LESSON 6

First Philosophy Must Examine the First Principle of Demonstration. The Nature of This Principle. The Errors about It

Chapters 3 & 4: 1005b 8-1006a 18

             326. And it is fitting that the person who is best informed about each class of things should be able to state the firmest principles of his subject. Hence he who understands beings as beings should be able to state the firmest principles of all things. This person is the philosopher.

             327. And the firmest of all principles is that about which it is impossible to make a mistake; for such a principle must be both the best known (for all men make mistakes about things which they do not know) and not hypothetical. For the principle which everyone must have who understands anything about beings is not hypothetical; and that which everyone must know who knows anything must be had by him when he comes to his subject. It is evident, then, that such a principle is the firmest of all.

             328. And let us next state what this principle is. It is that the same attribute cannot both belong and not belong to the same subject at the same time and in the same respect; and let us stipulate any other qualifications that have to be laid down to meet dialectical difficulties. Now this is the firmest of all principles, since it answers to the definition given; for it is impossible for anyone to think that the same thing both is and is not, although some are of the opinion that Heraclitus speaks in this way; for what a man says he does not necessarily accept. But if it is impossible for contraries to belong simultaneously to the same subject (and let us then suppose that the same things are established here as in the usual proposition , and if one opinion which expresses the contradictory of another is contrary to it, evidently the same man at the same time cannot think that the same thing can both be and not be; for one who is mistaken on this point will have contrary opinions at the same time. And it is for this reason that all who make demonstrations reduce their argument to this ultimate position. For this is by nature the starting point of all the other axioms.

Chapter 4

             329. Now as we have said (328), there are some who claimed that the same thing can both be and not be, and that this can be believed. And many of those who treat of nature adopt this theory. But now we take it to be impossible for a thing both to be and not be at the same time, and by means of this we shall show that this is the firmest of all principles.

             330. But some deem it fitting that even this principle should be demonstrated, and they do this through want of education. For not to know of what things one should seek demonstration and of what things one should not shows want of education. For it is altogether impossible that there should be demonstration of all things, because there would then be an infinite regress so that there would still be no demonstration. But if there are some things of which it is not necessary to seek demonstration, these people cannot say what principle they think to be more indemonstrable.

             331. But even in this case it is possible to show by refutation that this view is impossible, if only our opponent will say something. But if he says nothing, it is ridiculous to look for a reason against one who has no reason, on the very point on which he is without reason; for such a man is really like a plant. Now I say that demonstration by refutation is different from demonstration [in the strict sense], because he who would demonstrate this principle in the strict sense would seem to beg the question. But when someone argues for the sake of convincing another there will be refutation, not demonstration.

COMMENTARY

             596. He shows here that it is the first philosopher who is chiefly concerned with the first principle of demonstration; and in regard to this he does two things. First (326:C 596), he shows that it is the business of the first philosopher to consider this principle; and second (332:C 611), he begins to examine this principle ("The starting point").

             In regard to the first he does three things. First, he shows that it is the office of this science to consider the first principle of demonstration. Second (327:C 597), he indicates what this principle is ("And the firmest"). Third (329:C 606), he rejects certain errors regarding this same principle ("Now as we have said").

             In regard to the first point he uses the following argument. In every class of things that man is best informed who knows the most certain principles, because the certitude of knowing depends on the certitude of principles. But the first philosopher is best informed and most certain in his knowledge; for this was one of the conditions of wisdom, as was made clear in the prologue of this work (13:C 35), namely, that he who knows the causes of things has the most certain knowledge. Hence the philosopher ought to consider the most certain and firmest principles of beings, which he considers as the subject-genus proper to himself.

             597. And the firmest (327).

             Then he shows what the firmest or most certain principle is; and in regard to this he does two things. First (327:C 597), he states the conditions for the most certain principle; and then (328:C 600) he shows how they fit a single principle ("And let us").

