PART I — ON BOETHIUS’S DE TRINITATE (QUESTIONS V–VI)¶
On the Division of Speculative Science, Intelligible Matter, and the Termination of Mathematical Judgment
Source Work: Super Boetium De Trinitate (c. 1257–1259) · Switch to Diplomatic Latin · Summary · GEOMETOR Notes
Question V, Article 1 — Whether Speculative Science Is Fittingly Divided into Natural, Mathematical, and Divine¶
Latin Locus: q. 5, a. 1 · Commentary: Notes on q. 5, a. 1
[pars 3 q. 5 pr.] Here there is a twofold question. The first concerns the division of speculative science, which he sets down in the text. The second concerns the modes which he attributes to the parts of speculative science. Concerning the first, four points are asked.
[pars 3 q. 5 pr. 1] First: Whether the division is fitting whereby speculative science is divided into these three parts: natural, mathematical, and divine.
[pars 3 q. 5 pr. 2] Second: Whether natural philosophy treats of those things that exist in motion and matter.
[pars 3 q. 5 pr. 3] Third: Whether mathematical consideration is without motion and matter concerning those things that exist in matter.
[pars 3 q. 5 pr. 4] Fourth: Whether divine science treats of those things that exist without matter and motion.
[pars 3 q. 5 a. 1 arg. 1] We proceed thus to the first article. It seems that speculative science is unfittingly divided into these parts. For the parts of speculative science are those habits that perfect the contemplative part of the soul. But the Philosopher in Book VI of the Ethics states that the scientific faculty of the soul, which is its contemplative part, is perfected by three habits, namely wisdom, science, and understanding. Therefore these three are the parts of speculative science, and not those set down in the text.
[pars 3 q. 5 a. 1 arg. 2] Furthermore, \ Augustine says in Book VIII of The City of God that rational philosophy, which is logic, is contained under contemplative or speculative philosophy. Since, therefore, he makes no mention of it, it seems that the division is insufficient.
[pars 3 q. 5 a. 1 arg. 3] Furthermore, philosophy is commonly divided into the seven liberal arts, among which neither natural nor divine philosophy is contained, but only rational and mathematical philosophy. Therefore natural and divine philosophy ought not to have been set down as parts of speculative science.
[pars 3 q. 5 a. 1 arg. 4] Furthermore, the science of medicine seems above all to be operative, and yet within it one part is posited as speculative and another as practical. By the same reason, therefore, in all other operative sciences some part is speculative; and thus mention ought to have been made in this division of ethics or moral philosophy, even though it is active, on account of its speculative part.
[pars 3 q. 5 a. 1 arg. 5] Furthermore, the science of medicine is a certain part of physics, and likewise certain other arts that are called mechanical, such as the science of agriculture, alchemy, and others of this kind. Since, therefore, these are operative, it seems that natural philosophy ought not to have been placed unconditionally under speculative science.
[pars 3 q. 5 a. 1 arg. 6] Furthermore, a whole ought not to be divided over against its part. But divine science seems to stand as a whole with respect to physics and mathematics, since the subjects of the latter are parts of the subject of the former. For the subject of divine science, which is first philosophy, is being, of which mobile substance—which the natural philosopher considers—is a part, and likewise quantity—which the mathematician considers—as is evident in Book III of the Metaphysics. Therefore divine science ought not to be divided over against natural and mathematical science.
[pars 3 q. 5 a. 1 arg. 7] Furthermore, sciences are divided in the same manner as things are, as is said in Book III of On the Soul. Now philosophy treats of being, for it is the knowledge of being, as Dionysius says in his Letter to Polycarp. Since, therefore, being is primarily divided by potency and act, by the one and the many, and by substance and accident, it seems that the parts of philosophy ought to be distinguished by differences of this sort.
[pars 3 q. 5 a. 1 arg. 8] Furthermore, there are many other divisions of beings, concerning which there are sciences, that are more essential than these divisions by mobile and immobile and by abstract and non-abstract—for instance, by corporeal and incorporeal, animate and inanimate, and others of this kind. Therefore the division of the parts of philosophy ought rather to be taken according to differences of this sort than according to those touched upon here.
[pars 3 q. 5 a. 1 arg. 9] Furthermore, that science from which the others take their suppositions ought to be prior to them. Now all other sciences take suppositions from divine science, because it belongs to it to prove the principles of the other sciences. Therefore he ought to have placed divine science in order before the others.
[pars 3 q. 5 a. 1 arg. 10] Furthermore, mathematics presents itself to be learned prior to natural science, inasmuch as boys can easily learn mathematics, whereas only those more advanced can learn natural science, as is said in Book VI of the Ethics. Hence among the ancients this order is said to have been observed in learning the sciences: that men should study first logic, next mathematics, after which natural science, after this moral science, and finally divine science. Therefore he ought to have placed mathematics before natural science. And thus this division seems insufficient.
[pars 3 q. 5 a. 1 s. c. 1] On the contrary, that this division is fitting is proved through the Philosopher in Book VI of the Metaphysics, where he says: Wherefore there will be three philosophical and theoretical sciences: mathematics, physics, and theology.
[pars 3 q. 5 a. 1 s. c. 2] Furthermore, in Book II of the Physics three modes of sciences are set down, which also seem to pertain to these three.
[pars 3 q. 5 a. 1 s. c. 3] Furthermore, \ Ptolemy also employs this division at the beginning of the Almagest.
[pars 3 q. 5 a. 1 co. 1] I answer that the theoretical or speculative intellect is properly distinguished from the operative or practical intellect in this: that the speculative intellect has for its end the truth which it considers, whereas the practical intellect orders the truth considered toward operation as toward an end. And therefore the Philosopher says in Book III of On the Soul that they differ from one another by their end, and in Book II of the Metaphysics it is said that the end of speculative science is truth, whereas the end of operative science is action. Since, therefore, matter must be proportioned to the end, the matter of the practical sciences must be those things that can be produced by our work, so that knowledge of them can thus be ordered toward operation as toward an end. Conversely, the matter of the speculative sciences must be things that are not produced by our work; hence the consideration of them cannot be ordered toward operation as toward an end. And it is according to the distinction among these things that the speculative sciences must be distinguished.
[pars 3 q. 5 a. 1 co. 2] Yet it must be known that when habits or powers are distinguished according to their objects, they are not distinguished according to just any differences of objects, but according to those that belong per se to the objects insofar as they are objects. For to be an animal or a plant is accidental to a sensible thing insofar as it is sensible, and therefore the distinction of the senses is not taken from this, but rather from the difference of color and sound. Consequently, the speculative sciences must be divided through differences of speculative objects insofar as they are objects of speculation. Now to a speculative object, which is the object of a speculative power, something belongs on the side of the intellective power and something on the side of the habit of science whereby the intellect is perfected. On the side of the intellect, indeed, it belongs to it that it be immaterial, because the intellect itself is also immaterial; while on the side of science it belongs to it that it be necessary, because science is of necessary things, as is proved in Book I of the Posterior Analytics. Now everything necessary, insofar as it is such, is immobile; because everything that is moved, insofar as it is such, is capable of being and not being, either simply or in a certain respect, as is said in Book IX of the Metaphysics. Thus, therefore, separation from matter and motion, or application to them, belongs per se to the speculative object, which is the object of speculative science. And therefore the speculative sciences are distinguished according to the order of removal from matter and motion.
[pars 3 q. 5 a. 1 co. 3] Some speculative objects, therefore, are such that they depend on matter according to being, because they can exist only in matter. And these are subdivided: for some depend on matter both according to being and according to understanding, such as those in whose definition \ sensible matter is posited; hence they cannot be understood without sensible matter, just as in the definition of man it is necessary to include flesh and bones. And of these treats physics, or natural science. Others, however, are such that, although they depend on matter according to being, they do not depend on it according to understanding, because sensible matter is not posited in their definitions, such as line and number. And of these treats mathematics. Still other speculative objects are such that they do not depend on matter according to being, because they can exist without matter—whether they never exist in matter, such as God and an angel, or in some instances exist in matter and in others do not, such as substance, quality, being, potency, act, the one and the many, and things of this kind. Concerning all of these treats theology, that is, divine science, because foremost among the things known in it is God; by another name it is called metaphysics, that is, beyond physics, because it presents itself to be learned by us after physics, since we must arrive at insensible things from sensible ones. It is also called first philosophy, insofar as all the other sciences, receiving their principles from it, follow after it. Now it is not possible that there should be any things that depend on matter according to understanding and not according to being, because the intellect, considered in itself, is immaterial. And therefore there is no fourth genus of philosophy besides the aforesaid.
[pars 3 q. 5 a. 1 ad 1] To the first objection, therefore, it must be said that the Philosopher in Book VI of the Ethics determines concerning intellectual habits insofar as they are intellectual virtues. Now they are called virtues insofar as they perfect us in their operation, for virtue is that which makes its possessor good and renders his work good; and therefore according as the soul is variously perfected by speculative habits of this sort, he diversifies virtues of this kind. For there is one mode whereby the speculative part of the soul is perfected by understanding, which is the habit of principles, through which certain things become known of themselves, and another mode whereby conclusions demonstrated from principles of this sort are known—whether the demonstration proceeds from lower causes, as in science, or from the highest causes, as in wisdom. When, however, sciences are distinguished insofar as they are certain habits, they must be distinguished according to their objects, that is, according to the things concerning which the sciences treat. And it is thus that both here and in Book VI of the Metaphysics the three parts of speculative philosophy are distinguished.
[pars 3 q. 5 a. 1 ad 2] To the second it must be said that the speculative sciences, as is evident at the beginning of the Metaphysics, treat of those things whose knowledge is sought for their own sake. Now the things of which logic treats are not sought to be known for their own sake, but as a certain aid to the other sciences. And therefore logic is not contained under speculative philosophy as a principal part, but as something reduced to speculative philosophy, insofar as it furnishes speculation with its instruments—namely syllogisms, definitions, and other things of this kind, which we need in the speculative sciences. Hence according to \ Boethius in his Commentary on Porphyry, it is not so much a science as an instrument of science.
