COMMENTARY ON THE
POSTERIOR ANALYTICS OF ARISTOTLE

However, it has also been proved in the Prior Analytics that in figures other than the first, namely, in the second and third, one cannot form a circular syllogism, i.e., one through which each of the premises can be syllogized from the conclusion; or if one is formed, it is done not by using the premises already used but by using propositions other than those which appear in the first syllogism.

That this is so is obvious. For the second figure always yields a negative conclusion. Consequently, one premise must be affirmative and the other negative. However, it is true that if both are negative, nothing can be concluded; and if both are affirmative, a negative conclusion cannot follow. Therefore, it is not possible to use the negative conclusion and the negative premise to obtain the affirmative premise as a conclusion. Hence, if this affirmative is to be proved, it must be proved through propositions other than the ones originally used. Again, in the third figure the only conclusion ever obtained is particular. However, at least one premise must be universal; furthermore, if either premise is particular, a universal cannot be concluded. Hence it cannot occur that in the third figure each of the premises can be syllogized from the conclusion and the remaining premise.

For when we say that every man is an animal, it matters not whether it is also true that a non-man is an animal, or whether it is not true. Similarly, in the conclusion it matters not, Callias being an animal, whether nonCallias is an animal or not.

Now the reason for this is that the first is not limited to being said only *of the middle but can also be said of something else diverse from the middle and described by a negation of the riliddle (since the first is sometimes said of things other than the middle, as “animal” is said of things other than man; for it is said of horse, which is not man). Hence if the middle is taken the same and not the same, i.e., if an affirmative and a negative middle be taken, as when I say, “man” and “non-man” are animals, it contributes nothing to the conclusion. However, if the affirmation and negation are taken on the part of the major extreme, it does make a difference both as to the conclusion and as to the truth of the premises. For if man were not an animal, it would not be true that man is an animal, nor would it follow that Callias is an animal. Yet nothing more is verified by stating that man is an animal and is not a non-animal than by merely stating that man is an animal, for the same thing is conveyed by each. And thus it is clear that demonstrations do not use the principle that affirmation and negation are not simultaneously true, either on the part of the predicate or on the part of the subject.

Then (77a22) he shows how demonstrative sciences use the principle that “of anything there is either true affirmation or negation.” And he says that this principle is utilized in a demonstration leading to the impossible. For in this demonstration something is proved to be true by the fact that its opposite is false. (This of course would never happen, if it were possible for the two opposites to be false).

Nevertheless such a demonstration does not always employ this principle, for sometimes that opposite which is shown to be false is not a negation but an immediate contrary. For example, if a number were shown to be even on the ground that its opposite, namely, “it is odd,” is false, and this were done by leading to the impossible. Neither does it use this principle universally, i.e., in its universality, namely, under the terms “being” and “non-being,” but only so far as is sufficient for a genus or so far as it is narrowed to a generic subject. And I mean the first genus involved in the demonstration. For example, in leading to the impossible in geometry the terms would be “straight” and “non-straight” in the case where it is shown that some line is straight on the ground that it is false to state that it is not straight.

Then (77a26) he shows how the sciences as a community function relative to all common principles. In regard to this he does two things. First, he says that all the sciences share alike in the common principles in the sense that they all use them as items from which they demonstrate-which is to use them as principles. But they do not use them as things about which they demonstrate something, i.e., as subjects, or as things which they demonstrate, i.e., as conclusions.

Secondly (77a29), he shows that certain sciences employ the common principles in a manner other than has been described. For dialectics is concerned with common things, and a certain other science is concerned with common things, namely, first philosophy, whose subject is being and which considers the things which follow upon being as the proper attributes of being. Yet it should be noted that dialectics is concerned with common things under an aspect different from logic and first philosophy. For first philosophy is concerned with common things because its consideration is focused on those common things, namely, on being and on the parts and attributes of being. But because reason occupies itself with all things that are, and logic studies the operations of reason, logic will also be concerned with matters common to all things, i.e., with reason’s intentionalities which bear on all things, but not in such a way that logic has these common things as its subject-for logic considers as its subject the syllogism, enunciation, predication, and things of that type.

