first philosophy, inasmuch as all the other sciences, receiving their principles from it, come after it. Now there can be nothing that depends upon matter for its being understood but not for its being, because by it; very nature the intellect is immaterial. So there is no fourth kind of philosophy besides the ones mentioned.

Reply Obj. 1: In the Ethics the Philosopher considers the intellectual habits insofar as they are intellectual virtues. (Aristotle, Ethics, 6.1, 1139a12; 3, 1139b15–17; 5–6, 1140b31–1141b8.) Now they are called virtues because they perfect the intellect in its operation; for virtue makes its possessor good and renders his work good. (Aristotle, Ethics, 2.6, 1106a15–17.) So he distinguishes between virtues of this sort in as much as speculative habits perfect the intellect in different ways.

In one way the speculative part of the soul is perfected by understanding, which is the habit of principles, through which some things become known of themselves. In another way it is perfected by a habit through which conclusions demonstrated from these principles are known, whether the demonstration proceeds from inferior causes, as in science, or from the highest causes, as in wisdom.

But when sciences are differentiated insofar as they are habits, they must be distinguished according to their objects, that is, according to the things of which the sciences treat. And it is in this way that both here and in the Metaphysics speculative philosophy is distinguished into three parts. (Aristotle, Metaphysics, 6.1, 1026a18.)

Reply Obj. 2: As is evident in the beginning of the Metaphysics, the speculative sciences concern things the knowledge of which is sought for their own sake. (Aristotle, Metaphysics, 1.2, 982a14–17.) However, we do not seek to know the things studied by logic for themselves, but as a help to the other sciences. So logic is not included under speculative philosophy as a principal part but as something brought under speculative philosophy as furnishing speculative thought with its instruments, namely, syllogisms, definitions, and the like, which we need in the speculative sciences. Thus, according to Boethius, logic is not so much a science as the instrument of science. (Boethius, Commentary on Porphyry's Isagoge, I c. 3 (PL 64:74 B; CSEL 8:140).)

Reply Obj. 3: The seven liberal arts do not adequately divide theoretical philosophy; but, as Hugh of St. Victor says, seven arts are grouped together (leaving out certain other ones), because those who wanted to learn philosophy were first instructed in them. (Hugh of St. Victor, Didascalicon III c. 3 (PL 176:768 A; ed. Buttimer p. 53 lin. 7–8).) And the reason why they are divided into the trivium and quadrivium is that they are as it were paths introducing the quick mind to the secrets of philosophy. This is also in harmony with the Philosopher’s statement in the Metaphysics that we must investigate the method of scientific thinking before the sciences themselves. (Aristotle, Metaphysics, 2.5, 995a13–15.) And the Commentator says in the same place that before all the other sciences a person should learn logic, which teaches the method of all the sciences; and the trivium concerns logic. (Averroes, Commentary on Metaphysics, II comm. 15 (ed. Venetiis 1562 f. 35 rb).)

The Philosopher also says in the Ethics that the young can know mathematics but not physics, because it requires experience. (Aristotle, Ethics. 6.7, 1142a11–20.) So we are given to understand that after logic we should learn mathematics, which the quadrivium concerns. These, then, are like paths leading the mind to the other philosophical disciplines.

We may add that among the other sciences these are called arts because they involve not only knowledge but also a work that is directly a product of reason itself; for example, producing a composition, syllogism or discourse, numbering, measuring, composing melodies, and reckoning the course of the stars.

Other sciences (such as divine and natural science) either do not involve a work produced but only knowledge, and so we cannot call them arts, because, as the Metaphysics says, art is productive reason; (Aristotle, Metaphysics, 6.1, 1025b22.) or they involve some bodily activity, as in the case of medicine, alchemy, and other sciences of this kind. These latter, then, cannot be called liberal arts because such activity belongs to man on the side of his nature in which he is not free, namely, on the side of his body.

And although moral science is directed to action, still that action is not the act of the science but rather of virtue, as is clear in the Ethics. (Aristotle, Ethics, 1.3, 1095a4–6.) So we cannot call moral science an art; but rather in these actions virtue takes the place of art. Thus, as Augustine says, the ancients defined virtue as the art of noble and well-ordered living. (Augustine, City of God, 4.21 (PL 41:128; CCL 47:115; CSEL 40.1:188).)

Reply Obj. 4: As Avicenna says, the distinction between theoretical and practical is not the same when philosophy is divided into theoretical and practical, when the arts are divided into theoretical and practical, and when medicine is so divided. (Avicenna, Canon of Medicine, I fen 1 doctr.1 c.1, trans. Gerard of Cremona.)

For when we distinguish philosophy or the arts into theoretical and practical we must do so on the basis of their end, calling that theoretical which is directed solely to knowledge of the truth, and that practical which is directed to operation. However, there is this difference when we distinguish the whole of philosophy and the arts on this basis. We divide philosophy with respect to the final end or happiness, to which the whole of human life is directed.

For, as Augustine says, following Varro, there is no other reason for a man philosophizing except to be happy. (Augustine, City of God, 19.1.3 (PL 41:623; CCL 48:659; CSEL 40.2:366).) And since the philosophers teach that there is a twofold happiness, one contemplative and the other active, as is clear in the Ethics, they have accordingly also distinguished between two parts of philosophy, calling moral philosophy practical and natural and rational philosophy theoretical. (Aristotle, Ethics, 10.10–12, 1177a12–1178b32.)

But when they call some arts speculative and some practical, this is on the basis of some special ends of those arts; as when we say that agriculture is a practical art but dialectic is theoretical.

However, when we divide medicine into theoretical and practical, the division is not on the basis of the end. For on that basis the whole of medicine is practical, since it is directed to practice. But the above division is made on the basis of whether what is studied in medicine is proximate to, or remote from practice.

Thus we call that part of medicine practical which teaches the method of healing; for instance, that these particular medicines should be given for these abscesses. On the other hand, we call that part theoretical which teaches the principles directing a man in his practice, although not immediately; for instance, that there are three virtues, and that there are so many kinds of fever.

Consequently, if we call some part of a practical science theoretical, we should not on that account place that part under speculative philosophy.

Reply Obj. 5: One science is contained under another in two ways:

in one way, as its part, because its subject is part of the subject of that other science, as plant is part of natural body. So the science of plants is also contained under natural science as one of its parts.

In another way, one science is contained under another as subalternated to it. This occurs when in a higher science there is given the reason for what a lower science knows only as a fact. This is how music is contained under arithmetic.

Medicine, therefore, is not contained under physics as a part, for the subject of medicine is not part of the subject of natural science from the point of view from which it is the subject of medicine. For although the curable body is a natural body, it is not the subject of medicine insofar as it is curable by nature, but insofar as it is curable by art. But because art is nature’s handmaid in healing (in which art too plays a part, for health is brought about through the power of nature with the assistance of art), it follows that the reason for the practices used in the art must be based on the properties of natural things. So medicine is subalternated to physics, and for the same reason so too are alchemy, the science of agriculture, and all sciences of this sort.

We conclude, then, that physics in itself and in all its parts is speculative, although some practical sciences are subalternated to it.

Reply Obj. 6: Although the subjects of the other sciences are parts of being, which is the subject of metaphysics, the other sciences are not necessarily parts of metaphysics.

For each science treats of one part of being in a special way distinct from that in which metaphysics treats of being. So its subject is not properly speaking a part of the subject of metaphysics, for it is not a part of being from the point of view from which being is the subject of metaphysics; from this viewpoint it is a special science distinct from the others.

However, the science treating of potency, or that treating of act or unity or anything of this sort, could be called a part of metaphysics because these are considered in the same manner as being, which is the subject of metaphysics.

Reply Obj. 7: These parts of being require the same manner of consideration as being-in-general (ens commune) because they too are independent of matter. For this reason the science dealing with them is not distinct from the science of being-in-general.

Reply Obj. 8: The other diversities of things mentioned in the objection do not differentiate those things essentially as objects of knowledge. So the sciences are not distinguished according to them.

Reply Obj. 9: Although divine science is by nature the first of all the sciences, with respect to us the other sciences come before it. For as Avicenna says, the position of this science is that it be learned after the natural sciences, which explain many things used by metaphysics, such as generation, corruption, motion, and the like. (Avicenna, Commentary on Metaphysics, I c.3 (ed. Van Riet p. 20–23).)

It should also be learned after mathematics, because to know the separate substances metaphysics has to know the number and disposition of the heavenly spheres, and this is impossible without astronomy, which presupposes the whole of mathematics.

Other sciences, such as music, ethics, and the like, contribute to its fullness of perfection. Nor is there necessarily a vicious circle because metaphysics presupposes conclusions proved in the other sciences while it itself proves their principles. For the principles that another science (such as natural philosophy) takes from first philosophy do not prove the points which the first philosopher takes from the natural philosopher, but they are proved through other self-evident principles. Similarly the first philosopher does not prove the principles he gives the natural philosopher by principles he receives from him, but by other self-evident principles. So there is no vicious circle in their definitions.

Moreover, the sensible effects on which the demonstrations of natural science are based are more evident to us in the beginning. But when we come to know the first causes through them, these causes will reveal to us the reason for the effects, from which they were proved by a demonstration quia.

In this way natural science also contributes something to divine science, and nevertheless it is divine science that explains its principles. That is why Boethius places divine science last, because it is the last relative to us.

Reply Obj. 10: Although we should learn natural science after mathematics because the general proofs of natural science require experience and time, still, since natural things fall under the senses, they are by nature better known than the mathematical entities abstracted from sensible matter.

Article 2

Does natural philosophy treat of what exists in motion and matter?

Obj. 1: We proceed as follows to the second article: it seems that natural science does not treat of things that exist in motion and matter, for matter is the principle of individuation. Now, according to Plato’s doctrine, which is followed by Porphyry, no science treats of individual things but only of universals. (Porphyry, Isagoge.) Therefore, natural science does not treat of what is in matter.

Obj. 2: Again, science pertains to the intellect. But the intellect knows by abstracting from matter and from the conditions of matter. Therefore, no science can treat of what is not abstracted from matter.

Obj. 3: Again, as is clear in the Physics, the first mover is considered in natural science. (Aristotle, Physics, 8.9–13, 256a4–260a19; 21–22, 266a10–267b26.) But the first mover is free from all matter. Therefore, natural science does not treat only of what is in matter.

Obj. 4: Again, every science has to do with what is necessary. But whatever is moved, as such is contingent, as is proved in the Metaphysics. (Aristotle, Metaphysics, 9.9, 1050b11–25.) Therefore, no science can treat of what is subject to motion; and so neither can natural science.

Obj. 5: Again, no universal is subject to motion; for as is said in the beginning of the Metaphysics, it is not man in general who is healed, but this man. (Aristotle, Metaphysics, 1.1, 981a18–20.) But every science concerns that which is universal. Therefore natural science does not treat of what is in motion.

Obj. 6: Again, some of the things with which natural science deals are not subject to motion; for instance, the soul, as is shown in De anima, and the earth, as is proved in the De caelo et mundo. (Aristotle, De anima 1.6–8, 405b31–407b26; On the Heavens, 2.25–26, 296a24–297a6.) What is more, all natural forms neither come into being nor perish, and for the same reason they are not subject to motion, except accidentally. This is shown in the Metaphysics. (Aristotle, Metaphysics, 7.7, 1033b5–7.) Therefore not everything that physics considers is in motion.

