Cursus Philosophicus Thomisticus, Secunda Pars Artis Logicae

To explain the subordination of sciences, three things in particular must be explained: first, what constitutes subordination; second, how the subordinating science is said to know the reason why, and the subordinated science to know that; third, how a subordinated science can have the character of science in a subject in which the subordinating science is absent, and whose principles are only believed. We will treat this third matter in the next article.

Concerning the first point, authors commonly distinguish a THREEFOLD MODE of subordination, as can be seen in the Coimbra commentators, Posterior Analytics I, chapter 10, q. 2, and Fonseca, Metaphysics IV, chapter 3, q. 2. Some sciences are subordinated by reason of an end, others by reason of principles, and others by reason of a subject. On the part of the end, this occurs when one science regards a higher end and another a lower one and is subject to it; thus architectonic arts subordinate ministerial arts to themselves: bridle-making is subordinate to horsemanship, horsemanship to military science, and military science to political science. On the part of principles, it occurs when one science receives its principles from another. This can happen because it receives principles common to other sciences, as other sciences can receive them from Metaphysics and Logic; or because it receives its own proper principles, since that science cannot resolve them by itself into principles known per se, but receives them proved and taught by another, higher science, as Music receives from Arithmetic and Perspective from Geometry. Finally, on the part of the subject, sciences are said to be subordinated when the subject of one is contained under the subject of another. As St. Thomas notes in Posterior Analytics I, lect. 25¹, this happens in two ways: either one subject is contained essentially, as a species, under the subject of another—for example, the science of human beings concerns a subject contained under animal, and the science of the heavens concerns a subject contained under mobile being—or one subject is contained accidentally under another, as Music treats of sounding number and Perspective of the visual line, where “sounding” and “visual” add accidental differences to number and line.

Of these three modes of subordination, the first is improper, because subordination there does not always provide a manifestation of truth, but only service and command. This also occurs among the virtues in the will, as temperance is commanded by charity and religion. But being subject by command is one thing, and being subordinated in science is another, because scientific subordination involves dependence in the manifestation of truth.

The second mode is proper subordination. It is found without qualification when one science has no principles except those manifested by another science, so that it cannot resolve them by itself into principles known per se. For this reason our theology is subordinated to the beatific theology, as we will say shortly. If, however, a science can resolve its principles into principles known per se but sometimes receives some principle from another science, either for proving something without qualification or for defending it, then there is subordination in a certain respect.

The third mode produces subordination in the strictest sense when the subject of the lower science adds an accidental difference to the subject of the higher science, not an essential difference or proper attribute. The reason is that the subject of the subordinated science must be foreign to or distinct from the subject of the subordinating science, just as the sciences themselves are distinct, though one depends on the other. An essential species, however, does not make a subject foreign to its generic subject, since the same science that treats a genus also treats its species; it explains its subject through division just as it does through definition. Thus Philosophy, which treats of motion, also treats of the species of motion; and Metaphysics, which treats of being, treats of substance and of determinate beings. If a proper attribute is added, this does not make a distinct science, as though one science treated the subject and another its attributes; rather, every science demonstrates some attribute of its subject. Hence, if the same science treats of a common object and its species, it will also treat of common and specific attributes. Therefore, for proper subordination on the part of the subject, one subject must add an accidental difference to another, as “sounding” adds to number and “visual” to line.

From these points we gather the CONDITIONS required for the subordination of sciences, which can be reduced to three: first, the subject of the subordinated science must contract and add something to the subject of the subordinating science; second, it must add an accidental difference that makes the subject matter of the subordinated science foreign to that of the subordinating science; third, it must add an accidental difference that in that subject matter is the principle of special attributes and knowable truths. For example, some attributes are found in the visual line that are not found in a hot or cold line; the former therefore constitutes a distinct subordinated science, but the latter does not.

To explain this matter more fully, YOU WILL OBJECT: First, theology is subordinated to the beatific science, as St. Thomas teaches in Summa theologiae I, q. 1, art. 2, and yet both sciences treat of the same subject, namely, God. Therefore the subordination of sciences does not require the subjects to be distinct through the addition of an accidental difference.

