Commentary Aristotle Physics
Lecture 4
Error of more recent philosophers about the one and the many
Even the more recent of the ancient thinkers were alarmed lest the same thing should turn out to be both one and many. So some, like Lycophron, were led to omit “is,” and others to change the mode of expression and say “man whitened” instead of “is white” and “walks” instead of “is walking,” for fear that, if they added the word “is,” they should be making the one to be many—as if “one” and “being” were always used in one way.
What “is” may be many either in definition (for example “to be white” is one thing and “to be musical” another, yet the same thing may be both, so the one is many) or by division, as the whole and its parts.
On this point, indeed, they were already getting into difficulties and admitted that the one was many—as if there was any difficulty about the same thing being both one and many.
For these are not opposites, since “one” may mean either “one in potency” or “one in act.” If, then, we approach the thesis in this way, it seems impossible for all things to be one.
25. Having disproven the opinion of Parmenides and Melissus that being is one, the Philosopher here shows that certain later philosophers fell into the difficulty on the same basis.
Parmenides and Melissus erred because they did not know how to distinguish the uses of the term “one.” Thus, they said that what is one in a certain respect is one simply. But the later philosophers, also not knowing how to distinguish the uses of the term “one,” thought it absurd that the same thing should be in some way one and many. Yet, being convinced by the arguments, they were forced to believe it. And so Aristotle says that the later philosophers were alarmed (that is, fell into a difficulty similar to that of the ancients, Parmenides and Melissus) lest they be forced to say that one and the same thing is one and many. Now, this seemed absurd to both groups of philosophers. So, the earlier philosophers, holding that all is one, rejected all multiplicity. The later philosophers, on the other hand, tried to remove multiplicity from anything they held to be one.
26. Thus some, such as Lycophron, removed the verb is from propositions. They said that we must not say man is white, but rather white man. For they thought that man and white were in some way one; otherwise, white would not be predicated of man. And it seemed to them that the word is, since it is a verbal copula, must serve as a copula between two. And so, wishing to remove all multiplicity from that which is one, they said the verb is must not be used.
But because such speech seemed to be imperfect, and because an imperfect understanding was produced in the soul of the listener if names were spoken without the addition of any verb, some changed the mode of speech, wishing to correct this. They did not say white man, because of the imperfection of this mode of speech. Nor did they say man is white, lest they give the impression that there is multiplicity.
Rather, they said man whitened, because, by this expression whitened, a thing is not understood (as it seemed to them), but rather a certain change in the subject. And in like manner, they said that we must not say, man is walking, but man walks, lest by the addition of the verbal copula is, they make that which they thought to be one (namely, white man) to be many, as if one and being were used singularly, that is, in only one way and not in many.
27. But this is false, for that which is one in one respect can be many in some other respect, as what is one in subject can be many in concept. Thus, the white thing and the musical thing are the same in subject but many in concept; for the concept of music is one thing, and the concept of white is another. Hence it can be concluded that the one may be many.
This may happen also in another way. That which is actually one as a whole may be many according to a division of parts. Thus, the whole is one in its totality but it has multiplicity of parts. And, although those who wished to remove the verb is or alter it, as was said above, found some solution to the objection that things could be one in subject and many in definition, nevertheless on this point, namely, on the whole and parts, they, in their ignorance, failed to respond to the objection altogether, believing that it was something of a problem that the one should be many.
But it is not problematic if the one and the many are not taken as opposites. For the one in act and the many in act are opposed, but the one in act and the many in potency are not opposed. And, because of this, he adds that “one” is said in many ways—namely, one in potency and one in act. And so, nothing prohibits the same thing from being one in act and many in potency, as is clear with regard to the whole and the parts.
28. Finally, he draws the conclusion that he primarily intended, namely, that it is clear from the foregoing arguments that it is impossible for all beings to be one.
Lecture 5. The argument of Melissus is answered
Further, the arguments they use to prove their position are not difficult to expose. For both Melissus and Parmenides syllogized sophistically. Their premises are false, and their conclusions do not follow.
Or rather, the argument of Melissus is more gross and offers no difficulty at all. If you admit one ridiculous proposition, the rest follows—a simple enough proceeding.
The fallacy of Melissus is obvious. He supposes that if what is made always has a beginning, then what is not made has no beginning.
Then this also is absurd, that in every case there should be a beginning of a thing—not of the time and not only in the case of generation in the full sense but also in the case of coming to have a quality—as if change never took place suddenly.
