Commentary Aristotle Posterior Analytics
Lecture 14
Demonstration bears upon and proceeds from things which are per se
a18. Of accidents that are not essential according to our definition of essential there is no demonstrative knowledge; for since an accident, in the sense in which I here speak of it, may also not inhere, it is impossible to prove its inherence as a necessary conclusion.
a21. A difficulty, however, might be raised as to why in dialectic, if the conclusion is not a necessary connexion, such and such determinate premises should be proposed in order to deal with such and such determinate problems. Would not the result be the same if one asked any questions whatever and then merely stated one’s conclusion?
a24. The solution is that determinate questions have to be put, not because the replies to them affirm facts which necessitate facts affirmed by the conclusion, but because these answers are propositions which if the answerer affirm, he must affirm the conclusion and affirm it with truth if they are true.
a28. Since it is just those attributes within every genus which are essential and possessed by their respective subjects as such that are necessary it is clear that both the conclusions and the premises of demonstrations which produce scientific knowledge are essential; for accidents are not necessary.
Further, since accidents are not necessary, one does not necessarily have reasoned knowledge of a conclusion drawn from them (this is so even if the accidental premises are invariable but not essential, as in proofs through signs; for though the conclusion be actually essential, one will not know it as essential nor know its reason); but to have reasoned knowledge of a conclusion is to know it through its cause. We may conclude that the middle must be consequentially connected with the minor, and the major with the middle.
Of accidents that are not essential. After showing that demonstration proceeds from necessary things, the Philosopher then shows that it is concerned with things that are per se and proceeds from things that are per se.
In regard to this he does three things.
First, he shows that demonstration is concerned with things that are per se, that is, the conclusions of demonstrations are per se.
Second, he raises a problem, at: a difficulty, however (75a21).
Third, he shows that demonstration proceeds from things that are per se, that is, that the principles of demonstrations must be per se, at: since it is just those attributes (75a28).
He says therefore first (75a18) that demonstrative science cannot bear on accidents that are not per se in the way that 'per se' was explained above, namely, that a 'per se' accident is one in whose definition the subject is mentioned, as “even” or “odd” is a 'per se' accident of number. But “white” is not a 'per se' accident of animal, because animal is not mentioned in its definition.
That there cannot be demonstration bearing on accidents that are not per se he proves in the following way: An accident which is not per se might happen not to be present (and this is the accident under discussion). Therefore, if a demonstration were to bear on an accident which is not per se, it would follow that the conclusion of the demonstration would not be necessary: which is contrary to what has been established.
That an accident which is not 'per se' does not inhere necessarily can be obtained from the following: If an accident inheres necessarily and always in a subject, it must have its cause in the subject—in which case the accident cannot but inhere.
Now, this can occur in two ways:
in one way, when it is caused from the principles of the species, and such an accident is called a per se attribute or property;
in another way, when it is caused from the principles of the individual, and this is called an inseparable accident.
In either case every accident which is caused from the principles of the subject must, if it is defined, be defined in such a way as to mention the subject in its definition: for a thing is defined in terms of its proper principles. Thus it is clear that an accident which necessarily inheres in its subject must be a per se accident. Therefore, those that are not per se do not inhere of necessity.
It seems, however, that Aristotle is using the circular demonstration, which he previously repudiated. For he had proved earlier that a demonstration is concerned with necessary things, because it is concerned with things which are 'per se'; but now he shows that demonstration is concerned with things which are 'per se,' because it is concerned with things which are necessary.
The answer is that above Aristotle proved that demonstration is concerned with necessary things not only because it is concerned with things which are per se but also because of the definition of scientific knowing—and this was a true way to demonstrate. But the proof that demonstration is concerned with necessary things because it is concerned with things which are per se, is not a demonstration but an indication directed to a person who already knows that demonstration is concerned with things which are per se.
Then, at: a difficulty, however (75a21) he raises a problem.
First, he states the problem, saying that someone may perhaps object that if the conclusion which follows from contingent things or things which are per accidens is not necessary, why are inquiries made concerning contingent things or things which are per accidens, so that from such data one may reach a conclusion, since it is required of the syllogism that the conclusion follow of necessity.
That inquiries touching contingent things or things which are per accidens do occur is evident from his next statement, namely, that it makes no difference whether one inquires into contingent things and then gives his conclusion. As if to say: A conclusion can be drawn from contingent things that have been investigated and verified, just as from necessary things. For each employs the same syllogistic form.
Second, at: the solution is that determinate questions (75a24), he solves the difficulty and says that questions solved by contingent premises are not of such a nature that the conclusion is necessary absolutely, on the basis of the things investigated, that is, in virtue of the contingent premises, but because it is necessary for the one who admits the premises to admit the conclusion and to admit truth in the conclusion, if the things premised are true. It is as though he were saying that although a conclusion which is necessary with absolute necessity does not follow from contingent premises, yet it follows with the necessity of consequence according to which the conclusion follows from premises.
Then, at: since it is just those attributes (75a28) he shows that demonstration proceeds from things which are 'per se,' using the following argument: Demonstration proceeds from necessary things and bears on necessary things—and this because it is scientific, that is, makes one know scientifically. But things which are not 'per se' are not necessary, for they are per accidens and, being such, are not necessary, as has been stated above. On the other hand, those things bear with necessity on a genus which are 'per se' and belong to it according to what it is. It follows, therefore, that demonstration cannot be from anything or of anything but what is 'per se.'
He further shows that even if the premises were always both necessary and true but not 'per se,' one would not know the cause why [propter quid] of the conclusion. This is clear in syllogisms which prove through signs, for although the conclusion be 'per se,' one does not know it 'per se' nor 'propter quid.' For example, if someone were to prove that every element is corruptible on the ground that it is seen to grow old. This would be a proof through a sign but neither 'per se' nor 'propter quid,' because to know 'propter quid' one must know through the cause. Therefore, the middle must be the cause of that which is concluded in the demonstration. And this is obvious from the premises: for the middle must inhere in the third causatively, that is, 'per se,' and likewise the first in the middle. Here he calls the two extremes the first and the third.