Commentary Aristotle Physics
Lecture 6. The argument of Parmenides is answered
The same kind of argument holds good against Parmenides also, besides any that may apply specially to his view. The answer to him is that “this is false” and “that does not follow.”
His assumption that “what is” is used only simply is false, because it is used in several ways.
His conclusion does not follow because, if we take only white things, and if “white” has a single meaning, nevertheless what is white will be many and not one. For white will not necessarily be one by continuity nor in definition. “Whiteness” will be different from “what has whiteness.”
Nor does this mean that there is anything that can exist separately.
For “whiteness” and “that which is white” differ in definition, but not in the sense that they are things that can exist apart from each other.
But Parmenides did not see this distinction.
It is necessary for him, then, to assume not only that “being” has the same meaning whenever it is predicated, but further that it means what truly is and what is truly one. It must be so, for an accident is predicated of some subject, such that the subject to which “being” is attributed will not be, as it is something different from “being.” Something which is not will therefore be.
Hence “substance” will not be a predicate of anything else. For the subject cannot be a being, unless “being” means several things, in such a way that each is something. But it was supposed that “being” means only one thing.
If, then, “substance” is not attributed to anything, but other things are attributed to it, how does “substance” mean what truly is rather than what is not? Suppose that “substance” is also “white.” Since the definition of the latter is different (for being cannot even be attributed to white, as nothing is that is not “substance”), it follows that “white” is non-being—and that not in the sense of a particular non-being, but in the sense that it is not at all.
Hence, “substance” is not, for it is true to say that it is white, which we found to mean non-being. If, to avoid this, we say that even “white” means substance, it follows that “being” has more than one meaning.
In particular, then, being will not have magnitude, if it is substance. For each of the two parts must be in a different sense.
Substance is plainly divisible into other substances if we consider the mere nature of a definition. For instance, if “man” is what truly is, “animal” and “biped” must also be what truly is. For if not substances, they must be accidents—and if accidents, accidents either of man or of some other subject. But neither is possible.
An accident is either that which may or may not belong to the subject or that in whose definition the subject of which it is an accident is involved. Thus, “sitting” is an example of a separable accident, while “snubness” contains the definition of “nose,” to which we attribute snubness.
Further, the definition of the whole is not contained in the definitions of the contents or elements of the definitory formula—for instance, that of “man” in “two-footed” or that of “white man” in “white.”
If, then, this is so, and if “two-footed” is supposed to be an accident of man, either it must be separable, such that man might possibly not be “two-footed,” or the definition of “man” must come into the definition of “two-footed”—which is impossible, since the converse is the case.
If, on the other hand, we suppose that “two-footed” and “animal” are accidents not of man but of something else, and are not each of them a substance, then “man” will also be an accident of something else.
But what truly is, is not the accident of anything, and that of which both “two-footed” and “animal” are separately predicated is also the subject of “two-footed animal.” Are we then to say that the whole is composed of indivisibles?
36. Having disproved the argument of Melissus, here the Philosopher disproves the argument of Parmenides.
First, he disproves the argument.
Second, at “some thinkers did” (187a1; [47]), he rejects what has been said by some who have argued badly against Parmenides.
Concerning the first part, he makes two points.
First, he sets forth the ways in which the argument of Parmenides is to be refuted.
Second, at “his assumption” (186a24; [39]), he resolves the argument in these ways.
37. Concerning the first part, it must be known that, as is clear from Metaphysics 1, the argument of Parmenides was as follows: whatever is other than being is non-being; but what is non-being is nothing; therefore, whatever is other than being is nothing. But being is one; therefore, whatever is other than one is nothing; therefore, there is only one being.
And he concluded from this that it would be immobile, because it would not have anything by which it would be moved, nor would there be anything outside of it by which it would be moved.
Moreover, it is clear from their very arguments that, while Parmenides considered being under the account of being, and so held it to be one and finite, Melissus considered being from the point of view of matter. For Melissus considered being insofar as it is made or not made. And so he held being to be one and infinite.
38. Aristotle says, therefore (186a22), that the same approach must be used against the argument of Parmenides that was used against the argument of Melissus.
For as the argument of Melissus was answered on the basis that he assumed false propositions and did not draw his conclusions according to the correct form of the syllogism, so also the argument of Parmenides is answered partly because he assumed false propositions and partly because he did not draw his conclusions correctly.
He says, however, that there are also other appropriate ways of arguing against Parmenides. For it is possible to argue against Parmenides from the propositions that he assumed and that are in a certain respect true and probable.
But Melissus proceeded from what was false and improbable—for example, that being is not generated. Because of this, Aristotle did not argue against Melissus from the propositions that he assumed.
