Commentary Aristotle Posterior Analytics
Lecture 5
Whether a quod quid can be demonstrated by taking that which is required for a quod quid
a6. Can we nevertheless actually demonstrate what a thing essentially and substantially is, but hypothetically, that is, by premising (1) that its definable form is constituted by the ‘peculiar’ attributes of its essential nature; (2) that such and such are the only attributes of its essential nature, and that the complete synthesis of them is peculiar to the thing; and thus—since in this synthesis consists the being of the thing—obtaining our conclusion?
a9. Or is the truth that, since proof must be through the middle term, the definable form is once more assumed in this minor premise too?
a12. Further, just as in syllogizing we do not premise what syllogistic inference is (since the premises from which we conclude must be related as whole and part), so the definable form must not fall within the syllogism but remain outside the premises posited. It is only against a doubt as to its having been a syllogistic inference at all that we have to defend our argument as conforming to the definition of syllogism. It is only when someone doubts whether the conclusion proved is the definable form that we have to defend it as conforming to the definition of definable form which we assumed. Hence syllogistic inference must be possible even without the express statement of what syllogism is or what definable form is.
a20. The following type of hypothetical proof also begs the question. If evil is definable as the divisible, and the definition of a thing’s contrary—if it has one—is the contrary of the thing’s definition; then, if good is the contrary of evil and the indivisible of the divisible, we conclude that to be good is essentially to be indivisible.
a23. The question is begged because definable form is assumed as a premise,
a24. and as a premise which is to prove definable form. ‘But not the same definable form’, you may object. That I admit, for in demonstrations also we premise that ‘this’ is predicable of ‘that’; but in this premise the term we assert of the minor is neither the major itself nor a term identical in definition, or convertible, with the major.
a28. Again, both proof by division and the syllogism just described are open to the question why man should be animal-biped-terrestrial and not merely animal and terrestrial, since what they premise does not ensure that the predicates shall constitute a genuine unity and not merely belong to a single subject as do musical and grammatical when predicated of the same man.
a34. How then by definition shall we prove substance or essential nature? We cannot show it as a fresh fact necessarily following from the assumption of premises admitted to be facts—the method of demonstration: we may not proceed as by induction to establish a universal on the evidence of groups of particulars which offer no exception, because induction proves not what the essential nature of a thing is but that it has or has not some attribute. Therefore, since presumably one cannot prove essential nature by an appeal to sense perception or by pointing with the finger, what other method remains?
Can we nevertheless actually demonstrate. After showing that the 'quod quid' cannot be demonstrated either by convertible terms or by the method of division, the Philosopher here shows that it cannot be demonstrated by taking that which is required for a 'quod quid'.
First, he shows what he proposes.
Second, he concludes from all of the foregoing that there is no way in which 'quod quid' may be demonstrated, at: how, then, by definition (93a34).
Concerning the first he does two things.
First, he employs reasons proper to what he proposes.
Second, he employs a reason common to what is now being said and to what was said above, at: again, both proof (93a28).
Concerning the first he does two things.
First, he shows that the 'quod quid' cannot be demonstrated by taking that which pertains to the notion of its 'quod quid'.
Second, he shows that the 'quod quid' of this thing cannot be demonstrated by taking the 'quod quid' of some other thing, at: the following type (93a20).
First, he raises the question.
Second, he argues for his proposal, at: or is the truth (93a9).
He asks therefore first (93a6) whether one might demonstrate what something is according to its substance by supposing that the 'quod quid' of a thing can be obtained if one satisfies the conditions which are proper to the 'quod quid': (for example, if one were to prove that two-footed land animal is the 'quod quid' of man, having taken as middle the fact that this notion is converted with man and is composed of genus and difference); which are the only conditions required for a 'quod quid'. Furthermore, this whole, which has been stated, is proper to the 'quod quid' because it is the being or reality of it, that is, of that which is 'quod quid'. It is as though he were saying that being a convertible notion composed of a genus and difference is exactly the same as being the 'quod quid'.
Then, at: or is the truth (93a9) he lodges two objections against the above question, showing that the 'quod quid' cannot be demonstrated in the way it suggests.
The first of these is that just as the previously mentioned ways of demonstrating failed because they assumed the very thing in question, so too in the present instance. For it, too, assumes the 'quod quid erat esse', as for example when it is assumed that every convertible notion composed of genus and difference signifies the 'quod quid est'; consequently, the proof is not acceptable. For one must never take as middle the very thing the demonstration is intended to prove; rather it is necessary to demonstrate it through some other middle.
Then, at: further, just as in syllogizing (93a12) he gives the second reason, which is based on a likeness to a syllogism.
For when a person syllogizes, he is not required to use the definition of syllogism in order to syllogize; because the items from which a syllogism proceeds are such that each item is always either a whole proposition, that is, a universal or major proposition, or a part, that is, a particular or minor proposition subsumed under the major one. Consequently, the definition of a syllogism is not one of the things from which a syllogism proceeds. In like manner if someone wishes to syllogize the 'quod quid erat esse' of something, he is not required to mention what a 'quod quid erat esse' is; but he must have this in reserve in his mind over and above the items which are put in the definition or in the syllogism.