Obj. 7: Again, every creature is mutable for, as Augustine says, true immutability belongs to God alone. (Augustine, On the Nature of Good, 1 (PL 42:551; CSEL 25.2:855).) So if it is the task of natural science to consider what is in motion, it will be its business to consider all creatures, which clearly appears to be false.

On the contrary, it is the work of natural science to reach conclusions about natural things. Now, natural things are those in which there is a principle of motion; and, as the Metaphysics says, wherever there is motion there must be matter. (Aristotle, Metaphysics, 9.9, 1050b20–22.) So natural science treats of what is in motion and matter.

Moreover, these must be some speculative science dealing with what is in matter and motion, for otherwise the teaching of philosophy, which is knowledge of being, would be incomplete. Now no other speculative science treats of these things, for neither mathematics nor metaphysics does so. Therefore, natural science treats of them.

Moreover, the fact is clear from the statements of the Philosopher in the Metaphysics and the Physics. (Aristotle, Metaphysics, 6.1, 1026a13; Physics, 2.11, 198a27–31.)

I answer that it was the difficulty of this problem that drove Plato to posit ideas. Believing that all sensible things were always in flux, as Cratylus and Heraclitus taught, he thought there can be no science concerning them, as the Philosopher says in the Metaphysics. (Aristotle, Metaphysics, 1.10, 987a32–b1.) So he claimed that there were substances separated from the sense world, which might serve as the objects of science and of definitions. He made this mistake because he failed to distinguish what is essential from what is accidental. For it happens that by accident even the wise often fall into error, as is said in the Sophistic Refutations. (Aristotle, On Sophistical Refutations, 6, 168b6–8, trans. Boethius.)

Now, as is shown in the Metaphysics, we find in a sensible substance both the whole or the composite itself, and also its nature (ratio) or form; and it is the composite that is essentially generated and corrupted and not the nature or form, except accidentally. (Aristotle, Metaphysics, 7.15, 1039b20–24.) As the Metaphysics says, it is not house that is made, but this house. (Aristotle, Metaphysics, 7.15, 1039b24.) Now anything can be thought of without all the items that are not essentially related to it. Consequently, forms and natures, though belonging to things existing in motion, are without motion when they are considered in themselves; and so they can be the objects of sciences and of definitions, as the Philosopher says. As he proves, the sciences of sensible reality are not based upon the knowledge of certain substances separated from the sense world.

Natures of this kind, which are the objects of the sciences of real beings, are thought of without motion; and so they must be thought of without those conditions by reason of which motion belongs to mobile things. Now, because every motion is measured by time, and the primary motion is local motion (for without it there is no other motion), a thing must be subject to motion inasmuch as it exists here and now; and it exists under these conditions insofar as it is individuated by matter having determinate dimensions.

Consequently, natures of this kind, which make possible sciences of things subject to motion, must be thought of without determinate matter and everything following upon such matter; but not without indeterminate matter, because on its notion depends the notion of form that determines matter to itself. Thus the nature of man, which his definition signifies and which is the object of science, is considered without this flesh and these bones, but not absolutely without flesh and bones. And because individuals include determinate matter in their nature, whereas universals include common matter, as is said in the Metaphysics, the above-mentioned abstraction is not said to be the abstraction of form from matter absolutely, but the abstraction of the universal from the particular. (Aristotle, Metaphysics, 7.10, 1035b27–31.) Natures of this sort, thus abstracted, can be considered in two ways.

First, in themselves; and then they are thought of without motion and determinate matter. This happens to them only by reason of the being they have in the intellect.

Second, they can be viewed in relation to the things of which they are the natures; and these things exist with matter and motion. Thus they are principles by which we know these things, for everything is known through its form.

Consequently, in natural science we know mutable and material things existing outside the soul through natures of this kind; that is to say, natures that are immobile and considered without particular matter.

Reply Obj. 1: Matter is the principle of individuation only insofar as it exists with determinate dimensions, and in this sense natural science indeed abstracts from matter.

Reply Obj. 2: The intelligible form is a thing’s quiddity, for, as the De anima says, the object of the intellect is the quiddity of a thing. (Aristotle, De anima, 3.5, 430b28.) Now, as is said in the Metaphysics, the quiddity of a universal composite, like man or animal, includes within itself common but not particular matter. (Aristotle, Metaphysics, 7.10, 1035b27–31.) So the intellect regularly abstracts from determinate matter and its conditions; but in natural science it does not abstract from common matter, although matter itself is considered in natural science only in relation to form. For this reason the natural scientist is more concerned with form than with matter.

Reply Obj. 3: Natural science does not treat of the first mover as its subject or as part of its subject, but as the end to which natural science leads. Now the end does not belong to the nature of the thing of which it is the end, but it has a relation to it; as the end of a line is not the line but is related to it. So also the first mover is of a different nature from natural things, but it is related to them because it moves them. So it falls under the consideration of natural science, not in itself, but insofar as it is a mover.

Reply Obj. 4: Science treats of something in two ways: in one way, primarily and principally; and in this sense science is concerned universal natures, which are its very foundation. In another way it treats of something secondarily, as by a sort of reflection; and in this sense it is concerned with the things whose natures they are, inasmuch as, using the lower powers, it relates those natures to the particular things possessing them. For a knower uses a universal nature both as a thing known and as a means of knowing. Thus, through the universal nature of man we can judge of this or that particular man. Now, all universal natures of things are immutable; and so, in this respect, all science is concerned with what is necessary. But some of the things possessing these natures are necessary and immutable, whereas others are contingent and subject to movement, and in this respect sciences are said to be concerned with the contingent and mutable.

Reply Obj. 5: Although a universal is not mutable, it is nevertheless the nature of a mutable thing.

Reply Obj. 6: Although the soul and other natural forms are not themselves subject to motion, they are moved accidentally, and they are, moreover, the perfections of mutable things; and for this reason they come within the domain of natural science. But even though the earth as a whole is not moved (for it happens to be in its natural place, where a thing is at rest in virtue of the same nature through which it is moved to a place), nevertheless, when its parts are outside their proper place, they are moved to a place. Thus the earth falls within the domain of natural science both by reason of the immobility of the whole earth and by reason of the movement of its parts.

Reply Obj. 7: The mutability characteristic of all creatures is not with respect to any natural motion, but with respect to their dependence on God, separation from whom entails destruction of their very being. And that dependence falls under the consideration of metaphysics rather than under that of natural philosophy. Spiritual creatures, moreover, are mutable only with regard to choice; and this sort of motion is not the concern of the natural philosopher but rather of the metaphysician.

Article 3

Does mathematics treat, without motion and matter, of what exists in matter?

Obj. 1: We proceed as follows to the third article: it seems that mathematical thinking does not treat, without motion and matter, of what exists in matter, for since truth consists in the conformity of thing to intellect, there must be falsehood whenever we think of something otherwise than it is. If then in mathematics we consider what is in matter in abstraction from matter, we will consider it falsely; and so mathematics will not be a science, for every science is concerned with what is true.

Obj. 2: Again, as the Philosopher states, every science has the task of considering a subject and the parts of the subject. (Aristotle, Posterior Analytics, 1.18, 76b11–16.) Now in actual existence matter is a part of all material things. So it is impossible for a science to treat of what is in matter without treating of matter.

Obj. 3: Again, all straight lines are specifically the same. But the mathematician treats of straight lines by numbering them; otherwise he would not treat of the triangle and the square. It follows that he considers lines as specifically the same and numerically different. But it is clear from the above that matter is the principle differentiating things specifically the same. So the mathematician treats of matter.

Obj. 4: Again, no science completely abstracting from matter demonstrates through a material cause. But in mathematics some demonstrations are made which can only be reduced to a material cause, as when we demonstrate something about a whole by its parts. For, as the Physics says, parts are the matter of the whole. (Aristotle, Physics, 2.5, 195a16–20.) Thus in the Posterior Analytics the demonstration that the angle in a semi-circle is a right angle from the fact that each of its two parts is half of a right angle, is reduced to a material cause. (Aristotle, Posterior Analytics, 2.9, 94a20–34.) Therefore, mathematics does not entirely abstract from matter.

Obj. 5: Again, motion cannot exist without matter. But the mathematician ought to consider motion, because, since motion is measured relative to space, to consider the quantity of space, which pertains to the mathematician, and the quantity of motion, has the same nature and belongs to the same science. Therefore, the mathematician does not entirely leave matter out of consideration.

Obj. 6: Again, astronomy is a part of mathematics, and so too is the science of the moved sphere, the science of weights, and music, all of which treat of motion and mobile things So mathematics does not entirely abstract from matter and motion.

Obj. 7: Again, natural science is entirely concerned with matter and motion. But some conclusions are demonstrated alike by the mathematician and the natural scientist, for instance, whether the earth is round and whether it is in the middle of the universe. Therefore, mathematics cannot entirely abstract from matter. If it be said that mathematics abstracts only from sensible matter, the contrary seems true. Sensible matter seems to be particular matter, because what the senses perceive are particular things, and all the sciences abstract from this kind of matter. So mathematical thinking should not be called more abstract than that of the other sciences.

Obj. 8: Again, the Philosopher says that there are three branches of study: the first concerns what is mutable and corruptible, the second what is mutable and incorruptible, and the third what is immutable and incorruptible. (Aristotle, Physics, 2.11, 198a29–31.) As Ptolemy explains, the first is natural science the third divine science, and the second mathematics. (Ptolemy, Almagest, I c. 1 (ed. Heiberg p. 5, 13–6, 9v11) sec. versionem greco-lat.) Therefore mathematics concerns what is mutable.

On the contrary is the Philosopher’s statement in the Metaphysics. (Aristotle, Metaphysics, 6.1, 1026a14.)

Moreover, some things, although existing in matter, do not contain matter in their definition; for instance, curve, which differs in this respect from snub. Now philosophy should treat of all beings. Hence some part of philosophy must consider beings of this sort; and this is mathematics, for this does not belong to any other part.

Moreover, what is prior from the point of view of the intellect can be considered without what is posterior. Now mathematicals are prior to natural things existing in matter and motion, for the latter are so related to mathematicals that they add something to them, as is said in the De caelo et mundo. (Aristotle, On the Heavens, 3.3, 299a16.) Therefore, mathematical investigation can be without matter and motion.

I answer that in order to throw light on this question we must understand how the intellect in its operation is able to abstract. We must realize that, as the Philosopher says, the intellect has two operations, one called the understanding of indivisibles, by which it knows what a thing is, and another by which it joins and divides, that is to say, by forming affirmative and negative statements. (Aristotle, De anima, 3.5, 430a26–28.)

Now these two operations correspond to two principles in things.

The first operation concerns the nature itself of a thing, in virtue of which the object known holds a certain rank among beings, whether it be a complete thing, like some whole, or an incomplete thing, like a part or an accident.

The second operation has to do with a thing’s being (esse), which results from the union of the principles of a thing in composite substances, or, as in the case of simple substances, accompanies the thing’s simple nature.