But although the part of logic which is demonstrative is engaged in teaching about common intentionalities, the use of a demonstrative science does not consist in proceeding from common intentionalities to show anything about the things which are the subjects of the other sciences. But dialectics does this, for it goes from common intentions and argues to things that pertain to other sciences, whether they be proper or common things, but mainly common things. Thus, it argues that hatred is in the concupiscible appetite, because love is, on the ground that contraries are concerned with a same thing. Consequently, dialectics is concerned with common things not only because it treats concerning the common intentionalities of reason, which is common to all logic, but also because it argues about common characteristics of things. But any science that argues about the common characteristics of things must argue about the common principles, because the truth of the common principles is made manifest from the knowledge of common terms, as “being” and “non-being,” “whole” and “part” and the like.

It is significant that he says, “and any science which might attempt,” because first philosophy does not demonstrate the common principles, since they are absolutely indemonstrable, although some have unwittingly attempted to demonstrate them, as is stated in Metaphysics IV. Or else, because even though they cannot, strictly speaking, be demonstrated, the first philosopher attempts to uphold them in a way that is possible, namely, by contradicting those who deny them, appealing to things that must be conceded by them, though not to things which are more known.

We should understand, however, that a negative proposition is mediate, when both terms exist in some whole which is not the same but different for each. For if they are in the same whole, the proposition will be immediate, as “No rational being is irrational,” or “No biped is a quadruped.”

Then (79b5) he explains something he had presupposed, namely, “on condition that one of the extremes exist in some whole and that the other be not in the same,” saying that it is “clear from the ‘orderings’ of the various predicaments, which are” not mutually interchangeable. In other words, because that which is in one predicament is not in another, it is plain that B happens not to be in the whole in which A is, or vice versa, because one of the terms happens to be taken from one predicament in which the other is not found. Thus, let one ordering of the predicaments be ACD, say the predicament of substance, and another ordering be BEF, say the predicament of quantity. Then if none of those in the ordering ACD be predicated of none in the ordering BEF, while A is in P as in that most general item which is the principle of the whole first ering, it is plain that B is not in P, because then the orderings, i.e., the predicaments, would be interchanged. Similarly, if B is in some whole, say in E, it is plain that A is not in E.

Then (79b12) he indicates how a negative proposition may be immediate, saying that “if neither is in some whole,” i.e., neither A nor B, and A is not in B, it is necessary that this proposition, “No B is A,” be immediate. Because if a middle were taken to syllogize it, then one of them would have to be in some whole, for the syllogism would have to be made either in the first figure or in the second, since in the third figure a universal negative cannot be concluded, as is required for an immediate proposition. However, if it is made in the first, B would have to be in some whole, because B is the minor extreme, and in the first figure the minor proposition must always be affirmative. For a syllogism with the major affirmative and the minor negative cannot be formed in the first figure.

But if it be in the second figure, either may, i.e., A or B, may be in a whole, because in the second figure the first proposition may be negative in some moods and the minor in other moods. Of course it is never permitted, neither in the first nor the second, to have both propositions negative. And so it is required that when either proposition is affirmative, one of the extremes must be in some whole. Thus it is clear that a negative proposition is immediate, when neither of its terms is in some whole. This does not mean, however, that although neither is in some whole, a middle could be found to conclude it, namely, if one were to take a convertible middle, because it is necessary that such a middle be prior and better known. And this is either the genus itself or the definition, which is not without a genus.

Lecture 1
(89b21-90a35)
EACH OF THE FOUR QUESTIONS WHICH PERTAIN TO SCIENCE IS ONE WAY OR ANOTHER A QUESTION OF THE MIDDLE

b2l. The kinds of question— b26. Thus, when our question— b28. On the other hand,— b32. but for some objects— b38. Now when we ask— a2. (By distinguishing— a5. We conclude that in— a24. Cases in which the

After determining about the demonstrative syllogism in the first book, the Philosopher intends in this [second] book to treat concerning its principles. But there are two principles of the demonstrative syllogism, namely, its middle and the first indemonstrable propositions. Therefore this book is divided into two parts. In the first he determines concerning the knowledge of the middle in demonstrations. In the second concerning the knowledge of the first propositions (99b18) [L. 20]. For since it has been established in the first book that every doctrine and every discipline takes its start from pre-existing knowledge, and since in demonstrations the knowledge of the conclusion is acquired through some middle and through the first indemonstrable propositions, we are left with the task of investigating how these come to be known.

