Commentary Aristotle Posterior Analytics
Lecture 8
To attain quod quid through demonstration is not possible in all cases: relation of definition to demonstration b22. Now, while some things have a cause distinct from themselves, others have not. Hence it is evident that there are essential natures which are immediate, that is, are basic premises; and of these not only that they are but also what they are must be assumed or revealed in some other way. This too is the actual procedure of the arithmetician, who assumes both the nature and the existence of unit. On the other hand, it is possible (in the manner explained) to exhibit through demonstration the essential nature of things which have a ‘middle’, that is, a cause of their substantial being other than that being itself; but we do not thereby demonstrate it.
b28. Since definition is said to be the statement of a thing’s nature, obviously one kind of definition will be a statement of the meaning of the name, or of an equivalent nominal formula. A definition in this sense tells you, e.g., the meaning of the phrase ‘triangular character’. When we are aware that triangle exists, we inquire the reason why it exists. But it is difficult thus to learn the definition of things the existence of which we do not genuinely know—the cause of this difficulty being, as we said before, that we only know accidentally whether or not the thing exists. Moreover, a statement may be a unity in either of two ways, by conjunction, like the Iliad, or because it exhibits a single predicate as inhering not accidentally in a single subject. That then is one way of defining definition.
b38. Another kind of definition is a formula exhibiting the cause of a thing’s existence.
b39. Thus the former signifies without proving, but the latter will clearly be a quasi-demonstration of essential nature, differing from demonstration in the arrangement of its terms.
a2. For there is a difference between stating why it thunders, and stating what is the essential nature of thunder; since the first statement will be ‘Because fire is quenched in the clouds’, while the statement of what the nature of thunder is will be ‘The noise of fire being quenched in the clouds’. Thus the same statement takes a different form: in one form it is continuous demonstration, in the other definition. Again, thunder can be defined as noise in the clouds, which is the conclusion of the demonstration embodying essential nature.
a9. On the other hand, the definition of immediates is an indemonstrable positing of essential nature. We conclude then that definition is (a) an indemonstrable statement of essential nature, or (b) a syllogism of essential nature differing from demonstration in grammatical form, or (c) the conclusion of a demonstration giving essential nature.
a13. Our discussion has therefore made plain (1) in what sense and of what things the essential nature is demonstrable, and in what sense and of what things it is not; (2) what are the various meanings of the term definition, and in what sense and of what things it proves the essential nature, and in what sense and of what things it does not; (3) what is the relation of definition to demonstration, and how far the same thing is both definable and demonstrable and how far it is not.
Now, while some things have a cause. After showing that in some instances the quod quid is acquired through demonstration, the Philosopher now shows that this is not possible in all.
And in order to show this he repeats (94b22) that of some things there is a cause other than the thing, but of other things not. Therefore, because the 'quod quid' is acquired by a demonstration whose middle is a cause, it is manifest that there are certain things whose 'quod quid' must be taken as an immediate principle, in the sense that one must suppose both the to be and the quid of that thing, or manifest it by some means other than demonstration, say by an effect or by a likeness or some other way.
Here it should be noted that his statement that some things have a cause not distinct from themselves can be understood in three ways.
In one way, it means that it simply and absolutely has not a cause of its being. And this is proper to the First Principle alone, which is the cause of the being and truth of all things. For there is nothing to prevent even things which exist of necessity from having some cause of their necessity, as is stated in Metaphysics V. And therefore, although the Philosopher is speaking in the plural here, his words should not be taken to mean that there are several things which have no cause of their being.
In another way it can be understood as referring to the order of the causes of one thing. For it is clear that in things which have four causes, one cause is somehow the cause of another one. For since matter is for the sake of form and not vice versa, as is proved in Physics II, a definition which is based on the formal cause is the cause of the definition which is taken from the material cause of the same thing. And because the thing produced obtains a form in virtue of the action of the generator, it follows that the agent is somehow the cause of the form, and the definition the cause of the defined. Furthermore, every efficient cause acts for an end; hence, too, the definition taken from the end is somehow the cause of the definition which is taken from the efficient cause. Beyond this it is impossible to go in the genera of causes: hence the dictum that the end is the cause of the causes.
Yet in the individual genera of causes one can proceed from the subsequent to the prior; but definitions should be given through proximate causes. And according to this interpretation, we find it stated in certain books that definitions which are made in terms of the species have no middle by which they might be demonstrated, but that definitions made in terms of matter can have a middle, in the sense that definitions which are given according to the material cause can be demonstrated by those which are given according to the formal cause. But a definition which is given according to formal cause cannot be further demonstrated by an intrinsic principle of the thing which belongs in a proper way to the quod quid as entering into the essence of the thing. But if it were to be demonstrated by the efficient and final cause, one would have to say that a higher cause is related as formal to the lower. "However, these words are not present in the Greek version; hence they seem to be a Gloss introduced into the text by a copyist’s error".
Third, they could be understood in the sense that there are some things which do not have a cause in the generic subject of some science; as in the genus of number, with which arithmetic is concerned, one arrives at unity, which has no principle in this genus.
And this sense concurs with the example which the Philosopher adds when he states that the arithmetician accepts what unity is and that it is. And just as in the case of things that do not have something else as cause, so too in the case of things which can have a middle and whose cause is something else, their 'quod quid' can be manifested; in such a way, however, that the 'quod quid' is not demonstrated, but rather that the middle of demonstration is taken as 'quod quid'.