Now, since the truth of the intellect results from its conformity with reality, it is clear that in this second operation the intellect cannot truthfully abstract what is united in reality, because the abstraction would signify a separation with regard to the very being of the thing. For example, if I abstract man from whiteness by saying, “Man is not white,” I signify that there is a separation in reality. So if in reality man and whiteness are not separate, the intellect will be false. Through this operation, then, the intellect can truthfully abstract only those things that are separate in reality, as when we say, “Man is not an ass.”

Through the first operation, however, we can abstract things that are not separate in reality; not all, it is true, but some. For, since everything is intelligible insofar as it is in act, as the Metaphysics says, we must understand the nature itself or the quiddity of a thing either inasmuch as it is a certain act (as happens in the case of forms themselves and simple substances); or through that which is its act (as we know composite substances through their forms); or through that which takes the place of act in it (as we know prime matter through its relation to form, and a vacuum through the absence of a body in place). (Aristotle, Metaphysics, 9.10, 1051a30–32.) And it is from this that each nature is given its definition.

Therefore, when the nature itself is related to, and depends on something else, with regard to that which forms the definition (ratio) of the nature, and through which the nature itself is understood, clearly we cannot know the nature without that other thing. This is true whether they are connected as a part is united to a whole (as we cannot know foot without knowing animal, because that whereby foot has the nature of foot depends on that whereby animal is animal); or whether they are connected as form is united to matter, or as one part to another part, or as accident to subject (as we cannot know snub without nose); or even whether they are separated in reality (as we cannot know father without knowing son, although these relationships are found in different things).

But if one thing does not depend on another with regard to that which forms the definition of the nature, then the intellect can abstract the one from the other so as to know it without the other. This is true not only if they are separated in reality, like man and stone, but also if they are united in reality, whether they are joined as part and whole (as letter can be understood without syllable, but not vice versa, and animal without foot, but not conversely); or even if they are joined as form is united to matter and accident to subject (as whiteness can be understood without man and vice versa).

Accordingly, through its various operations the intellect distinguishes one thing from another in different ways. Through the operation by which it composes and divides, it distinguishes one thing from another by understanding that the one does not exist in the other. Through the operation, however, by which it understands what a thing is, it distinguishes one thing from another by knowing what one is without knowing anything of the other, either that it is united to it or separated from it. So this distinction is not properly called separation, but only the first.

lt is correctly called abstraction, but only when the objects, one of which is known without the other, are one in reality. For if we consider animal without considering stone, we do not say that we abstract animal from stone. It follows that since, properly speaking, we can only abstract objects united in existence, there are two sorts of abstraction corresponding to the two modes of union mentioned above, namely, the union of part and whole, and the union of form and matter. The first is that in which we abstract form from matter, and the second is that in which we abstract a whole from its parts.

Now a form can be abstracted from matter if the essential nature of the form does not depend on that particular kind of matter; but the intellect cannot abstract form from the kind of matter upon which the form depends according to its essential nature. Consequently, because all accidents are related to the underlying substance as form to matter, and because it is the nature of every accident to depend upon substance, no form of this kind can be separated from substance.

But accidents befall substance in a definite order. Quantity comes to it first, then quality, after that passivities (passiones) and actions. So quantity can be thought of in substance before the sensible qualities (because of which matter is called sensible) are considered in it. Quantity, then, according to its essential nature does not depend upon sensible matter but only upon intelligible matter. For, after accidents have been abstracted, substance is intelligible only to the intellect, because it is beyond the sense powers to comprehend substance. And abstract objects of this kind are the concern of mathematics; it treats of quantities and the properties of quantity, such as figures and the like.

Moreover, we cannot abstract a whole from just any parts. For there are some parts upon which the nature of the whole depends, namely, when the being of a particular whole consists in the composition of particular parts. It is in this way that a syllable is related to letters and a mixed body to the elements. Parts of this sort, which are necessary for understanding the whole because they enter into its definition, are called parts of the species and of the form.

There are some parts, however, that are accidental to the whole as such. The semicircle, for instance, is related to the circle in this way, for it is accidental to a circle that it be divided into two or more equal or unequal parts. But it is not accidental to a triangle that three lines are designated in it, for because of this a triangle is a triangle.

Similarly, it is an essential characteristic of man that there be found in him a rational soul and a body composed of the four elements. So man cannot be understood without these parts and they must be included in his definition; so they are parts of his species and form. But finger, foot, and hand, and other parts of this kind are outside the definition of man; and thus the essential nature of man does not depend on them and he can be understood without them. For whether or not he has feet, as long as he is constituted of a rational soul and a body composed of the elements in the proper mixture required by this sort of form, he will be a man. These parts are called parts of matter: they are not included in the definition of the whole, but rather the converse is true.

This is how all determinate (signatae) parts are related to man; for instance, this soul, this body, this nail, this bone, and so forth. These indeed are parts of the essence of Socrates and Plato, but not of man precisely as man; and therefore the intellect can abstract man from these parts. And this is the abstraction of the universal from the particular.

So there are two abstractions of the intellect. One corresponds to the union of form and matter or accident and subject. This is the abstraction of form from sensible matter. The other corresponds to the union of whole and part; and to this corresponds the abstraction of the universal from the particular. This is the abstraction of a whole, in which we consider a nature absolutely, according to its essential character, in independence of all parts that do not belong to the species but are accidental parts. But we do not find abstractions opposed to these, by which a part is abstracted from a whole by the intellect if it is one of the parts of matter in whose definition the whole is included, or it can even exist without the whole if it is one of the parts of the species, for instance, a line without a triangle, a letter without a syllable, or an element without a mixed body.

But in the case of things that can exist separately, separation rather than abstraction obtains. Similarly, when we say from is abstracted from matter, we do not mean substantial form, because substantial form and the matter correlative to it are interdependent, so that one is not intelligible without the other, because the appropriate act is in its appropriate matter. Rather, we mean the accidental forms of quantity and figure, from which indeed sensible matter cannot be abstracted by the intellect, because sensible qualities cannot be understood unless quantity is presupposed, as is clear in the case of surface and color. And neither can we understand something to be the subject of motion unless we understand it to possess quantity. Substance, however, which is the intelligible matter of quantity, can exist without quantity. Consequently, the consideration of substance without quantity belongs to the order of separation rather than to that of abstraction.

We conclude that there are three kinds of distinction in the operation of the intellect.

There is one through the operation of the intellect joining and dividing which is properly called separation and this belongs to divine science or metaphysics.

There is another through the operation by which the quiddities of things are conceived which is the abstraction of form from sensible matter, and this belongs to mathematics.

And there is a third through the same operation which is the abstraction of a universal from a particular, and this belongs to physics and to all the sciences in general, because science disregards accidental features and treats of necessary matters.

And because certain men (for example, the Pythagoreans and the Platonists) did not understand the difference between the last two kinds of distinction and the first, they fell into error, asserting that the objects of mathematics and universals exist separate from sensible things.

Reply Obj. 1: When the mathematician abstracts he does not consider something otherwise than it is. Thus, he does not think that a line exists without sensible matter, but he treats of a line and its properties without considering sensible matter. So there is no disagreement between his intellect and reality, because even in reality what belongs to the nature of a line does not depend upon that which makes matter sensible, but vice versa. Consequently, it is evident that there is no error in the one who abstracts, as is said in the Physics. (Aristotle, Physics, 2.3, 193b35.)

Reply Obj. 2: By “material” is meant not only that which has matter as a part, but also that which exists in matter; and in this way sensible line can be called something material. So this does not prevent a line from being understood without matter. For sensible matter is not related to a line as a part, but rather as the subject in which it exists, and this is also the case with a surface or body. Obviously, the mathematician does not treat of the kind of body that is in the category of substance, whose parts are matter and form, but rather the body in the category of quantity, constituted by three dimensions. Body, in this sense of the term, is related to body the category of substance (of which physical matter is a part) as accident to its subject.

Reply Obj. 3: Matter is the principle of numerical diversity or inasmuch as, being divided into many parts, and receiving in each part a form of the same nature, it constitutes many individuals of the same species. Now matter can be divided only if we presuppose quantity in it; if that is taken away, even substance remains indivisible. So the primary reason for the diversification of things of one species lies in quantity. And this is due to quantity because position, which is the arrangement of parts in place, is contained in its notion as a kind of formal difference. So even when the intellect has abstracted quantity from sensible matter, it is still possible to imagine numerically different things in the same species, for example, several equilateral triangles and several equal straight lines.

Reply Obj. 4: Mathematics does not abstract from every kind of matter but only from sensible matter. Now the parts of quantity that seem to be in a way the basis for a demonstration by means of a material cause are not sensible matter; rather, they pertain to intelligible matter, which indeed is found in mathematics, as is clear in the Metaphysics. (Aristotle, Metaphysics, 7.10, 1036a9–12.)

Reply Obj. 5: By its very nature motion is not in the category of quantity, but it partakes somewhat of the nature of quantity from another source, namely, according as the division of motion derives from either the division of space or the division of the thing subject to motion. So it does not belong to the mathematician to treat of motion, although mathematical principles can be applied to motion. Therefore, inasmuch as the principles of quantity are applied to motion, the natural scientist treats of the division and continuity of motion, as is clear in the Physics. (Aristotle, Physics, 6.2–6, 231b21–235b35.) And the measurements of motions are studied in the intermediate sciences between mathematics and natural science: for instance, in the science of the moved sphere and in astronomy.

Reply Obj. 6: Simple bodies and their properties remain in composite bodies although in a different way, as the proper qualities of the elements and their proper movements are found in a mixed body. What is proper to composite bodies, however, is not found in simple bodies. And so it is that the more abstract and simple the objects of a science are, the more applicable its principles are to the other sciences. Thus the principles of mathematics are applicable to natural things, but not visa versa, because physics presupposes mathematics; but the converse is not true, as is clear in the De caelo et mundo. (Aristotle, On the Heavens, 3.3, 299a13–17.)

So there are three levels of sciences concerning natural and mathematical entities.

Some are purely natural and treat of the properties of natural things as such, like physics, agriculture, and the like.

Others are purely mathematical and treat of quantities absolutely, as geometry considers magnitude and arithmetic numbers.

Still others are intermediate, and these apply mathematical principles to natural things; for instance, music, astronomy, and the like. These sciences, however, have a closer affinity to mathematics, because in their thinking that which is physical is, as it were, material, whereas that which is mathematical is, as it were, formal. For example, music considers sounds, not inasmuch as they are sounds, but inasmuch as they are proportionable according to numbers; and the same holds in other sciences. Thus they demonstrate their conclusions concerning natural things, but by means of mathematics. Therefore nothing prevents their being concerned with sensible matter insofar as they have something in common with natural science, but insofar as they have something in common with mathematics they are abstract.

Reply Obj. 7: Because the intermediate sciences mentioned above have something in common with natural science as regards what is material in their procedure, but differ from it as regards what is formal in it, nothing prevents these sciences from occasionally having the same conclusions as natural science. Nevertheless, they do not use the same means of demonstration, unless the sciences are mixed and one occasionally uses what belongs to another, as the natural scientist proves that the earth is round from the movement of heavy bodies, while the astronomer proves it by considering eclipses of the moon.

