LECTURE 9 (187 a 27-188 a 18)

THE OPINION OF ANAXAGORAS THAT THE PRINCIPLES ARE INFINITE IS REFUTED

             58. Having set forth the opinions of the natural philosophers concerning the principles, he here pursues one of these opinions, namely, that of Anaxagoras. For this opinion seemed to assign a common cause for all the species of motion.

             The discussion is divided into two parts. In the first part he sets forth Anaxagoras' argument; in the second part he raises objections against it, where he says, 'Now the infinite . . .' (187 b 7).

             Concerning the first part he makes three points. First he sets forth those things which Anaxagoras supposed and from which he argues. Secondly, where he says, 'The one, they reasoned . . .' (187 a 33), he sets forth the order of his argument. Thirdly, where he says, 'But things, as they say . . .' (187 b 2), he sets forth Anaxagoras' response to a certain tacit objection.

             59. Anaxagoras assumed two things from which he argued. The first of these is a point which is assumed by all of the natural philosophers, namely, that nothing comes to be from nothing. And Aristotle says that, because of this, Anaxagoras seemed to have held the opinion that the principles are infinite. For he accepted as true the common opinion of all philosophers of nature, namely, that what simply is not in no way comes to be. For they assumed this as a principle and then developed their different opinions.

             60. Lest they would be forced to hold that something new comes to be which previously was in no way at all, some held that all things from the beginning existed together, either in some one confused state, as Anaxagoras and Empedocles held, or in some natural principle, such as water, fire, and air, or some intermediate between these.

             And in accordance with this they posited two modes of production.

             Those who held that all things pre-existed together as in one material principle said that to come to be is nothing other than to be altered. For they said that all things come to be from that one material principle through its condensation and rarefaction.

             Others, however, who held that all things pre-existed together in some one confused state and mixture of many, said that the coming to be of things is only a joining together and a separation.

             All of these philosophers were deceived because they did not know how to distinguish between potency and act. For being in potency is, as it were, a mean between pure non-being and being in act. Therefore, those things which come to be naturally do not come to be from nonbeing simply, but from being in potency, and not, indeed, from being in act, as they thought. Hence things which come to be did not necessarily pre-exist in act, as they said, but only in potency.

             61. Next where he says, 'Moreover the fact that . . .' (187 a 32), he mentions the second thing which Anaxagoras assumed.

             Anaxagoras said that contraries come to be from each other. For we see the cold come to be from the hot, and vice versa. And from this he concluded that, since nothing comes to be from nothing, one of the contraries pre-exists in the other.

             And this is true, of course, in respect to potency. For the cold is in the hot in potency, but not in act, as Anaxagoras thought. For he was not aware of being in potency, which is a mean between pure non-being and being in act.

             62. Next where he says, 'The one, they reasoned . . .' (187 a 33), he sets forth the deductive order of the argument.

             Anaxagoras proceeded as follows. If something comes to be, it is necessary that it should come to be either from being or from nonbeing. But he excluded one of these alternatives--namely, that something should come to be from non-being. He does this because of the common opinion of the philosophers mentioned above. Whence he concluded that the remaining member was correct, namely, that a thing comes to be from being. For example, if air comes to be from water, then air pre-existed. For it cannot be said that air comes to be from water unless air pre-existed in water. Hence he wished to say that everything which comes to be from something pre-existed in that from which it comes to be.

             But because this seemed to be contrary to what appears to the senses (for it is not apparent to the senses that that which is generated from something pre-exists in it), he forestalled this objection by holding that that which comes to be from something pre-exists in it as certain most minute parts which are not sensible to us because of their smallness. For example, if air comes to be from water, certain minute parts of air are in the water, but not in that quantity in which it is generated. And so he said that by the gathering together of these parts of air by themselves, and by their separation from the parts of water, air comes to be.

             Having accepted, therefore, that everything which comes to be from something pre-exists in it, he further assumed that everything comes to be from everything. Whence he concluded that everything would be mixed in everything else as minute, non-sensible parts.

             And because an infinite variety of things can come to be from another, he said that infinite minute parts were in each thing.

             63. Next where he says, 'But things, as they say . . .' (187 b 2), he excludes a certain tacit objection.

             It is possible for someone to object as follows. If infinite parts of everything are in everything, it would follow that things neither differ from each other nor appear to differ from each other.

             Therefore, as if he were answering this objection, Anaxagoras says that things appear to differ from each other and are diversely named because of that which is dominant in them, even though there is an infinite number of minute parts contained in any mixture. And so nothing is purely and totally white or black or bone. Rather, that which abounds in each thing seems to be the nature of that thing.

             64. Next where he says, 'Now the infinite . . .' (187 b 7), Aristotle refutes the above mentioned position.

             Concerning this he makes two points. First he disproves the position absolutely. Secondly, where he says, '. . . and it is better . . .' (188 a 17), he compares it to the opinion of Empedocles.

