LECTURE 6 (186 a 23-b 35)

THE ARGUMENT OF PARMENIDES IS ANSWERED IN A NUMBER OF WAYS

             36. Having disproved the argument of Melissus, here the Philosopher disproves the argument of Parmenides.

             First he disproves the argument. Secondly, where he says, 'Some thinkers did . . .' (187 a 1), 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. Secondly, where he says, 'His assumption . . .' (186 a 24), he resolves the argument in these ways.

             37. Concerning the first part it must be known that the argument of Parmenides was as follows, as is clear from Metaphysics, I. 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 from this he concluded 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.

             It is clear, moreover, from their very arguments that Parmenides considered being under the aspect [secundum rationem] of being, and so held it to be one and finite; whereas 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, 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 which he assumed and which 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 which he assumed.

             39. Next where he says, 'His assumption . . .' (186 a 24), he follows the procedures just mentioned. First according to the first way, and secondly according to the second way, where he says, 'His conclusion does not follow . . .' (186 a 25).

             He says, therefore, first that Parmenides assumed false propositions because he held that what is, i.e., being, is used simply, i.e., in one way. Whereas in fact it is used in many ways.

             For being is used in one way for substance, in another way for accident; and the latter is used in many ways according to the different genera. Being also can 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, as it were, commonly 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 where he says, 'His conclusion does not follow . . .' (186 a 25), he follows the second method of answering the argument, i.e., that the argument of Parmenides does not draw its conclusion according to proper form.

             He shows this first in an example. And secondly, where he says, 'It is necessary for him . . .' (186 a 33), 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 of the fact that 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, i.e., from the fact that white is a continuum, it will not be one simply. For a continuum is in a certain respect many, as was said above.

             And in like manner white will not be one in definition [ratio], for the white and that which is receptive of the white are different in definition [ratio]. Furthermore there will not be something other than white, as it were, separated from it. For the white is not other than that which is receptive of it because the white is separable from that which is receptive of it, but because the definitions [ratio] 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 [ratio].

             41. Next where he says, 'It is necessary for him . . .' (186 a 33), 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 [ratio]. Secondly, where he says, 'In particular then . . .' (186 b 13), 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. Secondly, where he says, 'If, then, substance . . .' (186 b 4), 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 signify not some one being or what is predicated of some one thing. Rather it will signify what truly is, i.e., substance, and it will signify what is truly one, i.e., 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 (i.e., 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 nonbeing. 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, therefore, which is not will be' (186 b 1), 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, IV. Whence he concludes that if anything is truly being, as is supposed in the proposition 'whatever is other than being is nonbeing', 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 nature [ratio] of being, unless being should signify many, so that each of the many would be a being. But it was assumed by Parmenides that being signifies one only.

             43. Next where he says, 'If, then, substance . . .' (186 b 4), 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. Whence 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', i.e., substance, be signified by being rather than by non-being.

             But this cannot stand. For let it be held that that which truly is, i.e., 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, i.e., what is not substance, is not that which is, i.e., is not being. But what is other than being, i.e., 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 nonbeing 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. Whence it follows that being is non-being. And this indeed is impossible, because one contradictory is not predicated of another.

             Whence, if 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 many according to nature [ratio].

             44. Next where he says, 'In particular then . . .' (189 b 13), 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 and secondly with reference to the parts of definition [ratio], where he says, 'Substance is plainly divisible . . .' (186 b 14).

             He says, therefore, first 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 natures [ratio] of each of the parts are not the same, but different. Whence it follows that this one being is not a corporeal substance.

             45. Secondly, where he says, 'Substance is plainly divisible . . .' (186 b 14), he shows that this being cannot be a definable substance.

             For in a definition it is clear that that which truly is, i.e., the substance, is divided into many, each one of which is what truly is, i.e. substance, and each one of which has a different nature [ratio]. Let us suppose that man is one thing which truly is. 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, i.e., 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 which 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 [i.e., from two-footed and animal] 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 which 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, VI. 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. If, however, 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.

             That it would follow that man would be an accident of another if animal and two-footed were accidents of another, he shows as follows. What is said of both animal and two-footed taken separately may be said of them taken together, i.e., two-footed animal. And what is said of two-footed animal may be said of that which is from them, i.e., 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 in the passage beginning, 'But we must assume . . .' (186 b 33), Aristotle sets forth the second argument of Parmenides to show that being is one. And this argument is as follows. A being which 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 this either proceeds to infinity, which is impossible in itself, or else 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.