Commentary Aristotle Posterior Analytics
Lecture 4
Whether quod quid can be demonstrated by the method of division
b12. Nor, as was said in my formal logic, is the method of division a process of inference at all, since at no point does the characterization of the subject follow necessarily from the premising of certain other facts: division demonstrates as little as does induction. For in a genuine demonstration the conclusion must not be put as a question nor depend on a concession, but must follow necessarily from its premises, even if the respondent deny it. The definer asks ‘Is man animal or inanimate?’ and then assumes—he has not inferred—that man is animal. Next, when presented with an exhaustive division of animal into terrestrial and aquatic, he assumes that man is terrestrial. Moreover, that man is the complete formula, terrestrial-animal, does not follow necessarily from the premises: this too is an assumption, and equally an assumption whether the division comprises many differentiae or few. (Indeed as this method of division is used by those who proceed by it, even truths that can be inferred actually fail to appear as such.)
b25. For why should not the whole of this formula be true of man, and yet not exhibit his essential nature or definable form?
b26. Again, what guarantee is there against an unessential addition, or against the omission of the final or of an intermediate determinant of the substantial being?
b28. The champion of division might here urge that though these lapses do occur, yet we can solve that difficulty if all the attributes we assume are constituents of the definable form, and if, postulating the genus, we produce by division the requisite uninterrupted sequence of terms, and omit nothing; and that indeed we cannot fail to fulfill these conditions if what is to be divided falls whole into the division at each stage, and none of it is omitted; and that this—the dividendum—must without further question be (ultimately) incapable of fresh specific division.
b33. Nevertheless, we reply, division does not involve inference; if it gives knowledge, it gives it in another way. Nor is there any absurdity in this: induction, perhaps, is not demonstration any more than is division, yet it does make evident some truth. Yet to state a definition reached by division is not to state a conclusion: as, when conclusions are drawn without their appropriate middles, the alleged necessity by which the inference follows from the premises is open to a question as to the reason for it, so definitions reached by division invite the same question. Thus to the question ‘What is the essential nature of man?’ the divider replies ‘Animal, mortal, footed, biped, wingless’; and when at each step he is asked ‘Why?’, he will say, and, as he thinks, proves by division, that all animal is mortal or immortal: but such a formula taken in its entirety is not definition; so that even if division does demonstrate its formula, definition at any rate does not turn out to be a conclusion of inference.
Nor, as was said in my formal logic. After showing that 'quod quid' cannot be demonstrated with convertible terms, the Philosopher now shows that it cannot be demonstrated by the method of division.
And in regard to this he does two things.
First, he shows what he proposes.
Second, he excludes a certain solution, at: the champion of division (92b28).
Concerning the first he does two things.
First, he shows what he proposes by using a reason common to all things which are syllogized.
Second, he shows it with reasons proper to that which is 'quod quid', at: for why should not (92b25).
He says therefore first (92b12) that just as the quod quid cannot be demonstrated by convertible terms, so neither by the method of division through which, as a matter of fact, nothing is proved syllogistically, as was established in Resolutions Touching Figures, that is, in Prior Analytics I. For just as in the Posterior Analytics resolution to first principles is taught, so in the Prior Analytics resolution is made to certain first simple items which pertain to the arrangement of the syllogism in mood and figure.
That something cannot be syllogized by the method of division he proves from the fact that in this method, given the premises, the conclusion does not follow of necessity, which it should, considering the nature of a syllogism. Rather, the same thing happens in the method of division as happens in the method of induction. For one who induces through singulars to the universal does not demonstrate or syllogize from necessity. For when something is proved syllogistically, it is not necessary to make further inquiry concerning the conclusion or to ask that the conclusion be conceded; what is necessary is that the conclusion be true, if the premises laid down are true.
But, as he shows with certain examples, this does not happen in the method of division. For the method of division consists in assuming something common which is divided into at least two members, so that, one being removed, the other is concluded. For example, if beings are so divided that on the one hand is animal and on the other lifeless things, then having established that man is not a lifeless thing, it is concluded that he is animal. But this conclusion does not follow, unless the hearer grants that man is either an animal or a lifeless thing.