[pars 3 q. 5 a. 1 ad 3] To the third it must be said that the seven liberal arts do not sufficiently divide theoretical philosophy; rather, as Hugh of Saint Victor says in Book III of his Didascalicon, passing over certain others, seven are enumerated together because those who wished to learn philosophy were first instructed in these, and therefore they are distinguished into the trivium and the quadrivium, inasmuch as by these, as by certain pathways, the lively mind may enter into the secrets of philosophy. And this also accords with the words of the Philosopher, who says in Book II of the Metaphysics that the mode of science ought to be sought before the sciences; and the Commentator says in the same place that someone ought to learn logic, which teaches the mode of all the sciences, before all the other sciences, and to logic pertains the trivium. He also says in Book VI of the Ethics that mathematics can be known by boys, whereas physics cannot, since it requires experience. And thus we are given to understand that directly after logic mathematics ought to be learned, to which pertains the quadrivium; and so by these, as by certain pathways, the mind is prepared for the other philosophical disciplines. Or else these among the other sciences are called arts because they possess not only knowledge, but a certain work that belongs immediately to reason itself, such as constructing a syllogism or forming a discourse, numbering, measuring, forming melodies, and computing the courses of the stars. Other sciences, by contrast, either have no work, but knowledge alone, such as divine and natural science—whence they cannot bear the name of art, since art is called productive reason, as is said in Book VI of the Metaphysics—or they have a bodily work, such as medicine, alchemy, and others of this kind. Hence they cannot be called liberal arts, because acts of this sort belong to man on that side wherein he is not free, namely on the side of the body. Moral science, however, although it is for the sake of operation, nevertheless that operation is not the act of science, but rather of virtue, as is evident in the Ethics. Hence it cannot be called an art, but rather in those operations virtue takes the place of art. And therefore the ancients defined virtue as the art of living well and rightly, as Augustine says in Book IV of The City of God.
[pars 3 q. 5 a. 1 ad 4] To the fourth it must be said that, as \ Avicenna says at the beginning of his Medicine, the theoretical and the practical are distinguished in one way when philosophy is divided into theoretical and practical, in another way when the arts are divided into theoretical and practical, and in another way when medicine is so divided. For when philosophy, or even the arts, are distinguished by theoretical and practical, their distinction must be taken from the end, so that that is called theoretical which is ordered solely to the knowledge of truth, whereas that is called practical which is ordered to operation. Yet there is this difference when the whole of philosophy and when the arts are divided in this way: that in the division of philosophy regard is had to the end of beatitude, toward which the whole of human life is ordered. For as Augustine says in Book XX of The City of God from the words of Varro, man has no other reason for philosophizing except that he may be happy. Hence, since a twofold happiness is posited by the philosophers, one contemplative and the other active, as is evident in Book X of the Ethics, in accordance with this they also distinguished two parts of philosophy, calling moral philosophy practical, and calling natural and rational philosophy theoretical. When, however, certain arts are said to be speculative and others practical, regard is had to certain special ends of those arts, as if we should say that agriculture is a practical art, whereas dialectic is a theoretical one. When, on the other hand, medicine is divided into theoretical and practical, the division is not taken according to the end; for in that way the whole of medicine is contained under practical knowledge, inasmuch as it is ordered to operation. Rather, the aforesaid division is taken according as the things treated in medicine are proximate to, or remote from, operation. For that part of medicine is called practical which teaches the manner of operating for healing, as that such and such remedies are to be applied to such and such abscesses; whereas that part is called theoretical which teaches the principles by which a man is directed in operation, though not proximately, such as that the vital powers are three and that the genera of fevers are so many. Hence it is not necessary that, if some part of an active science is called theoretical, that part should on that account be placed under speculative philosophy.
[pars 3 q. 5 a. 1 ad 5] To the fifth it must be said that one science is contained under another in two ways. In one way, as a part of it, namely because its subject is a certain part of the subject of the other, just as a plant is a certain part of natural body; hence the science of plants is also contained under natural science as a part. In another way, one science is contained under another as subalternated to it, namely when in the higher science the propter quid is assigned for those things of which only the quia is known in the lower science, just as music is placed under arithmetic. Medicine, therefore, is not placed under physics as a part. For the subject of medicine is not a part of the subject of natural science under that precise aspect whereby it is the subject of medicine. For although the healable body is a natural body, nevertheless it is not the subject of medicine insofar as it is healable by nature, but insofar as it is healable by art. Yet because in healing that is also effected through art, art is the minister of nature—since health is brought to completion out of some natural power with the help of art—it follows that the propter quid regarding the operation of art must be taken from the properties of natural things. And on account of this, medicine is subalternated to physics, and for the same reason alchemy, the science of agriculture, and all things of this kind. And thus it remains that physics in itself and in all its parts is speculative, even though certain operative sciences are subalternated to it.
[pars 3 q. 5 a. 1 ad 6] To the sixth it must be said that although the subjects of the other sciences are parts of being, which is the subject of metaphysics, nevertheless the other sciences need not be parts of metaphysics. For each of the sciences takes one part of being according to a special mode of considering, distinct from the mode in which being is considered in metaphysics. Hence, properly speaking, its subject is not a part of the subject of metaphysics; for it is not a part of being according to that intelligible aspect whereby being is the subject of metaphysics, but when considered under this special aspect it is itself a special science shared in division alongside the others. On the other hand, the science that treats of potency, or of act, or of the one, or of anything of this sort could in this sense be called a part of metaphysics, because these possess the same mode of considering as being, which is treated in metaphysics.
[pars 3 q. 5 a. 1 ad 7] To the seventh it must be said that those parts of being demand the same mode of treatment as common being, because they too do not depend on matter; and therefore the science treating of them is not distinguished from the science that treats of common being.
[pars 3 q. 5 a. 1 ad 8] To the eighth it must be said that the other diversities of things upon which the objection touches are not per se differences of those things insofar as they are knowable; and therefore the sciences are not distinguished according to them.
[pars 3 q. 5 a. 1 ad 9] To the ninth it must be said that although divine science is by nature the first of all sciences, nevertheless with respect to us other sciences are prior. For as Avicenna says at the beginning of his Metaphysics, the order of this science is that it should be learned after the natural sciences, in which many things are determined that this science employs, such as generation, corruption, motion, and others of this kind. Similarly, it is learned after the mathematical sciences. For this science needs, for the knowledge of separate substances, to know the number and order of the celestial spheres, which is not possible without astronomy, for which the whole of mathematics is presupposed. Other sciences, such as music, moral sciences, and the like, contribute to its well-being. Nor, however, need there be a circle because metaphysics presupposes things proved in the other sciences while itself proving the principles of the others. For the principles that another science, namely natural science, receives from first philosophy do not prove the things that the first philosopher in turn receives from the natural philosopher; rather, those things are proved through other self-evident principles. And similarly, the first philosopher does not prove the principles that he hands over to the natural philosopher through principles received from him, but through other self-evident principles; and thus there is no circle in definition. Moreover, the sensible effects from which natural demonstrations proceed are better known with respect to us at the outset; but when through them we have arrived at the knowledge of first causes, from these latter there will become manifest to us the propter quid of those effects from which the causes were proved by a demonstration quia. And in this way natural science also contributes something to divine science, and yet through divine science its own principles are made known. And hence it is that Boethius places divine science last, because it is last with respect to us.
[pars 3 q. 5 a. 1 ad 10] To the tenth it must be said that although natural science presents itself to be learned after mathematics, inasmuch as its universal teachings require experience and time, nevertheless natural things, being sensible, are naturally more known than mathematical things abstracted from sensible matter.
Question V, Article 2 — Whether Natural Philosophy Treats of What Exists in Motion and Matter¶
Latin Locus: q. 5, a. 2 · Commentary: Notes on q. 5, a. 2
[pars 3 q. 5 a. 2 arg. 1] We proceed thus to the second article. It seems that natural science does not treat of those things that exist in motion and matter. For matter is the principle of individuation. Now no science treats of individuals, but of universals alone, according to the judgment of \ Plato set down in Porphyry. Therefore natural science does not treat of those things that exist in matter.
[pars 3 q. 5 a. 2 arg. 2] Furthermore, science pertains to the intellect. Now the intellect knows by abstracting from matter and from the conditions of matter. Therefore no science can treat of those things that are not abstracted from matter.
[pars 3 q. 5 a. 2 arg. 3] Furthermore, in natural science the first mover is treated, as is evident in Book VIII of the Physics. Yet he is immune from all matter. Therefore natural science does not treat solely of those things that exist in matter.
[pars 3 q. 5 a. 2 arg. 4] Furthermore, every science treats of necessary things. Yet everything that is moved, insofar as it is such, is contingent, as is proved in Book IX of the Metaphysics. Therefore no science can treat of mobile things, and consequently neither can natural science.
[pars 3 q. 5 a. 2 arg. 5] Furthermore, no universal is moved; for universal man is not healed, but this man, as is said at the beginning of the Metaphysics. Yet every science treats of universals. Therefore natural science does not treat of those things that exist in motion.
[pars 3 q. 5 a. 2 arg. 6] Furthermore, in natural science determinations are made concerning certain things that are not moved, such as the soul, as is proved in Book I of On the Soul, and the earth, as is proved in Book II of On the Heavens; moreover, all natural forms neither come to be nor are corrupted, and for the same reason are not moved except per accidens, as is proved in Book VII of the Metaphysics. Therefore not all the things of which physics treats exist in motion.
[pars 3 q. 5 a. 2 arg. 7] Furthermore, every creature is mutable, since true immutability belongs to God alone, as \ Augustine says. If, therefore, the consideration of things that exist in motion pertains to the natural philosopher, it will belong to him to consider all creatures, which appears manifestly false.
[pars 3 q. 5 a. 2 s. c. 1] On the contrary, it pertains to natural science to determine concerning natural things. Now natural things are those in which there is a principle of motion. Yet wherever there is motion, there must also be matter, as is said in Book IX of the Metaphysics. Therefore natural science treats of those things that exist in motion and matter.
[pars 3 q. 5 a. 2 s. c. 2] Furthermore, concerning those things that exist in matter and motion there must be some speculative science; otherwise the delivery of philosophy, which is the knowledge of being, would not be complete. Yet no other speculative science treats of these, since neither mathematics nor metaphysics does so. Therefore natural science treats of them.
[pars 3 q. 5 a. 2 s. c. 3] Furthermore, this is evident from what the Philosopher says in Book VI of the Metaphysics and in Book II of the Physics.
[pars 3 q. 5 a. 2 co. 1] I answer that on account of the difficulty of this question Plato was compelled to posit Ideas. For since, as the Philosopher says in Book I of the Metaphysics, he believed that all sensible things are continually in flux, in accordance with the opinion of Cratylus and Heraclitus, and consequently supposed that there could be no science of them, he posited certain substances separated from sensible things, concerning which there might be sciences and definitions might be given. Yet this failure arose from the fact that he did not distinguish what is per se from what is per accidens; for even the wise are frequently deceived according to what is accidental, as is said in Book I of On Sophistical Refutations. Now as is proved in Book VII of the Metaphysics, since in a sensible substance there are found both the whole itself, that is, the composite, and its intelligible nature, that is, its form, it is indeed the composite that is generated and corrupted per se, whereas the intelligible nature or form is not generated or corrupted per se, but only per accidens. For what comes to be is not to-be-a-house, as is said in the same place, but this house. Now each thing can be considered apart from all those things that are not related to it per se. Consequently, the forms and intelligible natures of things—even of things existing in motion—are without motion insofar as they are considered in themselves. And thus there are sciences and definitions of them, as the Philosopher says in the same place. Nor are the sciences of sensible substances founded upon the knowledge of certain substances separated from sensible things, as is proved there.
