Commentary Aristotle Metaphysics
Lecture 6. Are all substances considered by one science or by many?
And there is the problem of whether there is one science or many sciences which deal with all substances.
If there is not one science, then with what substances must this science deal?
But it is unreasonable that there should be one science of all substances, for then one science would demonstrate all per se accidents (if it is true that every demonstrative science speculates about the per se accidents of some subject by proceeding from common opinions).
Hence it is the office of the same science to study the per se accidents of the same subject genus by proceeding from the same opinions.
For it belongs to one science to consider that something is so, and it belongs to one science (whether to the same science or to another) to consider the principles.
Hence it belongs to one science to consider accidents, whether they are studied by these sciences or by one derived from them.
Further, there is the problem of whether this science is concerned only with substances, or also with accidents.
I mean, for example, that if a solid is a kind of substance, and also lines and surfaces, the question arises as to whether it is the function of the same science to know these and also the accidents of each genus of things about which the mathematical sciences make demonstrations, or whether it is the concern of a different science.
For if it is the concern of the same science, a particular one will undertake these demonstrations and this will be the one which deals with substance. However, there does not seem to be any demonstration of the quiddity.
But if it is the concern of a different science, which science will it be that studies the accidents of substances? For to solve this is very difficult.
Does the science of substance consider all substances as well as accidents?
393. Having debated two questions which pertain to the scope of investigation of this science, he now treats the third question which is about the study of substances and accidents.
This is divided into two parts inasmuch as he discusses two questions on this point.
The second begins where he says, furthermore, there is.
First, he raises the question of whether there is one science that considers all substances, or whether there are many sciences that consider different substances.
394. If there is not. Second, he argues the first side of the question with a view to showing that there is one science of all substances. For if there were not one science of all substances, then apparently it would be impossible to designate the substance which this science considers, because substance as substance is the primary kind of being. Hence it does not seem that one substance rather than another belongs to the consideration of the basic science.
395. But it is unreasonable. Third, he argues the other side of the question, saying that it is unreasonable to hold that there is one science of all substances. For it would follow that there would be one demonstrative science of all per se accidents. And this is true because every science which demonstrates certain accidents speculates about the per se accidents of some particular subject, and it does this from certain common conceptions. Therefore, since a demonstrative science considers the accidents only of some particular subject, it follows that the study of some subject genus belongs to the same science that is concerned with the study of the per se accidents of that genus, and vice versa, so long as demonstrations proceed from the same principles.
396. But sometimes it happens to be the function of some science to demonstrate from certain principles that a thing is so, and sometimes it happens to be the function of some science to demonstrate the principles from which it was demonstrated that a thing is so. This sometimes belongs to the same science and sometimes to a different one.
An example of its being the function of the same science is seen in the case of geometry, which demonstrates that a triangle has three angles equal to two right angles in virtue of the principle that the exterior angle of a triangle is equal to the two interior angles opposite to it. For to demonstrate this belongs to geometry alone.
An example of its being the function of a different science is seen in the case of music, which proves that a tone is not divided into two equal semitones because a ratio of nine to eight (which is superparticular) cannot be divided into two equal parts. But to prove this does not pertain to the musician, but to the arithmetician. It is evident, then, that sometimes sciences differ because their principles differ, so long as one science demonstrates the principles of another science by means of certain higher principles.
397. But if it is assumed that the principles are identical, sciences could not differ so long as the accidents are the same and the subject genus is the same, as if one science considered the subject and another its accidents. Hence it follows that that science which considers a substance will also consider its accidents, so that if there are many sciences which consider substances, there will be many sciences which consider accidents. But if there is only one science which considers substances, there will be only one science which considers accidents. But this is impossible, because it would then follow that there would be only one science, since there is no science which does not demonstrate the accidents of some subject. Therefore, it is not the function of one science to consider all substances.
398. This is treated in book 4 of this work, where it is shown that the examination of substance as substance belongs to the first science, whose province it is to consider being as being. Thus it considers all substances according to the common aspect of substance. Therefore, it belongs to this science to consider the common accidents of substance. But it belongs to the particular sciences, which deal with particular substances, to consider the particular accidents of substances, just as it belongs to the science of nature to consider the accidents of mobile substance. However, among substances there is also a hierarchy, for the first substances are immaterial ones. Hence the study of them belongs properly to first philosophy, just as the philosophy of nature would be first philosophy if there were no other substances prior to mobile bodily substances, as is stated below in book 6.
399. Further, there is the problem. Here he raises another question regarding the study of substance and accidents. Concerning this he does three things.
First, he raises the question of whether the investigation of this science is concerned with substance alone or also with the attributes that are accidents of substances. For example, if we say that lines, surfaces, and solids are substances of some sort, as some held, the question arises whether it belongs to the same science to consider such things and also their proper accidents, which are demonstrated in the mathematical sciences, or whether it belongs to another science.
400. For if it is the concern. Second, he argues one side of the question. For if it belongs to the same science to consider accidents and substances, then, since a science which considers accidents demonstrates accidents, it follows that a science which considers substance demonstrates substances. But this is impossible, for the definition of a substance, which expresses the quiddity, is indemonstrable. Hence it will not belong to the same science to consider substances and accidents.
401. But if it is the concern. Third, he argues the other side of the question. If different sciences consider substance and accident, it will not be possible to state which science it is that speculates about the accidents of substance, because the science which would do this would consider both, although this would seem to pertain to all sciences. For every science considers the per se accidents of its subject, as has been explained.
402. The Philosopher answers this question in book 4 of this work, saying that it is also the office of that science which is concerned with the study of substance and being to consider the proper accidents of substance and being. Yet it does not follow that it would consider each in the same way, that is, by demonstrating substance as it demonstrates accidents, but by defining substance and by demonstrating that accidents either belong to or do not belong to it. This is explained more fully at the end of book 9 of this work.