LECTURE 3 (185 a 20-b 27)

THE ASSERTION OF PARMENIDES AND MELISSUS THAT ALL THINGS ARE ONE BEING IS REFUTED

             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. Secondly, where he says, 'The physicists, on the other hand . . .' (187 a 11), 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, and secondly against their arguments, where he says, 'Further the arguments they use . . .' (186 a 5).

             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' which is the subject in this proposition. Secondly, where he says, 'Again, "one" itself . . .' (185 b 5), he uses an argument dealing with the 'one' which is the predicate.

             21. He says first that that which should be taken primarily as a principle in arguing against the aforesaid position is the fact that that which is, i.e., 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, i.e., 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, it must either 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. For 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. For he held that being was infinite, whence 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 where he says, 'Again "one" itself. . .' (185 b 5) he sets forth his second argument which deals with the 'one'.

             Concerning this he makes two points. First he gives the argument. Secondly, where he says, 'Even the more recent . . .' (185 b 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: either as the continuous is one, such as a line or a body, or as the indivisible is one, such as a point, or as those things are said to be one whose nature [ratio] or definition is one, as drink 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 which 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 this question, perhaps, 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 were the same as one of the parts, then for the same reason it would be the same as another of the parts. But things which 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 having no diversity of parts.

             23. Next where he says, 'But to proceed . . .' (185 b 18), 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 which 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 is not finite. For the finite and the infinite are found in quantity.

             24. Next where he says, 'But if all things . . .' (185 b 19), he shows how it cannot be said that all things are one in definition [ratio]. For if this were true, three absurdities would follow.

             The first is that contraries would be one according to definition [ratio], so 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, IV.

             The second absurdity is that the definitions [ratio] 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 that all beings would not only be one being, as they hold, but also they would be non-being or nothing. For things which are one in definition are so related that they may be used interchangeably as predicates. Whence 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 [ratio]. 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" ' (185 b 24).

             We must note however, that, as the Philosopher says in Metaphysics, IV, against those who deny principles there can be no unqualified demonstration which proceeds from what is more known simply. But we may use a demonstration to contradiction which proceeds from those things which are supposed by our adversary, which things are, for the time being, less known simply. And so the Philosopher, in this argument, uses many things which are less known than the fact that beings are many and not only one--the point about which he argues.