But the first part is divided into two parts. In the first he inquires what is a middle in demonstrations. In the second part he inquires how that middle is made known to us (90a36) [L. 2]. But because the middle in demonstrations is employed in order to make known something about which there might have been doubt or question, therefore in regard to the first he does two things. First, he lays down the number of questions. Secondly, from these questions he pursues his investigation by showing how the questions pertain to the middle of demonstrations (89b38). Regarding the first he does three things. First, he enumerates the questions. Secondly, he explains complex questions (89b26). Thirdly, simple questions (89b32).

He says therefore first (89b21) that the number of questions is equal to the number of things that are scientifically known. The reason for this is that science is knowledge acquired through demonstration. But things which we previously did not know are those of which we must seek knowledge by demonstration: for it is in regard to things which we do not know that we form questions. Hence it follows that the things we inquire about are equal in number to the things we know through science. But there are four things that we ask, namely, quia [i.e., is it a fact that], propter quid [i.e., why, or what is the cause or reason], si est [if it is, i.e., whether it is], quid est [what is it]. To these four can be reduced whatever is scientifically inquirable or knowable.

However in Topics I he divides questions or problems into four kinds in a different way, but all of them are included under one of the questions listed here, namely, the one called quia. For in the Topics he is concerned only with questions to be disputed dialectically.

Then (89b26) he clarifies the questions he laid down; and first of all the complex ones. To understand this it should be noted that science bears only on the true, and the true is not signified except by an enunciation; therefore, only the enunciation can be scientifically knowable and so inquirable. But, as it is stated in On Interpretation II, the enunciation is formed in two ways: in one way from a name and a verb without an appositive, as when it is stated that man is; in another way when some third item is set adjacent, as when it is stated that man is white.

Therefore the questions we form can be reduced either to the first type of enunciation so that we get, as it were, a simple question; or to the second type, and then the question will be, as it were, complex or put in number, because, namely, the question concerns the putting together of two items.

According to this latter type a twofold question can be formed: one of them is whether this is true which is stated. This question he expounds first, saying that when we ask concerning some thing whether that thing is this or that, so that in effect we are somehow putting it in number, namely, by taking two things one of which is predicate and the other subject, as when we ask if the sun is failing because of an eclipse or not, and is man an animal or not, then we are said to ask quia: not in the sense that the word “ quia ” functions as a question mark, but because we are asking in order to find out quia [i.e., that] it is so. An indication of this is that when we have discovered it through demonstration, we cease our questioning; and if we had known it at the very beginning, we would not have asked whether it is so. But inquiry does not cease until that is obtained which was asked. And so, since the question in which we ask whether this is this ceases once we have certified that it is so, it is clear what a question of this kind asks.

Then (89b28) he clarifies the next question which also puts in number, ‘I saying that when we know that it is so, we ask propter quid [i.e., why] it is so. For example, when we know that the sun is failing through an eclipse and that the earth is moved during an earthquake, we ask why the sun is failing or why the earth is being moved. Therefore we ask it in this way, namely, by putting in number.

Then (89b32) he clarifies the other two questions which do not put in number but are simple. And he says that we ask certain things in a manner different from the aforesaid questions, namely, by not putting in number; as when we ask whether or not there be centaurs, for in this case the question we ask concerning the centaur is simply whether it exists and not whether the centaur be this, say white, or not. And just as when we knew that this is this, we then asked why, so once we know of something simply that it is, we ask what it is, for example, what is God or what is man. These then and so many are the things we ask; and when we have found the answer, we are said to know scientifically.

Then (89b38) he shows how the aforesaid questions are related to the middle. Concerning this he does three things. First, he states what he intends. Secondly, he explains what he had said (90a2). Thirdly, he proves his proposition (90a5).