[pars 3 q. 5 a. 2 co. 2] Now intelligible natures of this sort, which the sciences treating of things consider, are considered without motion. Hence they must be considered apart from those conditions according to which motion belongs to mobile things. Now since every motion is measured by time, and the primary motion is local motion—upon the removal of which no other motion is present—something must be mobile insofar as it exists here and now. Yet this follows upon the mobile thing itself insofar as it is individuated by matter existing under designated dimensions. Hence intelligible natures of this sort, according to which there can be sciences of mobile things, must be considered without \ designated matter and without all the conditions consequent upon designated matter, yet not without undesignated matter, because upon the notion of such matter depends the notion of the form that determines matter for itself. Accordingly, the intelligible nature of man, which the definition signifies and according to which science proceeds, is considered without this flesh and without these bones, yet not without flesh and bones unconditionally. And because singulars include designated matter in their intelligible nature, whereas universals include common matter, as is said in Book VII of the Metaphysics, the aforesaid abstraction is not called the \ abstraction of form from matter unconditionally, but the abstraction of the universal from the particular.
[pars 3 q. 5 a. 2 co. 3] Intelligible natures of this sort, thus abstracted, can therefore be considered in two ways. In one way, in themselves, and thus they are considered without motion and designated matter; and this belongs to them only according to the being that they have in the intellect. In another way, insofar as they are compared to the things of which they are the intelligible natures, which things indeed exist in matter and motion; and thus they are principles of knowing those things, because every thing is known through its form. And consequently, through intelligible natures of this sort, immobile and considered without particular matter, knowledge is had in natural science of mobile and material things existing outside the soul.
[pars 3 q. 5 a. 2 ad 1] To the first objection, therefore, it must be said that matter is not the principle of individuation except insofar as it exists under designated dimensions. And in this respect natural science also abstracts from matter.
[pars 3 q. 5 a. 2 ad 2] To the second it must be said that the intelligible form is the \ quiddity of a thing; for the object of the intellect is what a thing is, as is said in Book III of On the Soul. Now the quiddity of a universal composite, such as man or animal, includes within itself universal matter, though not particular matter, as is said in Book VII of the Metaphysics. Hence the intellect universally abstracts from designated matter and its conditions, yet in natural science it does not abstract from common matter—even though in natural science too matter is considered only in relation to form. Hence form pertains more primarily to the consideration of the natural philosopher than matter does.
[pars 3 q. 5 a. 2 ad 3] To the third it must be said that the first mover is not treated in natural science as its subject or as a part of its subject, but as the term to which natural science leads. Now a term does not belong to the nature of the thing of which it is the term, yet it has a certain relation to that thing: just as the endpoint of a line is not a line, yet has a certain relation to it, so too the first mover is of a different nature from natural things, yet has a certain relation to them insofar as he imparts motion to them; and thus he falls under the consideration of the natural philosopher—not according to what he is in himself, namely, but insofar as he is a mover.
[pars 3 q. 5 a. 2 ad 4] To the fourth it must be said that science treats of something in two ways. In one way, primarily and principally, and thus science treats of the universal intelligible natures upon which it is founded. In another way, it treats of certain things secondarily and as it were by a certain reflection, and thus it treats of those things to which those intelligible natures belong, insofar as it applies those intelligible natures also to the particular things to which they belong, with the aid of the lower powers. For the knower uses the universal intelligible nature both as a thing known and as a medium of knowing; for through the universal nature of man I am able to judge concerning this man or that. Now the universal intelligible natures of things are all immobile, and therefore in this respect every science treats of necessary things. Yet among the things to which those intelligible natures belong, some are necessary and immobile, while others are contingent and mobile; and in this respect sciences are said to treat of contingent and mobile things.
[pars 3 q. 5 a. 2 ad 5] To the fifth it must be said that although the universal is not moved, it is nevertheless the intelligible nature of a mobile thing.
[pars 3 q. 5 a. 2 ad 6] To the sixth it must be said that the soul and other natural forms, although they are not moved per se, are nevertheless moved per accidens, and moreover they are perfections of mobile things, and in this respect they fall under the consideration of the natural philosopher. As for the earth, although as a whole it is not moved—which belongs to it insofar as it exists in its natural place, wherein a thing rests by the very same nature whereby it is moved toward that place—nevertheless its parts are moved toward their place whenever they are outside their proper place. And thus the earth falls under the consideration of the natural philosopher by reason both of the rest of the whole and of the motion of its parts.
[pars 3 q. 5 a. 2 ad 7] To the seventh it must be said that the mutability that belongs to every creature is not according to some natural motion, but according to dependence upon God—separated from whom, if creatures were left to themselves, they would fall away from what they are. Now this dependence pertains to the consideration of the metaphysician rather than of the natural philosopher. Moreover, spiritual creatures are mutable only according to choice, and such mutation does not pertain to the natural philosopher, but rather to the divine philosopher.
Question V, Article 3 — Whether Mathematical Consideration Is Without Motion and Matter Concerning Things That Exist in Matter (On Intelligible Matter)¶
Latin Locus: q. 5, a. 3 · Commentary: Notes on q. 5, a. 3
[pars 3 q. 5 a. 3 arg. 1] We proceed thus to the third article. It seems that mathematical consideration is not without matter concerning things that have their being in matter. For since truth consists in the adequation of thing and intellect, there must be falsehood whenever a thing is considered otherwise than it is. If, therefore, mathematics considers without matter things that exist in matter, its consideration will be false; and consequently it will not be a science, since every science is of true things.
[pars 3 q. 5 a. 3 arg. 2] Furthermore, according to the Philosopher in Book I of the Posterior Analytics, it belongs to every science to consider its subject and the parts of its subject. Now matter is a part of all things that are material in being. Therefore it cannot be that any science considers things existing in matter without considering matter.
[pars 3 q. 5 a. 3 arg. 3] Furthermore, all straight lines belong to the same species. Yet the mathematician considers straight lines by numbering them; otherwise he would not consider the triangle and the square. Therefore he considers lines insofar as they differ in number while agreeing in species. Now the principle whereby things agreeing in species differ from one another is matter, as is evident from what was said above. Therefore matter is considered by the mathematician.
[pars 3 q. 5 a. 3 arg. 4] Furthermore, no science that wholly abstracts from matter demonstrates through the material cause. Yet in mathematics certain demonstrations are made that cannot be reduced to anything other than the material cause, as when something is demonstrated of a whole from its parts. For parts are the matter of the whole, as is said in Book II of the Physics. Hence in Book II of the Posterior Analytics the demonstration whereby it is proved that the angle in a semicircle is a right angle, from the fact that each of its two parts is half a right angle, is reduced to the material cause. Therefore mathematics does not wholly abstract from matter.
[pars 3 q. 5 a. 3 arg. 5] Furthermore, motion cannot exist without matter. Yet the mathematician ought to consider motion; for since motion is measured according to space, it seems to belong to the same intelligible account and science to consider the quantity of space, which pertains to the mathematician, and the quantity of motion. Therefore the mathematician does not altogether set aside the consideration of matter.
[pars 3 q. 5 a. 3 arg. 6] Furthermore, astronomy is a certain part of mathematics, and likewise the science of the moving sphere, the science of weights, and music, in all of which consideration is given to motion and mobile things. Therefore mathematics does not totally abstract from matter and motion.
[pars 3 q. 5 a. 3 arg. 7] Furthermore, natural consideration is wholly concerned with matter and motion. Yet certain conclusions are demonstrated in common by the mathematician and the natural philosopher, such as whether the earth is round and whether it is in the middle of the heaven. Therefore it cannot be that mathematics wholly abstracts from matter. And if it should be said that it abstracts only from \ sensible matter, on the contrary: sensible matter seems to be particular matter, because sense is of particulars, and from this all sciences abstract. Therefore mathematical consideration ought not to be called more abstract than any of the other sciences.
[pars 3 q. 5 a. 3 arg. 8] Furthermore, the Philosopher in Book II of the Physics says that there are three inquiries: the first concerns the mobile and corruptible, the second the mobile and incorruptible, and the third the immobile and incorruptible. Now the first is natural, the third divine, and the second mathematical, as \ Ptolemy expounds at the beginning of the Almagest. Therefore mathematics treats of mobile things.
[pars 3 q. 5 a. 3 s. c. 1] On the contrary is what the Philosopher says in Book VI of the Metaphysics.
[pars 3 q. 5 a. 3 s. c. 2] Furthermore, there are certain things which, although they exist in matter, nevertheless do not admit matter into their definition, such as the curved, and in this it differs from the snub. Now philosophy ought to consider all beings. Therefore some part of philosophy must treat of things of this sort; and this is mathematics, since it pertains to no other part.
[pars 3 q. 5 a. 3 s. c. 3] Furthermore, those things that are prior according to understanding can be considered without those that are posterior. Now mathematical objects are prior to natural things, which exist in matter and motion; for natural things stand by way of addition to mathematical objects, as is said in Book III of On the Heavens. Therefore mathematical consideration can be without matter and motion.
[pars 3 q. 5 a. 3 co. 1] I answer that for the clarification of this question we must see how the intellect is able to abstract according to its operation. It must therefore be known that, according to the Philosopher in Book III of On the Soul, the operation of the intellect is twofold. One is called the understanding of indivisibles, whereby it knows concerning each thing what it is. The other is that whereby it composes and divides, namely by forming an affirmative or negative enunciation. And indeed these two operations correspond to two principles found in things. The first operation looks to the very nature of a thing, in virtue of which the thing understood holds a certain rank among beings, whether it be a complete thing, such as some whole, or an incomplete thing, such as a part or an accident. The second operation, however, looks to the very act of being of the thing, which results from the union of the principles of a thing in composites, or accompanies the simple nature itself of the thing, as in simple substances. And because the truth of the intellect arises from its conformity to the thing, it is evident that according to this second operation the intellect cannot truly abstract what is conjoined in reality, because in abstracting there would be signified a separation with respect to the very being of the thing—just as, if I abstract man from whiteness by saying, “Man is not white,” I signify that there is a separation in reality. Hence if in reality man and whiteness are not separated, the intellect will be false. By this operation, therefore, the intellect can truly abstract only those things that are separated in reality, as when one says, “Man is not an ass.” According to the first operation, however, it can abstract things that are not separated in reality—yet not all of them, but some. For since each thing is intelligible insofar as it is in act, as is said in Book IX of the Metaphysics, the nature itself or \ quiddity of a thing must be understood: either insofar as it is a certain act, as happens with forms themselves and simple substances; or through that which is its act, as composite substances are understood through their forms; or through that which stands to it in the place of act, as prime matter is understood through its relation to form and the void through the privation of a located body. And this is that from which each nature receives its intelligible account. Whenever, therefore, with respect to that whereby the intelligible account of a nature is constituted and through which the nature itself is understood, the nature itself bears an order to and dependence upon something else, then it is manifest that that nature cannot be understood without that other thing: whether they are conjoined by that conjunction whereby a part is conjoined to a whole—as a foot cannot be understood without the understanding of animal, because that from which a foot has the character of a foot depends upon that whereby an animal is an animal; or whether they are conjoined in the manner in which form is conjoined to matter, or one co-part to another, or an accident to its subject—as the snub cannot be understood without nose; or even whether they are separated in reality—as father cannot be understood without the understanding of son, even though these relations are found in diverse things. If, however, one thing does not depend upon the other with respect to what constitutes the intelligible account of its nature, then the one can be abstracted from the other by the intellect so as to be understood without it—not only if they are separated in reality, such as man and stone, but even if they are conjoined in reality: whether by that conjunction whereby part and whole are conjoined, just as a letter can be understood without a syllable, though not conversely, and an animal without a foot, though not conversely; or even if they are conjoined in the manner in which form is conjoined to matter and an accident to its subject, just as whiteness can be understood without man, and conversely.