Then, at: since definition is said (94b28) having shown how the 'quod quid' is related to demonstration, he shows how definition is related to demonstration.
Concerning this he does two things.
First, he shows how a definition is related to demonstration.
Second, he uses an example to manifest what he has stated, at: for there is a difference (95a2).
First, he lays down one type of definition which signifies 'quid est'.
Second, another type which signifies 'propter quid', at: another kind of definition (94b38).
Third, he shows how each of these definitions is related to demonstration, at: thus the former signifies (94b39).
In regard to the first he supposes first of all (94b28) that definition is a statement signifying the 'quod quid'. But if no other notion could be had of a thing except the definition, it would be impossible for us to know that some thing is, without knowing the 'quid est' of it; because it is impossible for us to know that a thing is except in virtue of some notion of that thing. For in regard to a thing completely unknown to us, we cannot know if it is or not. But we do find some other notion of a thing besides the definition, namely, a notion which explains the signification of a name, or a notion of the very thing named; which notion, however, is distinct from the definition, because it does not signify the 'quid est' as does a definition, but perhaps some accident. Thus one might find some notion which explains what the word 'triangle' means. Then having the 'quia est' in virtue of this notion, we would seek the 'propter quid' in order that we might thereby arrive at the 'quod quid'. But, as stated above, it is difficult to arrive at this in the case of things whose existence we do not know. Furthermore, the cause of this difficulty was mentioned above, namely, because when we do not know a thing to be by means of something of that thing, we do not know absolutely if it is or is not, but only according to an accident, as was explained above.
Then in order to distinguish the notion signifying the 'quid est' from the other notions, he adds that there are two ways in which a notion can be said to be one. For some are one by conjunction only: in this way even the Iliad, that is, the poem of the history of Troy, possesses a unity. (And this is the way the notion which explains a name or describes the thing named through its accidents is one, as when it is stated that man is a risible animal capable of discipline.) But a notion is also one insofar as it simply signifies one thing about one thing of which it is the notion, and this not in virtue of some accident. And such a notion is the definition signifying quid est, because the essence of anything is one. Thus, therefore, he concludes that what has been said, namely, that a definition is a notion of the 'quod quid', is one definition of a definition.
Then, at: another kind of definition (94b38) he lays down another type of definition.
He says that another definition of definition is that it is a notion manifesting the 'propter quid'.
Then, at: thus the former signifies (94b39) he shows how each of these definitions is related to demonstration, concluding from the foregoing that the first definition merely signifies, but does not demonstrate the 'quod quid'; whereas the second definition is, as it were, the definition of the 'quod quid' and differs from a demonstration by position alone, that is, in the ordering of the terms and propositions.
Then, at: for there is a difference (95a2) he uses examples to manifest what he had said.
First, he shows by examples what has been said.
Second, from the foregoing he gathers the various kinds of definition, at: on the other hand, the definition (95a9).
He says therefore (95a2) that it is one thing to say why it thunders and another what thunder is: because according to the opinion of those who state that the quenching of fire in a cloud is the cause of thunder, one is giving the 'propter quid' when he asserts thunder to be due to the fact that fire is quenched in a cloud; whereas one who asserts that thunder is the sound of fire being quenched in a cloud is stating what thunder is. Now, each of these signifies the same notion but not in the same way. For when one states that it thunders because fire is being quenched in a cloud, the notion is signified after the manner of a continuous demonstration, that is, not broken down into explicit propositions; yet all the terms of a demonstration are continually being taken. But when it is asserted that thunder is the sound of fire being quenched in the clouds, the notion is signified after the manner of a definition. But if we were to say that thunder is the sound in the clouds, no mention being made of the quenching of fire, it will be a definition signifying 'quid est', and will be merely the conclusion of a demonstration.
Then, at: on the other hand, the definition (95a9) he gathers together from the foregoing how many modes of definition there are insofar as they are relevant to demonstration.
First, he repeats something previously stated, namely, that in the case of things which do not have a cause, their definitions are to be taken as immediate principles. Hence he says here that the definition of immediate things, that is, of things not having causes, is as an indemonstrable positing of the 'quod quid'. From this, therefore, he concludes that there is a threefold genus of definition when considered relative to demonstration. For there is one definition which is an indemonstrable notion of a thing’s 'quod quid': this is the one which he said concerns immediate things. But another definition is that which is, as it were, a demonstrative syllogism of a thing’s 'quod quid' and differs from a demonstration merely by structure, that is, by a different acceptance and position of the phrasing, as when it is stated that thunder is the sound of fire being quenched in the clouds. The third is the definition which only signifies 'quod quid' and is the conclusion of a demonstration.
Then, at: our discussion has therefore (95a13) he summarizes what has been said.
He declares that it is plain from the foregoing in what way there is demonstration of the 'quod quid' and in what way not; namely, that the 'quod quid' can be taken from a demonstration but cannot be demonstrated. The things have also been pointed out in which there can be demonstration of the 'quod quid' according to the manner indicated (namely, in things having a cause) and those in which there cannot be (namely, in things not having a cause). It has also been indicated in how many ways definition is said to be: namely, that some signify quod quid, and others even the propter quid. It has also been stated how 'quod quid' is demonstrated, namely, so far forth as this is signified by a definition which signifies only 'quod quid'; and how it is not demonstrated, namely, insofar as in virtue of the definition not only the 'quid' but also the 'propter quid' are taken. It has also been pointed out how definition is related in various ways to demonstration; and how it comes about that there is demonstration of the definition of a same thing, and how this does not come about.