In regard to the first it should be noted that two of the aforesaid questions put in number and two do not. From the first member of each of these groups, he forms another grouping composed of the question that it is and the question if it is. And he says that when we ask that this is this, or when we simply ask concerning something, if it is, we are not asking anything else than whether or not a middle is to be found of that which we ask; and this is something not conveyed by the form of the question. For when I ask whether the sun is eclipsed or whether man exists, it is not obvious from the form of the question that I am asking whether there is some middle by which it might be demonstrated that the sun is eclipsed or that man exists; but if the sun is eclipsed or man does exist, the consequence is that some middle can be found to demonstrate the things which are inquired. For no one forms a question concerning immediate things which, although they are true, do not have a middle, since things of this sort, being evident, do not fall under a question. Thus, therefore, one who asks whether this is this or whether this absolutely is, as a consequence is asking whether there is a middle of this sort. For in the question if it is or that it is, one is asking whether that which is a middle exists, because that which is the middle is the reason of that concerning which one asks whether this is this or simply whether it is, as will be explained below. Nevertheless the question is not being asked under the aspect of middle.

Now it happens that having found the answer to what is asked by these two questions, one knows either that it is or if it is: one of which consists in knowing the existence absolutely; but the other in part, as when we know that man is white, because to be white does not signify the existence of man in his entirety but signifies him to be something. This is why when a man is becoming white, we do not say that he is coming to be absolutely, but in a qualified sense. But when it is asserted that man is, his existence is signified absolutely, so that when a man comes to be, he is said to become absolutely.

Therefore, when we know that it is and ask why it is, or when we know if it is and ask what it is, we are asking what is the middle. And as in the other cases, so here, this is gathered not from the form of the question but by way of concomitance. For one who seeks the cause why the sun is eclipsed is not seeking it as a middle which demonstrates, but he is seeking that which is a middle, because it is by way of consequence that once he has it, he can demonstrate. And the same applies to the question what is it.

Then (904) he manifests what he had said, namely, that that it is and if it is differ as in part and absolutely differ. For when we inquire whether the moon is waning or waxing, it is a question in part, since in a question of this type we are asking if the moon is something, namely, is it waning or has it waxed or not. But when we ask whether the moon exists or whether it is night, the question bears on existence absolutely.

Then (90a5) he proves his point, namely, that the aforesaid questions pertain to the middle. First, he proves it with a reason. Secondly, with a sign (90a24).

He concludes therefore first (90a5) from the explanation given above that in all the aforesaid questions one is either asking whether there is a middle, namely, in the question that it is and in the question if it is, or what the middle is, namely, in the question why and in the question what is it.

And he proves that the question why inquires what the middle is. For it is obvious that a cause is the middle in a demonstration which enables one to know scientifically, because to know scientifically is to know the cause of a thing. But it is precisely the cause that is being sought in all the above questions. That this is so he manifests first in regard to the question that. For when it is asked whether the moon is waning, then according to the manner explained above, what is being asked is whether or not something is the cause of this waning. Then he shows this for the question why. For once we know that something is the cause of the moon’s waning, we ask what the cause is; and this is to inquire why.

The same applies to the other two questions, as he shows in the following way. For he says that whether we assert not that something is this or that (for example, when I say that man is white or is a grammarian), but that the substance itself exists absolutely; or do not assert that some thing exists absolutely, but that some thing is something by putting in number (whether that something be a thing predicated per se or a thing predicated per accidens); no matter in which of these ways we take the thing to be, its cause is the middle for demonstrating it.

Then he explains what he means by a substance to exist absolutely when we inquire concerning the moon or the earth or a triangle or any other subject whether it is and then take some middle to demonstrate this. I say that a thing is something when we inquire concerning eclipse in regard to the moon, or equality or inequality in regard to triangle, or whether it is in the middle of the universe or not in regard to the earth. And he asserts that as far as the present point is concerned it makes no difference which way a thing is taken to be, because in all these cases what it is is the same as why.

He manifests this first of all in regard to the waning, of the moon. For if one asks what is the eclipse of the moon, the answer is that it is the absence of light in the moon because of the earth’s being set between it and the sun. And this same answer is given when it is inquired why the moon is eclipsed. For we say that the moon is eclipsed because there is a lack of light due to the earth’s opposition.