[pars 3 q. 5 a. 3 co. 2] Thus, therefore, the intellect distinguishes one thing from another differently according to its diverse operations: for according to the operation whereby it composes and divides, it distinguishes one thing from another through understanding that the one does not exist in the other. In the operation whereby it understands what each thing is, however, it distinguishes one from another while understanding what this thing is without understanding anything about the other—neither that it exists with it, nor that it is separated from it. Hence that latter distinction does not properly bear the name of separation, which belongs only to the former. Rather, this distinction is rightly called abstraction, yet only when the things of which one is understood without the other exist together in reality; for animal is not said to be abstracted from stone if animal is understood apart from the understanding of stone. Consequently, since abstraction, properly speaking, can occur only with things conjoined in being, corresponding to the two aforesaid modes of conjunction—namely that whereby part and whole are united, or form and matter—abstraction is twofold: one whereby form is abstracted from matter, and the other whereby a whole is abstracted from its parts. Now that form can be abstracted from some matter whose essential notion does not depend upon such matter; whereas from that matter upon which it does depend according to its essential notion, a form cannot be abstracted by the intellect. Accordingly, since all accidents stand to their underlying substance as form to matter, and the notion of every accident depends upon substance, it is impossible for any such form to be separated from substance. Yet accidents supervene upon substance in a certain order: for first quantity comes to it, next quality, and after that passions and motion. Hence quantity can be understood in the underlying substance before sensible qualities—from which matter is called sensible matter—are understood in it. And thus, according to the notion of its substance, quantity does not depend upon sensible matter, but solely upon \ intelligible matter. For substance, once accidents have been removed, remains comprehensible by the intellect alone, inasmuch as the sensitive powers do not reach to the comprehension of substance. And of abstracts of this kind treats mathematics, which considers quantities and the properties consequent upon quantities, such as figures and things of this sort.
[pars 3 q. 5 a. 3 co. 3] Nor can a whole be abstracted from just any parts whatsoever. For there are certain parts upon which the intelligible account of the whole depends, namely when to be such a whole consists precisely in being composed out of such parts, as a syllable stands to letters and a mixed body to the elements; and such parts are called parts of the species and of the form, without which the whole cannot be understood, since they are posited in its definition. Certain other parts, however, are accidental to the whole insofar as it is such, as a semicircle stands to a circle. For it is accidental to a circle that two equal or unequal parts of it, or even more, should be taken by division; whereas it is not accidental to a triangle that three lines be designated in it, because by that very fact a triangle is a triangle. In like manner, it belongs per se to man that there be found in him a rational soul and a body composed of the four elements; hence man cannot be understood without these parts, and they must be posited in his definition, so that they are parts of the species and form. Yet finger, foot, hand, and other parts of this kind are posterior to the understanding of man, whence the essential notion of man does not depend upon them, and man can be understood without them. For whether he has feet or not, so long as he is posited as conjoined out of a rational soul and a body mixed from the elements in the proper mixture that such a form requires, he will be a man. And these parts are called parts of matter, which are not posited in the definition of the whole, but rather conversely. And it is in this way that all designated parts stand to man, such as this soul and this body and this nail and this bone and things of this kind. For these parts are indeed parts of the essence of Socrates and of \ Plato, yet not of man insofar as he is man; and therefore man can be abstracted by the intellect from these parts, and such abstraction is that of the universal from the particular.
[pars 3 q. 5 a. 3 co. 4] And thus there are two abstractions of the intellect. One corresponds to the union of form and matter, or of accident and subject, and 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, which is the \ abstraction of the whole, wherein some nature is considered unconditionally according to its essential notion, apart from all parts that are not parts of the species, but accidental parts. Conversely, no abstractions opposite to these are found, whereby a part would be abstracted from a whole or matter from form: because a part either cannot be abstracted from the whole by the intellect—if it is one of the parts of matter, into whose definition the whole is placed—or else can even exist without the whole—if it is one of the parts of the species, as a line can exist without a triangle, a letter without a syllable, or an element without a mixed body. Now among things that can be divided in being, separation has place rather than abstraction. Similarly, when we say that form is abstracted from matter, this is not understood of substantial form, because substantial form and the matter corresponding to it depend mutually upon one another, so that the one cannot be understood without the other, inasmuch as a proper act comes to be in its proper matter. Rather, it is understood of the accidental form that is quantity and figure, from which indeed sensible matter cannot be abstracted by the intellect, since sensible qualities cannot be understood unless quantity is presupposed in understanding—as is evident with surface and color—nor can anything be understood to be the subject of motion that is not understood as quantified. Substance, however, which is the intelligible matter of quantity, can exist without quantity; hence to consider substance without quantity pertains rather to the genus of separation than to that of abstraction.
[pars 3 q. 5 a. 3 co. 5] Thus, therefore, a threefold distinction is found in the operation of the intellect. One is according to the operation of the intellect composing and dividing, which is properly called separation; and this belongs to divine science or metaphysics. The second is according to the operation whereby the quiddities of things are formed, which is the abstraction of form from sensible matter; and this belongs to mathematics. The third, according to the same operation, is the abstraction of the universal from the particular; and this belongs also to physics and is common to all the sciences, because in every science what is per accidens is set aside and what is per se is taken. And because certain thinkers did not understand the difference between the last two and the first, they fell into error, so as to posit mathematical objects and universals as separated from sensible things, as did the Pythagoreans and the Platonists.
[pars 3 q. 5 a. 3 ad 1] To the first objection, therefore, it must be said that the mathematician who abstracts does not consider a thing otherwise than it is. For he does not understand a line to exist without sensible matter; rather, he considers the line and its proper attributes without considering sensible matter. And thus there is no dissonance between intellect and thing, because even in reality what belongs to the nature of a line does not depend upon that which makes matter to be sensible, but rather conversely. And so it is evident that there is no falsehood in those who abstract, as is said in Book II of the Physics.
[pars 3 q. 5 a. 3 ad 2] To the second it must be said that “material” is predicated not only of that of which matter is a part, but also of that which has its being in matter; and in this way a sensible line can be called something material. Hence this does not prevent a line from being understood without matter. For sensible matter does not stand to a line as a part, but rather as the subject in which it has being; and the same holds for surface and body. For the mathematician does not consider body that is in the genus of substance, insofar as matter and form are its parts, but body insofar as it is in the genus of quantity, perfected by three dimensions; and as such it stands to body in the genus of substance—of which physical matter is a part—as an accident to its subject.
[pars 3 q. 5 a. 3 ad 3] To the third it must be said that matter is not the principle of numerical diversity except insofar as, being divided into many parts and receiving in each part a form of the same intelligible character, it constitutes several individuals of the same species. Now matter cannot be divided except on the presupposition of quantity, upon the removal of which every substance remains indivisible; and thus the primary ground of diversifying things that belong to one species lies in quantity. And this indeed belongs to quantity insofar as it possesses position as it were as a constitutive difference within its own notion, and position is nothing other than the order of parts. Hence even when quantity has been abstracted from sensible matter by the intellect, it still remains possible to imagine numerically diverse things of one species, such as several equilateral triangles and several equal straight lines.
[pars 3 q. 5 a. 3 ad 4] To the fourth it must be said that mathematical objects are not abstracted from every kind of matter, but solely from sensible matter. Now the parts of quantity, from which a demonstration taken in a certain manner from the material cause seems to be drawn, are not sensible matter, but pertain to intelligible matter, which is indeed found in mathematical objects, as is evident in Book VII of the Metaphysics.
[pars 3 q. 5 a. 3 ad 5] To the fifth it must be said that motion, according to its own nature, does not belong to the genus of quantity, though it participates somewhat in the nature of quantity from elsewhere, insofar as the division of motion is taken either from the division of space or from the division of the mobile thing. Consequently, to consider motion does not pertain to the mathematician, although mathematical principles can be applied to motion. Accordingly, insofar as the principles of quantity are applied to motion, the natural philosopher considers the division and continuity of motion, as is evident in Book VI of the Physics; while the measures of motions are treated in the sciences intermediate between mathematics and natural science, such as in the science of the moving sphere and in astronomy.
[pars 3 q. 5 a. 3 ad 6] To the sixth it must be said that in composite things simple things and their properties are preserved, though in another mode, just as the proper qualities of the elements and their proper motions are found in a mixed body; whereas what is proper to composites is not found in simple things. And hence it is that the more abstract a science is and the simpler the objects it considers, the more applicable its principles are to the other sciences. Consequently, the principles of mathematics are applicable to natural things, though not conversely, on account of which physics proceeds from the supposition of mathematics, and not conversely, as is evident in Book III of On the Heavens. And from this it follows that three orders of sciences are found concerning natural and mathematical things. Some are purely natural, considering the properties of natural things insofar as they are such, like physics, agriculture, and the like. Others are purely mathematical, determining concerning quantities unconditionally, as geometry treats of magnitude and arithmetic of number. Still others are intermediate sciences, which apply mathematical principles to natural things, such as music, astronomy, and the like. Yet these are more akin to mathematical sciences, because in their consideration what is physical is as it were material, whereas what is mathematical is as it were formal; just as music considers sounds, not insofar as they are sounds, but insofar as they are proportioned according to numbers, and the same holds in the others. On account of this, they demonstrate their conclusions concerning natural things, yet through mathematical middle terms; and therefore nothing prevents them from regarding sensible matter insofar as they share with natural science, for insofar as they share with mathematics, they are abstract.
