LESSON 13

Criticism of the Pythagoreans' Opinions

Chapters 8 & 9: 989b 24-990a 34

             98. But all those who make a study of all existing things, and who claim that some are sensible and others not, evidently make a study of both classes. And for this reason one should dwell at greater length on the statements they have made, whether they be acceptable or not, for the purposes of the present study which we now propose to make.

             99. Therefore, those who are called Pythagoreans used principles and elements which are foreign to the physicists; and the reason is that they did not take them from sensible things. For the objects of mathematics, with the exception of those that pertain to astronomy, are devoid of motion. Nevertheless they discuss and treat everything that has to do with the physical world; for they generate the heavens and observe what happens in regard to its parts, affections and operations. And in doing this they use up their principles and causes, as though they agreed with the others, i.e., the physicists, that whatever exists is sensible and is contained by the so-called heavens. But, as we have stated, the causes and principles [of which they speak] are sufficient to extend even to a higher class of beings, and are better suited to these than to their theories about the physical world.

             100. Yet how there will be motion if only the limited and unlimited and even and odd are posited as principles, they do not say. But how can there be generation or corruption, or the activities of those bodies which traverse the heavens, if there is no motion or change?

             101. And further, whether one grants them that continuous quantities come from these things, or whether this is demonstrated, how is it that some bodies are light and others heavy? For from what they suppose and state, they say nothing more about mathematical bodies than they do about sensible ones. Hence they have said nothing about fire, earth and other bodies of this kind, since they have nothing to say that is proper to sensible things.

             102. Further, how are we to understand that the attributes of number and number itself are [the causes] of what exists and comes to pass in the heavens, both from the beginning and now? And how are we to understand that there is no other number except that of which the world is composed? For when they [place] opportunity and opinion in one part of the heavens, and a little above or below them injustice and separation or mixture, and when they state as proof of this that each of these is a number, and claim that there already happens to be in this place a plurality of quantities constituted [of numbers], because these attributes of number correspond to each of these places, [we may ask] whether this number which is in the heavens is the same as that which we understand each [sensible] thing to be, or whether there is another kind of number in addition to this? For Plato says there is another. In fact, he also thinks that both these things and their causes are numbers, but that some are intellectual causes and others sensible ones.

Chapter 9

             Regarding the Pythagoreans, then, let us dismiss them for the present; for it is enough to have touched upon them to the extent that we have.

COMMENTARY

             201. Here he argues dialectically against the opinions of Pythagoras and Plato, who posited different principles than those which pertain to the philosophy of nature. In regard to this he does two things. First (98:C 201), he shows that a study of these opinions rather than those mentioned above belongs to the present science. Second (99:C 202), he begins to argue dialectically against these opinions ("Therefore those who").

             He says, first (98), then, that those who "make a study," i.e., an investigation, of all existing things, and hold that some are sensible and others non-sensible, make a study of both classes of beings. Hence an investigation of the opinions of those who spoke either correctly or incorrectly, belongs rather to the study which we now propose to make in this science. For this science deals with all beings and not with some particular class of being. Hence, the things which pertain to every class of being are to be considered here rather than those which pertain to some particular class of being.

             202. Therefore those who (99).

             Here he argues against the opinions of the foregoing philosophers. First (99), he argues against Pythagoras; and second (103:C 208), against Plato ("But those who posited Ideas").

             In regard to the first he does two things. First, he shows in what way Pythagoras agreed with the philosophers of nature, and in what way he differed from them. Second (100:C 204), he argues against Pythagoras' position ("Yet how").

             We must understand (99), then, that in one respect the Pythagoreans agreed with the philosophers of nature, and in another respect they differed from them. They differed from them in their position regarding principles, because they employed principles of things in a way foreign to the philosophers of nature. The reason is that they did not take the principles of things from sensible beings, as the natural philosophers did, but from the objects of mathematics, which are devoid of motion, and are therefore not physical. And the statement that the objects of mathematics are devoid of motion must be referred to those sciences which are purely mathematical, such as arithmetic and geometry. Astronomy considers motion, because astronomy is a science midway between mathematics and natural philosophy. For astronomy and the other intermediate sciences apply their principles to natural things, as is clear in Book II of the Physics.