Reply Obj. 8: As the Commentator says, the Philosopher there did not intend to distinguish between the speculative sciences, because the natural scientist treats of everything subject to motion, whether it be corruptible or incorruptible, while the mathematician as such does not treat of anything subject to motion. (Averroes, Commentary on Physics, II comm. 71 (ed. Venetiis 1562 f. 74r).) But he intended to distinguish between the things studied by the speculative sciences, which must be treated separately and in order, although these three sorts of things can be apportioned to the three sciences. For incorruptible and immobile beings pertain precisely to the metaphysician. However, mobile and incorruptible beings, owing to their uniformity and regularity, can be determined in their movements by mathematical principles; this cannot be said of beings that are mobile and corruptible. Therefore, as Ptolemy says, the second kind of beings is ascribed to mathematics through astronomy, while the third kind remains the proper domain of natural science alone.

Article 4

Does divine science treat of what exists without matter and motion?

Obj. 1: We proceed as follows to the fourth article: it seems that divine science does not treat of things separate from motion and matter, for divine science seems to he especially concerned with God. Now we can come to know God only by way of his visible effects, which are created in matter and motion, as it is said in the Epistle to the Romans, the invisible things of him, from the creation of the world, are clearly seen, being understood by the things that are made (Rom 1:20). Therefore, divine science does not abstract from matter and motion.

Obj. 2: Again, that to which motion in some way belongs is not entirely separate from motion and matter. But motion in some way belongs to God. Thus it is said in Wisdom 7:24 that the spirit of wisdom is mobile and more mobile than all mobile things. And Augustine says that God moves himself without time and place. (Augustine, On the Literal Interpretation of Genesis, 8.20 (PL 34:388; CSEL 28.1:259, 222).) Plato also asserted that the first mover moves itself. (Plato ut refert Averroes infra lin. 222: [See Q. 5, A. 4, Reply Obj. 2: Averroes, Commentary on Physics, VIII comm. 40 (ed. Venetiis 1562 f. 380 r).]) Therefore divine science, which treats of God, is not entirely separate from motion.

Obj. 3: Again, divine science must treat not only of God but also of angels. But angels change both with regard to choice, because they became bad after having been good, and also with regard to place, as is evident in the case of those who are sent as messengers. So the objects of divine science are not entirely separated from motion.

Obj. 4: Again, as the Commentator seems to say in the beginning of the Physics, every being is either pure matter, or pure form, or a composite of matter and form. (Averroes, Commentary on Physics, I comm. 1 (ed. Venetiis 1562 f. 6 r).) But an angel is not a pure form, because then he would be pure act, which is true of God alone. Neither is he pure matter. So he is a composite of matter and form. Therefore divine science does not abstract from matter.

Obj. 5: Again, divine science, the third part of speculative philosophy, is the same as metaphysics, whose subject is being, and especially substantial being. This is clear in the Metaphysics. (Aristotle, Metaphysics, 4.1, 1003a21.) But being and substance do not abstract from matter; otherwise there would be no material being. So divine science does not abstract from matter.

Obj. 6: Again, according to the Philosopher, it is the business of a science to consider not only a subject but also the divisions and attributes of that subject. (Aristotle, Posterior Analytics, 1.18, 76b11–16.) Now, as we have said, being is the subject of divine science. Therefore it is the business of this science to treat of all beings. But matter and motion are beings. Therefore they come under the consideration of metaphysics, and so divine science does not abstract from them.

Obj. 7: Again, divine science demonstrates by means of three causes: efficient, formal, and final, as the Commentator says. (Averroes, Commentary on Physics, I comm. 1 (ed. Venetiis 1562 f. 6 r).) But we cannot consider an efficient cause without taking motion into account; and the same thing is true of a final cause, as the Metaphysics says. (Aristotle, Metaphysics, 3.4, 996a26.) Thus, because the objects of mathematics are immobile, there are no demonstrations through these causes in that science. Consequently, divine science does not abstract from motion.

Obj. 8: Again, in theology we treat of the creation of the heavens and the earth, of acts of men, and many similar things that involve matter and motion. So theology does not seem to abstract from matter and motion.

On the contrary, the Philosopher says in the Metaphysics that first philosophy deals with things that can exist separately, that is, from matter, and with immobile things. (Aristotle, Metaphysics, 6.1, 1026a15.) Now first philosophy is divine science, as he says in the same place. Therefore divine science abstracts from matter and motion.

Moreover, the most excellent science deals with the most excellent beings. But the most excellent science is divine science. Therefore, since immaterial and immobile beings are the most excellent, divine science will treat of them.

Moreover, the Philosopher says in the beginning of the Metaphysics that divine science concerns first principles and causes. (Aristotle, Metaphysics, 1.1, 981b28.) Now these are immaterial and immobile. Therefore things of this sort are the objects of divine science.

I answer that in order to throw light on this question we must understand what science should be called divine science. We must realize indeed that if a science considers a subject-genus, it must investigate the principles of that genus, since science is perfected only through knowledge of principles, as the Philosopher explains in the beginning of the Physics. (Aristotle, Physics, 1.1, 184a12–14.) Now there are two kinds of principles.

Some are complete natures in themselves and nevertheless they are the principles of other things, as the heavenly bodies are principles of lower bodies and simple bodies are principles of mixed bodies. In the sciences, therefore, we study them not only insofar as they are principles, but also insofar as they are certain things in themselves. And for this reason they are considered not only in the science of the beings of which they are the principles, but also in a separate science. Thus there is a branch of natural science treating of heavenly bodies distinct from that treating of lower bodies, and there is one treating of the elements distinct from that treating of mixed bodies.

There are some principles, however, that are not complete natures in themselves, but only principles of natures, as unity is the principle of number, point the principle of line, and form and matter principles of natural bodies. Principles of this sort, then, are investigated only in the science dealing with the things of which they are principles.

Now just as there are certain common principles of any particular genus extending to all the principles of that genus, so too all beings, inasmuch as they share in being, have certain principles that are the principles of all beings. And as Avicenna says, these principles can be called common in two ways: (Avicenna, Sufficientia, I c. 2 (ed. Venetiis 1508 f. 14 va).)

first, by predication, as when I say that form is common to all forms because it is predicated of all;

second, by causality, as we say that the sun, which is numerically one, is the principle of all things subject to generation.

Now there are principles common to all beings not only in the first way (in this sense the Philosopher says that all beings have proportionately the same principles), (Aristotle, Metaphysics, 12.4, 1070a31–33, 1071a30–35.) but also in the second way, so that there are certain beings, each numerically one, which are the principles of all things. Thus the principles of accidents are reducible to the principles of substance, and the principles of perishable substances are reducible to imperishable ones, with the result that all beings are reducible to certain principles in a definite graded order.

And since the principle of the being of all things must be being in the highest degree as the Metaphysics says, (Aristotle, Metaphysics, 2.2, 993b26–31.) these principles must be most perfect and therefore supremely in act, so that they have no potentiality whatsoever, or the least possible, because actuality is prior to, and more excellent than potentiality, as the Metaphysics says. (Aristotle, Metaphysics, 9.7–10, 1049b4–1051a33.) For this reason they must be free from matter, which is in potency, and free from motion, which is actuality of that which exists in potency. Divine beings are of this sort, because if the divine exists anywhere, it exists especially in such a nature (that is to say, in a nature that is immaterial and immutable), as is said in the Metaphysics. (Aristotle, Metaphysics, 6.1, 1026a20.)

Accordingly, because these divine beings are the principles of all things and nevertheless they are complete natures in themselves, they can be studied in two ways:

first, insofar as they are the common principles of all things,

and second insofar as they are beings in their own right.

But even though these first principles are most evident in themselves, our intellect regards them as the eye of an owl does the light of the sun, as the Metaphysics says. (Aristotle, Metaphysics, 2.1, 993b9–11.) We can reach them by the light of natural reason only to the extent that their effects reveal them to us. It was in this way that the philosophers came to know them as is clear from the Epistle to the Romans: the invisible things of God . . . are clearly seen, being understood by the things that are made (Rom 1:20).

Philosophers, then, study these divine beings only insofar as they are the principles of all things. Consequently, they are the objects of the science that investigates what is common to all beings, which has for its subject being as being. The philosophers call this divine science. There is, however, another way of knowing beings of this kind, not as their effects reveal them, but as they reveal themselves. The Apostle mentions this way in his first epistle to the Corinthians: so the things also that are of God no man knows, but the Spirit of God. Now we have received not the spirit of this world, but the Spirit that is of God, that we may understand (1 Cor 2:12). And again, but to us God has revealed them by his Spirit (1 Cor 2:10). In this way we consider divine beings as they subsist in themselves and not only inasmuch as they are the principles of things.

Accordingly, there are two kinds of theology or divine science.

There is one that treats of divine things, not as the subject of the science but as the principles of the subject. This is the kind of theology pursued by the philosophers and that is also called metaphysics.

There is another theology, however, that investigates divine things for their own sakes as the subject of the science. This is the theology taught in Sacred Scripture. Both treat of beings that exist separate from matter and motion, but with a difference, for something can exist separate from matter and motion in two distinct ways.

First, because by its nature the thing that is called separate in no way can exist in matter and motion, as God and the angels are said to be separate from matter and motion.

Second, because by its nature it does not exist in matter and motion; but it can exist without them, though we sometimes find it with them. In this way being, substance, potency, and act are separate from matter and motion, because they do not depend on them for their existence, unlike the objects of mathematics, which can only exist in matter, though they can be understood without sensible matter.

Thus philosophical theology investigates beings separate in the second sense as its subjects, and beings separate in the first sense as the principles of its subject. But the theology of Sacred Scripture treats of beings separate in the first sense as its subjects, though it concerns some items in matter and motion insofar as this is needed to throw light on divine things.

Reply Obj. 1: When something is incorporated into a science only to throw light on something else, it does not belong to the science essentially, but, in a way, incidentally, as some mathematics are incorporated into the natural sciences. In this way nothing prevents some things in matter and motion being in divine science.

Reply Obj. 2: We do not attribute motion to God properly, but by a kind of metaphor, and this in two ways.

First, according as the operation of the intellect or will is improperly called motion; and in this way a person is said to move himself when he knows or loves himself. In this sense, as the Commentator says, the statement of Plato is true, that the first mover moves himself because he knows and loves himself. (Averroes, Commentary on Physics, VIII comm. 40 (ed. Venetiis 1562 f. 380 r).)

Second, according as the flowing forth of effects from their causes can be called a procession or motion of cause to effect insofar as the likeness of the cause is left in the effect itself; and so the cause, which previously existed in itself, afterward comes to be in the effect through its likeness. And in this way God, who has communicated his likeness to all creatures, in a certain respect is said to be moved by all of them or to go forward to all things. Dionysius frequently uses this manner of speaking. (Dionysius, The Divine Names, c. 5, nn. 9, 10; c. 9, nn. 1, 3, 9, 10; (PG 3:825A, 825B, 909B, 912A, 916C, 917A).) This also seems to be the meaning of the statement in Wisdom 7:24, that wisdom is more mobile than all mobile things, and that she reaches from end to end mightily (Wis 8:1). However, this is not motion in the proper sense the term, and so the argument does not follow.