[pars 3 q. 5 a. 3 ad 7] To the seventh it must be said that because the intermediate sciences, of which we have spoken, share with natural science in respect of what is material in their consideration, while differing from it in respect of what is formal in their consideration, nothing prevents these sciences from occasionally having the same conclusions as natural science. Nevertheless, they do not demonstrate through the same middle terms, except insofar as the sciences are intermingled and one occasionally uses what belongs to another—just as the natural philosopher proves the roundness of the earth from the motion of heavy bodies, whereas the astronomer proves it through the consideration of lunar eclipses.
[pars 3 q. 5 a. 3 ad 8] To the eighth it must be said that, as the Commentator says in the same place, the Philosopher does not intend there to distinguish the speculative sciences, since the natural philosopher determines concerning every mobile thing, whether corruptible or incorruptible, whereas the mathematician, insofar as he is such, does not consider anything mobile. Rather, he intends to distinguish the things concerning which the speculative sciences determine, which must be treated separately and in order—although those three genera of things can be appropriated to the three sciences. For incorruptible and immobile beings pertain precisely to the metaphysician. Mobile and incorruptible beings, however, on account of their uniformity and regularity, can be determined with respect to their motions through mathematical principles, which cannot be said of corruptible mobile things; and therefore the second genus of beings is attributed to mathematics by reason of astronomy, while the third remains proper to the natural philosopher alone. And it is in this way that Ptolemy speaks.
Question V, Article 4 — Whether Divine Science Treats of What Exists Without Matter and Motion¶
Latin Locus: q. 5, a. 4 · Commentary: Notes on q. 5, a. 4
[pars 3 q. 5 a. 4 arg. 1] We proceed thus to the fourth article. It seems that divine science does not treat of things separated from motion and matter. For divine science seems above all to treat of God. Yet we cannot arrive at the knowledge of God except through visible effects, which are constituted in matter and motion, according to Romans 1: For the invisible things of him, and so forth. Therefore divine science does not abstract from matter and motion.
[pars 3 q. 5 a. 4 arg. 2] Furthermore, that to which motion in some manner belongs is not altogether separated from motion and matter. Yet motion belongs in some manner to God; hence it is said in Wisdom 7 of the Spirit of Wisdom that it is mobile and more mobile than all mobile things. Moreover, \ Augustine says in Book VIII On Genesis that God moves himself without time and place, and \ Plato posited that the first mover moves itself. Therefore divine science, which determines concerning God, is not altogether separated from motion.
[pars 3 q. 5 a. 4 arg. 3] Furthermore, divine science ought to consider not only God, but also angels. Yet angels are moved both according to choice, inasmuch as from being good they became evil, and according to place, as is evident in those who are sent. Therefore the things that divine science considers are not altogether separated from motion.
[pars 3 q. 5 a. 4 arg. 4] Furthermore, as the Commentator seems to say at the beginning of the Physics, everything that exists is either pure matter, or pure form, or a composite of matter and form. Now an angel is not pure form, because then he would be pure act, which belongs to God alone; nor again is he pure matter. Therefore he is composed of matter and form. And consequently divine science does not abstract from matter.
[pars 3 q. 5 a. 4 arg. 5] Furthermore, divine science, which is set down as the third part of speculative philosophy, is the same as metaphysics, whose subject is being, and principally that being which is substance, as is evident in Book IV of the Metaphysics. Now being and substance do not abstract from matter; otherwise no being would be found that possessed matter. Therefore divine science does not abstract from matter.
[pars 3 q. 5 a. 4 arg. 6] Furthermore, according to the Philosopher in Book I of the Posterior Analytics, it pertains to a science to consider not only its subject, but also the parts and proper attributes of its subject. Now being is the subject of divine science, as has been said. Therefore it pertains to it to consider all beings. Yet matter and motion are certain beings. Therefore they pertain to the consideration of metaphysics, and consequently divine science does not abstract from them.
[pars 3 q. 5 a. 4 arg. 7] Furthermore, as the Commentator says in Book I of the Physics, divine science demonstrates through three causes, namely the efficient, the formal, and the final. Yet an efficient cause cannot be considered without considering motion, nor likewise can an end, as is said in Book III of the Metaphysics; hence in mathematical objects, because they are immobile, no demonstration is given through causes of this sort. Therefore divine science does not abstract from motion.
[pars 3 q. 5 a. 4 arg. 8] Furthermore, in theology determinations are made concerning the creation of heaven and earth, the acts of men, and many things of this kind that contain matter and motion within themselves. Therefore theology does not seem to abstract from matter and motion.
[pars 3 q. 5 a. 4 s. c. 1] On the contrary is what the Philosopher says in Book VI of the Metaphysics: that first philosophy is concerned with things separable—namely from matter—and immobile. Now first philosophy is divine science, as is said in the same place. Therefore divine science is abstracted from matter and motion.
[pars 3 q. 5 a. 4 s. c. 2] Furthermore, the noblest science treats of the noblest beings. Now divine science is the noblest science. Since, therefore, immaterial and immobile beings are the noblest, divine science will treat of them.
[pars 3 q. 5 a. 4 s. c. 3] Furthermore, the Philosopher says at the beginning of the Metaphysics that divine science treats of first principles and causes. Now things of this sort are immaterial and immobile. Therefore divine science treats of such things.
[pars 3 q. 5 a. 4 co. 1] I answer that for the clarification of this question we must know which science ought to be called divine science. It must indeed be known that whichever science considers some \ subject-genus must consider the principles of that genus, since science is brought to perfection only through the knowledge of principles, as is evident through the Philosopher at the beginning of the Physics. Yet there are two genera of principles. Some are both complete natures in themselves and nonetheless principles of other things, just as celestial bodies are certain principles of lower bodies and simple bodies are principles of mixed bodies. Consequently, these are considered in the sciences not only insofar as they are principles, but also insofar as they are certain things in themselves; and on account of this they are treated not only in the science that considers the things principled by them, but also have a separate science of their own—just as there is a certain part of natural science treating of celestial bodies distinct from that in which lower bodies are determined, and one treating of the elements distinct from that in which mixed bodies are treated. Other principles, however, are not complete natures in themselves, but are solely principles of natures—such as the unit of number, the point of a line, and the form and matter of a physical body; hence principles of this sort are treated only in the science in which the things principled are treated.
[pars 3 q. 5 a. 4 co. 2] Now just as every determinate genus has certain common principles that extend to all the principles of that genus, so too all beings, insofar as they share in being, have certain principles that are principles of all beings. And according to \ Avicenna in his Sufficientia, these principles can be called common in two ways: in one way by predication, as when I say that “form” is common to all forms because it is predicated of each; in another way by causality, as we say that the sun, which is one in number, is a principle for all generable things. Now there are common principles of all beings not only in the first way—which the Philosopher in Book XI of the Metaphysics expresses by saying that all beings have the same principles according to analogy—but also in the second way, so that there are certain things, numerically the same, existing as principles of all things: namely insofar as the principles of accidents are reduced to the principles of substance, and the principles of corruptible substances are reduced to incorruptible substances, and thus in a certain grade and order all beings are reduced to certain first principles. And because that which is the principle of being to all things must be maximally being, as is said in Book II of the Metaphysics, principles of this sort must be most complete, and therefore must be maximally in act, so as to have nothing or the least possible of potency, since act is prior to and more powerful than potency, as is said in Book IX of the Metaphysics. On account of this, they must exist without matter, which is in potency, and without motion, which is the act of that which exists in potency. And of this sort are divine things: for if the divine exists anywhere, in such a nature—namely immaterial and immobile—it above all exists, as is said in Book VI of the Metaphysics.
[pars 3 q. 5 a. 4 co. 3] Divine things of this sort, therefore, because they are principles of all beings and are nonetheless complete natures in themselves, can be treated in two ways: in one way, insofar as they are common principles of all beings; in another way, insofar as they are certain things in themselves. Yet although first principles of this sort are maximally known in themselves, our intellect nevertheless stands to them as the eye of an owl to the light of the sun, as is said in Book II of the Metaphysics, so that by the light of natural reason we can arrive at them only insofar as we are led to them through their effects. And it was in this way that the philosophers arrived at them, as is evident from Romans 1: The invisible things of God are clearly seen, being understood through the things that are made. Hence divine things of this sort are treated by the philosophers only insofar as they are principles of all things; and therefore they are treated thoroughly in that doctrine wherein are set forth the attributes common to all beings, which has for its subject being insofar as it is being; and among them this science is called divine science. There is, however, another mode of knowing things of this sort: not insofar as they are manifested through effects, but insofar as they manifest themselves. And the Apostle sets forth this mode in 1 Corinthians 2: The things that are of God no one knows except the Spirit of God. Now we have received not the spirit of this world, but the Spirit that is from God, that we may know. And in the same place: To us, however, God has revealed them through his Spirit. And in this mode divine things are treated insofar as they subsist in themselves, and not solely insofar as they are principles of things.
[pars 3 q. 5 a. 4 co. 4] Thus, therefore, theology or divine science is twofold. There is one in which divine things are considered not as the subject of the science, but as the principles of its subject, and such is the theology that the philosophers pursue, which by another name is called metaphysics. There is another, however, which considers divine things themselves for their own sake as the subject of the science, and this is the theology handed down in Sacred Scripture. Both, indeed, treat of things that are separated from matter and motion according to being, yet in diverse ways, according as something can be separated from matter and motion according to being in two ways. In one way, such that it belongs to the very notion of the thing called separated that it can in no way exist in matter and motion, as God and the angels are said to be separated from matter and motion. In another way, such that it does not belong to its notion that it exist in matter and motion, but it can exist without matter and motion, even though it is sometimes found in matter and motion. And in this way being, substance, potency, and act are separated from matter and motion, because they do not depend on matter and motion according to being, as mathematical objects did—which can never exist except in matter, even though they can be understood without \ sensible matter. Philosophical theology, therefore, determines concerning things separated in the second way as its subjects, and concerning things separated in the first way as the principles of its subject. The theology of Sacred Scripture, on the other hand, treats of things separated in the first way as its subjects, although certain things existing in matter and motion are treated in it insofar as the manifestation of divine things requires.
[pars 3 q. 5 a. 4 ad 1] To the first objection, therefore, it must be said that things assumed into a science solely for the manifestation of something else do not pertain per se to that science, but only as it were per accidens. For in this way certain mathematical truths are assumed into natural inquiries; and in this manner nothing prevents certain things existing in matter and motion from being present in divine science.
