Commentary Aristotle Posterior Analytics
Lecture 16
Demonstration is not of perishable but of eternal matters b21. It is also clear that if the premises from which the syllogism proceeds are commensurately universal, the conclusion of such a demonstration, that is, in the unqualified sense — must also be eternal.
Therefore, no attribute can be demonstrated nor known by strictly scientific knowledge to inhere in perishable things.
b24. The proof can only be accidental, because the attribute’s connexion with its perishable subject is not commensurately universal but temporary and special.
If such a demonstration is made, one premise must be perishable and not commensurately universal (perishable because only if it is perishable will the conclusion be perishable; not commensurately universal, because the predicate will be predicable of some instances of the subject and not of others); so that the conclusion can only be that a fact is true at the moment—not commensurately and universally.
b30. The same is true of definitions, since a definition is either a primary premise or a conclusion of a demonstration, or else only differs from a demonstration in the order of its terms.
b32. Demonstration and science of merely frequent occurrences—e.g., of eclipse as happening to the moon—are, as such, clearly eternal: whereas so far as they are not eternal they are not fully commensurate. Other subjects too have properties attaching to them in the same way as eclipse attaches to the moon.
It is also clear that if the premises. After concluding from the above that demonstration does not conclude from extraneous principles, the Philosopher intends to conclude something else from the above, namely, that demonstration is not of destructible things.
Concerning this he does two things.
First, he shows that demonstration is of eternal and not of destructible things.
Second, he shows how it is of things that occur now and then, at: demonstration and science (75b32; [142]).
Concerning the first he does two things.
First, he shows that demonstration is not of perishable but of eternal things.
Second, he shows that the same is true of definition, at: the same is true of definitions (75b30; [138]).
First, he proposes the intended conclusion.
Second, he sets down the reason proving it, at: if such a demonstration is made (75b24; [137]).
Therefore, first (75b21), he sets down two conclusions, one of which follows from the other. The first is that the conclusion of this demonstration which we are now discussing and which we can call demonstration in the full sense must be eternal: which, of course, follows from what has been stated so far, namely, that the propositions of a syllogism should be universal: which he signified by 'said of all.' The second conclusion is that neither demonstration nor science is of destructible things, that is, absolutely speaking, but only accidentally.
Then, at: if such a demonstration is made (75b24) he presents an argument to prove the proposed conclusions.
It is this: It is not the character of a destructible non-eternal conclusion to contain what is universally so, but what is so for a time and in certain instances. (For it has been established above that 'said of all' contains two things, namely, that it is not such as to be so in one case and not in another, or so at one time and not at another. But in destructible things we find that at one time something is so and at another not so. Hence it is clear that 'said of all' or “said universally” are not found in destructible things.) But where a conclusion is not universal, at least one of the premises is not universal. Therefore, a destructible conclusion must have followed from premises, one of which is not universal. Accordingly, when we add to this the fact that demonstration absolutely must be from what is universal, it follows that a demonstration cannot have a destructible conclusion, but must have an eternal one.
Then, at: the same is true of definitions (75b30) he shows that definition, too, is not of destructible but of eternal things.
The reason for this is that demonstration, both as to its principles and conclusions, is of eternal and not of destructible things. But a definition is either a principle of a demonstration, a conclusion of a demonstration, or a demonstration with a different ordering of its terms. Therefore, a definition is not of destructible, but of eternal things.
For a better understanding of this passage it should be noted that it is possible to give different definitions of the same thing, depending on the different causes mentioned. But causes are arranged in a definite order to one another: for the reason of one is derived from another. Thus the reason of matter is derived from the form, for the matter must be such as the form requires. Again, the agent is the reason for the form: for since an agent produces something like unto itself, the mode of the form which results from the action must be according to the mode of the agent. Finally, it is from the end that the reason of the agent is derived, for every agent acts because of an end. Consequently, a definition which is formulated from the end is the reason and cause proving the other definitions which are formulated from the other causes.
Therefore, let us lay down two definitions, one of which is formulated from the material cause, for example, that a house is a shelter composed of stones, cement and wood; the other being formulated from the final cause, namely, that a house is a shelter protecting us from the rain and heat and cold. Now, the first definition can be demonstrated from the second in the following way: Every shelter protecting us from rain, heat and cold should be composed of wood, cement and stones; but a house is such a thing: therefore... Thus it is clear that the definition formulated from the end is the principle of the demonstration, whereas the one formulated from the matter is the conclusion of the demonstration. However, the two can be combined in the following way to form one definition: A house is a shelter composed of the aforesaid, protecting us from rain, cold and heat. But such a definition contains all the elements of a demonstration, namely, a middle and a conclusion. Accordingly, such a definition is a demonstration differing merely in the arrangement of its terms, because the only way it differs from the demonstration is that it is not arranged in a syllogistic mode and figure.
Here we might remark that because demonstration, as well as definition, is not of destructible but of eternal things, Plato was led to posit “Ideas.” For since sensible things are destructible, it appeared that there could be neither demonstration nor definition of them. As a consequence it seemed necessary to postulate certain indestructible substances concerning which demonstrations and definitions could be given. These eternal substances are what he calls “Forms” or “Ideas.”
However, Aristotle opposed this opinion above, when he said that demonstration is not of destructible things except per accidens. For although those sensible things are destructible as individuals, nevertheless in the universal they have a certain everlasting status. Therefore, since demonstration is made about those sensible things universally and not individually, it follows that demonstration is not of destructible things except per accidens, but of eternal things per se.
Then, at: demonstration and science (75b32) he shows how there can be demonstration of things that occur now and then, saying “that there are science and demonstrations of things that occur frequently, as the eclipse of the moon,” which is not always. For the moon is not always being eclipsed, but only now and then. Now, things that occur frequently, so far as they are such, that is, so far as demonstrations are given concerning them, are always; but they are particular, so far as they are not always. But demonstration cannot be of particulars, as we have shown, but only of universals. Hence it is clear that these things, insofar as there is demonstration of them, are always. And as in the case of the eclipse of the moon, so in all kindred matters.
However, there are certain differences to be noted among them. For some are not always with respect to time, but they are always in respect to their cause, because it never fails that under given conditions the effect follows, as in the eclipse of the moon. For the moon never fails to be eclipsed when the earth is diametrically interposed between sun and moon.
But others happen not to be always even in respect to their causes, that is, in those cases where the causes can be impeded. For it is not always that from a human seed a man with two hands is generated, but now and then a failure occurs, owing to a defect in the efficient cause or material cause. However, in both cases the demonstration must be so set up that a universal conclusion may be inferred from universal propositions by ruling out whatever can be an exception either on the part of time alone, or also of some cause.