Reply Obj. 3: Divine science received through divine inspiration does not treat of the angels as its subject, but only as something incorporated into the science to throw light on its subject. For Sacred Scripture treats of the angels just as it does other creatures.

In the divine science taught by the philosophers, however, the angels, which they call Intelligences, are considered from the same point of view as the first cause or God, insofar as they are also secondary principles of things, at least through the movement of the spheres, though the angels themselves are subject to no physical motion.

Moreover, motion with respect to choice is reducible to the sense in which the act of the intellect or will is called motion, which is an improper sense of the term, motion being understood as operation.

Further, when angels are said to move in place, their motion is not with reference to enclosure in place but with reference to the activity they exercise in this or that place, or with reference to some other relation they have to place, although that relation is absolutely equivocal to that which a localized body has to place.

So it is clear that they do not move in the sense in which we say natural things move.

Reply Obj. 4: Act and potency are more common than matter and form. Therefore, even though we do not find the composition of form and matter in the angels we can still find potency and act in them. For matter and form are parts of a thing composed of matter and form; and so we find the composition of matter and form only in things with parts, one of which is related to the other as potency to act. Now what can be, can also not be; and so one part can be found with or without the other; and therefore, as the Commentator says, we find the composition of matter and form only in those things that are by nature corruptible. (Averroes, Commentary on Aristotle's On the Heavens, I comm. 20 (ed. Venetiis 1562 f. 15 r); Commentary on Metaphysics, VIII comm. 4 (ed. Venetiis 1562 f. 211 r) et comm. 12 (f. 220 r).)

Nor is the objection valid, that an accident may be eternally conserved in a subject, like shape in the heavens. For a heavenly body cannot exist without such a shape, since shape and all accidents in general follow upon substance as their cause. So a subject is related to its accidents not only as passive potency, but also in a way as an active power; and for this reason some accidents are naturally conserved forever in their subjects. But matter is not the cause of form in this way; and therefore all matter subject to form can cease to be subject to it, unless perhaps an extrinsic cause preserves it; thus we maintain that by the divine power even some bodies composed of contraries, like the bodies of those arisen from the dead, are incorruptible.

Now, since the essence of an angel is incorruptible by its nature, it is not composed of form and matter. But an angel does not exist of himself, and so he is potential to the being (esse) he receives from God. Consequently, the being (esse) received from God is related to his simple essence as act to potency. This is what is meant by saying that angels are composed of what they are (quod est) and that by which they are (quo est); being (esse) is understood as that by which they are and the angelic nature as what they are. However, even if angels were composed of matter and form, they would not be composed of sensible matter, from which both the objects of mathematics must be abstracted and those of metaphysics must be separated.

Reply Obj. 5: We say that being and substance are separate from matter and motion not because it is of their nature to be without them, as it is of the nature of ass to be without reason, but because it is not of their nature to be in matter and motion, although sometimes they are in matter and motion, as animal abstracts from reason, although some animals are rational.

Reply Obj. 6: The metaphysician deals with individual beings too, not with regard to their special natures, in virtue of which they are special kinds of being, but insofar as they share the common character of being. And in this way matter and motion also fall under his consideration.

Reply Obj. 7: Action and passion do not belong to things as they exist in thought but as they exist in reality. Now since the mathematician deals with things that are abstract only in thought, insofar as they come under his consideration they cannot be the principle or the end of motion. So the mathematician does not demonstrate by means of efficient and final causes. But the things the metaphysician deals with are separate, existing in reality, and these can be the principle and end of motion. So nothing prevents his demonstrating by means of efficient and final causes.

Reply Obj. 8: Just as faith, which is in a way the habit of the principles of theology, has for its object the first truth itself, and yet the articles of faith contain certain other things relating to creatures insofar as they have some connection with the first truth, in the same way theology is primarily concerned with God as its subject, but it includes many things about creatures as his effects, or as being in some way related to him.

Question 6

The methods of speculative science

The next question concerns the methods ascribed by Boethius to the speculative sciences. There are four points of inquiry in this connection.

1. Must we proceed according to the mode of reason in natural science, according to the mode of learning in mathematics, and according to the mode of intellect in divine science?

2. Should we entirely abandon the imagination in divine science?

3. Can our intellect behold the divine form itself?

4. Can our intellect behold the divine form by means of some speculative science?

Article 1

Must we proceed according to the mode of reason in natural science, of learning in mathematics, and of intellect in theology?

I

Obj. 1: On the first point we proceed as follows: it seems that we must no proceed according to the mode of reason in natural science, for rational philosophy is contra-distinguished from natural philosophy. But it seems to belong properly to rational philosophy to proceed according to the mode of reason. So this method is not appropriately ascribed to natural philosophy.

Obj. 2: Again, in the Physics the Philosopher frequently distinguishes between the methods of arriving at rational conclusions and physical conclusions. (Aristotle, Physics, 3.8, 204b4–10; 4.15, 217b29–32; 8.18, 264a8.) Therefore it is not the special characteristic of natural science to proceed rationally.

Obj. 3: Again, what is common to all the sciences should not be reserved to one. But every science proceeds by reasoning, advancing from effects to causes or from causes to effects or from certain signs. So this method should not be reserved to natural science.

Obj. 4: Again, in the Ethics the Philosopher distinguishes the reasoning part of the soul from the scientific part. (Aristotle, Ethics, 6.1, 1139a11.) But natural philosophy belongs to the scientific part. Therefore it is not appropriately said to proceed according to the mode of reason.

On the contrary, the De spiritu et anima says that reason is concerned with the forms of bodies. (Liber de spiritu et anima, c. 11 (PL 40:787).) Now it belongs most especially to natural philosophy to consider bodies. Therefore the rational method is appropriately attributed to it.

Moreover, Boethius says: when reason contemplates some universal nature, using neither imagination nor sense, it nevertheless comprehends imaginable and sensible things. (Boethius, On the Consolation of Philosophy, V pr. 4 (PL 63:850 A; CCL 94:97; CSEL 67:118).) Now it belongs to the natural philosopher alone to comprehend what is imaginable and sensible. Therefore the rational method is suitably attributed to natural philosophy.

II

Obj. 1: In the second place, it seems inappropriate to say that mathematics proceeds according to the mode of learning, for learning seems to be nothing else than the receiving knowledge. But we receive scientific knowledge in all branches of philosophy, because all proceed by means of demonstration. So it is common to all parts of philosophy to proceed according to the mode of learning; and so this procedure should not be made exclusive to mathematics.

Obj. 2: Again, the more certain something is, the easier it seems to learn it. But natural things seem to be more certain than mathematics because they are apprehended by the senses, from which all our knowledge takes its origin. Therefore this method belongs to the natural philosopher rather than to the mathematician.

Obj. 3: Again, as the Metaphysics says, in the sciences we begin at the point from which we learn more easily. (Aristotle, Metaphysics, 5.1, 1013a2–4.) But learning begins with logic, which must be mastered before mathematics and all the other sciences. Therefore it belongs to logic rather than to the other sciences to proceed according to the mode of learning.

Obj. 4: Again, the methods of natural and divine science are taken from powers of the soul, namely from reason and intellect. Therefore in the same way the method of mathematics ought to be taken from some power of the soul. So it is not appropriate to say that its method is to proceed according to the mode of learning.

On the contrary, to proceed according to the mode of learning is to proceed by demonstration and with certitude. But as Ptolemy says, mathematics alone, if one applies himself diligently to it, will give the inquirer after knowledge firm and unshaken certitude by demonstrations carried out with unquestionable methods. (Ptolemy, Almagest, I c. 1 (ed. Heiberg p. 6).) Therefore it is most characteristic of mathematics to proceed according to the mode of learning.

Moreover, this is evident from the Philosopher who, in several places in his works, calls the mathematical sciences disciplines. (Aristotle, Posterior Analytics, 1.1, 71a1; Topics, 7.2, 153a10–11; 8.4, 158b29.)

III

Obj. 1: In the third place, it seems that it is not appropriate to divine science to proceed according to the mode of intellect, for according to the Philosopher, there is understanding of principles, whereas there is science of conclusions. (Aristotle, Ethics, 6.3, 1139b31; 5, 1141a7.) But principles alone are not considered in divine science; some conclusions are also considered. Therefore to proceed according to the mode of intellect is not appropriate to divine science.

Obj. 2: Again, we cannot proceed intellectually with regard to those things that transcend every intellect. But divine things transcend every intellect, as Dionysius and the Philosopher say. (Dionysius, The Divine Names, c. 1, nn. 1, 4 (PG 3:588A, 593A); Liber de causis, prop. 5(6) (ed. Pattin p. 60).) Therefore they cannot be dealt with intellectually.

Obj. 3: Again, Dionysius says that angels have intellectual power inasmuch as they do not gather their divine knowledge from what is sensible and divided; but, as he adds, this is beyond the power of the soul. (Dionysius, The Divine Names, c. 7, n. 2 (PG 3:868B).) Therefore, since the divine science that is now under discussion is a science belonging to the human soul, it appears that its proper method is not to proceed intellectually.

Obj. 4: Again, theology seems particularly concerned with the things of faith. But understanding (intelligere) is the goal of the things of faith. Thus it is said in lsaiah, according to another version, unless you believe, you will not understand. So we should not say that proceeding intellectually about divine things is the method of theology but the goal.

On the contrary, the De spiritu et anima says that intellect (intellectus) has for its object created spirits, while understanding (intelligentia) has for its object God himself. (Liber de spiritu et anima, c. 11 (PL 40:787).) Now divine science is principally concerned with them. Therefore it seems proper to it to proceed intellectually.

Moreover, the method of a science must correspond to its subject matter. But divine things are intelligible in virtue of themselves. Therefore the method appropriate to divine science is to proceed intellectually.

I

To the first question, I answer that a method of proceeding in the sciences is called rational in three ways.

In one way, because of the principles from which we begin; for instance, when we proceed to prove something beginning with mental beings, like genus, species, opposite, and concepts of this sort, which the logicians study. In this sense a method will be called rational when in a science we use the propositions taught in logic; namely, when we use logic as having a teaching function in the other sciences. But this method of proceeding cannot belong properly to any particular science: it will fall into error unless it proceeds from its own proper principles. However, logic and metaphysics may properly and suitably use this method, because both are universal sciences and in a sense treat of the same subject.

In a second way, a method is called rational because of the end that terminates the thinking process. For the ultimate end that rational inquiry ought to reach is the understanding of principles, in which we resolve our judgments. And when this takes place, it is not called a rational procedure or proof but a demonstration. Sometimes, however, rational inquiry, cannot arrive at the ultimate end, but stops in the course of the investigation itself; that is to say, when several possible solutions still remain open to the investigator. This happens when we proceed by means of probable arguments, which by their nature produce opinion or belief, but not science. In this sense, rational method is opposed to demonstrative method. We can proceed by this rational method in all the sciences, preparing the way for necessary, proofs by probable arguments. This is another use of logic in the demonstrative sciences; not indeed as having a teaching function, but as being an instrument. In these two ways, then, a method is called rational from rational science, for, as the Commentator says, in both of them logic (which is another name for rational science) is used in the demonstrative sciences. (Averroes, Commentary on Physics, I comm. 35 (ed. Venetiis 1562 f. 23 r).)

