Commentary Aristotle Metaphysics
Lecture 2. The divisions of being and unity
Now, although being and unity are the same and are a single nature in the sense that they are associated like principle and cause, they are not the same in the sense that they are expressed by a single concept. Yet it makes no difference, even if we consider them to be the same; in fact, this will rather support our undertaking.
For “one man” and “human being” and “man” are the same thing; and nothing different is expressed by repeating the terms when we say, “This is a human being, a man, and one man.” And it is evident that they are not separated either in generation or in corruption. The same holds true of what is one. Hence it is evident that any addition to these expresses the same thing, and that unity is nothing else than being.
Further, the substance of each thing is one in no accidental way, and similarly it is something that is.
Hence there are as many species of being as there are of unity, of which it is the office of the same general science to treat. I mean, for example, sameness and likeness and other such attributes. And almost all contraries may be referred to this starting point. But these have been studied by us in our selection (that is, in our explanation or treatment) of contraries.
And there are just as many parts of philosophy as there are substances, so that there must be a first philosophy and one which is next in order to it. For being and unity are things that straightway have genera, and for this reason the sciences will correspond to these. For the term “philosopher” is used like the term “mathematician,” for mathematics too has parts, and there is a first and a second science and then others, following these among the mathematical sciences.
Metaphysics also treats of “being-one”
548. Here he proceeds to show that the study of common attributes such as one and many and same and different belongs to the consideration of one and the same science, and in regard to this he does two things.
First, he shows that this is true of each attribute taken separately by arguing from proper or specific principles.
Second, he shows that this is true of all attributes taken together by arguing from common principles, at and it is also evident.
First, he shows that the philosopher ought to investigate all these attributes.
Second, he tells us how to investigate them, at hence, since the term “one.”
First, he shows that it is the office of this science to consider unity and its species.
Second, he shows that it is the office of one and the same science to consider all opposites, at now, since it belongs to one science.
First, he shows that it is the office of this science to consider unity.
Second, he shows that it also belongs to it to examine the species of unity, at hence there are as many.
He therefore says first that being and unity are the same and are a single nature. He says this because some things are numerically the same which are not a single nature, but different natures (for example, Socrates, this white thing, and this musician). Now the terms “one” and “being” do not signify different natures, but a single nature. But things can be one in two ways: for some things are one which are associated as interchangeable things (like “principle” and “cause”), and some are interchangeable not only in the sense that they are one and the same numerically, but also in the sense that they are one and the same conceptually, like “garment” and “clothing.”
549. Now the terms “one” and “being” signify one nature according to different concepts, and therefore they are like the terms “principle” and “cause,” and not like the terms “tunic” and “garment,” which are wholly synonymous. Yet it makes no difference to his thesis if we consider them to be used in the same sense, as those things that are one both numerically and conceptually. In fact, this will rather support our undertaking, that is, it will serve his purpose better.
For he intends to prove that unity and being belong to the same study, and that the species of the one correspond to those of the other. The proof of this would be clearer if unity and being were the same both numerically and conceptually, rather than just numerically and not conceptually.
550. He proves that they are the same numerically by using two arguments.
He gives the first where he says, for “one man”, and it runs as follows. Any two things that when added to some third thing cause no difference are wholly the same. But when one and being are added to man or to anything at all, they cause no difference. Therefore, they are wholly the same. The truth of the minor premise is evident, for it is the same thing to say “man” and “one man.” And similarly it is the same thing to say “human being” and “the thing that is man,” and nothing different is expressed when we repeat the terms in saying, “This is a human being, a man, and one man.” He proves this as follows.
551. It is the same thing for man and the thing that is man to be generated and corrupted. This is evident from the fact that generation is a process toward being, and corruption a change from being to non-being. Hence a man is never generated without a human being being generated, nor is a man ever corrupted without a human being being corrupted. And those things that are generated and corrupted together are themselves one and the same.
552. And just as it has been said that being and man are not separated either in generation or in corruption, so too this is evident of what is one; for when a man is generated, one man is generated, and when a man is corrupted, one man is also corrupted.
It is clear, then, that the apposition of these expresses the same thing, and that, just because the term “one” or “being” is added to “man,” it is not to be understood that some nature is added to man. And from this it is clearly apparent that unity does not differ from being, because any two things that are identical with some third thing are identical with each other.
553. It is also evident from the foregoing argument that unity and being are the same numerically but differ conceptually; for if this were not the case they would be wholly synonymous, and then it would be nonsense to say, “a human being,” and “one man.” For it must be borne in mind that the term “man” is derived from the quiddity or the nature of man, and the term “thing” from the quiddity only; but the term “being” is derived from the act of being, and the term “one” from order or lack of division (for what is one is an undivided being). Now what has an essence, and a quiddity by reason of that essence, and what is undivided in itself are the same. Hence these three—“thing,” “being,” and “one”—signify absolutely the same thing but according to different concepts.
554. Further, the substance. Then he gives the second argument, which has to do with sameness or identity of subject. This argument is as follows.
Any two attributes which are predicated per se and not accidentally of the substance of each thing are the same in subject, or numerically. But unity and being are such that they are predicated per se and not accidentally of the substance of each thing, for the substance of a thing is one in itself and not accidentally. Therefore, the terms “being” and “one” signify the same thing in subject.