39. Next, at “his assumption” (186a24), he follows the procedures just mentioned.
First, according to the first way;
second, according to the second way, at “his conclusion does not follow” (186a25; [40]).
He first says, therefore, that Parmenides assumed false propositions, because he held that what is—namely, being—is used simply, that is, in one way. In fact, it is used in many ways. For “being” is used in one way for substance and in another way for accident; the latter is used in many ways according to the different genera. “Being” can also be used commonly for substance and accident. Hence, it is clear that the propositions assumed by Parmenides are true in one sense and false in another.
For when it is said that whatever is other than being is non-being, this is true if “being” is taken commonly, as it were, for substance and accident. If, however, “being” is taken for accident alone or for substance alone, this is false, as will be shown below. Likewise, when he says that being is one, this is true if “being” is taken for some one substance or for some one accident. But this will not be true in the sense that whatever is other than that being is non-being.
40. Next, at “his conclusion does not follow” (186a25), he follows the second method of answering the argument, namely, that the argument of Parmenides does not draw its conclusion according to proper form.
He shows this first in an example;
second, at “it is necessary for him” (186a32; [41]), he adapts this example to the problem at hand.
He says, therefore, first that it can be seen that the argument of Parmenides does not draw its conclusion properly, because the form of argumentation used is not efficacious in every matter. And this could not be true if a proper form of argumentation were used.
For if we take white in the place of being, and if we say that “white” signifies one thing only and is not used equivocally, and if we say that whatever is other than white is non-white, and whatever is non-white is nothing, then it will not follow that white would be one only. For it will not be necessary that all white things are one continuum.
Or, to put it differently, white will not necessarily be one by continuity; that is, from the fact that white is a continuum, it will not be one simply. For a continuum is many in a certain respect, as was said above. And in like manner, “white” will not be one in definition, for the white and that which is receptive of the white are different in definition.
Nevertheless, there will not be something other than white separated from it, as it were. The reason that the white is not other than that which is receptive of it is not because the white is separable from that which is receptive of it, but because the definitions of the white and of that which is receptive of it are different.
But it was not yet known at the time of Parmenides that something could be one in subject and many in definition, and thus he believed that, if there is nothing outside a certain subject, then it follows that it is one. But this is false on account of the multiplicity of parts, as well as on account of the different definitions of subject and accident.
41. Next, at “it is necessary for him” (186a32), he adapts this example to the matter at hand in order to show how what he has said of the white also applies to being.
Concerning this, he makes two points.
First, he shows that it does not follow that being is one simply. For subject and accident are different according to definition.
Second, at “in particular, then” (186b12; [44]), he shows that this does not follow, because of the multiplicity of parts.
Concerning the first part, he makes two points.
First, he shows that, when it is said that whatever is other than being is non-being, this being cannot be taken to mean accident alone.
Second, at if, then, “substance” (186b4; [43]), he shows that this “being” cannot be taken to mean substance alone.
42. He says, therefore, first that, when it is said that whatever is other than being is non-being, if being is said to signify one thing, then it will be necessary that it not signify any one being or what is predicated of any one thing. Rather, it will signify what truly is—namely, substance—and it will signify what is truly one, namely, the indivisible. For if being were to signify accident, then, since accident would be predicated of a subject, the subject could not be that to which the accident, which is called being, occurs.
For if whatever is other than being is non-being (that is, other than accident), and if the subject is other than the accident, which is here said to be being, then it follows that the subject is non-being. And so, when accident, which is being, is predicated of the subject, which is non-being, it follows that being is predicated of non-being.
Hence, Aristotle concludes, something that is not will therefore be; that is, it will follow that non-being is being. This, however, is impossible. For what is first of all assumed in the sciences is that contradictories are not to be predicated of each other, as is said in Metaphysics 4. Thus, he concludes that, if anything is truly being, as is supposed in the proposition whatever is other than being is non-being, it follows that it is not an accident inhering in something else. For in this case, its subject would not be a being. That is, this subject would not have the account of being unless being should signify “many,” such that each of the many would be a being. But it was assumed by Parmenides that being signifies one only.
43. Next, at if, then, “substance” (186b4), after he has concluded that being cannot refer to accident when it is said that whatever is other than being is non-being, he shows further that being cannot refer to substance either. Thus, he says that, if what truly is does not happen to something, but other things happen to it, then, in the proposition whatever is other than being is non-being, it is necessary that what truly is, substance, be signified by “being” rather than by “non-being.” But this cannot stand. For let it be held that that which truly is, namely, substance, is white. But white is not that which truly is. For it has already been said that that which truly is cannot happen to something. And this is so because what is not truly—namely, what is not substance—is not at all, namely, is not being. But what is other than being—namely, other than substance—is non-being.