Again, does it follow that being, if one, is motionless?
Why should not the whole of it move within itself, as parts of it do that are unities, such as this water? Again, why is qualitative change impossible?
Further, being cannot be one in form, though it may be in what it is made of. (Even some of the physicists hold it to be one in the latter way, though not in the former.) Man obviously differs from horse in form, and contraries from each other.
29. Having disproved the position of Parmenides and Melissus, here the Philosopher begins to answer their arguments.
Concerning this, he makes three points.
First, he shows how their arguments are to be answered;
second, at “the fallacy of Melissus” (186a10; [31]), he answers the argument of Melissus;
third, at “the same kind of argument” (186a22; [36]), he answers the argument of Parmenides.
30. He says that it is not difficult to answer the arguments with which Parmenides and Melissus reasoned. For each syllogized sophistically both in that they assumed false propositions and in that they did not observe the proper form of the syllogism. But the argument of Melissus is the more gross—that is, more vain and foolish—and offers no difficulty at all, that is, does not give rise to any doubt. For he assumed what is contrary to natural principles and what is manifestly false, namely, that being is not generated. And it is not a serious matter, granting one absurdity, if another should follow.
31. Next, at “the fallacy of Melissus” (186a10), he answers the argument of Melissus. The argument is as follows. What is made has a beginning. Therefore, what is not made has no beginning. But being is not made. Therefore, it has no beginning, and consequently has no end. But what has neither beginning nor end is infinite. Therefore, being is infinite. But what is infinite is immobile, for it would not have outside itself that by which it would be moved.
Furthermore, what is infinite is one, for if there were many, there must necessarily be something outside the infinite. Therefore, being is one and infinite and immobile.
Furthermore, in order to show that being is not generated, Melissus used a certain argument that some natural philosophers also used. Aristotle gives this argument below, near the end of book 1.
32. Aristotle disproves this argument of Melissus on four counts. He first argues against the statement of Melissus that if what is made always has a beginning, then what is not made has no beginning. This does not follow. Rather, it is a fallacy of the consequent.
For he argues from the denial of the antecedent to the denial of the consequent, when the correct form of argumentation would be the converse.
Hence, it does not follow that, if a thing that is made has a beginning, then that which is not made does not have a beginning. The correct conclusion would be that, if a thing does not have a beginning, then it is not made.
33. Second, at “then this also is absurd” (186a13), he disproves the argument under discussion with reference to the inference that, if something has no beginning, then it is infinite. For “beginning” may be taken in two ways.
In one way, we speak of a beginning of time and of generation. And this meaning of “beginning” is taken when it is said that what is made has a beginning or what is not made has no beginning.
In another sense, “beginning” is the beginning of a thing or a magnitude. And, in this sense, it would follow that, if a thing has no beginning, then it is infinite.
From this, it is clear that Melissus uses the term “beginning” as if it had one meaning only. Hence, Aristotle says that it is absurd to say that every case of beginning is the beginning of a thing, that is, of a magnitude, such that the beginning of time and of generation is not another meaning of the term. Nevertheless, a simple and instantaneous generation (which is the induction of a form in matter) does not have a beginning, for simple generation does not admit of a beginning. But there is a beginning for a whole alteration whose terminus is a generation, since this would not be an instantaneous change. And because of this terminus, this is sometimes called a “generation.”
34. Third, at “again, does it follow” (186a15), he disproves the above position with reference to its third inference: because being is infinite, it is immobile. He shows in two ways that this does not follow.
First, it does not follow in regard to local motion. For a part of water could be moved in water such that it is not moved to any extrinsic place. In this case, it would be moved by a joining and separation of the parts. And likewise, if the whole infinite body were water, it would be possible for the parts of it to be moved within the whole and not proceed outside the place of the whole.
Again, he disproves this with reference to the motion of alteration. For nothing prevents the infinite from being altered either as a whole or in its parts, for it would not be necessary to posit something outside the infinite to account for this.
35. Fourth, at “further, being cannot” (186a19), he disproves the given argument with reference to its fourth inference, by which it is concluded that, if being is infinite, it is one. For it does not follow that it is one according to species, but rather that it is one according to matter, just as some of the philosophers of nature have held that all things are one according to matter but not according to species. For it is obvious that man and horse differ in species, and in like manner, contraries differ from each other in species.