             Concerning the first part he makes two points. First he sets forth arguments to disprove the opinion of Anaxagoras. Secondly, where he says, 'The statement that . . .' (188 a 5), he disagrees with Anaxagoras' way of understanding his own position.

             Concerning the first part he gives five arguments.

             The first of these is as follows. Every infinite thing, in that respect in which it is infinite, is unknown. He explains why he says 'in that respect in which it is infinite'. If it is infinite in respect to multitude or magnitude, it will be unknown in respect to quantity. If, however, it is infinite in respect to species (for example, if it is composed of an infinite variety of species), then it will be unknown according to quality. And the reason for this is that what is known by the intellect is grasped by the intellect with respect to all that belongs to that thing. But this cannot happen with regard to something infinite. If, therefore, the principles of a thing are infinite, they must be unknown either in respect to quantity or in respect to species.

             But if the principles are unknown, those things which are from the principles must be unknown. He proves this as follows. We think that we know any composite when we know from what and from how many [principles] it is composed, i.e., when we know both the species and the quantity of the principles. It follows, therefore, from first to last that, if the principles of natural things are infinite, then natural things are unknown either in respect to quantity or in respect to species.

             65. At the point where he says, 'Further if the parts . . .' (187 b 14), he gives the second argument, which is as follows.

             If the parts of a whole do not have a determinate quantity, either great or small, but can be any size, either great or small, it is not necessary that the whole have a determinate greatness or smallness. Rather the whole could have any size. This is so because the quantity of the whole comes from the parts. (But this must be understood of the parts existing in act in the whole, as flesh and nerve and bone exist in an animal. Hence he says, '. . . by parts I mean components into which a whole can be divided and which are actually present in it' (187 b 15). And by this he excludes the parts of a continuous whole which are in the whole in potency.)

             But it is impossible that an animal or a plant or some such thing be related indeterminately to any size, whether great or small. For there is some quantity so large that no animal exceeds it in size. So also there is some quantity so small that no animal is found to be smaller. And the same must be said of plants. Therefore by denying the consequent it follows that the parts are not of indeterminate quantity. For what is true of the whole is true of the parts. But flesh and bone and things of this sort are parts of an animal, and fruits are parts of plants. Therefore it is impossible that flesh and bone and such things should have an indeterminate quantity, either greater or smaller. Therefore it is not possible that there should be certain parts of flesh or bone which are non-sensible because of smallness.

             66. It seems, however, that what is said here is contrary to the statement that a continuum is divisible to infinity. For if the continuous is divisible to infinity, and flesh is, indeed, a kind of continuum, it seems that flesh is divisible to infinity. Therefore, some part of flesh, according to a division to infinity, goes beyond every determinate smallness.

             But it must be pointed out that although a body, considered mathematically, is divisible to infinity, the natural body is not divisible to infinity. For in a mathematical body nothing but quantity is considered. And in this there is nothing repugnant to division to infinity. But in a natural body the form also is considered, which form requires a determinate quantity and also other accidents. Whence it is not possible for quantity to be found in the species of flesh except as determined within some termini.

             67. He gives the third argument where he says, 'Again according to the theory . . .' (187 b 23).

             Concerning this he makes two points. First he sets forth certain things which are the basis of the argument. Secondly, where he says, 'For let flesh . . .' (187 b 28), he sets forth the deductive order of the argument.

             Concerning the first part he proposes three things.

             The first is that according to the position of Anaxagoras, as was said above, all things are together. And from this Aristotle wishes to reduce Anaxagoras' argument to absurdity. For Anaxagoras said, as was pointed out, that all things which are of a certain kind, i.e., all things which are of like parts, such as flesh and bone and the like, are in each other, and do not come to be from nothing, but are separated from that in which they pre-exist. And each thing is named from that which abounds in it, i.e., from the largest number of parts existing in the thing.

             The second point is that everything comes to be from everything, as water comes to be by separation from flesh, and in the same way flesh comes to be from water.

             And the third point is that every finite body is reduced by a finite body. That is, if from some finite body, however large, a finite body, however small, is taken away, the smaller can be taken away from the larger until eventually the greater whole is consumed by the smaller through division.

             And from these three points Aristotle concludes what he primarily intended, namely, that each thing is not in each thing. And this is contrary to the first of these three points. For in arguments which lead to absurdity the denial of one of the premises is the final conclusion.

             68. Next where he says, 'For let flesh . . .' (187 b 28), he develops his argument and assumes what was concluded in the preceding argument.

             He says that if flesh is removed from water (since flesh is generated from water), and if again another separation of flesh is made from the remaining water, then although there will always remain a smaller quantity of flesh in the water, still the size of that flesh is not less than a certain smallness, i.e., there happens to be a certain small measure of flesh than which there will not be any smaller flesh, as is clear from the argument given above.

             Therefore, having established that there is some small particle of flesh than which there is no smaller, he proceeds as follows.

