Commentary Aristotle Posterior Analytics
Then, at: for it is clear (98b1) he shows that the observance of the three aforesaid rules is sufficient for defining, because the definition will have neither more nor less than it should.
That no more has been assigned than it should have is obvious from the first rule, namely, because the only things accepted are items predicated in quod quid; and it was necessary to accept such things. Likewise it will be clear that nothing has been omitted. For either the genus or the difference might be missing. But that the genus is not missing is clear from the second rule; for the first thing taken was the item without which the others do not exist, and which can exist without the others: and this is the genus. And with the genus the differences were then taken. But that all the differences have been taken is obvious from the third rule, since there can be no further subsequent difference taken after the one concerning which we have said that it has no difference; otherwise it would follow that what had been admitted to be the last would still differ with an essential difference, whereas it had been said that it does not have a difference.
Similarly, it is obvious from the foregoing that no difference has been left out in the meantime, namely, because first differences are always taken.
Hence it remains that for defining it is sufficient that the three aforesaid rules be observed.
Lecture 16
How to search for the definition of a thing by examining things similar to it and dissimilar
b7. To resume our account of the right method of investigation: We must start by observing a set of similar — that is, specifically identical — individuals, and consider what element they have in common. We must then apply the same process to another set of individuals which belong to one species and are generically but not specifically identical with the former set. When we have established what the common element is in all members of this second species, and likewise in members of further species, we should again consider whether the results established possess any identity, and persevere until we reach a single formula, since this will be the definition of the thing. But if we reach not one formula but two or more, evidently the definiendum cannot be one thing but must be more than one.
b15. I may illustrate my meaning as follows. If we were inquiring what the essential nature of pride is, we should examine instances of proud men we know of to see what, as such, they have in common; e.g., if Alcibiades was proud, or Achilles and Ajax were proud, we should find on inquiring what they all had in common, that it was intolerance of insult; it was this which drove Alcibiades to war, Achilles to wrath, and Ajax to suicide. We should next examine other cases, Lysander, for example, or Socrates, and then if these have in common indifference alike to good and ill fortune, I take these two results and inquire what common element have equanimity amid the vicissitudes of life and impatience of dishonour. If they have none, there will be two genera of pride.
b26. Besides, every definition is always universal and commensurate: the physician does not prescribe what is healthy for a single eye, but for all eyes or for a determinate species of eye.
b28. It is also easier by this method to define the single species than the universal, and that is why our procedure should be from the several species to the universal genera — this for the further reason too that equivocation is less readily detected in genera than in infimae species.
b31. Indeed, perspicuity is essential in definitions, just as inferential movement is the minimum required in demonstrations; and we shall attain perspicuity if we can collect separately the definition of each species through the group of singulars which we have established e.g., the definition of similarity not unqualified but restricted to colors and to figures; the definition of acuteness, but only of sound—and so proceed to the common universal with a careful avoidance of equivocation.
b38. We may add that if dialectical disputation must not employ metaphors, clearly metaphors and metaphorical expressions are precluded in definition: otherwise dialectic would involve metaphors.
To resume our account of the right method. After teaching how to investigate the 'quod quid' according to the most suitable method which is by division of the genus, the Philosopher now teaches another method.
Concerning this he does three things.
First, he describes the method.
Second, he gives examples, at: I may illustrate my meaning (98b15; [554]).
Third, he proves that this method is satisfactory, at: besides, every definition (98b26; [555]).
He says therefore first (98b7) that if someone is searching for the definition of some thing, he should examine things which are similar to it as well as things which are different from it. He shows how this should be done when he says that in those things which are similar, one should consider some item that is the same in all; for example, what is found to be the same in all men is that they all coincide in being rational. After that, one should investigate the things which agree with the first things in genus and are specifically the same among themselves, although specifically different from the things first taken, as horses from men. It is also necessary to investigate what is the same in these things, namely, these horses; say neighing. Then having taken what is the same in all of the former, that is, men, namely, rational, and what is the same in all the others, that is, horses, namely, neighing, the next step will be to consider again if anything is the same in those two, namely, in rational and neighing. And this method of investigating must be continued until one common formality is found. For this will be the definition of the thing. However, if such an investigation does not uncover one common formality, but leads to two or even several diverse formalities, it will be obvious that the thing whose definition is being sought will not be one thing according to essence but several. Consequently, it will not have one definition.