It might be remarked here that he quite fittingly compared division to induction. For in both cases one is required to suppose that he has listed all the things contained under some general heading; otherwise, the person inducing could not conclude a universal from the singulars he assumed, nor could the person dividing conclude to one member just because the others have been eliminated. Thus it is obvious that one cannot in virtue of the fact that Socrates and Plato and Cicero run, induce of necessity the conclusion that every man runs, unless his audience concedes that nothing more is contained under man than the ones listed. In like manner, one who divides cannot, in virtue of having proved that this colored object is neither white nor grey, conclude of necessity that it is black, unless his audience grants him that nothing else is contained under colored object than the things mentioned in the division.
And because a person investigating what man is must assume not only the genus which is animal but also the difference, he goes on to say in his example that if every animal is either of the land or of the water and it is established that because man is not a water animal, he is this whole which is 'land animal', that statement does not follow of necessity from the premises: rather it is further required that he suppose his audience to have granted him something, namely, that animal is sufficiently divided into those of the land and those of the water.
And because in some cases several divisions are used in obtaining the 'quod quid' of a thing, therefore, after laying down two divisions in his example, he adds that it makes no difference whether few or many are used. For the formality is the same in all.
And thus he concludes once more that those who proceed by the method of division, even in matters that could be syllogized, do not use a syllogized proof.
Then, at: for why should not (92b25) he induces two reasons proper to the 'quod quid'.
The first of these is that not everything which is truly predicated of something is predicated in 'quod quid' or signifies its essence. Therefore, even if it be conceded that one has sufficiently proved by the method of division that this whole, namely, 'land animal', is truly predicated of man, nevertheless it does not follow that it is predicated of it in 'quod quid' or that it shows the 'quod quid erat esse', that is, that it demonstrates the essence of the thing.
Then, at: again, what guarantee (92b26) he gives the second reason. For the essence of a thing is declared through certain definite items which may neither be added to or subtracted from. But there is nothing to hinder one who proceeds by the method of division from adding something over and above the items which suffice for showing the 'quod quid', or from subtracting some of the things which are necessary for this, or from going beyond and exceeding the essence of the thing, as when it is more common than the thing itself—which happens when the ultimate differences which contract common things are removed. Hence the 'quod quid' is not sufficiently proved by division. And this is what he concludes, namely, that in the method of division the above-mentioned conditions are not satisfied, that is, the conditions that what is concluded be predicated in 'quod quid' and that it neither exceed nor be exceeded.
Then, at: the champion of division (92b28) he excludes a certain solution.
First, he proposes it.
Second, he excludes it, at: nevertheless, we reply (92b33).
He says therefore first (92b28) that one might solve our objections by saying that when a division is made, one could be taking all the things that are predicated in quod quid, so that as a consequence of the division he accomplishes what was primarily intended, namely, that he obtains a definition signifying the 'quod quid' and leaves out nothing which is required for defining. And if he does these two things, namely, if all the items he assumes in the division are predicated in quod quid and all such things are included in the division so that nothing is left out, then it is necessary that what is obtained be the 'quod quid'. And the reason for this necessity is that in taking everything which is predicated in quod quid and leaving nothing out, that which is found must be something individual, that is, the individual notion of such a thing, so that no further division is required for it to be appropriate to this thing.
Then, at: nevertheless, we reply (92b33) he excludes this solution.
He says that even though under the aforesaid conditions something individual is necessarily obtained, as explained above, the method is nevertheless not syllogistic; although it might make one know the 'quod quid' in some other way. And this is not unbecoming, namely, that something be manifested in a way other than by a syllogism: for one who uses induction does not prove anything syllogistically, but yet he does manifest something. That one who reaches a definition by way of division does not achieve a syllogism he shows by something similar. For if a conclusion is induced from a major proposition, the second proposition being omitted, and the person concluding declares that this must follow from the premises, the hearer could ask why it is necessary—which is something that does not happen in a syllogistic proof. Hence such a method of arguing is not syllogistic. Similarly, in terms of division no syllogism is achieved, because the question why always remains. Thus, if someone wishing to disclose what man is were to assert by the method of division that man is a two-footed mortal animal, or one that has two feet but no wings, then as he adds one item to another in his division, he could be asked in regard to each one, 'why' is it necessary. For one who sets out to manifest a 'quod quid' by division will not only assert but also prove—in keeping with what he thinks—that everything which exists is mortal or immortal. And although it be granted that through this division he might be demonstrating his proposition, nevertheless it is not necessary that the notion so concluded be a definition; for perhaps the items out of which such a notion is formed are not predicated in quod quid or exceed the substance of the thing defined. But even though such a notion might happen to be a definition, it is nevertheless not proved by the syllogism to be a definition, as is clear from what has been established above.