Chapter II. On inspecting the prior divisively, how definition is destroyed.

CHAPTER II. On inspecting the prior divisively, how definition is destroyed.

But of that which is to inspect divisively with respect to this, that the assigned definition is not from things prior simply, three places or considerations are taken according to the number of those things toward which one inspects. But if the place is numbered according to the mode of inspecting in these matters, then there are four places, because according to inspection toward the same thing both the second and the third will be received. The first among these is if an opposite is defined through an opposite, as if good is defined through evil; and this is an inspection toward contraries, or toward the opposition of contraries; and evil and good are contraries insofar as they are received in acts and habits. But the cause why such a definition is destroyed is that it is not stated through things truly proper. For those things which are contrarily opposed are simultaneous in nature; for they have one genus and are constituted by contrary and coequal differences; and therefore it is necessary that they be true simultaneously. For to some people the same discipline seems to belong to each of two contraries; and according to this one is not better known than the other. And thus an assigned definition of an opposite and through an opposite is not from prior things, and therefore it is destroyed, so that it is not a definition.

And if it is objected that contraries according to Aristotle in the tenth book of first philosophy ¹ are reduced to privation and habit, but privation and habit are not true simultaneously, but have themselves as prior and posterior, it must be said that this objection comes from a false understanding of the Philosopher in the Metaphysics. For they are not reduced to privation and habit except according to cause, and not according to the mode of opposition which is received in the opposed forms of opposites, because this is impossible; and so the introduced consideration stands.

But one must not be unaware that in certain opposites some opposed things are not, or cannot otherwise be, defined unless the account of one is in the account of the other, as in relatives; for example, double is not yet defined without half, which is also relatively opposed. And to speak universally, whatever things are and are said toward another, and are not toward another only according to being said, for all things which through themselves are said toward another and are relatives, this very being which they have is to be toward that thing, and by their very name they are thus said toward another, because they have themselves toward another according to the being by which they are defined. Therefore it is not possible to know one through definition without the other, because it is necessary that one correlative be taken in the definition of the other. But it must be subtly understood that then, when one relative is placed in the definition of the other, it is not placed in the definition as defining; nor in this way is one of the relatives in the other as defining in the defined thing, but rather it is in the definition of the other as that toward which its definition is given according to that toward which it is said according to the being of the relative which is toward it, and for this it is received in the definition as the terminus toward which the definition stands extrinsically; and in this way no unsuitability stands. On account of this one must subtly know the natures of opposites, and in all things of this sort which are assumed for terminating the problem according to this place one must use those things which are opposed as will seem expedient for the proposal.

But another place of this consideration is by inspecting what is prior in nature, if one has used in the definition even the same thing as that which is defined; for then it is not defined through things prior simply, because the same thing is not prior in nature to itself. For this sometimes lies hidden when it has been done in definitions, when he has posited the same thing, but not under the same name of the defined thing, rather with the account of it posited in place of the name. Thus if someone, wishing to define the sun, said that the sun is a white star which appears by day. And the reason of this is that he places the same thing in its own definition, because by using day in the definition, he also uses the sun. But to detect such errors in definitions, one must use or take definitions of the name, and place definitions in place of the name. Thus, since day, if it is defined, is the bearing or motion of the sun above the earth, it is plain that one who stated the bearing of the sun above the earth in the name of day also stated the sun; on account of which in defining the sun he uses day.

Again, the third place of this consideration, by inspecting what is prior in nature, is that one must consider whether he uses in the definition that which is divided contrariwise with the defined thing; but things divided contrariwise are coequal. As one who defined an abundant number, which is an odd number, saying that the abundant or odd number is that which is greater by a unit or exceeds the perfect, that is, the even number; for those things which are divided from diverse sides from the same proximate genus are simultaneous in nature, that is, they are received through a coequal division. But abundant and perfect are coequally divided from the same genus, which is number, from diverse sides; for both these, even and odd, are numbers, and are coequal species in this genus which is number. And therefore one of them is not prior to the other according to nature.

Likewise, on the contrary, one must inspect whether he has defined superior things through inferior things according to a straight line. The example of this is if someone in defining should call a perfect number that which is divided bipartitely; or in defining good should say that it is the habit of virtue. For he uses bipartite in the definition of the perfect or even through derivation from two; for to be divided bipartitely is the same as to be divided into two. But two are certain perfect things, that is, even numbers. And virtue is a certain good, or a species and subjective part of good. On account of this these two also, and virtue, are inferior to those things, the perfect and the good, because those are genera, and these are their subjective parts; and so in those these are said, because they are in them in act and in understanding, and thus they are taken toward the same thing in the definition.

Furthermore, there is another reason for the same point, that one who uses the inferior things of superiors must also use the same thing if the definition is put in place of the name. For one who uses virtue in the definition of good uses good itself in the definition of good, if the definition of virtue is put in place of the name; this can be done, as has often been said in what went before. Therefore he uses good in the definition of good, because virtue is a certain special good in which good is in act and in understanding. Likewise, in the same way, one who uses what is bipartite in the definition of the perfect also uses the perfect, because to be divided into two signifies to be divided bipartitely, as was said a little before. But two are certain perfect or even things, and thus the same thing is taken in the definition of itself. Therefore two things are posited in this one consideration: both that he takes what is posterior in the definition of what is prior, and that he takes the same thing in the definition of itself; and so he does not make a definition from prior and better known things. Therefore, by concluding universally according to the aforesaid things, it must be said that one common place is to have made a definition not through prior and more evident things, from which definition is destroyed; but the parts of that place are those which have been stated.