[pars 3 q. 5 a. 4 ad 2] To the second it must be said that being moved is not attributed to God properly, but as it were metaphorically, and this in two ways. In one way, insofar as the operation of intellect or will is improperly called motion, according to which someone is said to move himself when he understands or loves himself. And in this way the saying of Plato can be verified, who said that the first mover moves itself because, namely, it understands and loves itself, as the Commentator says in Book VIII of the Physics. In another way, insofar as the very efflux of caused things from their causes can be named a procession or a certain motion of the cause into the thing caused, inasmuch as a likeness of the cause is left in the effect itself, and thus the cause, which previously existed in itself, afterward comes to be in the effect through its likeness. And in this way God, who has imparted his likeness to all creatures, is in a certain respect said to move through all things or to proceed toward all things—a manner of speaking that Dionysius frequently employs. And in this way too seems to be understood what is said in Wisdom 7, that wisdom is more mobile than all mobile things, and that she reaches mightily from end to end. Yet this is not being moved properly speaking, and therefore the argument does not follow.
[pars 3 q. 5 a. 4 ad 3] To the third it must be said that divine science received through divine inspiration does not treat of angels as its subject, but solely as things assumed for the manifestation of its subject; for Sacred Scripture treats of angels just as it does of other creatures. In the divine science handed down by the philosophers, however, angels—whom they call Intelligences—are considered under the same aspect as the first cause, which is God, insofar as they too are secondary principles of things, at least through the motion of the spheres, while to the Intelligences themselves no physical motion can belong. Now motion according to choice reduces to that mode wherein the act of intellect or will is called motion, which is an improper expression taking motion for operation. Moreover, the motion whereby they are said to be moved locally is not according to local circumscription, but according to the operation that they exercise in this or that place, or according to some other relation that they bear to place, wholly equivocal with respect to the relation that a located body bears to place. Hence it is evident that motion does not belong to them in the sense in which natural things are said to exist in motion.
[pars 3 q. 5 a. 4 ad 4] To the fourth it must be said that act and potency are more common than matter and form; and therefore in angels, even though composition of form and matter is not found, potency and act can nevertheless be found in them. For matter and form are parts of a composite of matter and form, and consequently composition of matter and form is found only in things whereof one part stands to the other as potency to act. Now what is able to be is also able not to be; hence it is possible for one part to be found both with the other and without the other, and therefore, according to the Commentator in Book I of On the Heavens and Book VIII of the Metaphysics, composition of matter and form is found only in things that are by nature corruptible. Nor is it an obstacle that some accident may be perpetually preserved in some subject, such as figure in the heaven; for a celestial body cannot exist without such figure, and all accidents follow upon substance as upon their cause, so that a subject stands to its accidents not only as passive potency, but also in a certain manner as active potency, and therefore certain accidents are naturally perpetuated in their subjects. Matter, however, is not in this way the cause of form, and therefore every matter underlying some form is also capable of not underlying it, unless perhaps it be restrained by an extrinsic cause—just as we hold that by divine power even certain bodies composed of contraries are incorruptible, such as the bodies of the risen. Now the essence of an angel is by its nature incorruptible, and therefore there is in it no composition of form and matter. Yet because an angel does not have being from himself, he stands in potency to the being that he receives from God, and thus the being received from God stands to his simple essence as act to potency. And this is what is meant by saying that they are composed of that which is and that whereby it is, taking the act of being itself as that whereby it is and the nature of the angel itself as that which is. Even if angels were composed of matter and form, however, they would still not be composed of sensible matter, from which mathematical objects must be abstracted and metaphysical objects separated.
[pars 3 q. 5 a. 4 ad 5] To the fifth it must be said that being and substance are called separated from matter and motion not because it belongs to their notion to exist without matter and motion—in the way it belongs to the notion of an ass to exist without reason—but because it does not belong to their notion to exist in matter and motion, even though they sometimes exist in matter and motion, just as animal abstracts from reason even though some animal is rational.
[pars 3 q. 5 a. 4 ad 6] To the sixth it must be said that the metaphysician also considers individual kinds of beings, not according to their proper notions whereby they are such or such a being, but insofar as they participate in the common notion of being; and in this way matter and motion also pertain to his consideration.
[pars 3 q. 5 a. 4 ad 7] To the seventh it must be said that acting and being acted upon do not belong to beings insofar as they exist in consideration, but insofar as they exist in reality. Now the mathematician considers things that are abstract in consideration alone; hence it does not belong to those things, insofar as they fall under the mathematician’s consideration, to be the principle and end of motion, and therefore the mathematician does not demonstrate through efficient and final causes. The things that the divine philosopher considers, however, exist separated in the nature of things, and are such as can be the principle and end of motion; hence nothing prevents him from demonstrating through efficient and final causes.
[pars 3 q. 5 a. 4 ad 8] To the eighth it must be said that just as faith, which is as it were the habit of the principles of theology, has for its object the First Truth itself, and yet certain other things pertaining to creatures are contained in the articles of faith insofar as they touch upon the First Truth in some way, in the very same manner theology treats principally of God as its subject, while assuming many things concerning creatures as his effects or as bearing a relation to him in any way whatsoever.
Question VI, Article 1 — Whether One Must Proceed Rationally in Natural Things, Disciplinably in Mathematics, and Intellectually in Divine Things¶
Latin Locus: q. 6, a. 1 · Commentary: Notes on q. 6, a. 1
[pars 3 q. 6 pr.] Next we inquire concerning the modes which he attributes to the speculative sciences. And concerning this, four points are asked.
[pars 3 q. 6 pr. 1] First: Whether one must proceed rationally in natural things, disciplinably in mathematical things, and intellectually in divine things.
[pars 3 q. 6 pr. 2] Second: Whether in divine things the imagination must be altogether relinquished.
[pars 3 q. 6 pr. 3] Third: Whether our intellect is able to behold the divine form itself.
[pars 3 q. 6 pr. 4] Fourth: Whether this can come about by way of any speculative science.
[pars 3 q. 6 a. 1 arg. 1] We proceed thus to the first article. It seems that one ought not to proceed rationally in natural things. For rational philosophy is divided over against natural philosophy. Now to proceed rationally seems to pertain properly to rational philosophy. Therefore it is not fittingly attributed to natural philosophy.
[pars 3 q. 6 a. 1 arg. 2] Furthermore, in the Physics the Philosopher frequently distinguishes between rational and physical procedures leading to certain conclusions. Therefore it is not proper to natural science to proceed rationally.
[pars 3 q. 6 a. 1 arg. 3] Furthermore, what is common to all the sciences ought not to be appropriated to one alone. Yet every science proceeds by reasoning, advancing discursively either from effects to causes, or from causes to effects, or from certain signs. Therefore this mode ought not to be appropriated to natural science.
[pars 3 q. 6 a. 1 arg. 4] Furthermore, in Book VI of the Ethics the ratiocinative part of the soul is distinguished by the Philosopher over against the scientific part. Now natural philosophy pertains to the scientific part. Therefore proceeding rationally is not fittingly attributed to it.
[pars 3 q. 6 a. 1 s. c. 1] On the contrary is what is said in the book On Spirit and Soul, namely that reason is concerned with the forms of bodies. Now to consider bodies pertains above all to the natural philosopher. Therefore proceeding rationally is fittingly attributed to him.
[pars 3 q. 6 a. 1 s. c. 2] Furthermore, in Book V of The Consolation of Philosophy \ Boethius says: Reason, when it looks upon something universal, making use of neither imagination nor sense, nevertheless comprehends things imaginable and sensible. Now to comprehend things imaginable and sensible pertains to the natural philosopher alone. Therefore a rational procedure is fittingly attributed to the natural philosopher.
[pars 3 q. 6 a. 1 arg. 11] Further, it seems unfitting to say that mathematics proceeds disciplinably—that is, by way of learning. For discipline seems to be nothing other than the reception of science. Yet in every part of philosophy science is received, since all proceed demonstratively. Therefore to proceed disciplinably is common to all parts of philosophy, and consequently ought not to be appropriated to mathematics.
[pars 3 q. 6 a. 1 arg. 12] Furthermore, the more certain something is, the easier it seems to be for there to be learning concerning it. Now natural things seem to be more certain than mathematical objects, because they are grasped by sense, from which all our cognition takes its origin. Therefore this mode belongs rather to the natural philosopher than to the mathematician.
[pars 3 q. 6 a. 1 arg. 13] Furthermore, as is said in Book V of the Metaphysics, the starting point in the sciences is that from which easier learning comes about. Now the starting point of learning is taken from logic, which must be learned prior to mathematics and to all the other sciences. Therefore the disciplinary mode belongs to logic more than to the other sciences.
[pars 3 q. 6 a. 1 arg. 14] Furthermore, the modes of natural science and of divine science are taken from powers of the soul, namely from reason and intellect. Similarly, therefore, the mode of mathematics ought also to be taken from some power of the soul; and thus its mode is unfittingly set down as proceeding disciplinably.
[pars 3 q. 6 a. 1 s. c. 11] On the contrary, to proceed disciplinably—by way of learning—is to proceed demonstratively and with certitude. Now as \ Ptolemy says at the beginning of the Almagest, the mathematical genus alone, if one devotes diligent inquiry to it, will yield to its students firm and unshakable conviction in knowledge, as through demonstration wrought by indubitable paths. Therefore to proceed disciplinably is most proper to the mathematician.
[pars 3 q. 6 a. 1 s. c. 12] Furthermore, this is evident through the Philosopher, who in many places in his books names the mathematical sciences “disciplines.”
[pars 3 q. 6 a. 1 arg. 21] Further, it seems that proceeding intellectually is not a fitting mode for divine science. For according to the Philosopher, understanding is of principles, whereas science is of conclusions. Yet not all the truths handed down in divine science are principles, since some are also conclusions. Therefore proceeding intellectually is not fitting for divine science.
[pars 3 q. 6 a. 1 arg. 22] Furthermore, in matters that exceed every intellect we cannot proceed intellectually. Yet divine things exceed every intellect, as Dionysius says in Chapter 1 of On the Divine Names and the Philosopher in the Book of Causes. Therefore they cannot be treated intellectually.
[pars 3 q. 6 a. 1 arg. 23] Furthermore, Dionysius says in Chapter 7 of On the Divine Names that angels possess intellectual power insofar as they do not gather divine cognition from sensible things or from divided realities. Yet this is beyond the power of the soul, as is added in the same place. Since, therefore, the divine science now under discussion is a science belonging to the human soul, it seems that its proper mode is not to treat its objects intellectually.
[pars 3 q. 6 a. 1 arg. 24] Furthermore, theology seems chiefly to treat of things pertaining to faith. Yet in things pertaining to faith, understanding is the end; hence it is said in Isaiah 7 according to another reading: Unless you believe, you shall not understand. Therefore proceeding intellectually concerning divine things ought to be posited not as the mode of theology, but as its end.
[pars 3 q. 6 a. 1 s. c. 21] On the contrary is what is said in the book On Spirit and Soul, namely that intellect deals with created spirits, whereas intelligence deals with God himself. Now divine science treats chiefly of both of these. Therefore proceeding intellectually seems to be proper to it.