For these notions of a syllogism and of a definition function in defining and syllogizing as rules of art which an artisan must respect in his works. Now, an artisan who makes a knife does not do so by establishing the rules according to which he works, but in the light of the rules he has in his mind he examines whether the knife was made well. So, too, a person who syllogizes does not mention the notion of a syllogism as he syllogizes, but in view of the notion of a syllogism he examines the syllogism he made, in order to see whether it is good.
Hence if a person should wonder, once a syllogism has been formed, whether it syllogized or not, the one who formed the syllogism can settle this doubt by showing that it does syllogize, on the ground that a syllogism is such and such a thing. So, too, a person who intends to syllogize the 'quod quid erat esse' should have reserved in his mind the notion of what a 'quod quid erat esse' is, so that if someone should say that a 'quod quid erat esse' has not been syllogized, he can answer that it has, because such and such is put down as the 'quod quid erat esse'. Thus, therefore, it is clear that a person who syllogizes a 'quod quid erat esse' should not state what a syllogism is or what a 'quod quid erat esse' is.
Then, at: the following type of hypothetical (93a20) he shows that the 'quod quid' of one thing cannot be demonstrated from the 'quod quid' of another thing.
Concerning this he does two things.
First, he proposes what he intends.
Second, he proves what he proposes, at: the question is begged (93a23).
He says therefore first (93a20) that the 'quod quid' is not proved, if someone wished to prove it by supposing the 'quod quid' of some other thing; for example, if someone were to proceed in such a way as to assume that the being or reality of divisible and of evil is the same, that is, that division is the 'quod quid' of evil, and then argued in the following manner: “In all things which have a contrary the 'quod quid' of one contrary is a contrary; but the contrary of good is evil, and of divisible the contrary is indivisible: therefore, it follows that indivisible is the 'quod quid' of the good.” And these examples are taken according to Plato’s opinion that the notion of the one and of the good are the same. For we notice that everything seeks unity as its own good. But one is the same as indivisible; and so in virtue of the opposition it follows that evil is the same as divisible. For everything shuns division of the self, because through division it tends to what is shattered and imperfect.
Then, at: the question is begged (93a23) he proves what he has proposed, namely, that the 'quod quid' cannot be demonstrated:
and this by giving two reasons.
The first of these is that even according to this method one demonstrates by assuming the 'quod quid erat esse', and thus he assumes what he should have proved.
Then, at: and as a premise (93a24) he gives the second reason, saying that not only is it improper to take the 'quod quid erat esse' when demonstrating, but this impropriety is compounded when one takes a 'quod quid erat esse' to demonstrate a 'quod quid erat esse': because even in demonstrations in which this is proved of this, say a proper attribute of a subject, a 'quod quid erat esse' is taken as middle; nevertheless the one so taken is not the very thing which was to be concluded or something which has the same notion and is converted. But good and indivisible, and evil and divisible, have the same notion; and each pair is converted, because one being posited, the other is posited, and vice versa.
Then, at: again, both proof by division (93a28) he presents a common reason against anyone who demonstrates from supposition and division.
And he says that the same opposition is directed against both, namely, against one who tries to demonstrate the 'quod quid' by division and against one who proceeds by laying down the 'quod quid' in the syllogism. For clearly a definition signifies something which is one: hence to signify this oneness the items laid down in the definition should be arranged without a conjunction; thus one should say that man is a two-footed land animal, but not that man is an animal and two-footed. Hence if anyone desires to prove the 'quod quid', he must prove that one thing is formed from the things assumed. But it is not required, according to the above-cited methods of division and supposition, that one predicate be formed from these items which are taken for defining: since there might be several, for example, if one should state that man is grammatical and musical. It seems therefore that according to the ways mentioned above, the 'quod quid' is not proved.
Then, at: how, then, by definition (93a34) he concludes from the foregoing that there is no way to prove the 'quod quid'.
He says: If, then, the 'quod quid' cannot be proved either by convertible terms or division or opposition, how will the definer be able to demonstrate the substance of a thing or the 'quod quid'? For it is now clear from the foregoing that he does not prove it according to the method whereby, in virtue of items that are per se known, one manifests that something else must follow through things which are said—which is required for a demonstration. However, besides these three modes there is a fourth, namely, through induction. But it turns out that the 'quod quid' cannot be proved by manifest singulars, namely, in such a way that something is predicated of all and is not anything that might be otherwise: because one who thus proceeds by induction will not demonstrate the quod quid but will demonstrate that something is or is not; for example, that every man is an animal, or that no animal is a stone. But no other method is available for demonstrating the 'quod quid', save perhaps the method of demonstrating something to the senses, as when something is pointed out with the finger.
But it is obvious that this method cannot be invoked in the present instance, because the 'quod quid' is not an object of sense but of intellect, as it is stated in On the Soul III. It remains, therefore, that there is no way in which the 'quod quid' can be demonstrated.