Commentary Aristotle Physics
Lecture 3. Refutation of Parmenides and Melissus
The most pertinent question with which to begin will be this: in what sense is it asserted that all things are one? For that which “is” is used in many senses. Do they mean that all things “are” substance or quantities or qualities? And, further, are all things one substance (one man, one horse, or one soul) or one particular quality (white or hot or some other such thing)?
These are all very different doctrines and all impossible to maintain. For if both substance and quantity and quality are, then being will be many whether these exist independently of each other or not. If, on the other hand, it is asserted that all things are quality or quantity, then, whether substance exists or not, an absurdity results—if the impossible can properly be called absurd. For none of these except substance can exist independently, for everything is predicated of substance as subject.
Now, Melissus says that being is infinite. It is, then, a quantity, since the infinite is in the category of quantity, whereas substance or quality or passion cannot be infinite except accidentally—that is, if at the same time they are also quantities. For to define the infinite, you must use quantity in your formula, but not substance or quality. If, then, being is both substance and quantity, it is two, not one; but if only substance, it is not infinite and has no magnitude, for to have that, it will have to be a quantity.
Again, “one” itself, no less than “being,” is used in many senses, so we must consider in what sense the word is used when it is said that the all is one. Now, we say either that the continuous is one or that the indivisible is one, or that things are said to be one when their essence is one and the same, as “vintage” and “wine.” If they are one in the sense of continuous, then it is many, for the continuous is infinitely divisible.
There is, indeed, a difficulty about part and whole, perhaps not relevant to the present argument, yet deserving consideration on its own account, namely, whether the part and the whole are one or more than one, and how they can be one or many, and if they are more than one, in what sense they are more than one.
(It is similar with the parts of wholes that are not continuous.)
Further, if each of the two parts is indivisibly one with the whole, the difficulty arises that they will be indivisibly one with each other also.
But to proceed: if their one is one as indivisible, nothing will have quantity or quality, and so the one will not be infinite, as Melissus says—nor, indeed, limited, as Parmenides says, for though the limit is indivisible, the limited is not.
But, if all things are one in the sense of having the same definition, like “raiment” and “dress,” then it turns out that they are maintaining the Heraclitean doctrine, for it will be the same thing “to be good” and “to be bad,” and “to be good” and “to be not good,” and so the same thing will be “good” and “not good,” and “man” and “horse.”
In fact, their view will be not that all things are one, but that they are nothing, and that “to be of such-and-such a quality” is the same as “to be of such-and-such a size.”
20. After he has set forth the opinions of the philosophers concerning principles, here Aristotle argues against them.
First, he argues against those who spoke unnaturally about nature.
Second, at “the physicists, on the other hand” (187a12; [53]), he argues against those who spoke of nature in a natural way.
Concerning the first part, he makes two points.
First, he argues against the position of Melissus and Parmenides;
second, against their arguments, at “further, the arguments they use” (186a5; [29]).
Concerning the first part, he makes two points.
First, he argues against the position that “being is one” by using an argument dealing with the “being” that is the subject in this proposition.
Second, at again, “one” itself (185b5; [22]), he uses an argument dealing with the “one” that is the predicate.
21. He says first (185a20) that that which should be taken primarily as a principle in arguing against the position just given is the fact that that which “is”—namely, being—is said in many ways. For we must ask of those who say that being is one how they are using “being”: whether they take it for substance, or for quality, or for one of the other genera. And because substance is divided into the universal and the particular—that is, into first and second substance—and further into many species, we must ask the following questions. Do they say that being is one as one man, or as one horse, or as one soul, or as one quality, such as white or hot or some other such thing? For it makes a great difference which of these is said.
Hence, if being is one, either it must be substance and accident together or it must be accident alone or substance alone.
If, however, it is substance and accident together, then being will not be one only, but two. Nor does it differ with reference to this whether substance and accident are together in one thing as one or as different. For even though they are together in one thing, they are not one simply, but one in subject. And so, by positing substance with accident, it follows that they are not one simply, but many.