             If from water flesh is separated, and again other flesh, the process of separation will either stop or it will not. If it stops, then there is no flesh in the remaining water, and everything will not be in everything. If it does not stop, then some part of flesh will always remain in the water. Thus in the second separation the remaining flesh is smaller than in the first, and in the third it is smaller than in the second. And since we cannot proceed to infinity in smallness of parts, as was said, then the smallest parts of flesh are equal and infinite in number in some finite body of water. Otherwise separation could not proceed to infinity. It follows, therefore, that if the separation does not stop, but flesh is always removed from water to infinity, then in some finite magnitude, e.g., water, there are certain things which are finite in respect to quantity, and equal to each other, and infinite in respect to number, namely, the infinite smallest parts of flesh. But this is impossible and contrary to what was said above, namely, that every finite body is reduced by some finite body. Therefore the first point, namely, that everything is in everything, as Anaxagoras held, is also impossible.

             69. We must note that it is not without reason that the Philosopher used the term 'equal' in stating the last absurdity to which this position leads. For if the nature of quantity is considered, it is not absurd that an infinity of unequal parts be in a finite body. For if a continuum is divided according to the same proportion, it will be possible to proceed to infinity, for example, if we take a third of a whole, and then a third of the third, and so on. In this case, however, the parts were not taken as equal in quantity. But if the division is made according to equal parts, we will not be able to proceed to infinity even if we consider only the nature [ratio] of quantity which is found in a mathematical body.

             70. He gives his fourth argument where he says, 'Another proof may be added . . .' (187 b 35). The argument is as follows.

             Every body becomes a smaller one when something is taken from it, because every whole is greater than its parts. Since then the quantity of flesh is determinately great or small, as is clear from what was said above, there must be some smallest bit of flesh. Therefore from this nothing can be separated, because the remaining flesh would be smaller than this smallest piece of flesh. Therefore it is impossible that everything comes to be from everything by separation.

             71. At the point where he says, 'Lastly in each . . .' (188 a 3), he gives his fifth argument, which is as follows. If infinite parts of each thing are in each thing, and everything is in everything, it follows that infinite parts of flesh and infinite parts of blood and brain are in an infinite number of bodies. And regardless of how much is separated, the same amount would always remain. Therefore it would follow that the infinite is in the infinite infinitely. But this is unthinkable.

             72. Next where he says, 'The statement that . . .' (188 a 5), he disproves the position of Anaxagoras according to Anaxagoras' own understanding of it.

             He does this in two ways. First he shows that Anaxagoras did not understand his own position. Secondly, where he says, 'Nor is Anaxagoras . . .' (188 a 13), he shows that Anaxagoras did not have sufficient evidence for holding this position.

             He says, therefore, first that although Anaxagoras has in a certain respect spoken the truth, he himself did not understand what he said when he held that the process of separation would never end. For accidents can never be separated from substance; yet he held that there was a mixture not only of bodies but also of accidents. When something becomes white, he said that this happened by an abstraction of white from the previously existing mixture. If then colours and other accidents of this sort are mixed together, as he said, and if someone on this supposition says all things that are mixed can be separated, it would follow that there would be white and healthy, and yet there would be no subject of which these are predicated and in which they are. But this is impossible. Therefore the truth is that if accidents are in the mixture it is impossible that all mixed things can be separated.

             Another absurdity results from the following. Anaxagoras held that all things were mixed from the very beginning, but intellect began to separate them. Now any intellect which attempts to do what cannot be done is not worthy of the name intellect. Hence that intellect will be inconsistent, intending the impossible, if it truly wishes this, i.e., wishes to separate things completely. For this is impossible both from the point of view of quantity, because there is no smallest magnitude, as Anaxagoras said, for from any small quantity something can be subtracted, and from the point of view of quality, because accidents are not separable from their subjects.

             73. Next where he says, 'Nor is Anaxagoras . . .' (188 a 13), he disproves this position by reason of the fact that Anaxagoras did not have sufficient evidence.

             Since Anaxagoras saw that a thing is made large by the coming together of many small parts which are similar, as a stream is made from many brooks, he believed this to be the case for all things. And thus Aristotle says that Anaxagoras did not correctly understand the generation of things of the same species, i.e., he did not understand that a thing is not always generated by things which are similar in respect to species. For some things are both generated from and are resolved into things like unto themselves, as clay is divided into bricks; in other instances, however, this is not so. For some things are generated from that which is dissimilar. And in these instances there is not merely one mode of production. For some things are made by alteration from that which is unlike, as the sides of a house are made from clay and not from sides; whereas other things are made by composition, as the house is not made of houses, but of sides. It is in this way that air and water come to be from each other, i.e., as from the unlike.

             Another reading here is 'as the sides are from the house'. And thus he sets forth a twofold way in which things come to be from the unlike, i.e., through composition, as the house is made of sides, and by resolution, as the sides come to be from the house.

             74. Next where he says, '. . . and it is better . . .' (188 a 17), he disproves the position of Anaxagoras by comparing it with the opinion of Empedocles. He says that it is better to make the principles smaller in number and finite, as Empedocles does, than to make them many and infinite, as does Anaxagoras.