555. That the terms “being” and “one” are predicated per se and not accidentally of the substance of each thing can be proved as follows. If being and one were predicated of the substance of each thing by reason of something added to it, being would have to be predicated also of the thing added, because anything at all is one and a being.
But then there would be the question of whether being is predicated of this thing (the one added) either per se or by reason of some other thing that is added to it in turn. And if the latter were the case, then the same question would arise once again regarding the last thing added, and so on to infinity. But this is impossible. Hence the first position must be held, namely, that a thing’s substance is one and a being of itself and not by reason of something added to it.
556. But it must be noted that Avicenna felt differently about this; for he said that the terms “being” and “one” do not signify a thing’s substance, but something added to it. He said this of “being” because, in the case of anything that derives its existence from something else, the existence of such a thing must differ from its substance or essence. But the term “being” signifies existence itself. Hence it seems that being or existence is something added to a thing’s essence.
557. He spoke in the same way of “one,” because he thought that the one which is interchangeable with being and the one which is the principle of number are the same. And the “one” which is the principle of number must signify a reality added to the substance; otherwise, number, since it is composed of ones, would not be a species of quantity, which is an accident added to substance. He said that this kind of “one” is interchangeable with “being,” not in the sense that it signifies the very substance of a thing or being, but in the sense that it signifies an accident belonging to every being, just as the ability to laugh belongs to every man.
558. But in regard to the first point he does not seem to be right, for even though a thing’s existence is other than its essence, it should not be understood to be something added to its essence after the manner of an accident, but something established, as it were, by the principles of the essence. Hence the term “being,” which is applied to a thing by reason of its very existence, designates the same thing as the term applied to it by reason of its essence.
559. Nor does it seem to be true that the one or unity which is interchangeable with being and that which is the principle of number are the same, for nothing that pertains to some special genus of being seems to be characteristic of all beings. Hence the unity which is limited to a special genus of being—discrete quantity—does not seem to be interchangeable with universal being. For, if unity is a proper and per se accident of being, it must be caused by the principles of being as being, just as any proper accident is caused by the principles of its subject. But it is not reasonable that something having a particular mode of being should be adequately accounted for by the common principles of being as being. It cannot be true, then, that something which belongs to a definite genus and species is an accident of every being.
560. Therefore, the kind of unity which is the principle of number differs from that which is interchangeable with being; for the unity which is interchangeable with being signifies being itself, adding to it the notion of undividedness, which, since it is a negation or a privation, does not posit any reality added to being. Thus unity differs from being in no way numerically, but only conceptually; for a negation or a privation is not a real being, but a being of reason, as has been stated.
However, the kind of unity which is the principle of number adds to substance the notion of a measure, which is a special property of quantity and is found first in the unit. And it is described as the privation or negation of division which pertains to continuous quantity, for number is produced by dividing the continuous. Hence number belongs to mathematical science, whose subject cannot exist apart from sensible matter but can be considered apart from sensible matter. But this would not be so if the kind of unity which is the principle of number were separate from matter in being and existed among the immaterial substances, as is true of the kind of unity which is interchangeable with being.
561. Hence there are as many. Then he concludes that it is the business of the philosopher to consider the parts of unity, just as it is to consider the parts of being.
First, he proves this;
second, he shows that there are different parts of philosophy corresponding to the different parts of being and unity, at and there are just.
He first says that since being and unity signify the same thing, and the species of things that are the same are themselves the same, there must be as many species of being as there are of unity, and they must correspond to each other.
For just as the parts of being are substance, quantity, quality, and so on, in a similar way the parts of unity are sameness, equality, and likeness. For things are the same when they are one in substance, equal when they are one in quantity, and like when they are one in quality. And the other parts of unity could be taken from the other parts of being, if they were given names. And just as it is the office of one science, philosophy, to consider all parts of being, in a similar way it is the office of this same science to consider all parts of unity, such as sameness, likeness and so forth. And to this starting point, namely, unity, almost all contraries may be referred.
562. He adds this qualification because in some cases this point is not so evident. Yet it must be true; for since one member of every pair of contraries involves privation, they must be referred back to certain primary privatives, among which unity is the most basic. And plurality, which stems from unity, is the cause of otherness, difference, and contrariety, as will be stated below. He says that this has been treated in our selection, or extract, of contraries, that is, a treatise which is the part selected to deal with contraries, namely, book 10 of this work.
563. And there are. Here he shows that the parts of philosophy are distinguished in reference to the parts of being and unity. He says that there are as many parts of philosophy as there are parts of substance, of which being and unity chiefly are predicated, and of which it is the principal intention or aim of this science to treat. And because the parts of substance are related to each other in a certain order (for immaterial substance is naturally prior to sensible substance), then among the parts of philosophy there must be a first part.
Now that part which is concerned with sensible substance is first in the order of instruction, because any branch of learning must start with things that are better known to us. He treats of this part in books 7 and 8 of this work.
But that part which has to do with immaterial substance is prior both in dignity and in the aim of this science. This part is treated in book 12 of this work.
Yet whatever parts are first must be continuous with the others, because all parts have unity and being as their genus. Hence all parts of this science are united in the study of being and unity, although they are about different parts of substance. Thus it is one science inasmuch as the foregoing parts are things that correspond to these, that is, to unity and being, as common attributes of substance.
In this respect the philosopher resembles the mathematician. For mathematical science has different parts, one of which is primary, as arithmetic, another secondary, as geometry, and others following these in order, as optics, astronomy, and music.