Commentary Aristotle Posterior Analytics
a6. To define and divide one need not know the whole of existence.
a7. Yet some hold it impossible to know the differentiae distinguishing each thing from every single other thing without knowing every single other thing; and one cannot, they say, know each thing without knowing its differentiae, since everything is identical with that from which it does not differ, and other than that from which it differs.
a11. Now, first of all this is a fallacy: not every differentia precludes identity, since many differentiae inhere in things specifically identical, though not in the substance of these nor essentially.
a13. Second, when one has taken one’s differing pair of opposites and assumed that the two sides exhaust the genus, and that the subject one seeks to define is present in one or other of them, and one has further verified its presence in one of them; then it does not matter whether or not one knows all the other subjects of which the differentiae are also predicated. For it is obvious that when by this process one reaches subjects incapable of further differentiation one will possess the formula defining the substance.
a19. Moreover, to postulate that the division exhausts the genus is not illegitimate if the opposites exclude a middle; since if it is the differentia of that genus, anything contained in the genus must lie on one of the two sides.
a23. In establishing a definition by division one should keep three objects in view: (1) the admission only of elements in the definable form, (2) the arrangement of these in the right order, (3) the omission of no such elements.
a25. The first is feasible because one can establish genus and differentia through the topic of the genus, just as one can conclude the inherence of an accident through the topic of the accident.
a28. The right order will be achieved if the right term is assumed as primary, and this will be ensured if the term selected is predicable of all the others but not all they of it; since there must be one such term. Having assumed this we at once proceed in the same way with the lower terms; for our second term will be the first of the remainder, our third the first of those which follow the second in a ‘contiguous’ series, since when the higher term is excluded, that term of the remainder which is ‘contiguous’ to it will be primary, and so on.
a34. Our procedure makes it clear that no elements in the definable form have been omitted: we have taken the differentia that comes first in the order of division, pointing out that animal, e.g., is divisible exhaustively into A and B, and that the subject accepts one of the two as its predicate. Next we have taken the differentia of the whole thus reached, and shown that the whole we finally reach is not further divisible — that is, that as soon as we have taken the last differentia to form the concrete totality, this totality admits of no division into species.
b1. For it is clear that there is no superfluous addition, since all these terms we have selected are elements in the definable form; and nothing lacking, since any omission would have to be a genus or a differentia. Now, the primary term is a genus, and this term taken in conjunction with its differentiae is a genus: moreover the differentiae are all included, because there is now no further differentia; if there were, the final concrete would admit of division into species, which, we said, is not the case.
To define and divide one need not know. After presenting the truth concerning the division of the genus which is used in defining, the Philosopher here excludes two errors.
In regard to the first one he does three things:
First (98a6) he excludes the error and says that it is not necessary that one who defines by dividing should know all the things which exist in the world.
Second, at: yet some hold it impossible (98a7) he sets forth the opinion of those who make this error.
For some have said that it is not possible to know the difference between one thing and everything else, unless everything else is known, as is plain in regard to any two given things, whose difference we cannot know unless we know both things. However, they added that the quid est of something cannot be known, unless the difference between it and everything else is known. For that wherein something is not different is identical with it, whereas that by which something differs is other than it. But we cannot know what a thing is, unless we know what is the same as it and what is other than it. According to this, therefore, they concluded that something cannot be known unless everything is known.
Third, at: now, first of all (98a11) he disproves what they say in two ways.
First, he destroys the statement according to which it is said that that by which something differs is something other. For we are now speaking about what is the same and what is other according to the essence which the definition signifies. But it is obvious that even in the same species there are many accidental differences which neither diversify the substance of the species which the definition signifies, nor are in it per se. Hence it follows that not every difference makes something other in such a way that it must be known if one is to define.
Second, at: second, when one has taken (98a13), he disproves it another way.
For, since one who proposes to define by dividing must take opposing differences in such a way that everything contained under the divided whole falls under this member or that member of the division, and must subsume under one or the other of the members that whose definition is sought (if he knows that the thing he intends to define is contained under that member of the division), then it makes no difference, so far as his intent is concerned, whether he knows or does not know the things of which the opposing differences might be predicated.