             203. Now Pythagoras agreed with the philosophers of nature concerning the things whose principles he sought; for he discussed and treated all natural beings. He dealt with the generation of the heavens, and observed everything that happens to the parts of the heavens, by which are meant the different spheres, or also the different stars. He also considered what happens to its affections, or to the eclipses of the luminous bodies; and what happens to the operations and motions of the heavenly bodies, and their effects on lower bodies. And he used up causes on particular things of this kind by applying to each one its proper cause. He also seemed to agree with the other philosophers of nature in thinking that that alone has being which is sensible and is contained by the heavens which we see. For he did not posit an infinite sensible body as the other philosophers of nature did. Nor again did he hold that there are many worlds, as Democritus did. He therefore seemed to think that there are no beings except sensible ones, because he assigned principles and causes only for such substances. However, the causes and principles which he laid down are not proper or limited to sensible things, but are sufficient for ascending to higher beings, i.e., intellectual ones. And they were better fitted to these than the theories of the natural philosophers which could not be extended beyond sensible things, because these philosophers claimed that principles are corporeal. But since Pythagoras posited incorporeal principles, i.e., numbers, although he only posited principles of sensible bodies, he came very close to positing principles of intelligible beings, which are not bodies, as Plato did later on.

             204. Yet how (100).

             Here he gives three arguments against the opinion of Pythagoras. The first is this: Pythagoras could not explain how motion originates in the world, because he posited as principles only the limited and unlimited and the even and odd, which he held to be principles as substance, or material principles. But he had to admit that there is motion in the world. For how could there be generation and corruption in bodies, and how could there be any activities of the heavenly bodies, which occur as a result of certain kinds of motion, unless motion and change existed? Evidently they could not exist in any way. Hence, since Pythagoras considered generation and corruption and the operations of the heavenly bodies without assigning any principle of motion, his position is clearly unsatisfactory.

             205. And further (101).

             Here he gives the second argument. For Pythagoras claimed that continuous quantities are composed of numbers. But whether he proves this or takes it for granted, he could not give any reason on the part of numbers as to why some things are heavy and others light. This is clear from the fact that his theories about numbers are no more adapted to sensible bodies than they are to the objects of mathematics, which are neither heavy nor light. Hence they obviously said nothing more about sensible bodies than they did about the objects of mathematics. Therefore, since sensible bodies, such as earth and fire and the like, considered in themselves, add something over and above the objects of mathematics, it is evident that they said nothing proper in any true sense about these sensible bodies. Thus it is also evident that the principles which they laid down are not sufficient, since they neglected to give the causes of those [attributes] which are proper to sensible bodies.

             206. Further, how are we (102).

             Here he gives the third argument, which is based on the fact that Pythagoras seemed to hold two contrary [positions]. For, on the one hand, he held that number and the attributes of number are the cause both of those events which occur in the heavens and of all generable and corruptible things from the beginning of the world. Yet, on the other hand, he held that there is no other number besides that of which the substance of things is composed; for he held that number is the substance of things. But how is this to be understood, since one and the same thing is not the cause of itself? For Pythagoras says that the former position may be demonstrated from the fact that each one of these sensible things is numerical in substance; because in this part of the universe there are contingent beings, about which there is opinion, and which are subject to time inasmuch as they sometimes are and sometimes are not. But if generable and corruptible things were partly above or partly below, there would be disorder in the order of the universe: either after the manner of injustice, i.e., insofar as some being would receive a nobler or less noble place than it ought to have; or after the manner of separation, i.e., in the sense that, if a body were located outside its own place, it would be separated from bodies of a like nature; or after the manner of mixture and mingling, provided that a body located outside its proper place must be mixed with some other body, for example, if some part of water occupied a place belonging to air or to earth. In this discussion he seems to touch on two ways in which a natural body conforms to its proper place: one pertains to the order of position, according to which nobler bodies receive a higher place, in which there seems to be a kind of justice; and the other pertains to the similarity or dissimilarity between bodies in place, to which separation and mingling may be opposed. Therefore, insofar as things have a definite position, they are fittingly situated in the universe. For if their position were changed ever so little, something unfitting would result, inasmuch as it has been stated and shown that all parts of the universe are arranged in a definite proportion; for every definite proportion is numerical. And it was from this that Pythagoras showed that all things would be numbers. But, on the other hand, we see that the continuous quantities established in different places are many and different, because the particular places in the universe correspond to the proper attributes by which bodies are differentiated. For the attributes of bodies which are above differ from those which are below. Hence, since Pythagoras by means of the above argument affirms that all sensible things are numbers, and we see that the difference in sensible bodies is attributable to difference in place, the question arises whether the number which exists "in the heavens," i.e., in the whole visible body which comprises the heavens, is merely the same as that which must be understood to be the substance of each sensible thing, or whether besides this number which constitutes the substance of sensible things there is another number which is their cause. Now Plato said that there is one kind of number which is the substance of sensible things, and another which is their cause. And while both Plato himself and Pythagoras thought that numbers are both sensible bodies themselves and their causes, Plato alone considered intellectual numbers to be the causes of things that are not sensible, and sensible numbers to be the causes and forms of sensible things. And since Pythagoras did not do this, his position is unsatisfactory.

             207. In concluding Aristotle says that these remarks about the Pythagoreans' opinions will suffice; for it is enough to have touched upon them to this extent.