Commentary Aristotle Posterior Analytics
Lecture 13
Demonstration proceeds from necessary things b5. Demonstrative knowledge must rest on necessary basic truths; for the object of scientific knowledge cannot be other than it is.
b6. Now, attributes attaching per se to their subjects attach necessarily to them: for essential attributes are either elements in the essential nature of their subjects, or contain their subjects as elements in their own essential nature. (The pairs of opposites which the latter class includes are necessary because one member or the other necessarily inheres.) It follows from this that premises of the demonstrative syllogism must be connexions essential in the sense explained: for all attributes must inhere essentially or else be accidental, and accidental attributes are not necessary to their subjects.
b13. We must either state the case thus, or else premise that the conclusion of demonstration is necessary and that a demonstrated conclusion cannot be other than it is, and then infer that the conclusion must be developed from necessary premises. For though you may reason from true premises without demonstrating, yet if your premises are necessary you will assuredly demonstrate — in such necessity you have at once a distinctive character of demonstration.
b18. That demonstration proceeds from necessary premises is also indicated by the fact that the objection we raise against a professed demonstration is that a premise of it is not a necessary truth — whether we think it altogether devoid of necessity, or at any rate so far as our opponent’s previous argument goes.
b22. This shows how naive it is to suppose one’s basic truths rightly chosen if one starts with a proposition which is (1) popularly accepted and (2) true, such as the sophists’ assumption that to know is the same as to possess knowledge. For (1) popular acceptance or rejection is no criterion of a basic truth, which can only be the primary law of the genus constituting the subject matter of the demonstration; and (2) not all truth is ‘appropriate’.
b27. A further proof that the conclusion must be the development of necessary premises is as follows. Where demonstration is possible, one who can give no account which includes the cause has no scientific knowledge. If, then, we suppose a syllogism in which, though A necessarily inheres in C, yet B, the middle term of the demonstration, is not necessarily connected with A and C, then the man who argues thus has no reasoned knowledge of the conclusion, since this conclusion does not owe its necessity to the middle term; for though the conclusion is necessary, the mediating link is a contingent fact.
b32. Or again, if a man is without knowledge now, though he still retains the steps of the argument, though there is no change in himself or in the fact and no lapse of memory on his part; then neither had he knowledge previously. But the mediating link, not being necessary, may have perished in the interval; and if so, though there be no change in him nor in the fact, and though he will still retain the steps of the argument, yet he has not knowledge, and therefore had not knowledge before. Even if the link has not actually perished but is liable to perish, this situation is possible and might occur. But such a condition cannot be knowledge.
a1. When the conclusion is necessary, the middle through which it was proved may yet quite easily be non-necessary. You can in fact infer the necessary even from a non-necessary premise, just as you can infer the true from the not true. On the other hand, when the middle is necessary the conclusion must be necessary; just as true premises always give a true conclusion. Thus, if A is necessarily predicated of B and B of C, then A is necessarily predicated of C. But when the conclusion is nonnecessary the middle cannot be necessary either. Thus: let A be predicated non-necessarily of C but necessarily of B, and let B be a necessary predicate of C; then A too will be a necessary predicate of C, which by hypothesis it is not.
a13. To sum up, then: demonstrative knowledge must be knowledge of a necessary nexus, and therefore must clearly be obtained through a necessary middle term; otherwise its possessor will know neither the cause nor the fact that his conclusion is a necessary connexion. Either he will mistake the non-necessary for the necessary and believe the necessity of the conclusion without knowing it, or else he will not even believe it — in which case he will be equally ignorant, whether he actually infers the mere fact through middle terms or the reasoned fact and from immediate premises.
Demonstrative knowledge must rest. Having finished his treatment of that which is said 'of all' and 'per se' and 'universally,' all of which we use in demonstration, the Philosopher now begins to discuss the items from which demonstration proceeds.
And there are two parts.
In the first he shows what demonstration of the reasoned fact [demonstration 'propter quid'] proceeds from.
In the second what demonstration of the fact [demonstration 'quia'] proceeds from, at: knowledge of the fact (78a22; [192]).
In the first he shows the sort of things from which a demonstration proceeds.
In the second, what the principles of demonstration are, at: as regards both these primary truths (76a32; [152]).
The first is divided into three parts.
In the first he shows that demonstration issues from necessary things.
In the second that it issues from things that are per se, at: of accidents that are not essential (76a26; [120]).
In the third that it proceeds from proper principles, at: it follows that we cannot (75a38; [127]).
Concerning the first he does two things.
First, he shows that demonstration should proceed from necessary things.
Second, he proves certain things he had presupposed, at: a further proof that the conclusion (74b27; [116]).
