LESSON 9

The Nature of Contraries

  Chapter 7: 1057a 18-1057b 34

             878. And since there can be an intermediate between contraries, and some contraries admit of intermediates, intermediates must be composed of contraries.

             879. For all intermediates and the things of which they are the intermediates belong to the same genus. For we call those things intermediates into which something undergoing change must first change; for example, if one should pass from the top-string note to the bottom-string note, assuming that the passage is made through the intervening register, he will first come to the intermediate sounds. And the same thing is true in the case of colors; for if one will pass from white to black, he will first come to purple and to gray before he comes to black; and it is similar in the case of other things. But it is not possible except accidentally for a change to take place from one genus to another, for example, from color to figure. Hence intermediates and the things of which they are the intermediates must belong to the same genus.

             880. But all intermediates are intermediates between certain things that are opposed; for it is only from these that change in the strict sense can arise. And for this reason there cannot be intermediates between things that are not opposed; for otherwise there would be a change which is not from opposites.

             881. For the opposites involved in contradiction admit of no intermediates, for this is what contradiction is: an opposition of which one or the other part applies to anything whatever and which does not have an intermediate. But of other opposites some are relative, some privative, and some contrary. And between those terms that are relative and not contrary there is no intermediate. The reason is that they do not belong to the same genus; for what is the intermediate between knowledge and the knowable object? There is an intermediate, however, between the large and the small.

             882. Now if intermediates belong to the same genus, as we have shown (879), and are intermediates between things that are contrary, they must be composed of these contraries.

             883. For there will be some genus of these contraries or there will not. And if there is some genus such that it is something prior to the contraries, there will be contrary differences prior to the species, constituting them as contrary species of the genus; for species are composed of genus and differences. Thus, if white and black are contraries and the one is an expanding color and the other a contracting color, the differences "expanding" and "contracting" will be prior. Hence these things that are contrary to each other will be prior. But contrary differences are more truly contrary [than contrary species].

             884. And the other species, the intermediate ones, will be composed of genus and differences; for example, all colors intermediate between white and black must be defined by a genus (which is color) and by differences. But these differences will not be the primary contraries; and if this were not the case, every color would be either white or black. Hence the intermediate species are different from the primary contraries.

             885. And the primary differences will be "expanding" and "contracting," because these are primary. Moreover, it is necessary to investigate those contraries which belong to the same genus and to discover the things of which their intermediates are composed. For things belonging to the same genus must either be composed of things that are incomposite in the same genus, or must be incomposite in themselves. For contraries are not composed of each other, and thus are principles; but either all intermediates are incomposite, or none of them are. But something comes about from contraries. Hence change will affect this before reaching the contraries, for it will be less than one contrary and greater than the other, and thus this will be an intermediate between the contraries. All the other intermediates, then, are composites; for that intermediate which is greater than one contrary and less than the other is composed in a sense of these contraries of which it is said to be greater than one and less than the other. And since there are no other things belonging to the same genus which are prior to the contraries, all intermediates will be composed of contraries. All inferiors, then, both contraries and intermediates, must be composed of the primary contraries.

             886. Hence it is evident that all intermediates belong to the same genus; that they are intermediates between contraries; and that they are composed of contraries.

COMMENTARY

             2097. Having expressed his views about contraries, the Philosopher now does the same thing with regard to the intermediates between contraries; and concerning this he does two things. First (878:C 2097), he indicates what his plan is. He says that, since there can be an intermediate between contraries, as has been shown above (850:C 2042), and some contraries have an intermediate, it is necessary to show that intermediates are composed of contraries. He not only does this but also proves certain points needed for this proof.

             2098. For all intermediates (879).

             Then he carries out his plan; and in regard to this he does three things. First (879:C 2098), he shows that intermediates belong to the same genus as contraries. Second (880:C 2101), he shows that there are intermediates only between contraries ("But all intermediates"). Third (882:C 2098), he establishes his main thesis, that intermediates are composed of contraries ("Now if intermediates").

             He accordingly says, first (879), that all intermediates belong to the same class as the things of which they are the intermediates. He proves this by pointing out that intermediates are defined as that into which a thing undergoing change from one extreme to another first passes.

             2099. He makes this clear by two examples. First, he uses the example of sounds; for some sounds are low and some are high and some are intermediate. And strings on musical instruments are distinguished by this distinction of sounds; for those strings which yield low pitched sounds are called "top-strings" because they are the basic ones, and those which yield high pitched sounds are called "bottom-strings." Hence, if a musician wishes to proceed step by step from low sounds to high ones, and so to pass through an intermediate register, he must first come to the intermediate sounds. Second, he makes this clear by using colors. For if a thing is changed from white to black, it must first pass through the intermediate colors before it reaches black. The same thing is true of other intermediates.

             2100. It is evident, then, that change passes from intermediates to extremes and the reverse. But things belonging to diverse genera are changed into each other only accidentally, as is clear with regard to color and figure; for a thing is not changed from color to figure or vice versa, but from color to color, and from figure to figure. Hence intermediates and extremes must belong to the same genus.

             2101. But all intermediates (880).

             Here he shows that intermediates stand between contraries; and in regard to this he does two things. First, he shows that intermediates must stand between opposites. Second (881:C 2102), he indicates the kind of opposites between which they stand, namely, contraries ("For the opposites").

             He accordingly says, first (880), that all intermediates must stand between opposites. He proves this as follows: changes arise, properly speaking, only from opposites, as is proved in Book I of the Physics; for properly speaking a thing changes from black to white; and what is sweet comes from black only accidentally inasmuch as it is possible for something sweet to become white. But intermediates stand between things which are changed into each other, as is evident from the definition of intermediates given above (879:C 2098). Therefore it is impossible that intermediates should not stand between opposites; otherwise it would follow that change would not proceed from opposites.