Hence it follows that white is non-being, not only in the sense that it is not this being, as a man is not this being, which is an ass, but also in the sense that it is not in any way. For he says that whatever is other than being is non-being, and what is non-being is nothing. From this, therefore, it follows that non-being would be predicated of that which truly is, because white is predicated of substance, which truly is. And white does not signify being, as was said. Thus it follows that being is non-being. And this indeed is impossible, because one contradictory is not predicated of another. If, then, in order to avoid this inconsistency, we say that “true being” signifies not only the subject but also the white itself, it follows that “being” will signify many. And thus there will not be only one being, for subject and accident are several according to definition.
44. Next, at “in particular, then” (186b12), he shows, because of the multiplicity of parts, that it does not follow from the argument of Parmenides that there is only one being.
He shows this first with reference to quantitative parts;
second, with reference to the parts of definition, at “substance is plainly divisible” (186b14; [45]).
Therefore, he first says that, if “being” signifies only one thing, not only will it not be accident with subject, but neither will it be a magnitude. For every magnitude is divisible into parts. But the account of each of the parts is not the same, but different. Hence it follows that this one being is not a corporeal substance.
45. Second, at “substance is plainly divisible” (186b14), he shows that this being cannot be a definable substance. For in a definition, it is clear that what truly is, the substance, is divided into many, each one of which is what truly is—namely, substance—and each one of which has a different account.
Let us suppose that man is one thing that truly exists. Since man is a two-footed animal, it is necessary that “animal” be and that “two-footed” be. And each of these will be what truly is, namely, substance. And, if they are not substances, they are accidents, either of man or of some other thing. But it is impossible that they be accidents of man.
And, to make this clear, he assumes two things.
First, he assumes that “accident” is used in two ways.
One type of accident is separable and, as such, can be in something or not in it, for example, to sit.
Another type of accident is inseparable and per se. And this latter is the accident in whose definition is placed the subject in which it is. For example, the snub is a per se accident of nose, because nose is placed in the definition of the “snub.” For the “snub” is a curved nose.
The second thing he assumes is that, if certain things are placed in the definition of that which is defined, or in the definition of the things on which the definition depends, then it is impossible that the whole definition of that which is defined be placed in the definition of these certain things. Thus, “two-footed” is placed in the definition of “man” and certain other things are placed in the definition of “two-footed” or “animal,” from which man is defined.
Hence it is impossible that “man” be placed in the definition of “two-footed” or in the definition of any of the things that fall in the definition of “two-footed” or of “animal.” Otherwise, we would have a circular definition and one and the same thing would be both prior and posterior, better-known and less-known. For every definition is from the prior and the better known, as is said in Topics 6.4.
And for the same reason, when “white” is placed in the definition of “white man,” it is impossible for “white man” to be placed in the definition of “white.” These things having been assumed, the argument is as follows.
If two-footed is an accident of man, it must be either a separable accident (and thus it could happen that man is not two-footed, which is impossible) or an inseparable accident (and thus it will be necessary that man be placed in the definition of “two-footed”). But this also is impossible, because “two-footed” is placed in the definition of “man.” It is impossible, therefore, that two-footed be an accident of man. For the same reason, “animal” cannot be an accident.
But if it is said that both are accidents of something else, it would follow that man also would be an accident of something else. But this is impossible, for it has already been said above that that which truly is, is an accident of nothing. But man was assumed to be that which truly is, as is clear from what was said above.
He shows in the following way that it would follow that man would be an accident of another if animal and two-footed were accidents of some other thing. What is said of both animal and two-footed taken separately may be said of them taken together, namely, two-footed animal. And what is said of two-footed animal may be said of that which is from them—namely, man—because man is nothing other than a two-footed animal.
Therefore, it is clear that, if being is held to be one only, we cannot hold that there are quantitative parts, or parts of a magnitude, or parts of a definition. Therefore, it follows that every being is numerically indivisible. Otherwise, while holding being to be one, we would be forced to posit a multiplicity because of the parts.
46. The Commentator, however, says that, beginning at “but what truly is” (186b33), Aristotle sets forth the second argument of Parmenides to show that being is one. And this argument is as follows. A being that is one is substance and not accident (and by “substance” he means body). If, however, that body is divided into two halves, it will follow that being is predicated of each half and of the union of the two. And either this proceeds to infinity, which is impossible in itself, or the being is divided into points. But this also is impossible. Hence it follows that being is an indivisible one. But this exposition is fabricated and contrary to the intention of Aristotle, as is sufficiently clear from an examination of the letter of the text according to the first explanation.