LESSON 12

Are Unity and Being the Substance and Principle of All Things?

Chapter 4: 1001a 4-1001b 25

             266. But the most difficult problem which has to be considered, and the one which is most necessary for a knowledge of the truth, is whether unity and being are the substance of existing things, and whether each of them is nothing else than unity and being. Or whether it is necessary to investigate what being and unity themselves are, as though there were some other nature which underlies them.

             267. For some think that reality is of the former sort, and some of the latter. For Plato and the Pythagoreans thought that being and unity were nothing else [than themselves], and that this is their nature, their substance being simply unity and being. But among the other philosophers [there are different opinions] about the nature of unity. Empedocles, for example, as though reducing it to something better known, says that unity is being; for he would seem to say that this is love, since this is the cause why unity belongs to all things. Others say that this unity and being of which existing things consist and have been made is fire, and others say it is air. And those who hold that there are many elements say the same thing; for they must also speak of unity and being in as many ways as they say there are principles.

             268. But if anyone holds that unity and being are not substances, it will follow that no other universals are such; for these are the most universal of all. But if there is no one-in-itself or being-in-itself, there will hardly be any other things that exist apart from what are called singular things. Further, if unity is not a substance, evidently number will not exist as another reality separate from existing things; for number is units, and a unit is truly something one. But if there is a one-in-itself and being-in-itself, the substance of these must be unity itself and being itself. For nothing else is predicated universally of all things but these two.

             269. But, on the other hand, if there is to be a one-in-itself and being-in-itself, there is great difficulty in seeing how there will be anything else besides these. I mean, how will there be more beings than one? For that which differs from being does not exist. Hence according to Parmenides' argument it must follow that all beings are one, and that this is being.

             270. But there is a difficulty in either case; for whether unity itself is not a substance, or whether there is a unity itself, it is impossible for number to be a substance. Now it has already been stated why this follows if unity is not a substance; but if it is, the same difficulty will arise with regard to being. For from something outside of being something else will be one; for it must be not one. But all beings are either one or many, each of which is a one.

             271. Further, if unity itself is indivisible, according to Zeno's axiom it will be nothing. For that which when added does not make a thing greater or when subtracted does not make it smaller, this, he says, does not belong to the realm of existing things, as though it were evident that whatever has being is a continuous quantity. And if it is a continuous quantity, it is corporeal; for this in every respect is a being. But other quantities, for example, a surface and a line, when added in one way will make a thing greater, but in another way they will not; and a point and a unit will do so in no way.

             272. But this philosopher speculates clumsily, and it is possible for a thing to be indivisible in such a way that some answer may be made against him; for when something of this kind is added it will not make a thing greater but more.

             273. Yet how will continuous quantity come from such a unity or from many of them? For this would be like saying that a line is made up of points.

             274. But even if someone were to think that the situation is such that number has come, as some say, from unity itself and from something else that is not one, none the less it would be necessary to inquire why and how the thing which has come to be would sometimes be a number and sometimes a continuous quantity, if that not-one were inequality and the same nature in either case. For it is not clear how continuous quantities would be produced from unity and this principle, or from some number and this principle.

COMMENTARY

             488. Having asked whether the principles of things are the same or different, the Philosopher now asks how unity itself could have the nature of a principle; and in regard to this he does three things. First (266:C 488), he asks whether unity itself is a principle; second (275:C 502), he asks whether numbers, which arise or follow from unity, are the principles of things ("And connected with"); and third (284:C 515), whether the Forms, which are certain separate unities, are the principles of things ("But in general").

             In regard to the first he does three things. First, he raises the question. Second (267:C 489), he gives the opinions on both sides ("For some think"). Third (268:C 490), he advances arguments on both sides ("But if anyone").

             He says, first (266), that of all the different questions which have been raised, one is more difficult to consider because of the weight of the arguments on both sides, and that this question is also one about which it is necessary to know the truth, because our decision about the substances of things depends on it. Now this question is whether unity and being are the substances of things, not so that either of them must be attributed to some other nature which would be informed, as it were, by unity and being, but rather so that the unity and being of a thing are its substance; or, in an opposite way, whether it is necessary to ask what that thing is to which unity and being properly belong, as though there were some other nature which is their subject.