First, he makes a connection with what went before.
Second, he proves his proposition, at: now, attributes attaching per se (74b6; [110]).
Third, he draws a conclusion from the aforesaid, at: this shows how naive it is (74b22; [114]).
He says therefore first (74b5), as an inference from what has already been established, that if there be demonstrative science, that is, if science is acquired through demonstration, it must issue from necessary principles. The necessity of this inference is clear, because that which is known scientifically cannot be otherwise than it is, as was pointed out in the definition of scientific knowing.
Then, at: now, attributes attaching per se (74b6), he shows that demonstration issues from necessary things.
First, with a reason.
Second, with a sign, at: that demonstration proceeds (74b19; [113]).
With respect to the first he gives two reasons.
The first (74b6) is this: Things predicated per se are in a thing necessarily. (And he manifests this in two of the modes of predicating per se:
in the first mode, because the things predicated per se are “in that which is what,” that is, in the definition of the subject. But whatever is put in the definition of anything is predicated of it necessarily.
In the second mode, because certain subjects are put in “that which is the what of things predicated of them,” that is, in the definition of their predicates. And if these are opposites, one or other of them is necessarily in the subject: thus, either “odd” or “even” is in number, as we showed above).
Now, it is clear that it is from principles of this kind, namely, per se, that a demonstrative syllogism proceeds. (And this is proved by the fact that whatever is predicated, is predicated either per se or per accidens, and that things predicated per accidens are not necessary). Therefore, since it is not a demonstration but rather a sophistic syllogism that issues from things that are per accidens, it follows that demonstration proceeds from necessary things.
Furthermore, it should be noted that, since in a demonstration a proper attribute is proved of a subject through a middle which is the definition, it is required that the first proposition (whose predicate is the proper attribute, and whose subject is the definition which contains the principles of the proper attribute) be per se in the fourth mode, and that the second proposition (whose subject is the subject itself and the predicate its definition) must be in the first mode. But the conclusion, in which the proper attribute is predicated of the subject, must be per se in the second mode.
Then, at: we must either state the case thus (74b14) he sets forth the second reason and it is this: “Demonstration is concerned with the necessary and the demonstrated,” that is, the conclusion of the demonstration cannot be other than it is.
This statement is to be taken as the principle proving our proposition that demonstration proceeds from necessary things. And from what has been said, the truth of this principle is obvious. From this principle one argues thus: a necessary conclusion cannot be scientifically known save from necessary principles; but a demonstration makes a necessary conclusion scientifically known: therefore, it must proceed from necessary principles. Herein lies the difference between a demonstration and other syllogisms. For in the latter it is enough if one syllogizes from true principles. Nor is there any other type of syllogism in which it is required to proceed from the necessary: in a demonstration alone must this be observed. And this is proper to a demonstration, that is, to proceed from the necessary.
Then, at: that demonstration proceeds (74b18) he proves the same thing in the following way, using a sign: Suit is brought against an argument solely on the ground that something is wanting that should have been observed in that argument. But against one who believes that he has demonstrated, we bring the charge that the things from which he proceeded are not necessarily true, whether we are convinced that they could be otherwise than stated, or whether we bring a charge of reason, that is, for the sake of disputing. Therefore, demonstration should proceed from necessary things.
Then, at: this shows how naive it is (74b22) he draws a conclusion from the foregoing, saying that "this," namely, the fact that a demonstration must conclude from necessary things, "shows" that they are obtuse who assumed that they rightly chose the principles of demonstration, if the proposition they chose was probable or true, as the Sophists do, that is, those who appear wise but are not. For scientific knowing consists in nothing less than having science, namely, from demonstration. But when something is probable or improbable, it is not certain whether it is first or not first, whereas that on which a demonstration bears must be first in some genus and be true. This does not mean that a demonstrator may take anything that is first: it must be first in that genus with respect to which he is demonstrating. Thus, arithmetic does not choose what is first in regard to magnitude, but in regard to number.
It should be noted that Sophists are not taken here as they are in the book of Sophistical Refutations, that is, who proceed from things that seem probable but are not, or seem to syllogize but do not. For just as some are called Sophists, that is, seeming to be wise but not really so, inasmuch as they appear by their arguments to be scientific knowers but are not, so dialectical arguments, if they seem to prove demonstratively but do not, are sophistic.
Then, at: a further proof that the conclusion (74b27), he proves something he had presupposed.
And concerning this he does two things.
First, he shows that a necessary conclusion cannot be scientifically known from non-necessary principles.
Second, that although the necessary cannot be scientifically known from the non-necessary, it can nevertheless be syllogized, at: when the conclusion is necessary (75a1; [118]).
