Commentary Aristotle Posterior Analytics
Lecture 38
Universal demonstration is stronger than particular demonstration
b22. (4) Demonstration is syllogism that proves the cause, that is, the reasoned fact, and it is rather the commensurate universal than the particular which is causative (as may be shown thus: that which possesses an attribute through its own essential nature is itself the cause of the inherence, and the commensurate universal is primary; hence the commensurate universal is the cause). Consequently commensurately universal demonstration is superior as more especially proving the cause, that is the reasoned fact.
b28. (5) Our search for the reason ceases, and we think that we know, when the coming to be or existence of the fact before us is not due to the coming to be or existence of some other fact, for the last step of a search thus conducted is eo ipso the end and limit of the problem. Thus: ‘Why did he come?’ ‘To get the money — wherewith to pay a debt — that he might thereby do what was right.’ When in this regress we can no longer find an efficient or final cause, we regard the last step of it as the end of the coming — or being or coming to be — and we regard ourselves as then only having full knowledge of the reason why he came. If, then, all causes and reasons are alike in this respect, and if this is the means to full knowledge in the case of final causes such as we have exemplified, it follows that in the case of the other causes also full knowledge is attained when an attribute no longer inheres because of something else. Thus, when we learn that exterior angles are equal to four right angles because they are the exterior angles of an isosceles, there still remains the question ‘Why has isosceles this attribute?’ and its answer ‘Because it is a triangle, and a triangle has it because a triangle is a rectilinear figure.’ If rectilinear figure possesses the property for no further reason, at this point we have full knowledge — but at this point our knowledge has become commensurately universal, and so we conclude that commensurately universal demonstration is superior.
a3. (6) The more demonstration becomes particular the more it sinks into an indeterminate manifold, while universal demonstration tends to the simple and determinate. But objects so far as they are an indeterminate manifold are unintelligible, so far as they are determinate, intelligible: they are therefore intelligible rather in so far as they are universal than in so far as they are particular. From this it follows that universals are more demonstrable: but since relative and correlative increase concomitantly, of the more demonstrable there will be fuller demonstration. Hence the commensurate and universal form, being more truly demonstration, is the superior.
a11. (7) Demonstration which teaches two things is preferable to demonstration which teaches only one. He who possesses commensurately universal demonstration knows the particular as well, but he who possesses particular demonstration does not know the universal. So that this is an additional reason for preferring commensurately universal demonstration. And there is yet this further argument:
a14. (8) Proof becomes more and more proof of the commensurate universal as its middle term approaches nearer to the basic truth, and nothing is so near as the immediate premise which is itself the basic truth. If, then, proof from the basic truth is more accurate than proof not so derived, demonstration which depends more closely on it is more accurate than demonstration which is less closely dependent. But commensurately universal demonstration is characterized by this closer dependence, and is therefore superior. Thus, if A had to be proved to inhere in D, and the middles were B and C, B being the higher term would render the demonstration which it mediated the more universal.
a21. Some of these arguments, however, are dialectical. The clearest indication of the precedence of commensurately universal demonstration is as follows: if of two propositions, a prior and a posterior, we have a grasp of the prior, we have a kind of knowledge — a potential grasp — of the posterior as well. For example, if one knows that the angles of all triangles are equal to two right angles, one knows in a sense—potentially—that the isosceles’ angles also are equal to two right angles, even if one does not know that the isosceles is a triangle; but to grasp this posterior proposition is by no means to know the commensurate universal either potentially or actually.
a28. Moreover, commensurately universal demonstration is through and through intelligible; particular demonstration issues in sense-perception.
The preceding arguments constitute our defense of the superiority of commensurately universal to particular demonstration.
Demonstration is syllogism. After answering the arguments which favored the false side, the Philosopher now introduces arguments for the true side, namely, to show that universal demonstration is the more powerful.
In regard to this he sets down seven reasons, adding them to the previous solutions from which the proposition can also be concluded, as was clear from the above.
The first reason (85b22), is this: Demonstration is a syllogism showing the cause and 'propter quid': (for this is the way scientific knowing takes place, as stated above.) But the universal does this better than the particular. For as was shown in the first solution, something is per se in the universal more than in the particular. But that in which something is per se is the cause of this something: (for the subject is the cause of the proper attribute which is in it per se). However, the first thing in which the proper attribute is present is the universal, as is clear from what has been stated above. Hence it is plain that, properly speaking, the cause is that which is universal. From this he concludes the proposition, namely, that universal demonstration is more valuable as better declaring the cause and 'propter quid'.
Then, at: our search for the reason ceases (85b28) he gives the second reason.
This reason is taken from the final causes. Here it should be pointed out that something is the end of another thing both in regard to becoming and in regard to being: in regard to becoming, as generation is for the sake of form; in regard to being, as a house is for the sake of habitation.