Then he manifests the same idea with another example. For if one asks what is a chord, the answer is given that it is a numerical ratio according to high and low notes. Again, if one asks why a high note and a low note are concordant, the answer is given that it is because the high note and the low note have a numerical ratio. And so the question what is it and the question why reduce to the same thing subjectively, although they differ in formality. Hence because the question why leads us to inquire what the middle is, as has been shown, what is left is that when one asks what is it, the middle is likewise inquired.

Then he shows the same thing in regard to the question that. For, as has been said, concordance is a numerical ratio between high and low notes. Men, therefore, one asks whether a high and low note concord, he is inquiring whether there is some numerical ratio of the high and low note; and this is the middle for demonstrating that a high and a low note concord. Consequently in the question that, one inquires whether there is a middle. But once we have found that there is a numerical ratio of the high and low note, we then ask what that ratio is: and this is to ask what or why.

Here Aristotle seems to say that the definition of a proper attribute is the middle in demonstration. However it must be remarked that the definition of the proper attribute cannot be completed without the definition of the subject. For it is obvious that the principles which the definition of the subject contains are the principles of the proper attribute. Hence a demonstration will not reach the first cause unless one takes as the middle of demonstration the definition of the subject. And so the proper attribute must be concluded of the subject by means of the definition of the proper attribute; furthermore, the definition of the proper attribute must be concluded of the subject through the definition of the subject. This is why it was laid down at the very beginning that one must know beforehand the what is it not only of the proper attribute but of the subject also; which would not be required unless the definition of the proper attribute were concluded of the subject through the definition of the subject.

This is clear from the following example: If we wish to demonstrate of triangle that it has three angles equal to two right angles, we first take as middle the fact that it is a figure having an exterior angle equal to its two opposite interior angles-which is, as it were, the definition of a proper attribute. But this in turn must be demonstrated by the definition of the subject, so that we would say: “Every closed figure of three straight lines has an exterior angle equal to its two opposite interior angles; but the triangle is such a figure. Therefore...” And the same is true if we were to demonstrate that a high note concords with a low note: for we would state the definition of the attribute which in this case consists in their having a numerical ratio; but then to demonstrate this attribute we would have to take the definition of high note and of low note. For a low note is one which is apt to act on the sense for a long time, whereas a high note is one which does so for a short time: but between the long and the short there is a numerical ratio. Therefore, there is a numerical ratio between a high note and a low note. And if the high note and the low note were defined some other way, it would make no difference. For in any case something pertaining to quantity would have to appear in their definition, so that it would be necessary to conclude that there is a numerical ratio between them.

Then (90a44) he manifests his point by means of a sensible sign. And he says that those cases in which the middle is perceptible by sense clearly show that every question is a question concerning a middle, because, namely, when the middle is known through the senses, no room is left for a question. For we ask one of the aforesaid questions in matters pertaining to sense, when the middle does not appear: thus, we ask whether or not there is an eclipse of the moon because we do not sensibly perceive the middle which is the cause making the moon to be eclipsed. But if we were to situate ourselves in a place above the moon, we would see how the moon became eclipsed by entering the earth’s shadow. Then we would no longer ask if it is or why it is, but both would at once be obvious to us.

But because someone could object that sense-perception bears on singulars—whereas it is universals that are being asked about, just as it is universals that are scientifically known—and consequently, it does not seem that the matter under question can be made known through sense; therefore, as though in answer to this objection he adds that it is precisely because we do sense the particular (namely, that this body of the moon enters this shadow of the earth), that we happen at once to know the universal. For our sense would observe the fact that the light of the sun is now blocked by the earth’s opposition; and through this it would be clear to us that the moon is now eclipsed. And because we would conjecture that the eclipse of the moon always occurs in this way, the sense knowledge of the singular would immediately become a universal in our science.

And so from this example he concludes that knowing the quod quid [ quod quid refers to any or all of the items that constitute the essential nature of a thing.] and the why are the same. For from the fact that we observe the earth situated between the sun and moon, we would know scientifically both what an eclipse of the moon is and why the moon is eclipsed. And one of these, namely, the knowledge what it is, is reduced to the science by which we know that something simply is, and not that something is in some thing. But the why is reduced to our knowledge of things that are in some thing, as when we say that three angles are equal to or greater than or less than two right angles.