If, however, it is said that being is accident only and not substance, this is altogether impossible, since accident can in no way be without substance. For every accident is said of substance as of its subject, and the very definition of accident involves this.
If, however, it is said that being is substance only, without accident, then it follows that it would not be a quantity, for quantity is an accident. And this is contrary to the position of Melissus, who held that being was infinite, from which it follows that it is quantity, because the infinite, properly speaking, does not exist except in quantity. And substance and quality and the like are not said to be infinite except accidentally, insofar as they are, for instance, together with quantity. Since, then, Melissus held being to be infinite, he cannot hold that it is substance without quantity.
If, therefore, being is substance and quantity together, it follows that being is not one only, but two. If, however, it is substance alone, it is not infinite, because it will not have magnitude or quantity. Hence what Melissus says—namely, that being is one—can in no way be true.
22. Then, at again, “one” itself (185b5), he sets forth his second argument that deals with the one.
Concerning this, he makes two points.
First, he gives the argument.
Second, at “even the more recent” (185b25; [25]), he shows how some have erred in the solution of this question.
He says first that, just as “being” is said in many ways, so also is “one.” And so, we must consider in what way they say that all things are one. For “one” is used in three ways: as the continuous is one, such as a line or a body; as the indivisible is one, such as a point; or as those things are said to be one whose account or definition is one, as “vintage” and “wine” are said to be one.
First, therefore, he shows that we cannot say that all are one by continuity, because a continuum is in a certain respect many. For every continuum is divisible to infinity, and so contains many in itself as parts. Hence, whoever holds that being is a continuum must hold that it is in a certain respect many.
And this is true not only because of the number of the parts but also because of the difference that seems to exist between the whole and the parts. For there is a question whether the whole and the parts are one or many. And, although perhaps this question does not pertain to the matter at hand, it is nevertheless worthy of consideration for its own sake.
And here we consider not only the continuous whole but also the contiguous whole whose parts are not continuous, such as the parts of a house, which are one by contact and composition. It is clear that that which is a whole accidentally is the same as its parts. But this is not true of that which is a whole simply.
For if that which is a whole simply is the same as one of the parts, then it would for the same reason be the same as another of the parts. But things that are identical with the same thing are identical with each other. And thus it would follow that both parts, if they are held simply to be the same as the whole, would be identical with each other. Hence it would follow that the whole would be indivisible, with no diversity of parts.
23. Next, at “but to proceed” (185b16), he shows that it is impossible for all to be one as the indivisible is one. For that which is indivisible cannot be a quantity, since every quantity is divisible. As a result of this, it cannot be a quality, if it is understood that we are speaking of a quality that is founded upon quantity. And, if it is not a quantity, it cannot be finite (as Parmenides has said), nor can it be infinite (as Melissus has said). For an indivisible terminus, such as a point, is an end and not ended, for the finite and the infinite are found in quantity.
24. Next, at “but if all things” (185b19), he shows how it cannot be said that all things are one in definition. For if this were true, three absurdities would follow.
The first is that contraries would be one according to definition, such that the definitions of good and evil would be the same, just as Heraclitus held the definitions of contraries to be the same (as is made clear in Metaphysics 4).
The second absurdity is that the definitions of the good and the non-good would be the same, because non-good follows upon evil. And thus it would follow that the definitions of being and non-being would be the same. And it would also follow not only that all beings would be one being, as they hold, but also that they would be non-being or nothing. For things that are one in definition are so related that they may be used interchangeably as predicates. Thus, if being and nothing are one according to definition, then it follows that, if all are one being, all are nothing.
The third absurdity is that the different genera, such as quantity and quality, would be the same according to definition. He sets forth this absurdity where he says, “to be of such-and-such a quality” is the same as “to be of such-and-such a size.”
However, we must note that, as the Philosopher says in Metaphysics 4, against those who deny principles there can be no unqualified demonstration that proceeds from what is more known simply. But we may use a “demonstration to contradiction,” which proceeds from those things that are supposed by our adversary—which things are, for the time being, simply less known. And so, in this argument, the Philosopher uses many things that are less known than the fact that beings are many and not only one—the point about which he argues.