He proves the first with two reasons, one of which (74b27) is this:
If one does not have an argument which shows the cause why [that is, propter quid], he does not know scientifically, even though a syllogism be had; because to know scientifically is to know the cause of a thing, as we stated above. But an argument which infers a necessary conclusion from non-necessary principles does not show the cause why.
To clarify this he gives an example, using general terms. Assume that the conclusion, “Every C is A,” is necessary, and that it is demonstrated by a middle, B, which is not a necessary middle but a contingent one, so that, for example, one of the propositions, “Every B is A,” and “Every C is B,” or both, are contingent. Now, it is obvious that through this contingent middle, namely, B, one cannot obtain scientific knowledge propter quid of the necessary conclusion, “Every C is A.” For if the cause on which something depends is removed, the effect must be removed. But this middle, being contingent, can be withdrawn, whereas the conclusion, since it is necessary, cannot be withdrawn. It follows, therefore, that a necessary conclusion cannot be scientifically known through a contingent middle.
The second reason, at: or again, if a man (74b32) is this: “If a man is without scientific knowledge now, then even though he possesses the same argument he had up to now, and he has been kept sound,” that is, has not ceased to be, “and the thing known has not changed; and if he has not forgotten, then obviously he has not known scientifically.”
In this passage the Philosopher mentions four ways in which a person loses the science he once had: one way is when there slips from his mind the argument through which he formerly knew scientifically. Another is through the destruction of the knower. A third is by a change occurring in the thing known: thus if, while you are sitting, I know that you are sitting, this knowledge perishes when you are not sitting. The fourth way is by forgetting. Hence if none of these ways has occurred, then, if a person does not know a thing scientifically now, he never did know it.
Now, one who holds a necessary conclusion in virtue of a contingent middle, no longer knows it scientifically when the middle ceases to be, for the middle no longer exists, even though he retains the same argument and the fact remains the same, and he has not forgotten anything. Therefore, even when the middle had not ceased to be, he did not know scientifically. But that a contingent middle is liable to perish he proves by the fact that whatever is not necessary must at some time perish. And even though the middle has not perished, nevertheless, because it is not necessary, it is obvious that it is liable to perish. Now, when something contingent is put forward, its result is not impossible but possible and contingent. But what followed in our case was impossible, namely, that one should have had science of something and later not have had it, all the conditions described above prevailing. And this follows from the fact that a contingent middle has perished, which, although it may not be true [that it has], is nevertheless liable to, as has been said.
Then, at: when the conclusion is necessary (75a1) he shows that although a necessary conclusion cannot be scientifically known through a contingent middle, nevertheless a necessary conclusion can be syllogized from a non-necessary middle.
Hence he says that nothing hinders a necessary conclusion from being obtained through a non-necessary middle, as witness the case in which something is syllogized with a dialectical syllogism, although not with a demonstrative syllogism which causes science. For the necessary happens to be syllogized from the non-necessary, just as the true happens to be syllogized from the untrue—although the converse does not occur. For when the middle is necessary, the conclusion too will be necessary; similarly, from true premises something true is concluded. But that the necessary is always concluded from necessary premises he proves thus: “Let A be necessary of B,” that is, let this proposition, “Every B is A,” be necessary, “and the latter of C,” that is, let “Every C is B” also be necessary. Now, from these two necessary things follows a third necessary thing, namely, the conclusion, “Every C is A.” For it has been proved in the Prior Analytics that “from two propositions of necessity follows a conclusion of necessity.”
Then by way of consequence he shows that if the conclusion were not necessary, the middle could not be necessary. For example, suppose that this conclusion, “Every C is A,” is not necessary, but that the two premises are necessary. According to our previous doctrine it follows that the conclusion is necessary—which is contrary to the supposition in our example, namely, that the conclusion not be necessary.
Then, at: to sum up, then (75a13) he infers from the aforesaid the conclusion originally intended, saying that since a thing must be necessary if it is made known by way of demonstration, it is clear from the foregoing that a demonstration must rest on a necessary middle. For otherwise it would not be scientifically known that the conclusion is necessary, neither propter quid nor quia, since the necessary cannot be known through the non-necessary, as we have shown.
But if someone rests on an argument based on a non-necessary middle, he will be in one of two states. For since he does not actually know in a scientific way, he will either believe that he does know in a scientific way, if he assumes a non-necessary middle as necessary, or he will not presume that he knows in a scientific way, that is, if he believes that he does not have a necessary middle. And this is to be universally understood both of scientific knowledge 'quia', in which something is known through mediate principles, and of science 'propter quid', in which something is known through immediate principles. The difference between these two will be explained later.