             He accordingly gives, first (327), the three conditions for the firmest principle. The first is that no one can make a mistake or be in error regarding it. And this is evident because, since men make mistakes only about those things which they do not know, then that principle about which no one can be mistaken must be the one which is best known.

             598. The second condition is that it must "not be hypothetical," i.e., it must not be held as a supposition, as those things which are maintained through some kind of common agreement. Hence another translation reads "And they should not hold a subordinate place," i.e., those principles which are most certain should not be made dependent on anything else. And this is true, because whatever is necessary for understanding anything at all about being "is not hypothetical," i.e., it is not a supposition but must be self-evident. And this is true because whatever is necessary for understanding anything at all must be known by anyone who knows other things.

             599. The third condition is that it is not acquired by demonstration or by any similar method, but it comes in a sense by nature to the one having it inasmuch as it is naturally known and not acquired. For first principles become known through the natural light of the agent intellect, and they are not acquired by any process of reasoning but by having their terms become known. This comes about by reason of the fact that memory is derived from sensible things, experience from memory, and knowledge of those terms from experience. And when they are known, common propositions of this kind, which are the principles of the arts and sciences, become known. Hence it is evident that the most certain or firmest principle should be such that there can be no error regarding it; that it is not hypothetical; and that it comes naturally to the one having it.

             600. And let us next (328).

             Then he indicates the principle to which the above definition applies. He says that it applies to this principle, as the one which is firmest: it is impossible for the same attribute both to belong and not belong to the same subject at the same time. And it is necessary to add "in the same respect"; and any other qualifications that have to be given regarding this principle "to meet dialectical difficulties" must be laid down, since without these qualifications there would seem to be a contradiction when there is none.

             601. That this principle must meet the conditions given above he shows as follows: it is impossible for anyone to think, or hold as an opinion, that the same thing both is and is not at the same time, although some believe that Heraclitus was of this opinion. But while it is true that Heraclitus spoke in this way, he could not think that this is true; for it is not necessary that everything that a person says he should mentally accept or hold as an opinion.

             602. But if one were to say that it is possible for someone to think that the same thing both is and is not at the same time, this absurd consequence follows: contraries could belong to the same subject at the same time. And "let us suppose that the same things are established," or shown, here as in the usual proposition established in our logical treatises. For it was shown at the end of the Perihermineas that contrary opinions are not those which have to do with contraries but those which have to do with contradictories, properly speaking. For when one person thinks that Socrates is white and another thinks that he is black, these are not contrary opinions in the primary and proper sense; but contrary opinions are had when one person thinks that Socrates is white and another thinks that he is not white.

             603. Therefore, if someone were to think that two contradictories are true at the same time by thinking that the same thing both is and is not at the same time, he will have contrary opinions at the same time; and thus contraries will belong to the same thing at the same time. But this is impossible. It is impossible, then, for anyone to be mistaken in his own mind about these things and to think that the same thing both is and is not at the same time. And it is for this reason that all demonstrations reduce their propositions to this proposition as the ultimate opinion common to all; for this proposition is by nature the starting point and axiom of all axioms.

             604. The other two conditions are therefore evident, because, insofar as those making demonstrations reduce all their arguments to this principle as the ultimate one by referring them to it, evidently this principle is not based on an assumption. Indeed, insofar as it is by nature a starting point, it clearly comes unsought to the one having it and is not acquired by his own efforts.

             605. Now for the purpose of making this evident it must be noted that, since the intellect has two operations, one by which it knows quiddities, which is called the understanding of indivisibles, and another by which it combines and separates, there is something first in both operations. In the first operation the first thing that the intellect conceives is being, and in this operation nothing else can be conceived unless being is understood. And because this principle--it is impossible for a thing both to be and not be at the same time--depends on the understanding of being (just as the principle, every whole is greater than one of its parts, depends on the understanding of whole and part), then this principle is by nature also the first in the second operation of the intellect, i.e., in the act of combining and separating. And no one can understand anything by this intellectual operation unless this principle is understood. For just as a whole and its parts are understood only by understanding being, in a similar way the principle that every whole is greater than one of its parts is understood only if the firmest principle is understood.