[pars 3 q. 6 a. 1 s. c. 22] Furthermore, the mode of a science ought to correspond to its matter. Now divine things are intelligible in themselves. Therefore the mode fitting to divine science is to proceed intellectually.
[pars 3 q. 6 a. 1 co. 1] I answer to the first question that a procedure followed in the sciences is called rational in three ways. In one way, on the side of the principles from which one proceeds, as when someone proceeds to prove something from the works of reason—of which sort are genus, species, opposite, and intentions of this kind that logicians consider. And thus a procedure will be called rational when in some science one employs propositions handed down in logic, namely insofar as we use logic as a teaching science within the other sciences. Yet this mode of proceeding cannot properly belong to any particular science, in which error arises unless one proceeds from proper principles. This happens properly and fittingly, however, in logic and in metaphysics, inasmuch as both sciences are common and treat in a certain manner of the same subject.
[pars 3 q. 6 a. 1 co. 2] In a second way, a procedure is called rational from the term at which one stops in proceeding. For the ultimate term to which the inquiry of reason ought to lead is the understanding of principles, into which we resolve when judging; and when this indeed comes about, the procedure or proof is not called rational, but demonstrative. Sometimes, however, the inquiry of reason cannot be brought all the way to the aforesaid term, but comes to rest in the inquiry itself—namely when a path toward either side of a contradiction still remains open to the inquirer; and this happens when one proceeds through probable reasons, which by nature produce opinion or belief rather than science. In this sense, a rational procedure is divided over against a demonstrative one; and in this way one can proceed rationally in any science whatsoever, so that from probable arguments the way may be prepared for necessary proofs. And this is another mode in which we employ logic in the demonstrative sciences—not indeed as teaching, but as logic in use. In both of these two ways a procedure is denominated rational from rational science, for in these ways logic, which is called rational science, is employed in the demonstrative sciences, as the Commentator says in Book I of the Physics.
[pars 3 q. 6 a. 1 co. 3] In a third way, a procedure is called rational from the rational power, namely insofar as in proceeding we follow the proper mode of the rational soul in knowing; and in this sense a rational procedure is proper to natural science. For natural science in its procedures observes the proper mode of the rational soul in two respects. First, in that just as the rational soul receives the knowledge of intelligible things—which are more known by nature—from sensible things—which are more known with respect to us—so natural science proceeds from things that are more known with respect to us and less known by nature, as is evident in Book I of the Physics, and demonstration through a sign or an effect is above all employed in natural science. Second, because since it belongs to reason to advance discursively from one thing to another, this is observed above all in natural science, wherein from the knowledge of one thing one arrives at the knowledge of another thing, as from the knowledge of an effect to the knowledge of its cause. Nor does one proceed merely from one thing to another according to notion while not distinct in reality, as if one proceeded from animal to man. For in the mathematical sciences one proceeds solely through things that belong to the essence of the thing, since they demonstrate solely through the formal cause; and therefore in them nothing is demonstrated of one thing through another thing, but through the proper definition of that thing itself. For even if certain demonstrations are given concerning the circle from the triangle or conversely, this occurs only insofar as the triangle exists potentially in the circle and conversely. In natural science, however, wherein demonstration takes place through extrinsic causes, something is proved of one thing through another wholly extrinsic thing. And thus the mode of reason is observed above all in natural science, and on account of this natural science among the others is most conformed to the human intellect. Proceeding rationally is therefore attributed to natural science, not because it belongs to it alone, but because it belongs to it preeminently.
[pars 3 q. 6 a. 1 ad 1] To the first objection, therefore, it must be said that that argument proceeds concerning a procedure called rational in the first way; for in that sense a rational procedure is proper to rational science and divine science, though not to natural science.
[pars 3 q. 6 a. 1 ad 2] To the second it must be said that that argument proceeds concerning a procedure called rational in the second way.
[pars 3 q. 6 a. 1 ad 3] To the third it must be said that the mode of reason is observed in all the sciences to the extent that one proceeds from one thing to another according to notion, yet not to the extent that one proceeds from one reality to another; rather, this latter is proper to natural science, and thus proceeding rationally is attributed to it, as has been said.
[pars 3 q. 6 a. 1 ad 4] To the fourth it must be said that the Philosopher there sets down the ratiocinative and the opinative as the same, whence it is evident that this pertains to the second mode assigned above. Now to the ratiocinative or opinative faculty the Philosopher in the same place attributes human doable actions, of which moral science treats, by reason of their contingency. Hence it may be gathered from what has been said that the first mode of rationality is most proper to rational science, the second to moral science, and the third to natural science.
[pars 3 q. 6 a. 1 co. 11] To the second question it must be said that proceeding disciplinably—by way of learning—is attributed to mathematical science not because it alone proceeds disciplinably, but because this belongs to it preeminently. For since to learn is nothing other than to receive science from another, we are said to proceed disciplinably when our procedure leads to certain knowledge, which is called science; and this indeed happens above all in the mathematical sciences. For since mathematics stands midway between natural and divine science, it is more certain than either. It is more certain than natural science because its consideration is freed from motion and matter, whereas natural consideration is engaged with matter and motion. Now from the fact that natural consideration deals with matter, its cognition depends upon more factors—namely upon the consideration of matter itself, of form, of material dispositions, and of the properties that follow upon form in matter. Yet wherever one must consider more factors in order to know something, cognition is more difficult; hence in Book I of the Posterior Analytics it is said that that science is less certain which exists by way of addition, as geometry is less certain than arithmetic. Moreover, from the fact that its consideration deals with mobile things that do not behave uniformly, its cognition is less firm, because its demonstrations hold for the most part, inasmuch as things sometimes happen otherwise. Consequently, the closer any science approaches to singulars—such as operative sciences like medicine, alchemy, and moral science—the less certitude they are able to possess, on account of the multitude of factors that must be considered in such sciences, the omission of any one of which entails error, and on account of their variability.
[pars 3 q. 6 a. 1 co. 12] Furthermore, the procedure of mathematics is more certain than the procedure of divine science, because the realities of which divine science treats are further removed from sensible things, from which our cognition takes its start—both with respect to separate substances, toward the knowledge of which what we receive from sensible things leads insufficiently, and with respect to the attributes common to all beings, which are maximally universal and thus maximally removed from the particulars falling under sense. Mathematical objects themselves, however, fall under sense and underlie the imagination, such as figure, line, number, and the like. Consequently, the human intellect, receiving from \ phantasms, grasps the knowledge of these things more easily and more certainly than that of some separate Intelligence, or even than the \ quiddity of substance, act and potency, and other things of this kind. Thus it is evident that mathematical consideration is easier and more certain than natural and theological consideration, and much more so than the other, operative sciences; and therefore mathematics above all is said to proceed disciplinably. And this is what Ptolemy says at the beginning of the Almagest: One might call the other two genera of theoretical inquiry opinion rather than scientific conception: the theological on account of its unmanifest and incomprehensible character, and the physical on account of the instability and obscurity of matter; the mathematical genus alone will yield to its students firm and unshakable conviction in inquiry, as assuredly through demonstration wrought by indubitable paths.
[pars 3 q. 6 a. 1 ad 11] To the first objection on this point, therefore, it must be said that although learning is received in every science, nevertheless in mathematics it is received more easily and more certainly, as has been said.
[pars 3 q. 6 a. 1 ad 12] To the second it must be said that although natural things underlie sense, nevertheless on account of their fluidity they do not possess great certitude once they pass outside actual sensation, such as mathematical objects possess—which exist without motion and yet exist in \ sensible matter according to being, and thus are able to fall under sense and the imagination.
[pars 3 q. 6 a. 1 ad 13] To the third it must be said that in learning we begin from what is easier, unless necessity requires otherwise. For sometimes in learning it is necessary to begin not from what is easier, but from that upon the knowledge of which the knowledge of subsequent matters depends. And for this reason in learning one must begin from logic—not because it is easier than the other sciences, for indeed it involves the greatest difficulty since it treats of second intentions, but because the other sciences depend upon it insofar as it teaches the mode of proceeding in all the sciences. Now one must know the mode of science before science itself, as is said in Book II of the Metaphysics.
[pars 3 q. 6 a. 1 ad 14] To the fourth it must be said that the mode of the sciences is taken from the powers of the soul by reason of the mode in which the powers of the soul act. Hence the modes of the sciences correspond not simply to the powers of the soul, but to the modes in which the powers of the soul can proceed, which are diversified not by the powers alone, but also by the objects; and thus the mode of every science need not be denominated from some power of the soul. Nevertheless, it can be said that just as the mode of physics is taken from reason insofar as it receives from sense, and the mode of divine science from intellect insofar as it considers something nakedly, so too the mode of mathematics can be taken from reason insofar as it receives from the imagination.
[pars 3 q. 6 a. 1 co. 21] To the third question it must be said that just as proceeding rationally is attributed to natural philosophy because in it the mode of reason is observed above all, so proceeding intellectually is attributed to divine science because in it the mode of intellect is observed above all. Now reason differs from intellect as multitude from unity. Hence Boethius says in Book IV of The Consolation of Philosophy that reason stands to intelligence in the same way as time stands to eternity and a circle to its center. For it is proper to reason to be diffused around many things and out of them to gather one simple cognition. Hence Dionysius says in Chapter 7 of On the Divine Names that souls possess rationality insofar as they discursively circle around the truth of existing things, and in this they fall short of the angels; yet insofar as they roll many things together into one, they are in a certain manner made equal to the angels. Intellect, conversely, considers first one simple truth and within that grasps the knowledge of a whole multitude, just as God, by understanding his own essence, knows all things. Hence Dionysius says in the same place that angelic minds possess intellectuality insofar as they uniformly understand the intelligibles of divine realities.
[pars 3 q. 6 a. 1 co. 22] Thus it is evident that rational consideration terminates at intellectual consideration according to the way of resolution, insofar as reason gathers one simple truth out of many. Conversely, intellectual consideration is the principle of rational consideration according to the way of composition or discovery, insofar as the intellect comprehends a multitude within one unity. That consideration, therefore, which is the term of all human ratiocination is supremely intellectual consideration. Now the entire consideration of resolving reason across all the sciences terminates at the consideration of divine science. For reason, as was said earlier, sometimes proceeds from one thing to another in reality, as when demonstration takes place through extrinsic causes or effects: by composing when one proceeds from causes to effects, and as it were by resolving when one proceeds from effects to causes, inasmuch as causes are simpler than effects and abide more immobily and uniformly. The ultimate term of resolution along this path, therefore, is reached when one arrives at the highest and simplest causes, which are the separate substances. At other times, however, reason proceeds from one thing to another according to notion, as when the procedure follows intrinsic causes: by composing when one proceeds from the most universal forms to more particularized ones, and by resolving when one proceeds conversely, inasmuch as what is more universal is simpler. Now the maximally universal principles are those that are common to all beings; and therefore the ultimate term of resolution along this path is the consideration of being and of the attributes belonging to being insofar as it is such. Now these—namely separate substances and what is common to all beings—are the very realities that divine science considers, as was said above. Hence it is manifest that its consideration is supremely intellectual. And from this it also follows that it bestows principles upon all the other sciences insofar as intellectual consideration is the principle of rational consideration, on account of which it is called first philosophy; and nonetheless it is learned after physics and the other sciences insofar as intellectual consideration is the term of rational consideration, on account of which it is called metaphysics, as it were beyond physics, because it presents itself after physics along the path of resolution.