Then, at: I may illustrate my meaning (98b15) he elucidates what he had said with an example.
He says that if we would investigate what magnanimity is, we should first of all consider certain magnanimous persons, in order to learn what is the one item they have insofar as they are magnanimous. Thus, Alcibiades was said to be magnanimous, and so were Achilles and Ajax; all of whom have one item in common—not to tolerate insults. The sign of this is that Alcibiades fought rather than accept insults; Achilles went mad from anger; Ajax committed suicide. Then we should consider this in others who are said to be magnanimous, say in Lysander and Socrates. For they have this in common that they were unmoved by good fortune or bad, but were indifferent to both. Therefore, let us take these two items, namely, equanimity in the face of the vicissitudes of life and intolerance of insults, and see if there is anything common to them.
For in this consists the notion of magnanimity. For example, we might say that these two things are due to the fact that a person considers himself worthy of great things. For it is from this attitude that a man does not tolerate insults and it is also from this attitude that he scorns fluctuations affecting external goods as being trifles.
But if nothing common is to be found in the two items taken, the species of magnanimity would not be one but two. Hence one common definition could not be given.
Then, at: besides, every definition (98b26) he shows that the above method is well adapted to finding the 'quod quid'.
Concerning this he does two things.
First, he shows that the method is suitable.
Second, he shows what should be avoided in this method, at: we may add that if dialectical (98b38; [559]).
Concerning the first he does two things.
First, he shows that the above method is suitable as to its result, namely, as to arriving at something common.
Second, as to its procedure, namely, inasmuch as it starts with particular cases, at: it is also easier by this method (98b28; [557]).
He says therefore first (98b26) that it was said advisedly that one who is investigating the 'quod quid' must reach something common, because every definition of something is given insofar as that thing is considered in its universality, and not as it is considered in this or that individual. For a physician does not define health as it exists in this eye of this man, but either as it is universally and absolutely in regard to all men, or he distinguishes health according to various species; for example, when he says this to be health for the cholerics, or for the bilious.
Then, at: it is also easier by this method (98b28) he shows that this method is satisfactory as to procedure, inasmuch as it proceeds from the less common to the more common.
And this in two ways.
First, by reason of facility. For a discipline begins from the easier things. But it is easier to define something singular, that is, something less common, than something universal, which is more common; inasmuch as equivocations are less likely to be detected in universals, because they are less determinate, than in things which are undifferentiated, that is, in things which are not divided by specific differences. Accordingly, one must define by ascending from singulars to universals.
Second, at: indeed, perspicuity is essential (98b31), he shows the same thing by reason of evidence.
For just as in demonstrations one should syllogize by presupposing something which is evident and obvious, so too in terms, that is, in definitions. (For no one can pass to a knowledge of something which is unknown except by means of something known, whether he intends to know quia est, which is made known through demonstration, or quid est, which is done by definition.) But this happens, that is, something evident preexists, if it is defined or happens to be defined separately, that is, distinctly, by means of items that are predicated singularly, that is, which belong to this or that thing properly and distinctively.
Thus, if someone desires to know what similar is, he will not examine every single thing which can be called similar, but only some similar things; for example, how things are similar in color, and how something is accounted similar in figure. For it is from the unity of color that things are said to be similar in color; but in the realm of figure, two things are similar because corresponding angles are equal and the sides proportional. Likewise in other things: if someone desires to define sharp, he will not examine everything which can be called sharp, but he will consider sharp as applied to a sound. Hence it is clear that one who follows this method when he defines is automatically avoiding the possibility of equivocation.
Consequently, it is clear that this is a practical method of defining, that is, the method of passing from the less common to the more common, inasmuch as it is easier in special things to define what is special, and univocation can be more easily recognized in such things.