             2102. For the opposites (881).

             Then he indicates the kinds of opposites that can have intermediates. He says that there cannot be any intermediates whatsoever between the opposite terms of a contradiction; for contradictory opposition is such that one part of it must belong to any type of subject, whether it be a being or a non-being. For we must say that any being or non-being either is sitting or is not sitting. Thus it is evident that contradictories have no intermediate.

             2103. But in the case of other opposites some involve relations, some privation and form, and some contraries. Now of opposites which are relative, some are like contraries which are related to each other on an equal basis, and these have an intermediate. But some do not have the character of contraries, for example, those which are not related to each other on an equal basis, as knowledge and a knowable object; and these do not have an intermediate. And the reason is that intermediates and extremes belong to the same genus. But these things do not belong to the same genus, since the one is related in itself, as knowledge, but the other is not, as the knowable object. How, then, can there be an intermediate between knowledge and the knowable object? But there can be "an intermediate" between the large and the small, and this is the equal, as has been stated above (881:C 2102). The same thing is true of those things which are related to each other as contraries. He does not mention how things which are opposed privatively have an intermediate or how they do not, and how this opposition somehow pertains to contrariety, because he has explained these points above (851-3:C 2043-53).

             2104. Now if intermediates (882).

             Third, he proves the point that constitutes his main thesis. He says that, if intermediates belong to the same genus as extremes, as has been shown (879:C 2098), and if again there are intermediates only between contraries, as has also been shown (882:C 2104), then intermediates must be composed of the contraries between which they stand.

             2105. For there will (883).

             Then he proves his thesis; and in regard to this he does three things. First, he proves that contrary species have prior contraries of which they are composed. He proceeds as follows: there must either be a genus of contraries or not. But if there is no genus of contraries, contraries will not have an intermediate; for there is an intermediate only between those things which belong to one genus, as is evident from what has been said. But if those contraries which are assumed to have an intermediate have some genus which is prior to the contraries themselves, there must also be different contraries prior to contrary species, which make and constitute contrary species from this one genus. For species are constituted of genus and differences.

             2106. He makes this clear by an example. If white and black belong to contrary species and have one genus, color, they must have certain constitutive differences, so that white is a color capable of expanding vision, and black is a contracting color. Therefore the differences "contracting" and "expanding" are prior to white and to black. Hence, since in each case there is a contrariety, it is evident that some contraries are prior to others; for contrary differences are prior to contrary species; and they are also contrary to a greater degree because they are causes of the contrariety in these species.

             2107. However, it must be understood that, while "expanding" and "contracting" as referred to vision are not true differences which constitute white and black, but rather are their effects, still they are given in place of differences as signs of them, just as differences and substantial forms are sometimes designated by accidents. For the expansion of vision comes from the strength of the light, whose fullness constitutes whiteness. And the contraction of vision has as its cause the opposite of this.

             2108. And the other (884).

             He shows too that intermediate species have prior intermediates of which they are composed. He says that, since intermediates are species of the same genus, and all species are constituted of genus and differences, intermediates must be constituted of genus and differences; for example, any colors that are intermediate between white and black must be defined by their genus, color, and by certain differences; and these differences of which intermediate colors are composed cannot be the immediate "primary contraries," i.e., the differences which constitute the contrary species of white and black. Again, any color must be intermediate between white and black; for black is a contracting color and white an expanding color. Hence the differences which constitute intermediate colors must differ according to the different contraries which are constitutive of contrary species. And since differences are related to differences as species are to species, then just as intermediate colors are intermediate species between contrary species, in a similar fashion the differences which constitute them must be intermediate between the contrary differences which are called primary contraries.

             2109. And the primary (885).

             Then he shows that intermediate differences are composed of contrary differences. He says that primary contrary differences are those which can expand and contract sight, so that these differences constitute a primary type of which we compose every species of a genus. But if certain contraries did not belong to the same genus, we would still have to consider of which of these contraries the intermediates would be composed. This is not difficult to understand in the case of those things which belong to the same genus, because all things belonging to the same genus "must either be incomposite," i.e., simple things, or they must be composed "of incomposites," i.e., of simple things, which belong to the same genus. For contraries are not composed of each other, because white is not composed of black, nor black of white; nor is the contracting composed of the expanding or the reverse. Hence contraries must be principles, because the simple things in any genus are the principles of that genus.

             2110. But it is necessary to say that all intermediates are composed either "of simple things," i.e., of contraries, or they are not, because the same reasoning seems to apply to all. But it cannot be said that they are not, because there is an intermediate which is composed of contraries, and according to this it is possible for change to first affect intermediates before it affects extremes. This becomes evident as follows: that in which change first occurs admits of difference in degree in relation to the two extremes; for something becomes slightly white or slightly black before it becomes completely white or completely black; and it is what is less white that becomes plain white, and what is less black that becomes plain black. And it also comes closer to white than to plain black, and closer to black than to plain white. Thus it is evident that the thing which change first affects admits of difference in degree in relation to both extremes; and for this reason contraries must have an intermediate. It follows, then, that all intermediates are composed of contraries; for the same intermediate which is more and less in relation to both extremes must be composed of both unqualified extremes, in reference to which it is said to be more and less. And since there are no extremes which are prior to contraries in the same genus, it follows that the two contrary differences which constitute intermediates are composed of contrary differences. Thus intermediates must come from contraries. This is evident because "all inferiors," i.e., all species of a genus, both contraries and intermediates, are composed of primary contraries, i.e., differences.

             2111. Hence it is evident (886).

             He brings his discussion to a close by summarizing what has been said above about intermediates. This part of the text is clear.