For example, if I divide animal into rational and irrational, and assume that man is contained under animal in the way we have proposed, it is not required that I know the things of which irrational is predicated or how they differ from one another. For it is obvious that if someone proceeds in this way, namely, by dividing the genus into its first differences and taking the definitum [thing being defined] as subsumed under one of the members and then dividing until certain items are reached that cannot be further divided by essential differences, then by proceeding in this manner he will have the definition of the substance which he was seeking.
Therefore, the persons mentioned above were deluded for failing to distinguish between something in common and in detail. For it is required of one who knows what something is, that he know all things in common but not in detail. For example, one who knows what man is must know that it is through being an animal that man is distinguished from all things that are not animals, and through being rational that man is distinguished from all things that are not rational. But it is not required that he know anything more about these others than is included in the general notion of 'non-animal' or 'irrational'.
Then, at: moreover, to postulate (98a19) he excludes the second error.
For someone might believe that whoever uses division for defining must assume that the entire whole is contained under the members of the division. But he says that this is not necessary, if the opposites through which the division is made are immediate; because the divided whole is necessarily contained under one of the opposites, provided the first differences of the genus were taken. For differences which are immediate when compared to a lower genus are not immediate if compared to a higher genus. For example, even and odd are immediate if compared to number of which they are proper differences, but not if they are compared to quantity.
Then, at: in establishing a definition (98a23), after rejecting things which are not required in the divisions of the definitum, he shows what is really required.
First, he proposes what he intends.
Second, he manifests his proposal, at: the first is feasible (98a25; [548]).
He says therefore first (98a23) that in order to achieve a term, that is, a definition, by the method of division three things must be observed:
first, that the things which are taken be predicated in 'quod quid';
second, that they be arranged according to what is first and what is second;
third, that everything taken pertain to the 'quod quid' and that nothing be omitted.
Then, at: the first is feasible (98a25) he manifests his proposal.
First, he shows how these three rules can be observed.
Second, he shows that it is enough to observe those three rules, at: for it is clear that there (98b1; [551]).
In regard to the first point he does three things.
First (98a25), he shows how the first rule is observed, saying that this one (namely, that one take things which are predicated in quod quid) is observed, first of all, by the fact that a person can form syllogisms to show that what is assumed is in the thing (as is done when there is dispute about whether something is an accident); second, to show that it is predicated in quod quid (as is done when there is dispute about a genus).
Second, at: the right order will be achieved (98a28), he shows how the second rule is observed, namely, that there be a correct ordering of the parts.
And he says that the parts of a definition are arranged as they should, if one takes what is first—and he will do this, if he first takes that which is implied by the other things that are taken later, and not conversely. For this is more common and prior. But such a thing must be taken in the definition as a genus, as when it is stated that man is an animal, two-legged and walking. For if he is a two-legged walker, he is an animal; but not vice versa. Therefore, when I have taken animal as first, the same method must be observed in arranging the other items. For the second item to be employed in the definition will be that which according to the foregoing description will be first among all the others; likewise, the third item to be taken will be that which is first in respect of the items had, that is, following. For it will always turn out that when the more general item has been removed, that which is had, that is, that which immediately follows, will be first in regard to all the other items, say a fourth and a fifth, if that many parts are needed for the definition.
Third, at: our procedure makes it clear (98a34), he shows how the third rule can be observed.
And he says that it will be obvious that all items pertaining to the 'quod quid' are present in the definition according to the aforesaid method, because when we divide the genus, we take its first differences, under which the divisum is universally contained; for example, that every animal is this or that, that is, rational or irrational, and we assume that what we intend to define is this, that is, rational. And again we take this whole, namely, rational animal, and divide it by its proper differences; but when we arrive at the ultimate difference, it will be impossible to divide by other specific differences, but as soon as the ultimate difference is added, the thing whose definition is being sought will differ in no way from the assembled whole, that is, from the description formed by all the parts that were taken. Thus, man does not differ specifically from any of those of whom 'rational mortal animal' is predicated.