LESSON 5

Contrariety Is the Greatest and Perfect Difference

Chapter 4: 1055a 3-1055a 33

             842. But since it is possible for things which differ from each other to differ to a greater or lesser degree, there is a greatest difference.

             843. And I call this difference contrariety. That this is the greatest difference becomes clear by induction; for things which differ generically cannot pass into each other, but they are too far apart and cannot be compared; and those things which differ specifically arise from contraries as their extremes. But the distance between extremes is the greatest; therefore the distance between contraries is the greatest.

             844. Now what is greatest in each class is perfect (or complete); for that is greatest which nothing exceeds, and that is perfect beyond which it is impossible to find anything else; for the perfect difference is an end, just as other things are said to be perfect because they have attained their end. For there is nothing beyond the end, since in every case it is what is ultimate and contains everything else. There is nothing beyond the end, then, and what is perfect needs nothing else. It is therefore clear from these remarks that contrariety is the perfect or complete difference. And since things are said to be contrary in many ways, it follows that difference will belong to contraries perfectly in proportion to the different types of contrariety.

             845. Since this is so, it is evident that one thing cannot have many contraries; for there can be nothing more extreme than the extreme (since, if there were, it would be the extreme); nor can there be more than two extremes for one distance.

             846. And in general this is evident if contrariety is difference, and difference must be between two things. Hence this will also be true of the perfect difference.

             847. And the other formulations of contraries must also be true. For the perfect difference is the greatest, since in the case of things which differ generically it is impossible to find any difference greater than in those which differ specifically; for it has been shown (843) that there is no difference between things in a genus and those outside it, and for those specifically different the perfect difference is the greatest. And contraries are things which belong to the same genus and have the greatest difference; for the perfect difference is the greatest difference between them. And contraries are things which have the greatest difference in the same subject; for contraries have the same matter. And contraries are things which come under the same potency and have the greatest difference; for there is one science of one class of things, and in these the perfect difference is the greatest.

COMMENTARY

             2023. Having settled the issue about the one and the many, and about the attributes which naturally accompany them, of which one is contrariety, which is a kind of difference, as has been pointed out (840:C 2021), here the Philosopher explains contrariety, because the investigation of it involves a special difficulty. This is divided into two parts. In the first (842:C 2023) he shows that contrariety is the greatest difference. In the second (887:C 2112) he inquires whether contraries differ generically or specifically ("That which is").

             The first part is divided into two. In the first he settles the issue about contraries. In the second (878:C 2097) he deals with their intermediates ("And since").

             The first part is divided into two. In the first he settles the issue about the nature of contraries. In the second (857:C 2059) he raises certain difficulties about the points which have been established ("But since one thing").

             The first part is divided into two. In the first he shows what contrariety is. In the second (848:C 2036) he establishes what is true of contrariety as compared with the other kinds of opposition ("The primary contrariety").

             In treating the first part he does two things. First, he gives a definition of contrariety. Second (847:C 2032), he reduces all the other definitions which have been assigned to contraries to the one given ("And the other").

             In regard to the first he does two things. First, he gives the definition of contrariety. Second (844:C 2027), he draws a corollary from this definition ("Now what is").

             In regard to the first he does two things. First (842), he shows that there is a greatest difference, as follows: there is some maximum in all things which admit of difference in degree, since an infinite regress is impossible. But it is possible for one thing to differ from something else to a greater or lesser degree. Hence it is also possible for two things to differ from each other to the greatest degree; and therefore there is a greatest difference.

             2024. And I call (843).

             Second, he shows by an induction that contrariety is the greatest difference; for all things which differ must differ either generically or specifically. Now those things which differ generically cannot be compared with each other, being too far apart to admit of any difference of degree between them. This is understood to apply to those things which are changed into each other, because a certain process or way of change of one thing into another is understood from the fact that at first they differ more and afterwards less, and so on until one is changed into the other. But in the case of things which differ generically we do not find any such passage of one thing into another. Hence such things cannot be considered to differ in degree, and so cannot differ in the highest degree. Thus in things which differ generically there is no greatest difference.

