LESSON 5

Are the Principles of Demonstration and Substance

Considered by One Science or by Many?

Chapter 2: 996b 26-997a 15

             198. But with respect to the principles of demonstration there is also the problem whether they are studied by one science or by many. By principles of demonstration I mean the common axioms from which [all] demonstrations proceed, e.g., "everything must either be affirmed or denied," and "it is impossible both to be and not to be at the same time," and all other such propositions. Is there one science which deals with these principles and with substance or are there different sciences? And, if not one, which of the two must be called the one that is now being sought?

             199. Now it would be unreasonable that these things should be studied by one science; for why should the study of these be proper to geometry rather than to any other science? In a similar way, then, if this study pertains to any science but cannot pertain to all, an understanding of these principles is no more proper to the science which studies substance than it is to any other science.

             200. But at the same time how will there be a science of these principles? For we already know what each one of them is; and therefore the other arts use them as something known. However, if there is demonstration of them, there will have to be some subject-genus, and some of the principles will have to be properties and others axioms. For there cannot be demonstration of all things, since demonstration must proceed from something, and be about something, and [be demonstration] of certain things. It follows, then, that there is a single genus of demonstrable things; for all demonstrative sciences use axioms.

             201. But on the other hand, if the science which considers substance differs from the one which considers axioms, which of these sciences is the more important and prior one? For axioms are most universal and are the principles of all things. And if it does not belong to the philosopher to establish the truth and falsity [of these principles], to what other person will it belong?

COMMENTARY

             387. Having debated the first question, which had to do with the study of causes, Aristotle's intention here is to argue dialectically about the science which is concerned with the study of the first principles of demonstration; and in regard to this he does three things. First (198:C 387), he raises the question. Second (199:C 388), he argues one side of the question ("Now it would be"). Third (201:C 391), he argues on the other side of the question ("But on the other hand").

             Accordingly, he states, first (198), the problem relating to the first principles of demonstration, namely, whether the study of these principles belongs to one science or to many. Further, he explains what the principles of demonstration are, saying that they are the common conceptions of all men on which all demonstrations are based, i.e., inasmuch as the particular principles of the proper demonstrated conclusions derive their stability from these common principles. And he gives an example of first principles, especially this one, that everything must either be affirmed or denied [of some subject]. Another principle which he mentions is that it is impossible for the same thing both to be and not to be at the same time. Hence the question arises whether these principles and similar ones pertain to one science or to many. And if they pertain to one science, whether they pertain to the science which investigates substance or to another science. And if to another science, then which of these must be called wisdom, or first philosophy, which we now seek.

             388. Now it would be (199).

             Here he argues one side of the question with a view to showing that it is not the office of one science to consider all first principles, i.e., the first principles of demonstration and substance. He gives two arguments, of which the first runs thus: since all sciences employ these principles of demonstration, there seems to be no reason why the study of them should pertain to one science rather than to another; nor again does it seem reasonable that they should be studied by all sciences, because then it would follow that the same thing would be treated in different sciences; but that would be superfluous. Hence it seems to follow that no science considers these principles. Therefore, for the very same reason that it does not belong to any of the other sciences to give us a knowledge of such principles, for this reason too it follows that it does not belong to the science whose function it is to consider substance.

             389. But at the same time (200).

             Here he gives the second argument, which runs thus. In the sciences there are two methods by which knowledge is acquired. One is that by which the whatness of each thing is known, and the other is that by which knowledge is acquired through demonstration. But it does not belong to any science to give us a knowledge of the principles of demonstration by means of the first method, because such knowledge of principles is assumed to be prior to all the sciences. For "we already know" what each one of them is, i.e., we know from the very beginning what these principles signify, and by knowing this the principles themselves are immediately known. And since such knowledge of principles belongs to us immediately, he concludes that all the arts and sciences which are concerned with other kinds of cognitions make use of these principles as things naturally known by us.

             390. But it is proved in the same way that a knowledge of these principles is not presented to us in any science by means of demonstration, because if there were demonstration of them, then three principles would have to be considered, namely, some subject-genus, its properties and the axioms. In order to clarify this he adds that there cannot be demonstration of all things; for subjects are not demonstrated but properties are demonstrated of subjects. Concerning subjects, however, it is necessary to know beforehand whether they exist and what they are, as is stated in Book I of the Posterior Analytics. The reason is that demonstration must proceed from certain things as principles, which are the axioms, and be about something, which is the subject, and [be demonstration] of certain things, which are properties. Now according to this it is immediately evident of one of these three, i.e., the axioms, that they are not demonstrated, otherwise there would have to be certain axioms prior to the axioms; but this is impossible. Therefore, having dismissed this method of procedure as obvious, he proceeds to consider the subject-genus. For since one science has one subject-genus, then that science which would demonstrate axioms would have one subject-genus. Thus there would have to be one subject-genus for all demonstrative sciences, because all demonstrative sciences use axioms of this kind.

             391. But on the other hand (201).

             Here he argues the other side of the question. For if it is said that there is one science which deals with such principles, and another which deals with substance, the problem will remain as to which of these sciences is the more important and prior one. For, on the one hand, since the axioms are most universal and are the principles of everything that is treated in any of the sciences, it seems that the science which deals with such principles is the most important one. Yet, on the other hand, since substance is the first and principal kind of being, it is evident that first-philosophy is the science of substance. And if it is not the same science which deals with substance and with the axioms, it will not be easy to state to which of the other sciences it belongs to consider the truth and falsity of these axioms, i.e., if it does not belong to first philosophy, which considers substance.

             392. The Philosopher answers this question in Book IV (321:C 590) of this work. He says that the study of the axioms belongs chiefly to the [first] philosopher inasmuch as it pertains to him to consider being in general, to which first principles of this kind essentially belong, as is most evident in the case of the very first principle: it is impossible for the same thing both to be and not to be [at the same time]. Hence all the particular sciences use principles of this kind just as they use being itself, although it is the first philosopher who is chiefly concerned with this. And the first argument is solved in this way. But the second argument is solved thus: the [first] philosopher does not consider principles of this kind in such a way as to make them known by defining them or by demonstrating them in an absolute sense, but by refutation, i.e., by arguing disputatively against those who deny them, as is stated in Book IV (331:C 608).