Second, if the subordinated science has as its subject something contracted by an accidental difference, it follows that it has an accidental being as its object. The visual line and sounding number, for example, are accidental beings. But there is no per se science of accidental being.

Third: Either that accidental difference is accidental to the object in the being of the thing or in the being of what is knowable. If in the being of the thing, this contributes nothing to subordination: many sciences treat of a subject determined by an accidental difference and yet are not subordinated to a higher science. Philosophy treats of mobile being but is not subordinated to a science of being; Medicine treats of a healthful body but is not subordinated to Philosophy, which treats of body. Likewise, there would be no reason why the visual line or sounding number, for example, should constitute a subject of subordination, while a line or number with another accident, such as a colored or hot line, a visible number, or something similar, should not. If the difference is in the being of what is knowable, it follows that the subordinating and subordinated sciences differ only accidentally, since they differ by an accidental difference in the being of what is knowable; yet Music and Arithmetic differ essentially.

Finally, Metaphysics proves the principles of all the sciences and thereby subordinates the others. Yet the other sciences do not add an accidental difference to its subject, since nothing adds an accidental difference to being, which is transcendental. Therefore, and so on.

To the first, the reply is that our theology is not subordinated to the beatific science on the part of the subject, as though a foreign and distinct subject were subordinated to the subject of a higher science, but on the part of principles and evidence: theology receives from the beatific or divine science evidence for the principles that it now believes by faith. This suffices for true and proper subordination, insofar as the evidence of one science's principles depends on another. Our theology does not, however, have all the conditions required for subordination on the part of the subject, because in fact it does not have a subject different from the beatific science's subject. Thus on the part of the subject there is no subordination but identity: it does not add an accidental difference to the subordinating science's subject but regards the same subject under a different formal aspect, namely, as virtually revealed, whereas the beatific science regards it as clearly seen. See Cajetan, Summa theologiae I, q. 1, art. 2.

To the second: Authors hold various opinions about the subject of a subordinated science. Some think that there can be science of accidental being, provided it is not accidental being by chance or fortune. See the Coimbra commentators, Posterior Analytics I, chapter 10, q. 2, art. 1. This reduces to what others say: the object of the subordinated science is one accidentally in the being of the thing but per se in the being of what is knowable. This clearly admits that there can be science of accidental being. But it conflicts with the very character of accidental being, because such a being does not consist of one genus and difference, and consequently does not have one definition. Since a definition is a principle of science, the unity of science depends on the unity of that definition, as we will say in the next question; we said more about this above, qq. 5 and 7.

The reply, then, is that the subordinated science does not have as its subject that aggregate considered as accidental being, constituted from an accidental difference and the subject of a higher science. Rather, it regards one of those things per se, though not absolutely, but as modified and connoted by the other. For example, Perspective treats of the visual insofar as it is modified by and connotes line. It is therefore no problem that a subject should be per se knowable and ground necessary truths, even though to ground them it requires something accidental as a connoted and oblique feature. For many properties or proportions do not belong to a thing absolutely, but on the supposition of some state or condition that is accidental to it yet required per se for the property to follow. Rest, for example, does not follow a stone absolutely, but insofar as it is at the center. Similarly, some properties or proportions follow the visual or the sounding, not absolutely, but the visual as it is in a line and the sounding as it is in number. Thus they do not belong to something constituted and aggregated accidentally, but to one thing per se with the connotation of another.

To the third, the reply is that the subordinated science adds an accidental difference to its subject on the part of the thing itself, but in such a way that this is a required condition for a per se truth to result, one that is truly knowable through dependence on the subject of the higher science. The stated conditions must therefore all be present for subordination: the accidental difference must help constitute different proportions or connections of truth, and these necessary truths or connections must then depend, for their manifestation, on the principles of the higher science's subject. Thus the proportions of the visual line depend per se on the principles of line, and those of sounding number on the principles of number. The truths of mobile being, however, do not depend on the principles of being as such; the science of mobile being resolves itself into per se known principles of its own genus, rather than proving them by resolution into principles of another science, as subordination requires. If a line or number is given a difference that does not constitute a special per se demonstrable truth, such as the line's being hot or cold, or if the manifestation of those truths does not depend on the subject of the higher science, this cannot constitute subordination.

