Commentary Aristotle Physics
The second point is that everything comes to be from everything, as water comes to be by separation from flesh and flesh likewise comes to be from water.
The third point is that every finite body is exhausted by a finite body. 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 this is how the reductio ad absurdum works: the conclusion contradicts some premise.
68. Next, at “for let flesh” (187b27), 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 will not fall below a certain magnitude; that is, 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 smallest particle of flesh than which there is no smaller, he proceeds as follows. If flesh is separated from water, and again other flesh, either the process of separation will 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—namely, water—there are certain things that are finite in respect to quantity and equal to each other, but 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 definition 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, such as 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 account of quantity that is found in a mathematical body.
70. He gives his fourth argument at “another proof may be added” (187b35). 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, nothing can be separated from this, 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 finally, in each (188a2), 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, at “the statement that” (188a5), 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.
Second, at “nor is Anaxagoras” (188a13; [73]), he shows that Anaxagoras did not have sufficient evidence for holding this position.
Therefore, he says 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, colors and other accidents of this sort are mixed together, as he said, and if someone says, on this supposition, that all things that are mixed can be separated, it would follow that there would be white and healthy but 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 problem results from this. Anaxagoras held that all things were mixed from the very beginning, but intellect began to separate them. Now, any intellect that attempts to do what cannot be done is not worthy of the name “intellect.”
Hence, that intellect will be inconsistent, intending the impossible, if he truly wishes, that is, 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, since something can be subtracted from any small quantity—and from the point of view of quality, because accidents are not separable from their subjects.
73. Next, at “nor is Anaxagoras” (188a13), 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 that 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; that is, he did not understand that a thing is always generated by things that 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 pieces of clay, but in other instances, 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; but 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, that is, 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: through composition, as the house is made of sides, and by resolution, as the sides come to be from the house.
74. Next, at “and it is better” (188a17), 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.