In a third way, a method is called rational from the rational power, that is, inasmuch as in our procedure we follow the manner proper to the rational soul in knowing, and in this sense the rational method is proper to natural science. For in its procedures natural science keeps the characteristic method of the rational soul in two ways.

First, in this respect, that just as the rational soul receives from sensible things (which are more knowable relatively to us) knowledge of intelligible things (which are more knowable in their nature), so natural science proceeds from what is better known to us and less knowable in its own nature. This is evident in the Physics. (Aristotle, Physics, 1.1, 184a16–21.) Moreover, demonstration by means of a sign or an effect is used especially in natural science.

Second, natural science uses a rational method in this respect, that it is characteristic of reason to move from one thing to another; and this method is observed particularly in natural science, where we go from the knowledge of one thing to the knowledge of another; for example, from the knowledge of an effect to the knowledge of its cause.

And the procedure in natural science is not only a movement from one thing to another distinct from it in the mind and not in reality, as when we go from the concept animal to the concept man. In the mathematical sciences we proceed only by means of what is of the essence of a thing, since they demonstrate only through a formal cause. In these sciences, therefore, we do not demonstrate something about one thing through another thing, but through the proper definition of that thing. It is true that some demonstrations about the circle are made by means of the triangle or vice versa, but this is only because the triangle is potentially in the circle and vice versa.

But in natural science, where demonstration takes place through extrinsic causes, something is proved of one thing through another thing entirely external to it. So the method of reason is particularly observed in natural science; and on this account natural science among all the others is most in conformity with the human intellect.

Consequently, we say that natural science proceeds rationally, not because this is true of it alone, but because it is especially characteristic of it.

Reply Obj. 1: That argument is based on the method that is called rational in the first way. In this sense a rational method is proper to rational and divine science, but not to natural science.

Reply Obj. 2: That argument is based on the method that is called rational in the second way.

Reply Obj. 3: The method of reason is observed in all the sciences insofar as they proceed from one item to another that is mentally distinct from it, but not in the sense that they go from one thing to another thing. As has been said, that is proper to natural science.

Reply Obj. 4: In that place the Philosopher considers the reasoning and deliberative parts of the soul to be identical: so it is clear that they are related to the second mode of rational procedure mentioned above. In the same place, moreover, because of their contingency he assigns human actions, which are the objects of moral science, to the reasoning or deliberative part of the soul. From what has been said, then, we can gather that the first mode of rationality is most characteristic of rational science, the second of moral science, and the third of natural science.

II

To the second question, I answer that mathematical science is said to proceed according to the mode of learning, not because it alone does so, but because this is especially characteristic of it. For, since learning is nothing else than the taking of knowledge from another, we are said to proceed according to the mode of learning when our procedure leads to certain knowledge, which is called science. Now this occurs particularly in the mathematical sciences. Because mathematics is situated between natural and divine science, it is more certain than either. It is more certain than natural science because its investigation is not bound up with motion and matter, while the investigation of natural science centers upon matter and motion. Now from the very fact that natural science deals with matter, its knowledge depends upon many factors, upon the consideration of matter itself, of form, and of the material dispositions and properties accompanying form in matter. And whenever there are many factors to be considered in order to know something, knowledge is more difficult. Thus the Posterior Analytics says that a science is less certain that results from adding on some item, as geometry adds something to arithmetic. (Aristotle, Posterior Analytics, 1.41, 87a31–34.) If the inquiry in a science is about things that are mobile and lack uniformity, its knowledge is less exact because its demonstrations are often valid only in the majority of cases, owing to the fact that things sometimes happen differently. So, too, the more a science draws close to particulars (as do practical sciences like medicine, alchemy, and ethics), the less certain they can be because of the many factors to be taken into account in these sciences, the omission of any one of which will lead to error, and also because of their variability.

The method of mathematics is also more certain than the method of divine science, because the objects of divine science are further removed from sensible things, from which our knowledge takes its origin. This is true both in the case of the separate substances (to which our knowledge of the sense world gives us inadequate access), and also in the case of the principles common to all things (which are most universal and therefore furthest removed from the particular things falling under the senses). But mathematical entities do fall under the senses and they are objects of our imagination; for example, figures, lines, numbers, and the like. So the human intellect, which takes its knowledge from images, knows these things with greater ease and certainty than it does a separate Intelligence, or even the nature of substance, act, potency, and the like. It is clear, then, that mathematical inquiry, is easier and more certain than physical and theological, and much more so than that of the other sciences that are practical, and for this reason it is said especially to proceed according to the mode of learning. This is what Ptolemy asserts in the beginning of the Almagest: “Let us call the other two kinds of theoretical knowledge opinion rather than science: theology because of its obscurity and incomprehensibility, physics because of the instability and obscurity of matter. The mathematical type of investigation alone will give the inquirer firm and unshaken certainty through demonstrations carried out by unquestionable methods.” (Ptolemy, Almagest, I c. 1 (ed. Heiberg p. 6).)

Reply Obj. 1: Although we learn in all the sciences, nevertheless, as we have said, we do so with greater ease and certitude in mathematics.

Reply Obj. 2: Natural things come under the senses; but because of their instability when they begin to exist in reality they do not have the great certitude of the objects of mathematics. These latter are not subject to change; and yet they exist in sensible matter, and as such they can come under the senses and imagination.

Reply Obj. 3: In learning we begin with what is easier, unless necessity dictates otherwise. For sometimes in learning it is necessary to start, not with what is easier, but with that on which the knowledge of subsequent matters depends. That is why in acquiring knowledge we must begin with logic, not because it is easier than other sciences (for it involves the greatest difficulty, concerned as it is with second intentions), but because the sciences depend on it inasmuch as it teaches the method of proceeding in all the sciences. And, as the Metaphysics says, we must know the method of science before science itself. (Aristotle, Metaphysics, 2.5, 995a13.)

Reply Obj. 4: The method of the sciences is taken from the powers of the soul because of the way in which these powers operate. So the methods of the sciences do not correspond to the soul’s powers, but rather to the ways in which these powers can operate, and these are diversified not only according to the powers, but also according to their objects. So it is not necessary that the method of every science be named after a power of the soul. However, we can say that just as the method of physics is taken from reason inasmuch as it gets its objects from the senses, and the method of divine science is taken from the intellect inasmuch as it understands something purely and simply, so also the method of mathematics can be taken from reason inasmuch as it obtains its objects from the imagination.

III

To the third question, I answer that just as we attribute the rational method to natural philosophy because it adheres most closely to the method of reason, so we attribute the intellectual method to divine science because it adheres most closely to the method of intellect. Now reason differs from intellect as multitude does from unity. Thus Boethius says that reasoning is related to understanding as time to eternity and as a circle to its center. (Boethius, On the Consolation of Philosophy, IV pr. 6 (PL 63:817 A; CCL 94:80; CSEL 67:98).) For it is distinctive of reason to disperse itself in the consideration of many things, and then to gather one simple truth from them. Thus Dionysius says, souls have the power of reasoning in that they approach the truth of things from various angles, and in this respect they are inferior to the angels; but inasmuch as they gather a multiplicity into unity they are in a way equal to the angels. (Dionysius, The Divine Names, c. 7, n. 2 (PG 3:868B).)

Conversely, intellect first contemplates a truth one and undivided and in that truth comprehends a whole multitude, as God, by knowing his essence, knows all things. Thus Dionysius says: angelic minds have the power of intellect in that they understand divine truths in a unified way. (Dionysius, The Divine Names, c. 7, n. 2 (PG 3:868B).)

It is clear, then, that rational thinking ends in intellectual thinking, Following the process of analysis, in which reason gathers one simple truth from many things. And again, intellectual thinking is the beginning of rational thinking, following the process of synthesis, in which the intellect comprehends a multiplicity in unity. So the thinking that is the terminus of all human reasoning is supremely intellectual.

Now all rational thinking in all the sciences, following the way of analysis, terminates in the knowledge of divine science. For, as we have said, reason sometimes advances from one thing to another in the order of reality; for example, when a demonstration is made through external causes or effects, by synthesis when we go from causes to effects, by analysis when we proceed from effects to causes, for causes are more simple, unchangeable, and uniformly constant than their effects.

Consequently, the ultimate end of analysis in this process is attainment d the highest and most simple causes, which are the separate substances. At other times, however, reason advances from one item to another distinct in the mental order, as when we proceed according to intrinsic causes, by synthesis when we go from the most universal forms to the more particular ones, by analysis when we proceed conversely, because what is more universal is more simple. Now that which is most universal is common to all beings; and so the ultimate end of analysis in this process is the consideration of being and the properties of being as being.

And, as we said above, these are the objects of divine science; namely, the separate substances and that which is common to all beings. It is evident, therefore, that its thinking is supremely intellectual. It also follows that divine science gives principles to all the other sciences, because intellectual thinking is the starting point of rational thinking; and for this reason it is called first philosophy. Nevertheless it is learned after physics and the other sciences, because intellectual thinking is the terminus of rational thinking. For this reason it is called “metaphysics,” as if to say “beyond physics,” for in the process of analysis it comes after physics.

Reply Obj. 1: We say that divine science proceeds intellectually not as though it makes no use of reason, moving forward from principles to conclusions, but because its reasoning most closely approaches intellectual consideration and its conclusions are closest to its principles.

Reply Obj. 2: God is beyond the comprehension of every created intellect, but he is not beyond the uncreated intellect, since in knowing himself he comprehends himself. However, he is above the intellect of everyone here on earth as regards knowing what he is, but not as regards knowing that he is, The blessed in heaven, however, also know what he is, because they see his essence. Nevertheless divine science is not only about God. It is concerned with other things as well, which are not beyond the human intellect even in its present state as regards knowing what they are.

Reply Obj. 3: As we said above, human thought at its terminus in a way approaches angelic knowledge; not that it equals it, but bears a resemblance to it. So Dionysius says: souls, by reducing multitude to unity, are rightly considered the equal of the angelic intelligences, as far as this is proper and possible to souls. (Dionysius, The Divine Names, c. 7, n. 2 (PG 3:868C).)

Reply Obj. 4: The knowledge of faith also belongs in a special way to understanding (intellectus). For we do not possess the things of faith through the investigation of reason, but we hold them by simply receiving understanding. But we are said not to understand them because the intellect does not have a full knowledge of them. That indeed is promised to us as our reward.

Article 2

Should we entirely abandon the imagination in divine science?

Obj. 1: We proceed as follows to the second article: it seems that in divine science we must turn to images, for divine science was never more appropriately taught than in Sacred Scripture. But treating of the divine in Sacred Scripture we resort to images when divine things are described for us under sensible figures. Therefore in divine science we must turn to images.

Obj. 2: Again, we grasp divine things only by the intellect; and this is why, as we have said, we must proceed intellectually when treating of them. But, as the Philosopher says, it is impossible to understand without the imagination. (Aristotle, De anima, 1.2, 403a8; 3.6, 431a16.) Therefore in divine science we must resort to images.