[pars 3 q. 6 a. 1 ad 21] To the first objection on this point, therefore, it must be said that proceeding intellectually is attributed to divine science not as though it did not reason by proceeding from principles to conclusions, but because its ratiocination is closest to intellectual consideration, and its conclusions closest to its principles.
[pars 3 q. 6 a. 1 ad 22] To the second it must be said that God is above every created intellect with respect to comprehension, though not above the uncreated intellect, since in understanding himself he comprehends himself. With respect to the cognition whereby it is known what he is, however, he is above every intellect of a wayfarer in this life, though not with respect to the cognition whereby it is known that he exists; whereas by the blessed it is also known what he is, because they see his essence. Moreover, divine science treats not of God alone, but also of other realities that do not exceed the human intellect even in the state of this present life with respect to knowing what they are.
[pars 3 q. 6 a. 1 ad 23] To the third it must be said that, as was stated above, human consideration with respect to its term attains in a certain manner to angelic cognition—not by equality, indeed, but by a certain assimilation. Hence Dionysius says in Chapter 7 of On the Divine Names that souls, by rolling many things together into one, are counted worthy of intellective acts equal to those of the angels, so far as is proper and possible to souls.
[pars 3 q. 6 a. 1 ad 24] To the fourth it must be said that the cognition of faith also pertains preeminently to the intellect; for we do not receive those truths through the investigation of reason, but hold them by a simple acceptance of the intellect. Yet we are said not to understand them insofar as the intellect does not possess full cognition of them—which indeed is promised to us as our reward.
Question VI, Article 2 — Whether in Divine Things Imagination Must Be Altogether Relinquished (Why Mathematical Judgment Terminates at the Imagination)¶
Latin Locus: q. 6, a. 2 · Commentary: Notes on q. 6, a. 2
[pars 3 q. 6 a. 2 arg. 1] We proceed thus to the second article. It seems that in divine things one must be led to imaginations. For divine science is never handed down more fittingly than in Sacred Scripture. Yet in Sacred Scripture, when treating of divine things, we are led to imaginations, inasmuch as divine things are described to us under sensible figures. Therefore in divine things one must be led to imaginations.
[pars 3 q. 6 a. 2 arg. 2] Furthermore, divine things are grasped solely by the intellect, whence one must also proceed intellectually in them, as has been said. Yet there is no understanding without a \ phantasm, as the Philosopher says in Books I and III of On the Soul. Therefore in divine things one must be led to imaginations.
[pars 3 q. 6 a. 2 arg. 3] Furthermore, divine things become known to us above all through the illumination of the divine ray. Yet as Dionysius says in Chapter 1 of The Celestial Hierarchy, it is impossible for the divine ray to shine upon us otherwise than enveloped in a variety of sacred veils; and he calls images of sensible things “sacred veils.” Therefore in divine things one must be led to imaginations.
[pars 3 q. 6 a. 2 arg. 4] Furthermore, in dealing with sensible things one must proceed imaginatively. Now we receive our knowledge of divine things from sensible effects, according to Romans 1: The invisible things of God are clearly seen, being understood through the things that are made. Therefore in divine things one must be led to imaginations.
[pars 3 q. 6 a. 2 arg. 5] Furthermore, in cognitive matters we are regulated above all by that which is the principle of cognition, just as in natural things we are regulated by sense, from which our cognition begins. Now the principle of intellectual cognition in us is the imagination, since phantasms stand to our intellect in the same way that colors stand to sight, as is said in Book III of On the Soul. Therefore in divine things one must be led to the imagination.
[pars 3 q. 6 a. 2 arg. 6] Furthermore, since the intellect makes no use of a bodily organ, the action of the intellect is not impeded by an injury to a bodily organ except insofar as it turns toward the imagination. Yet through an injury to a bodily organ, namely the brain, the intellect is impeded in the consideration of divine things. Therefore the intellect, in considering divine things, is led to the imagination.
[pars 3 q. 6 a. 2 s. c. 1] On the contrary is what Dionysius says in Chapter 1 of Mystical Theology, speaking to Timothy: Do thou, O friend Timothy, in regard to mystical visions, abandon the senses. Now the imagination treats solely of sensible things, since it is a motion produced by sense in act, as is said in Book II of On the Soul. Since, therefore, considerations of divine things are supremely mystical, in them we ought not to be led to imaginations.
[pars 3 q. 6 a. 2 s. c. 2] Furthermore, in the consideration of every science one must avoid that which produces error within it. Yet as \ Augustine says in Book I of On the Trinity, the primary error concerning divine things belongs to those who endeavor to transfer what they know of corporeal things to divine things. Since, therefore, the imagination treats solely of corporeal things, it seems that in divine things we ought not to be led to imaginations.
[pars 3 q. 6 a. 2 s. c. 3] Furthermore, a lower power does not extend to what is proper to a higher power, as is evident through \ Boethius in Book V of The Consolation of Philosophy. Now to know divine and spiritual things pertains to intellect and intelligence, as is said in the book On Spirit and Soul. Since, therefore, as is said in the same place, the imagination ranks below intelligence and intellect, it seems that in divine and spiritual things we ought not to be led to the imagination.
[pars 3 q. 6 a. 2 co. 1] I answer that in every cognition two things must be considered, namely its beginning and its term. The beginning pertains indeed to apprehension, whereas the term pertains to judgment, for it is there that cognition is brought to completion. Now the beginning of all our cognition lies in sense, because from the apprehension of sense arises the apprehension of fantasy, which is a motion produced by sense, as the Philosopher says, and from this in turn arises intellective apprehension in us, since phantasms stand to the intellective soul as objects, as is evident in Book III of On the Soul.
[pars 3 q. 6 a. 2 co. 2] Yet the term of cognition is not always uniform: for sometimes it is in sense, sometimes in the imagination, and sometimes in the intellect alone. For sometimes the properties and accidents of a thing that are manifested by sense sufficiently express the nature of the thing, and then the judgment that the intellect makes concerning the nature of the thing must conform to those things that sense manifests concerning the thing. And of this sort are all natural things, which are determined to \ sensible matter; and therefore in natural science cognition must terminate at sense, namely so that we judge of natural things in the way sense manifests them, as is evident in Book III of On the Heavens; and whoever neglects sense in natural things falls into error. And these are natural things, which are concrete with sensible matter and motion both according to being and according to consideration.
[pars 3 q. 6 a. 2 co. 3] There are other things, however, the judgment of which does not depend upon what is perceived by sense, because although according to being they exist in sensible matter, nevertheless according to their definitive notion they are abstracted from sensible matter. Now the judgment concerning each thing is made above all according to its definitive notion. Yet because according to their definitive notion they do not abstract from every kind of matter, but solely from sensible matter, and once sensible conditions have been removed there remains something imaginable, in such things judgment must be taken according to what the imagination manifests. Now of this sort are mathematical objects. And therefore in mathematical inquiries cognition according to judgment must \ terminate at the imagination, not at sense, because mathematical judgment surpasses the apprehension of sense. Hence the judgment concerning a mathematical line is sometimes not the same as that concerning a sensible line—for instance, in the truth that a straight line touches a sphere at a single point alone, which belongs to a separate straight line, though not to a straight line in matter, as is said in Book I of On the Soul.
[pars 3 q. 6 a. 2 co. 4] Still other things exceed both what falls under sense and what falls under the imagination, such as those that are altogether independent of matter both according to being and according to consideration; and therefore the cognition of such things according to judgment ought to terminate neither at the imagination nor at sense. Nevertheless, from the things apprehended by sense or imagination we arrive at the knowledge of these realities: either by way of causality, as a cause is gauged from its effect—not as commensurate with the effect, but as surpassing it; or by way of transcendence; or by way of negation, when we separate from realities of this sort everything that sense or imagination apprehends; and Dionysius sets down these modes of knowing divine things from sensible ones in the book On the Divine Names. In divine inquiries, therefore, we can make use of both sense and imagination as beginnings of our consideration, yet not as terms—namely so that we would judge divine things to be such as the things apprehended by sense or imagination are. Now to be led to something is to terminate at it. Consequently, in divine things we ought to be led neither to the imagination nor to sense; in mathematical things, however, to the imagination and not to sense; while in natural things, even to sense. And on account of this, those err who strive to proceed uniformly in these three parts of speculative science.
[pars 3 q. 6 a. 2 ad 1] To the first objection, therefore, it must be said that Sacred Scripture does not set divine things before us under sensible figures so that our intellect may remain there, but so that from them it may ascend to immaterial realities; hence it even hands down divine truths through figures of lowly things, so as to afford less occasion for remaining in such figures, as Dionysius says in Chapter 2 of The Celestial Hierarchy.
[pars 3 q. 6 a. 2 ad 2] To the second it must be said that in the present state of life the operation of our intellect is never without a phantasm with respect to the beginning of cognition; yet it is not necessary that our cognition always terminate at phantasms—namely so that we would judge what we understand to be such as what fantasy apprehends.
[pars 3 q. 6 a. 2 ad 3] To the third it must be said that that authority of Dionysius speaks with respect to the beginning of cognition, and not with respect to its term.
[pars 3 q. 6 a. 2 ad 5] To the fifth it must be said that that argument holds when the principle of cognition leads sufficiently to that of which knowledge is sought; and sense is such a principle in natural things, though not in divine things, as has been said.
[pars 3 q. 6 a. 2 ad 6] To the sixth it must be said that the phantasm is the principle of our cognition, as that from which the operation of the intellect begins—not as something passing away, but as something permanent, like a certain foundation of intellectual operation, just as the principles of demonstration must remain throughout every process of science—since phantasms stand to the intellect as objects in which it inspects whatever it inspects, either through a perfect representation or through negation. Consequently, when the cognition of phantasms is impeded, the cognition of the intellect must be wholly impeded even in divine matters. For clearly we cannot understand that God is the cause of bodies, or transcends all bodies, or is without corporeity, unless we imagine bodies; yet our judgment of divine things is not formed according to the imagination. And therefore, although the imagination is necessary in every consideration of divine things during the present state of life, one must nevertheless never be led to terminate at it in divine matters.