He says, therefore, that we search for the 'reason why' something is done or 'why' something is, until we reach the point where there is nothing further to assign than this point reached, as the reason why that comes to be or is, whose 'reason why' is sought. And when we find this, then we think that we know the 'propter quid': the reason being that that which is ultimate in this way, that is, leaving nothing further to be sought, is truly the end and terminus which is being sought when we seek the 'propter quid'. And he gives this example: if we should ask why someone went out, and the answer is given, “to get money,” and this in order to pay a debt, and “this for this other reason,” namely, so that he is not guilty of injustice; and we continue in this way until there is nothing further for the sake of which as for an end—as when we arrive at the ultimate end, which is happiness—we will say that it was for this, as for an end, that he went. And it is the same in all other things that are or are done for the sake of an end: when we arrive at it, we will know best the reason why he went. Thus, if things are so related in the other causes as they are in the final cause, namely, that we know fully when the last one has been reached, then we will know best in the others, when we shall have arrived at the fact that “this is in this” no longer because of something else. And this happens when we shall have reached the universal. To elucidate this he offers the following example: If we should ask concerning this particular triangle, why its exterior angles are equal to four right angles, the answer will be that this happens to this triangle because it is isosceles; and it is so for the isosceles, because it is a triangle; and it is so for a triangle, because it is such and such a rectilinear figure. If no further step can be taken, then we know in the best way. But this happens when the universal has been reached. Therefore, the universal demonstration is stronger than the particular.
Then, at: the more demonstration becomes particular (86a3) he gives the third reason.
He says that the more one proceeds toward particulars, the nearer one gets to what is infinite; because, as it is stated in Physics III, the infinite is appropriate to matter which is the principle of individuation. On the other hand, the more one proceeds toward the universal, the nearer he gets to what is simple and to the end itself; because the universal reason is taken on the part of the form, which is simple and which has the character of an end insofar as it terminates the infinitude of matter. Now, it is obvious that infinite things as such are not scientifically knowable; rather to the extent that they are finite, to that extent are they knowable; because the principle of knowing a thing is not the matter but the form. Therefore, it is obvious that universals are scientifically more knowable than particulars. Consequently, they are also more demonstrable, because a demonstration is a syllogism that makes one know scientifically. But a demonstration of the more demonstrable is more powerful; for things which are described one in terms of the other grow apace. But demonstration is described in terms of the demonstrable. Consequently, since universals are more demonstrable, universal demonstration will be the more powerful demonstration.
Then, at: demonstration which teaches two things (86a11) he gives the fourth reason and it is this:
Since the end of demonstration is scientific knowledge, the more things a demonstration enables one to know, the more powerful it is. And this is what he states, namely, that a demonstration, according to which a man knows one thing and something additional, is more preferable to one according to which a man knows only the one. But a man who has knowledge of the universal knows also the particular, so long as he knows that the particular is contained under the universal. Thus, one who knows that every mule is sterile, knows that this animal, which he recognizes to be a mule, is sterile. But one who knows the particular does not on that account know the universal. For if I know that this mule is sterile, I do not on that account know that every mule is sterile. It remains, therefore, that universal demonstration, through which the universal is known, is stronger than particular, through which the particular is known.
Then, at: proof becomes more and more proof (86a14) he gives the fifth reason, and it is this:
The nearer to the first principle the middle of a demonstration is, the more powerful is the demonstration. He proves this on the ground that if a demonstration which proceeds from an immediate principle is more certain than one which does not proceed from an immediate, but from a mediate, principle, then it is necessary that to the extent that a demonstration proceeds from a middle nearer an immediate principle, the more powerful it is. But a universal demonstration proceeds from a middle nearer the principle which is an immediate proposition. And he exemplifies this with terms. For if one is required to demonstrate A, which is the most universal, of B, which is the most particular, say “substance” of man, and B and C, say 'living' and 'animal' be taken, such that B is more general than C, as 'living' than 'animal', it is obvious that B, which is the more universal, will be immediate to A; consequently, more will be known through it than through C, which is less universal. Hence it remains that universal demonstration is more powerful than particular.
But he remarks that some of the above reasons are “logical,” because, namely, they proceed from common principles which are not proper to demonstration; especially the third and fourth, which take as their middle something which is common to all knowledge. However, the other three, namely, the first, second and fifth, seem to be more analytic, proceeding as they do from principles proper to demonstration.
Then, at: some of these arguments (86a21) he gives the sixth reason.
He says that the primacy of universal demonstration over particular is most evident from the very propositions from which the two demonstrations proceed. For the universal demonstration proceeds from universal propositions, whereas the particular demonstration proceeds from a particular proposition. Now, the comparison between universal and particular propositions is such that one who has knowledge of the former, that is, of the universal, somehow knows the latter, namely, in potency. For the particulars are potentially in the universal, as the parts are potentially in a whole. Thus, if one knows that every triangle has three angles equal to two right angles, he already knows it potentially of isosceles. But one who knows something in a particular way does not on that account know it universally either potentially or actually. For the universal proposition is neither potentially nor actually contained in the particular. Therefore, if that demonstration is more powerful which proceeds from stronger propositions, it follows that universal demonstration is more powerful.
It should be noted that this reason does not differ from the fourth one given above, except that in the fourth one the comparison was made between the conclusions which are known through demonstration, whereas here the comparison is between the propositions from which the demonstration proceeds.
Then, at: moreover, commensurately universal (86a28) he gives the seventh reason.
It is this: the universal demonstration is intelligible, that is, is terminated in the intellect, because it finishes in a universal which is known only by the intellect. On the other hand, a particular demonstration, although it begins in the intellect is terminated in sense, because it concludes a particular which is directly known by sense, and the reason demonstrating reaches out to the particular through a certain application or reflexion. Now, since intellect is more powerful than sense, it follows that universal demonstration is stronger than particular.
Finally, he concludes that this is clear in virtue of all that has been said above.