             2025. However, in the case of things which differ specifically there must be a greatest difference between contraries, because reciprocal processes of generation arise from contraries as their extremes. And an intermediate arises from an extreme or vice versa, or an intermediate also arises from an intermediate, as gray is produced from black or from red. Yet generations of this kind do not arise from two things as extremes; for when something passes from black to gray in the process of generation, it can still pass farther to some color which differs to a greater degree. But when it has already become white, it cannot continue farther to any color which differs to a greater degree from black, and there it must stop as in its extreme state. This is why he says that processes of generation arise from contraries as extremes. But it is evident that the distance between extremes is always the greatest. Hence it follows that contraries have the greatest difference among things which differ specifically.

             2026. And since we have shown that things which differ generically are not said to have a greatest difference, although there is a greatest difference, it follows that contrariety is nothing else than the greatest difference.

             2027. Now what is greatest (844).

             He draws two corollaries from what has been said. The first is that contrariety is the perfect difference. This is proved as follows. What is greatest in any class is the same as what is perfect. This is clear from the fact that that is greatest which nothing exceeds; and that is perfect to which nothing can be added. Hence the difference of the greatest and that of the perfect [from a common referent] are seen to be the same.

             2028. That that is perfect to which nothing external can be added is evident, because all things are said to be perfect when they go up to the end. Now there is nothing beyond the end, because the end is what is ultimate in every case and contains the thing. Hence nothing lies beyond the end, nor does what is perfect need anything external, but the whole is contained under its own perfection. Thus it is evident that the perfect difference is one which goes up to the end.

             2029. Therefore, since contrariety is the greatest difference, as has already been proved (843:C 2024), it follows that it is the perfect difference. But since things are said to be contrary in many ways, as will be stated later (849:C 2039), not all contraries are said to differ perfectly; but it follows that all contraries differ perfectly in the way in which contrariety belongs to them, i.e., to some primarily and to others secondarily.

             2030. Since this is so (845).

             Here he gives the second corollary. He says that, since the foregoing remarks are true, it is evident that one thing cannot have many contraries. He proves this in two ways. He does this, first, on the grounds that contrariety is the greatest and perfect difference between extremes. But there can be no more than two extremes of one distance; for we see that one straight line has two end points. Further, there is nothing beyond the extreme. If, then, contrariety is one distance, it is impossible for two things to be equally opposed as extremes to one contrary, or for one to be more contrary and another less so, because whatever is less contrary will not be an extreme but will have something beyond it.

             2031. And in general (846).

             He now proves the same thing in another way. He says that since contrariety is a kind of difference, and every difference is a difference between two things, then the perfect difference must also be a difference between two things. Thus one thing has only one contrary.

             2032. And the other (847).

             Next he shows that all the definitions of contraries which have been given are seen to be true on the basis of the definition of contrariety posited above (842:C 2023). He gives "four formulations," i.e., definitions, of contraries assigned by other thinkers. The first is that contraries are things which have the greatest difference. Now this is seen to be true on the basis of the foregoing definition, since contrariety is the perfect difference, and this causes things to differ most. For it is evident from what has been said that in the case of things which differ generically nothing can be found which differs more than things which differ specifically, because there is no difference as regards those things which lie outside the genus, as has been stated. And of things which differ specifically the greatest difference is between contraries. Hence it follows that contraries are things which differ most.

             2033. The second definition is that contraries are attributes which differ to the greatest degree in the same genus. This is also seen to be true on the basis of the foregoing definition, because contrariety is the perfect difference. But the greatest difference between things which belong to the same genus is the perfect difference. Hence it follows that contraries are attributes which have the greatest difference in the same genus.

             2034. The third definition is that contraries are attributes which have the greatest difference in the same subject. This is also seen to be true on the basis of the foregoing definition; for contraries have the same matter since they are generated from each other.

             2035. The fourth definition is that contraries are attributes which have the greatest difference "under the same potency," i.e., the same art or science; for science is a rational potency, as has been stated in Book IX (746:C 1789). This definition is also seen to be true on the basis of the foregoing definition, because there is one science of one class of things. Therefore, since contraries belong to the same genus, they must come under the same potency or science. And since contrariety is the perfect difference in the same genus, contraries must have the greatest difference among those things which come under the same science.