To the fourth, the reply is that Metaphysics is the highest science because its object is higher and more universal than those of the other sciences, and it proceeds from first principles. The other sciences do not, however, receive the manifestation and proof of their principles from it, because they have principles known from their terms, into which they resolve per se. Any science that resolves itself per se into principles known per se is not subordinated; for subordination, it must have principles manifested and proved by another science. Metaphysics does explain and defend the principles of the other sciences by reducing them to impossibility, but it does not prove and demonstrate them a priori. And if the other sciences sometimes proceed in their demonstrations from principles of Metaphysics, just as they sometimes proceed from principles of Logic, as we said in q. 1, art. 5, this does not mean that they are subordinated to those sciences without qualification. It is not total dependence on another science for the evidence of one's principles, such that one has no principles known per se into which to resolve them; rather, it is being helped in some proof by principles of another science as an external and transferred proof. This is subordination in a certain respect.

Concerning the SECOND POINT, namely, how to understand the Philosopher's statement that “it belongs to the subordinating science to know the reason why, but to the subordinated science to know that”: setting aside the various explanations that can be seen in Master Soto, on this first book, q. 5, ad 6, and the Coimbra commentators on chapter 10 of this book, q. 2, art. 3, we say first that the Philosopher did not state absolutely that a subordinated science knows that, as if every subordinated science knew that—or, worse, as some understand it, that the subordinating science reaches the subordinated science's conclusions in its own determinate subject matter, whereas the subordinated science reaches them from effects and by demonstration of the fact. Rather, the Philosopher said that it is proper to the sciences of sensible things—that is, those that descend to sensible matter—to know that, whereas it belongs to mathematicians to know the reason why. That is, among the sciences subordinated to Mathematics, those that extend to sensible things know by the science of the fact, because they reach sensible things by induction and descend to experience. If they wish to know the reason why for the very same things they know by experience, they must use principles taught by Mathematics, or by the subordinating science. For example, a surgeon says that circular wounds heal more slowly, first from long experience and second from the circular figure itself. But if the surgeon wishes to give the cause and explanation, he must turn to Geometry, which says that a circular figure joins its parts with greater difficulty because it lacks angles. Thus we are not compelled to verify Aristotle's proposition in every subordinated science, but only in one that descends to sensible things. Such a science can reach sensible things in singulars and use induction from them, which is to know by the science of the fact. To know the reason why, however, it must borrow principles from a higher science and apply them to the sensible matter it treats. Therefore, a subordinated science is not said to know that with respect to the subordinating science's principles that it uses, but with respect to the conclusions it can know from those principles applied to its own matter and also reach through experience itself. It knows them by the science of the fact not precisely insofar as it is subordinated, but insofar as it is sensible and descends to sensible effects.

FROM THIS YOU WILL GATHER TWO POINTS: First, when the subordinating science is said to know the reason why, this does not mean that it knows the subordinated science's conclusions themselves and descends to demonstrate them. That cannot hold unless the subordinating science changes its abstraction and descends to the matter of another science, which would change the species of that science, derived as it is from abstraction and a different immateriality. Thus, as Cajetan aptly notes in Posterior Analytics I, chapter 12, the subordinating science is said to know the reason why in isolation and in general, not as applied to this particular matter: it teaches principles only in general, which are later applied by the subordinated science to its determinate matter. Geometry does not demonstrate that circular wounds heal more slowly; the geometer treats nothing about wounds, but only teaches in general that a circular figure, because it lacks angles, joins together with greater difficulty, which he demonstrates abstractly. The surgeon takes this principle and applies it to his own subject matter, showing that circular wounds join more slowly.

Second, when the subordinated science is said to know that, this should not be understood privatively, as if it demonstrated only the fact and in no way the reason why. By taking principles from the subordinating science it truly demonstrates the reason why; indeed, the chief point of subordination is that, taking principles from a higher science, it demonstrates its own conclusions. But because it does not have those principles from itself or resolve them from itself into principles known per se, but receives them as made known by another, higher science, the higher science is credited with knowing the reason why: its principles are taken and applied to the matter of the lower science so that the lower science's own conclusions may be demonstrated through their reasons. Those conclusions are also known further through experience itself, and thus that science is said to know them by the science of the fact through its own resources, that is, through experience and effects.