             606. Now as we have said (329).

             Then he shows how some men erred regarding this principle; and in regard to this he does two things. First, he touches on the error of those who rejected the foregoing principle; and second (330:C 607) he deals with those who wished to demonstrate it ("But some").

             He accordingly says that some men, as was stated above about Heraclitus (328:C 601), said that the same thing can both be and not be at the same time, and that it is possible to hold this opinion; and many of the philosophers of nature adopt this position, as will be made clear below (354:C 665). For our part, however, we now take as evident that the principle in question is true, i.e., the principle that the same thing cannot both be and not be; but from its truth we show that it is most certain. For from the fact that a thing cannot both be and not be it follows that contraries cannot belong to the same subject, as will be said below (353:C 663). And from the fact that contraries cannot belong to a subject at the same time it follows that a man cannot have contrary opinions and, consequently, that he cannot think that contradictories are true, as has been shown (328:C 603).

             607. But some (330).

             Then he mentions the error of certain men who wished to demonstrate the above-mentioned principle; and in regard to this he does two things. First, he shows that it cannot be demonstrated in the strict sense; and second (331:C 608), that it can be demonstrated in a way ("But even").

             Thus he says, first (330), that certain men deem it fitting, i.e., they wish, to demonstrate this principle; and they do this "through want of education," i.e., through lack of learning or instruction. For there is want of education when a man does not know what to seek demonstration for and what not to; for not all things can be demonstrated. For if all things were demonstrable, then, since a thing is not demonstrated through itself but through something else, demonstrations would either be circular (although this cannot be true, because then the same thing would be both better known and less well known, as is clear in Book I of the Posterior Analytics , or they would have to proceed to infinity. But if there were an infinite regress in demonstrations, demonstration would be impossible, because the conclusion of any demonstration is made certain by reducing it to the first principle of demonstration. But this would not be the case if demonstration proceeded to infinity in an upward direction. It is clear, then, that not all things are demonstrable. And if some things are not demonstrable, these men cannot say that any principle is more indemonstrable than the above-mentioned one.

             608. But even in this case (331).

             Here he shows that the above-mentioned principle can be demonstrated in a certain respect. He says that it may be demonstrated by disproof. In Greek the word is {elegktikos} which is better translated as by refutation, for an {elegchos} is a syllogism that establishes the contradictory of a proposition, and so is introduced to refute some false position. And on these grounds it can be shown that it is impossible for the same thing both to be and not be. But this kind of argument can be employed only if the one who denies that principle because of difficulties "says something," i.e., if he signifies something by a word. But if he says nothing, it is ridiculous to look for a reason against one who does not make use of reason in speaking; for in this dispute anyone who signifies nothing will be like a plant, for even brute animals signify something by such signs.

             609. For it is one thing to give a strict demonstration of this principle, and another to demonstrate it argumentatively or by refutation. For if anyone wished to give a strict demonstration of this principle, he would seem to be begging the question, because any principle that he could take for the purpose of demonstrating this one would be one of those that depend on the truth of this principle, as is clear from what has been said above (330:C 607). But when the demonstration is not of this kind, i.e., demonstration in the strict sense, there will then be disproof or refutation at most.

             610. Another text states this better by saying, "But when one argues for the sake of convincing another, there will then be refutation but not demonstration"; i.e., when a process of this kind from a less well known to a better known principle is employed for the sake of convincing another man who denies this, there will then be disproof or refutation but not demonstration; i.e., it will be possible to have a syllogism which contradicts his view, since what is less known absolutely is admitted by the opponent, and thus it will be possible to proceed to demonstrate the above-mentioned principle so far as the man is concerned but not in the strict sense.