             489. For some think (267).

             Here he gives the opinions on each side of the question. He says that some philosophers thought that reality was of one kind, and some of another. For Plato and the Pythagoreans did not hold that unity and being are the attributes of some nature, but that they constitute the nature of things, as though being itself and unity itself were the substance of things. But some philosophers, in speaking about the natural world, attributed unity and being to certain other natures, as Empedocles reduced the one to something better known, which he said is unity and being; and this seems to be love, which is the cause of unity in the world. But other philosophers of nature attributed these to certain elementary causes, whether they posited one first principle, as fire or air, or more than one. For since they would hold that the material principles of things are the substances of things, it was necessary that each of these should constitute the unity and being of things; so that whichever one of these anyone might hold to be a principle, he would logically think that through it being and unity would be attributed to all things, whether he posited one principle or more than one.

             490. But if anyone (268).

             Here he gives arguments on both sides of the question. First, he gives arguments in support of the view of Plato and Pythagoras. Second (269:C 493), he gives arguments on the other side of the question, in support of the view of the philosophers of nature ("But, on the other hand").

             In regard to the first (268), he makes use of elimination as follows. It is necessary to hold either that unity and being, separate and existing apart, are a substance, or not. Now if it is said that unity and being are not a substance, two untenable consequences will follow. The first of these is this: unity and being are said to be the most universal of all, and therefore, if unity and being are not separate in such a way that unity itself or being itself is a certain substance, it will then follow that no universal is separate. Thus it will follow that there is nothing in the world except singular things, which seems to be inappropriate, as has been stated in earlier questions (C 443).

             491. The other untenable consequence is this. Number is nothing else than units, because number is composed of units; for a unit is nothing else than unity itself. Therefore, if unity itself is not separate as a substance existing of itself, it will follow that number will not be a reality separate from those things which are found in matter. This can be shown to be inappropriate in view of what has already been stated above. Hence it cannot be said that unity and being are not a substance which exists by itself.

             492. Therefore, if the other part of the division is conceded, that there is something which is unity itself and being itself, and that this exists separately, it must be the substance of all those things of which unity and being are predicated. For everything that is separate and is predicated of many things is the substance of those things of which it is predicated. But nothing else is predicated of all things in as universal a way as unity and being. Therefore unity and being will be the substance of all things.

             493. But, on the other hand (269).

             Then he argues the other side of the question; and he gives two arguments. The second (271:C 496) of these begins where he says, "Further, if unity itself."

             In regard to the first he does two things. First, he gives the argument. Second (270:C 494), he shows how the question is made difficult as a result of the argument given ("But there is a difficulty in either case").

             The first (269) argument, then, is as follows: if there is something which is itself being and unity as something existing separately, it will be necessary to say that unity is the very same thing as being. But that which differs from being is non-being. Therefore it follows, according to the argument of Parmenides, that besides the one there is only non-being. Thus all things will have to be one, because it could not be held that that which differs from the one, which is essentially separate, is a being.

             494. But there is a difficulty (270).

             Here he shows how this argument creates a difficulty in the case of the position of Plato, who held that number is the substance of things. He says that Plato faces a difficulty in either case, whether it is said that this separate one is a substance or not. For whichever view is held, it seems impossible that number should be the substance of things. For if it is held that unity is not a substance, it has already been stated (269:C 493) why number cannot be held to be a substance.

             495. But if unity itself is a substance, the same problem will arise with respect to both unity and being. For either there is some other unity besides this unity which exists separately of itself, or there is not. And if there is no other, a multitude of things will not exist now, as Parmenides said. But if there is another unity, then that other unity, since it is not unity itself, must have as a material element something that is other than unity itself, and, consequently, other than being. And that material element from which this second unity comes to be, will have not to be a being. Thus a multitude of beings cannot be constituted from this unity which exists apart from unity itself, because all beings are either one or many, each of which is a one. But this one has as its material element something that is neither unity nor being.

             496. Further, if unity (271).

             Here he gives the second argument; and in regard to this he does three things. First (271:C 496), he gives the argument. Second (272:C 498), he criticizes it ("But this"). Third (273:C 499), he shows that the difficulty remains ("Yet how will continuous quantity").