Obj. 3: Again, we know the divine especially through divine illumination. But as Dionysius says, it is impossible for the divine light to illumine us from above unless it be hidden within the covering of many sacred veils. (Dionysius, The Celestial Hierarchy, c. 1, n. 2 (PG 3:121BC).) And he calls these sacred veils images of sensible things. So in divine science we must turn to images.

Obj. 4: Again. when dealing with what is sensible we must make use of the imagination. But we know divine things from sensible effects, according to the statement of the Epistle to the Romans: “The invisible things of God... are clearly seen, being understood by the things that are made.” Therefore in divine science we must resort to images.

Obj. 5: Again, in cognitive matters we are guided especially by the starting point of knowledge; for instance in the sciences of nature we are guided by the senses, from which our knowledge begins. Now in us intellectual knowledge begins in the imagination, since images are related to our intellect as colors to sight, as the De anima says. (Aristotle, De anima, 3.6, 431a14.) Therefore in divine science we must go to the imagination.

Obj. 6: Again, since the intellect does not use a bodily organ, an injury to such an organ hinders the action of the intellect only insofar as it turns to the imagination. Now the intellect is hindered in its consideration of divine things through an injury of a bodily organ, namely the brain. Therefore in considering divine things the intellect resorts to the imagination.

On the contrary, Dionysius says in his Mystical Theology, speaking to Timothy: O beloved Timothy, in mystic contemplation abandon the senses. (Dionysius, Mystical Theology, c. 1, n. 1 (PG 3:997B).) But the imagination has to do only with the sensible, for it is a movement produced by the sense in act, as the De anima says. (Aristotle, De anima, 2.30, 429a1.) Therefore, since the considerations of divine things are eminently mystical, we should not have recourse to images in them.

Moreover, in the procedure of any science we should avoid what leads to error in it. But, as Augustine says, the principal error regarding divine things is the mistake of those who try transfer to them what they know of the corporeal world. (Augustine, On the Trinity, 1.1.1 (PL 42:819; CCL 50:27).) Therefore, since the imagination has to do only with the corporeal, it seems that in divine science we should not go to images.

Moreover, as is clear from Boethius, a lower power does not extend to that which is proper to a higher power. (Boethius, On the Consolation of Philosophy, V pr. 4 (PL 63:849; CCL 94:97; CSEL 67:117).) But it belongs to an intellect and to an intelligence to know the divine and the spiritual, as is said in the De spiritu et anima. (Liber de spiritu et anima c. 11 (PL 40:787).) Therefore, since, as is said in the same work, imagination is below intelligence and intellect, it seems that in the domain of the divine and the spiritual we should no go to the imagination.

I answer that in all knowledge two factors must be taken into account: the beginning and the end. Knowledge begins with apprehension but it ends with judgment, for it is there that knowledge is completed. Now all our knowledge begins in the senses; from sense perception results the apprehension of the imagination (which is a movement arising from sensory knowledge, as the Philosopher says), (Aristotle, De anima, 2.30, 429a1.) and from it in turn springs our intellectual apprehension, for images are like objects to the intellectual soul, as is clear in the De anima. (Aristotle, De anima, 3.6, 431a14.) But knowledge does not always terminate in the same way. Sometimes it terminates in the senses, sometimes in the imagination, and sometimes in the intellect alone.

In some cases the properties and accidents of a thing disclosed by the senses adequately reveal its nature, and then the intellect’s judgment of that nature must conform to what the senses reveal about it. All natural things, which are bound up with sensible matter, are of this kind. So the terminus of knowledge in natural science must be in the senses, with the result that we judge of natural beings as the senses manifest them, as is evident in the De caelo et mundo. (Aristotle, On the Heavens, 3.7, 306a16.) Accordingly, the man who neglects the senses when dealing with natural things falls into error. By natural things I mean those that are bound up with sensible matter and motion both in existence and in thought.

Our judgment about some things, however, does not depend upon what the sense perceives, because even though they exist in sensible matter they abstract from it when their essences are defined, and we judge of anything chiefly according to the definition of its essence. But because they do not abstract from every kind of matter when their essences are defined but only from sensible matter, and because an object for the imagination remains after sensible characteristics have been set aside, we must judge about such things according to what the imagination reveals. Now the objects of mathematics are of this kind. Accordingly, the knowledge we have through judgment in mathematics must terminate in the imagination and not in the senses, because mathematical judgment goes beyond sensory perception. Thus, the judgment about a mathematical line is not always the same as that about a sensible line. For example, that a straight line touches a sphere at only one point is true of an abstract straight line but not of a straight line in matter, as is said in the De anima. (Aristotle, De anima, 1.2, 403a12–16.)

There are other beings, however, that transcend both that which falls under the senses and that which falls under the imagination; namely, those that are entirely independent of matter both with respect to their being and with respect to their being understood. So, when we know things of this kind through judgment, our knowledge must terminate neither in the imagination nor in the senses. Nevertheless we reach some knowledge of them through the objects of the senses and the imagination, either by way of causality (as when from an effect we come to know its cause, which is not proportionate to the effect but transcends it), or by way of transcendence, or by way of negation (as when we separate from such beings whatever the sense or imagination apprehends). These are the means of knowing divine things from the sensible world proposed by Dionysius in his Divine Names. (Dionysius, The Divine Names, c. 7, n. 3 (PG 3:872A).)

It follows that we can use the senses and the imagination as the starting points but not as the termini of our knowledge of divine things, so that we judge them to be the sort of objects the sense or the imagination apprehends. Now to go to something is to terminate at it. Therefore, we should go neither to the imagination nor to the senses in divine science, to the imagination and not to the senses in mathematics, and to the senses in the natural sciences. For this reason they aree in error who try to proceed in the same way in these three parts of speculative science.

Reply Obj. 1: Sacred Scripture does not present divine things to us under sensible images so that our intellect may stop with them, but that it may rise from them to the immaterial world. Thus, as Dionysius says, it even teaches the divine through symbols of base objects in order to offer less occasion of stopping with them. (Dionysius, The Celestial Hierarchy, c. 2, nn. 2, 3 (PG 3:140A, 141B).)

Reply Obj. 2: The operation of our intellect in its present state is never without an image as regards the beginning of knowledge. But our knowledge need not always terminate at images, so that, in other words, we judge the objects of our understanding to be of the same kind as the objects of the imagination.

Reply Obj. 3: The text of Dionysius refers to the beginning of knowledge and not to its end, which is reached when we know divine things from their sensible effects by the three methods described above; but not in such a way that we must form our judgment of the divine according to the manner of being of these sensible effects.

Reply Obj. 4: That argument is valid when the starting point of knowledge adequately leads to the object we seek to know. This is the way the senses are the starting point in the natural sciences, but not, as we have said, in divine science.

Reply Obj. 5: An image is the starting point of our knowledge, for it is that from which the operation of the intellect begins; not that it passes away, but it remains as the foundation of intellectual activity, just as the principles of demonstration must remain throughout the whole process of science. This is because images are related to the intellect as objects in which it sees whatever it sees, either through a perfect representation or through a negation. Consequently, when our knowledge of images is impeded, we must be completely incapable of knowing anything with our intellect even about divine things. Clearly, we cannot know that God causes bodies, or transcends all bodies, or is not a body, if we do not form an image of bodies; but our judgment of what is divine is not made according to the imagination. Consequently, even though in our present state of life the imagination is necessary in all our knowledge of the divine, with regard to such matters we must never terminate in it.

Article 3

Can our intellect behold the divine form itself?

Obj. 1: We proceed as follows to the third article: It seems that we are unable to behold the divine form itself, at least in this life, for as Dionysius says, if anyone seeing God understood what he saw, he did not see God himself but one of his creations. (Dionysius, Letter 1: to Gaius, (PG 3:1065A).) Now the divine form is God himself. Therefore we are not able to behold the divine form itself.

Obj. 2: Again, the divine form is the divine essence itself. Now no one in the present life can see God through his essence. Therefore neither can he behold the divine form.

Obj. 3: Again, if we see the form of something, we have some knowledge of that thing. But according to Dionysius, our intellect is most united to God when it knows absolutely nothing of him. (Dionysius, Mystical Theology, c. 1, n. 3 (PG 3:1001A).) Therefore we are unable to behold the divine form.

Obj. 4: Again, as was said above, all our knowledge begins from the senses. But what we perceive by the senses is inadequate to reveal the divine form or even the other separate substances. Therefore we are unable to behold the divine form itself.

Obj. 5: Again, according to the Philosopher, our intellect is related to what is most evident as the eye of an owl to the sun. (Aristotle, Metaphysics, 2.1, 993b9–11.) But the eye of an owl cannot see the sun at all. Therefore neither can our intellect see the divine form itself or other separate forms, which are nature’s most evident beings.

On the contrary, the Apostle says in the Epistle to the Romans: the invisible things of God are clearly seen by a creature of the world (that is, by man), his eternal power also and divinity. Now the divine form is simply the divinity itself. Therefore in some way we can know the divine form with our intellect.

Moreover, commenting on the text of Genesis, I have seen God face to face (32:30), the gloss of Gregory says, unless a person somehow beheld it (namely, divine truth), he would not feel himself incapable of beholding it. (Glossa ordinaria, at Genesis 32:30 (PL 76:292 C; CCL 143 B, 1196).) But we feel that we cannot perfectly see the divine essence. Therefore in some way we do behold it.

Moreover, Dionysius says that the human mind gradually becomes accustomed to rise from the world of sense to heights beyond this world, which are nothing else than the separate forms. (Dionysius, The Celestial Hierarchy, c. 2, n. 5 (PG 3:145B).) Therefore we can somehow know the separate forms.

I answer that, we know a thing in two ways: in one way when we know that it is, and in another way when we know what it is.

Now in order to know what anything is, our intellect must penetrate its quiddity or essence either directly or by means of other things that adequately reveal its quiddity.

But in this life our intellect cannot directly penetrate the essence of God or other separate essences, because it directly extends to images, to which it bears the same relation as sight does to color, as the De anima says. (Aristotle, De anima, 3.6, 431a14.) So the intellect can directly conceive the quiddity of a sensible reality but not of an intelligible reality. Thus Dionysius says, according to our way of knowing, we cannot immediately attain to the contemplation of the invisible. (Dionysius, The Celestial Hierarchy, c. 2, n. 2 (PG 3:140A).)

There are some invisible things, however, whose quiddity or nature is perfectly revealed by the known quiddities of sensible things; and we can also know what these intelligible objects are, although indirectly. For instance, from the fact that we know what man and animal are, we come to know adequately the relation of one to the other, and from this we know what a genus and a species are.

But the sensible natures known to us do not adequately reveal the divine essence or even other separate essences, since naturally considered they do not belong to one genus; and quiddity and all such terms predicated almost equivocally of sensible things and of these substances. That is why Dionysius calls the likenesses of sensible things, transferred to immaterial substances, unlike likenesses, which intellectual beings participate in one way and sensible beings in another. (Dionysius, The Celestial Hierarchy, c. 2, n. 4 (PG 3:141C).) Consequently, we cannot have adequate knowledge of the former from the latter by way of likeness or even by way of causality, because the effects of those substances found in lower beings do not measure up to their powers so that we can come to know the essence of their cause in this way.

