Lecture 1 — Each of the four questions which pertain to science is one way or another a question of the middle

b21. The kinds of question we ask are as many as the kinds of things which we know. They are in fact four: (1) whether the connexion of an attribute with a thing is a fact, (2) what is the reason of the connexion, (3) whether a thing exists, (4) What is the nature of the thing.

b26. Thus, when our question concerns a complex of thing and attribute and we ask whether the thing is thus or otherwise qualified — whether, e.g., the sun suffers eclipse or not — then we are asking as to the fact of a connexion. That our inquiry ceases with the discovery that the sun does suffer eclipse is an indication of this; and if we know from the start that the sun suffers eclipse, we do not inquire whether it does so or not.

b28. On the other hand, when we know the fact we ask the reason; as, for example, when we know that the sun is being eclipsed and that an earthquake is in progress, it is the reason of eclipse or earthquake into which we inquire. Where a complex is concerned, then, those are the two questions we ask;

b32. but for some objects of inquiry we have a different kind of question to ask, such as whether there is or is not a centaur or a God. (By ‘is or is not’ I mean ‘is or is not, without further qualification’; as opposed to ‘is or is not [e.g.] white’.) On the other hand, when we have ascertained the thing’s existence, we inquire as to its nature, asking, for instance, ‘what, then, is God?’ or ‘what is man?’. These, then, are the four kinds of question we ask, and it is in the answers to these questions that our knowledge consists.

b38. Now, when we ask whether a connexion is a fact, or whether a thing without qualification is, we are really asking whether the connexion or the thing has a ‘middle’; and when we have ascertained either that the connexion is a fact or that the thing is — that is, ascertained either the partial or the unqualified being of the thing-and are proceeding to ask the reason of the connexion or the nature of the thing, then we are asking what the ‘middle’ is.

a2. (By distinguishing the fact of the connexion and the existence of the thing as respectively the partial and the unqualified being of the thing, I mean that if we ask ‘does the moon suffer eclipse?’, or ‘does the moon wax?’, the question concerns a part of the thing’s being; for what we are asking in such questions is whether a thing is this or that, that is, has or has not this or that attribute: whereas, if we ask whether the moon or night exists, the question concerns the unqualified being of a thing.)

a5. We conclude that in all our inquiries we are asking either whether there is a ‘middle’ or what the ‘middle’ is: for the ‘middle’ here is precisely the cause, and it is the cause that we seek in all our inquiries. Thus, ‘Does the moon suffer eclipse?’ means ‘Is there or is there not a cause producing eclipse of the moon?’, and when we have learnt that there is, our next question is, ‘What, then, is this cause? for the cause through which a thing is — not is this or that, that is, has this or that attribute, but without qualification is — and the cause through which it is — not is without qualification, but is this or that as having some essential attribute or some accident — are both alike the middle’. By that which is without qualification I mean the subject, e.g., moon or earth or sun or triangle; by that which a subject is (in the partial sense) I mean a property, e.g., eclipse, equality or inequality, interposition or non-interposition. For in all these examples it is clear that the nature of the thing and the reason of the fact are identical: the question ‘What is eclipse?’ and its answer ‘The privation of the moon’s light by the interposition of the earth’ are identical with the question ‘What is the reason of eclipse?’ or ‘Why does the moon suffer eclipse?’ and the reply ‘Because of the failure of light through the earth’s shutting it out’. Again, for ‘What is a concord? A commensurate numerical ratio of a high and a low note’, we may substitute ‘What ratio makes a high and a low note concordant? Their relation according to a commensurate numerical ratio.’ ‘Are the high and the low note concordant?’ is equivalent to ‘Is their ratio commensurate?’; and when we find that it is commensurate, we ask ‘What, then, is their ratio?’.

Cases in which the ‘middle’ is sensible show that the object of our inquiry is always the ‘middle’: we inquire, because we have not perceived it, whether there is or is not a ‘middle’ causing, e.g., an eclipse. On the other hand, if we were on the moon we should not be inquiring either as to the fact or the reason, but both fact and reason would be obvious simultaneously. For the act of perception would have enabled us to know the universal too; since, the present fact of an eclipse being evident, perception would then at the same time give us the present fact of the earth’s screening the sun’s light, and from this would arise the universal. Thus, as we maintain, to know a thing’s nature is to know the reason why it is; and this is equally true of things in so far as they are said without qualification to he as opposed to being possessed of some attribute, and in so far as they are said to be possessed of some attribute such as equal to right angles, or greater or less.

It is clear, then, that all questions are a search for a ‘middle’.

The kinds of question. 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, at: as to the basic premises (100b18; [582]). For since it has been established in the first book that every doctrine and every discipline takes its start from preexisting 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, at: let us now state how essential nature (91a36; [418]).

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.

Second, from these questions he pursues his investigation by showing how the questions pertain to the middle of demonstrations, at: now, when we ask (90b38; [412]).

Regarding the first he does three things.

First, he enumerates the questions.

Second, he explains complex questions, at: thus, when our question (90b26; [409]).

Third, simple questions, at: but for some objects (90b32; [411]).

He says therefore first (90b21) 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' [that is, is it a fact that], 'propter quid' [that is, why, or what is the cause or reason], 'si est' [if it is, that is, 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, at: thus, when our question (90b26) 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' [that is, 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 he clarifies the next question which also puts in number, ‘I saying that when we know that it is so, we ask propter quid [that is, why] it is so, at: on the other hand, when we know (90b28).

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 he clarifies the other two questions which do not put in number but are simple, at: but for some objects (90b32).

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, at: now, when we ask (90b38) he shows how the aforesaid questions are related to the middle.

Concerning this he does three things.

First, he states what he intends.

Second, he explains what he had said, at: by distinguishing the fact (91a2; [413]).

Third, he proves his proposition, at: we conclude that in all our inquiries (91a5; [414]).

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.

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, at: by distinguishing the fact (91a2) 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 he proves his point, namely, that the aforesaid questions pertain to the middle, at: we conclude that in all (91a5).

First, he proves it with a reason.

Second, with a sign, at: cases in which the ‘middle’ (91a5; [416]).

He concludes therefore first (91a5) 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 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, at: cases in which the ‘middle’ (91a5) 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.

Finally, he summarizes and concludes the main point, namely, that it is clear from the foregoing that in all questions there is question of the middle.