             He says first (271), then, that if this separate unity is indivisible, there follows from this the other position, which Zeno assumed, that nothing exists. For Zeno supposed that that which when added does not make a thing greater and when taken away does not make it smaller, is nothing in the real order. But he makes this assumption on the grounds that continuous quantity is the same as being. For it is evident that this is not a continuous quantity--I mean that which when added does not make a thing greater and when subtracted does not make it smaller. Therefore, if every being were a continuous quantity, it would follow that that which when added does not make a thing greater and when subtracted does not make it smaller, is non-being.

             497. And better still, if any particular thing were to bear this out, every being would have to be a corporeal continuous quantity. For anything added to or subtracted from a body in any one of its dimensions, makes the body greater or less. But other continuous quantities, such as lines and surfaces, become greater insofar as one dimension is added, whereas others do not. For line added to line in length causes increase in length but not in width; and surface added to surface causes increase in width and in length but not in depth. But a point and a unit do not become greater or less in any way. Hence according to Zeno's axiom it would follow that a point and a unit are non-beings in an absolute sense, whereas a body is a being in every respect, and surfaces and lines are beings in one respect and non-beings in another respect.

             498. But this (272).

             Here he criticizes the argument which has been given. He says that Zeno, by proposing such an axiom, speculated "clumsily," i.e., in an unskilled and rude manner, so that according to him there cannot by anything indivisible. And for this reason some answer must be given to the foregoing argument; and if not to the point at issue, at least to the man. Now we say that even though a unity when added to something else does not make it larger, it does cause it to be more. And it is sufficient for the notion of being that in the case of what is continuous it should make a thing larger, and that in the case of what is discrete it should make it more.

             499. Yet how will (273).

             Then he states the difficulty which still faces the Platonists after the above solution. And he advances two difficulties. The first of these is that the Platonists held that the one which is indivisible is the cause not only of number, which is a plurality, but also of continuous quantity. Therefore, if it is granted that when a one is added it makes a thing more, as would seem to suffice for the one which is the cause of number, how will it be possible for continuous quantity to come from an indivisible one of this kind, or from many such ones, as the Platonists held? For this would seem to be the same thing as to hold that a line is composed of points. For unity is indivisible just as a point is.

             500. But even if someone (274).

             Here he gives the second difficulty. He says that if anyone were to think that the situation is such that number is the result of the indivisible one and of something else which is not one, but participates in the one as a kind of material nature, as some say, the question would still remain why and how that which comes from the one as form and from another material nature, which is called the not-one, is sometimes a number and sometimes a continuous quantity. The difficulty would be most acute if that material not-one were inequality, as is implied in the continuously extended, and were to be the same reality. For it is not clear how numbers come from this inequality as matter and from the one as form; nor again is it clear how continuous quantities come from some number as form and from this inequality as matter. For the Platonists held that number comes from a primary one and a primary two, and that from this number and material inequality continuous quantity is produced.

             501. The solution of this problem is treated by Aristotle in the following books. For the fact that there is something separate, which is itself one and being, he will prove below in Book XII (1078:C 2553), when he establishes the oneness of the first principle which is separate in an absolute sense, although it is not the substance of all things which are one, as the Platonists thought, but is the cause and principle of the unity of all things. And insofar as unity is predicated of other things it is used in two ways. In one way it is interchangeable with being, and in this way each thing is one by its very essence, as is proved below in Book IV (301:C 548); and unity in this sense adds nothing to being except merely the notion of undividedness. Unity is used in another way insofar as it has the character of a first measure, either in an absolute sense or with respect to some genus. And this unity if it is both a minimum in the absolute sense and indivisible, is the one which is the principle and measure of number. But if it is not both a minimum in an absolute sense and indivisible, it will not be a unit and measure in an absolute sense, as a pound in the case of weights and a half-tone in the case of melodies, and a foot in the case of lengths. And nothing prevents continuous quantities from being composed of this kind of unity. He will establish this in Book X (822:C 1940) of this work. But because the Platonists thought that the one which is the principle of number and the one which is interchangeable with being are the same, they therefore held that the one which is the principle of number is the substance of each thing, and consequently that number, inasmuch as it is composed of many substantial principles, makes up or comprises the substance of composite things. But he will treat this question at greater length in Books XIII and XIV of this work.