Accordingly, in the present life it is absolutely impossible to know the essence of immaterial substances, not only by natural knowledge but also by revelation; for, as Dionysius says, the light of divine revelation comes to us adapted to our condition. Thus even though revelation elevates us to know something of which we should otherwise be ignorant, it does not elevate us to know in any other way than through sensible things. Thus Dionysius says: it is impossible for the divine light to illumine us from above unless it be hidden within the covering of many sacred veils. (Dionysius, The Celestial Hierarchy, c. 1, n. 2 (PG 3:121B).)

Now knowledge by way of the sensible is inadequate to enable us to know the essences of immaterial substances. So we conclude that we do not know what immaterial forms are, but only that they are, whether by natural reason based upon created effects or even by revelation, by means of likenesses taken from sensible things.

It should be noticed, however, that we cannot know that a thing is without knowing in some way what it is, either perfectly or at least confusedly, as the Philosopher says we know things defined before we know the parts of their definition. (Aristotle, Physics, 1.1, 184a23–b12.) For if a person knows that man exists and wants to find out what man is by definition, he must know the meaning of the term “man.” And this is possible only if he somehow forms a concept of what he knows to exist, even though he does not know its definition. That is to say, he forms a concept of man by knowing a proximate or remote genus and accidental characteristics which reveal him externally. For our knowledge of definitions, like that of demonstrations, must begin with some previous knowledge. Similarly, therefore, we cannot know that God and other immaterial substances exist unless we know somehow, in some confused way, what they are.

Now we cannot do this by knowing a proximate or remote genus, for God is in no genus, since his essence is not distinct from his being; a condition required in all genera, as Avicenna says. (Avicenna, Commentary on Metaphysics, 8.4 (ed. Van Riet p. 402).) Created immaterial substances, however, are indeed in a genus; but even though from the viewpoint of logic they share the same remote genus of substance with sensible substances, from the viewpoint of physics they do not belong to the same genus, as neither do heavenly and terrestrial bodies. For the corruptible and the incorruptible do not belong to the same genus, as the Metaphysics says. (Aristotle, Metaphysics, 10.12, 1058b26–28.) For the logician considers concepts in themselves; and from this point of view nothing prevents the immaterial and the material, or the incorruptible and the corruptible, from having something in common.

But the philosopher of nature and the metaphysician treat of essences as existing in reality; and therefore they say that there are different genera wherever they find diverse modes of potency and act, and consequently diverse modes of being. Neither has God any accidental characteristics, as we will prove later. If other immaterial substances have such characteristics, we do not know them.

Accordingly, we cannot say that we know immaterial substances obscurely by knowing their genus and observable accidents. Instead of knowing the genus of these substances, we know them by negations; for example, by understanding that they are immaterial, incorporeal, without shapes, and so on. The more negations we know of them the less vaguely we understand them, for subsequent negations limit and determine a previous negation as differences do a remote genus.

Our knowledge of the heavenly bodies is also negative for the most part, because they belong to a different genus from that of inferior bodies. We know, for instance, that they are not light or heavy, or hot or cold. And instead of accidental characteristics in these substances we have their connections with sensible ones, either with regard to the relationship of cause to effect or with regard to the relationship of transcendence.

We conclude, then, that in the case of immaterial forms we know that they exist; and instead of knowing what they are we have knowledge of them by way of negation, by way of causality, and by way of transcendence. These are the same ways Dionysius proposes in his Divine Names; (Dionysius, The Divine Names, c. 7, n. 3 (PG 3:872A).) and this is how Boethius understands that we can know the divine form by removing all images, and not that we know that it is.

The solution of the opposing arguments is clear from what has been said: for the first arguments are based on perfect knowledge of what a thing is, the others on imperfect knowledge of the sort described.

Article 4

Can our intellect behold the divine form through some speculative science?

Obj. 1: We proceed as follows to the fourth article: it seems that we can come to behold the divine form through the speculative sciences, for: as Boethius says here, theology is a part of speculative science. But, as he says, it belongs to theology to behold the divine form itself. Therefore we can arrive at a knowledge of that form through the speculative sciences.

Obj. 2: Again, there is a speculative science treating of immaterial substances, namely divine science. Now any science treating of a substance beholds the form of that substance, because all knowledge is by means of form, and according to the Philosopher all demonstration begins with essence. (Aristotle, Posterior Analytics, 1.23, 78a22ff.) Therefore we can behold separate forms through the speculative sciences.

Obj. 3: Again, according to the philosophers, the ultimate happiness of man is to understand the separate substances For, since happiness is the most perfect activity, it must have to do with the most excellent things falling under the intellect, as we can learn from the Philosopher in the Ethics. (Aristotle, Ethics, 10.10, 1177a12–21.) Now the happiness described by the philosophers is an activity springing from wisdom, since wisdom is the most perfect virtue of the most perfect power: the intellect; and, as the Ethics says, this activity is happiness. Through wisdom, therefore, we understand the separate substances. Now wisdom is a speculative science, as is clear in the Metaphysics and Ethics. (Aristotle, Metaphysics, 1.1, 981b28–982a2; Ethics, 6.5, 6, 1141a18–20b2.) So we can understand the separate substances through the speculative sciences.

Obj. 4: Again, if something is unable to reach the end for which it exists it is to no purpose. But the inquiry in all the speculative sciences is directed to a knowledge of the separate substances as to its end, because in any class of things the most perfect is the goal [of all the rest], Therefore if substances of this sort cannot be understood through the speculative sciences, all of them would be to no purpose, which is absurd.

Obj. 5: Again, everything directed by nature to an end has been previously endowed with principles by which it is able to arrive at that end and by which it also tends toward that end; for the principles of natural motions are within a thing. Now the end of man to which he is directed by nature is to know the immaterial substances, as both the saints and the philosophers teach. So man is naturally endowed with principles of that knowledge. But everything we can arrive at from naturally known principles is included in one of the speculative sciences. Therefore the knowledge of immaterial substances pertains to some speculative sciences.

On the contrary, the Commentator says that there are two possible consequences of this position. (Averroes, Commentary on De Anima, III comm. 36 (ed. Venetiis 1562 f. 182v–83r; Crawford p. 494–95).) Either the speculative sciences are not yet perfect, because we have not discovered the sciences by which we can know the separate substances, and this owing to the fact we do not yet understand these substances because of our ignorance of some principles. Or if it happens because of some defect in our nature that we cannot discover the speculative sciences by which these substances may be known, it follows that, if some men can discover these sciences, we and they are men only in an equivocal sense. The first of these is improbable; the second is impossible. So we cannot understand these substances through some speculative sciences.

Moreover, in the speculative sciences we search after definitions, by which we understand the essences of things through the division of a genus into differences and through the examination of a thing’s causes and accidents, which contribute a great deal to our knowledge of the essence. But we cannot know these in the case of immaterial substances, because, as we have already said, from the viewpoint of physics they have no genus in common with the sensible substances known to us. And either they do not have a cause, as in the case of God, or their cause is deeply hidden from us, as in the case of the angels. Their accidents are also unknown to us. So there can be no speculative science through which we may come to understand immaterial substances.

Moreover, in the speculative sciences we know the essences of things through definitions. Now a definition is a phrase made up of a genus and differences. But the essences of these substances are simple and there is no composition in their quiddities, as is clear from the Philosopher and the Commentator. (Aristotle, Metaphysics, 9.11, 1051b26–28. Averroes, Commentary on Metaphysics, IX comm. 22.) So we cannot understand these substances through the speculative sciences.

I answer that, in the speculative sciences we always proceed from something previously known, both in demonstrating propositions and also in finding definitions. For just as one comes to know a conclusion by means of propositions previously known, so also from the concept of a genus and difference and from the causes of a thing he comes to know its species. But it is impossible to go on to infinity in this case, because then all science would cease, both as regards demonstrations and as regards definitions, since the infinite cannot be traversed. So inquiry in all the speculative sciences works back to something first given, which one does not have to learn or discover (otherwise he would have to go on to infinity), but which he knows naturally. Such are the indemonstrable principles of demonstration (for example, Every whole is greater than its part, and the like), to which all demonstrations in the sciences are reducible. Such, too, are the first conceptions of the intellect (for example, being, one, and the like), to which all definitions in the sciences must be reduced. From this it is clear that the only things we can know in the speculative sciences, either through demonstration or definition, are those that lie within the range of these naturally known principles.

Now these principles are revealed to man by the light of the agent intellect, which is something natural to him; and this light makes things known to us only to the extent that it renders images actually intelligible; for in this consists the operation of the agent intellect, as the De Anima says. (Aristotle, De anima, 3.4, 430a15.) Now images are taken from the senses. So our knowledge of the above-mentioned principles begins in the senses and memory, as is evident from the Philosopher. (Aristotle, Posterior Analytics, 2.20, 100a3–11.) Consequently, these principles do not carry us beyond that which we can know from the objects grasped by the senses.

Now we cannot know the essence of the separate substances through that which we take from the senses. This is clear from what was said above. But through sensible things we can arrive at a knowledge of the existence of these substances and of some of their characteristics. So we cannot know the quiddity of any separate substance by means of a speculative science, though the speculative sciences enable us to know the existence of these substances and some of their traits; for instance, that they are intellectual, incorruptible, and the like.

This is also the teaching of the Commentator. (Averroes, Commentary on De anima, III comm. 36 (ed. Venetiis 1562 f. 182 r B; Crawford p. 493).) Avempace (Ibn-Bajja) was of the opposite opinion; he thought that the quiddities of sensible things adequately reveal immaterial quiddities; but, as the Commentator says, this is clearly false, because quiddity is predicated of both almost in an equivocal sense.

Reply Obj. 1: Boethius does not intend to say that through the science of theology we can contemplate the essence of the divine form itself, but only that is transcends all images.

Reply Obj. 2: Some things are knowable to us through themselves; and in clarifying them the speculative sciences use the definitions of these objects to demonstrate their properties, as in the case of the sciences that demonstrate through causes. Other things are not knowable to us through themselves but through their effects. If the effect is proportionate to its cause, we take the quiddity itself of the effect as our starting point to prove that the cause exists and to investigate its quiddity, from which in turn its properties are demonstrated. But if the effect is not proportionate to its cause, we take the definition of the effect as the starting point to prove only the existence of the cause and some of its properties, while the quiddity of the cause remains unknown. This is what happens in the case of the separate substances.

Reply Obj. 3: Man’s happiness is twofold. One is the imperfect happiness found in this life, of which the Philosopher speaks, and this consists in contemplating the separate substances through the habit of wisdom. But this contemplation is imperfect and such as is possible in our present life, not such that we can know their quiddity. The other is the perfect happiness of heaven, where we will see God himself through his essence and the other separate substances. But this happiness will not come through a speculative science; it will come through the light of glory.

Reply Obj. 4: As we have said, the speculative sciences are directed to an imperfect knowledge of the separate substances.

Reply Obj. 5: We are endowed with principles by which we can prepare for that perfect knowledge of separate substances but not with principles by which to reach it. For even though by his nature man is inclined to his ultimate end, he cannot reach it by nature but only by grace, and this owing to the loftiness of that end.