Commentary Aristotle Posterior Analytics
Lecture 6
Whether quod quid can be shown by demonstration or definition
b3. To put it another way: how shall we by definition prove essential nature? He who knows what human—or any other—nature is, must know also that man exists; for no one knows the nature of what does not exist—one can know the meaning of the phrase or name ‘goat-stag’ but not what the essential nature of a goat-stag is.
b7. But further, if definition can prove what is the essential nature of a thing, can it also prove that it exists? And how will it prove them both by the same process, since definition exhibits one single thing and demonstration another single thing, and what human nature is and the fact that man exists are not the same thing?
b11. Then too we hold that it is by demonstration that the being of everything must be proved—unless indeed to be were its essence; and, since being is not a genus, it is not the essence of anything. Hence the being of anything as fact is matter for demonstration; and this is the actual procedure of the sciences, for the geometer assumes the meaning of the word triangle, but that it is possessed of some attribute he proves. What is it, then, that we shall prove in defining essential nature? Triangle? In that case a man will know by definition what a thing’s nature is without knowing whether it exists. But that is impossible.
b18. Moreover it is clear, if we consider the methods of defining actually in use, that definition does not prove that the thing defined exists: since even if there does actually exist something which is equidistant from a centre, yet why should the thing named in the definition exist? Why, in other words, should this be the formula defining circle? One might equally well call it the definition of mountain copper. For definitions do not carry a further guarantee that the thing defined can exist or that it is what they claim to define: one can always ask why.
b26. Since, therefore, to define is to prove either a thing’s essential nature or the meaning of its name, we may conclude that definition, if it in no sense proves essential nature, is a set of words signifying precisely what a name signifies.
b28. But that were a strange consequence; for (1) both what is not substance and what does not exist at all would be definable, since even non-existents can be signified by a name:
b30. (2) all sets of words or sentences would be definitions, since any kind of sentence could be given a name; so that we should all be talking in definitions, and even the Iliad would be a definition:
b32. (3) no demonstration can prove that any particular name means any particular thing: neither, therefore, do definitions, in addition to revealing the meaning of a name, also reveal that the name has this meaning.
b35. It appears then from these considerations that neither definition and syllogism nor their objects are identical, and further that definition neither demonstrates nor proves anything, and that knowledge of essential nature is not to be obtained either by definition or by demonstration.
To put it another way. After considering each of the ways in which something might be demonstrated and showing that none can demonstrate the 'quod quid', the Philosopher now shows what he proposes through common reasons.
Concerning this he does three things.
First, he lays down something which is necessary for proving what he proposes.
Second, he shows what he proposes, at: but further, if definition (93b7; [462]).
Third, he sums up what has been stated, at: it appears then from these (93b35; [469]).
He says therefore first (93b3) that there does not seem to be any possible way for a person to demonstrate that some 'quod quid' is man: and this because whoever knows a 'quod quid' to be of man or of any other thing is required to know that the thing exists. For since there is no quiddity or essence of a non-being, it is impossible to know the 'quod quid' of something which is not; but one might know the meaning of the name or have a notion composed of several names. Thus a person is capable of knowing the meaning of the word 'tragelaphus' or 'goat-stag', because it signifies an animal composed of goat and stag, but it is impossible to know the 'quod quid' of a goat-stag, because there is no such thing given in nature.
Then, at: but further, if definition (93b7) from what has been established he goes on to prove what he proposed.
In regard to this he does two things.
First, he shows that the 'quod quid' cannot be shown by demonstration.
Second, that it cannot be shown by definition, at: since, therefore, to define (93b26).
In regard to the first he presents three reasons.
The first of these (93b7) is the following: just as a definition is brought forward to manifest something which is one in the sense that from the parts of the definition something is formed which is one per se and not one per accidens, so a demonstration which employs a definition as its middle must demonstrate something which is one; for the conclusion must be proportionate to the middle. Consequently, it is clear that one cannot in virtue of one and the same definition demonstrate things that are diverse. But the quod quid of man is one thing and his being or existence is another—(for it is only in the First Principle of being, Who is being essentially, that to be and quiddity are one and the same; in all other things, which are beings by participation, the to be has to be other than the quiddity.) Therefore, it is not possible to demonstrate both the quid and the quia with the same demonstration.
Then, at: then too we hold (93b11) he presents the second reason and it is this: According to a common opinion of wise men, it is necessary that all that is, the whole demonstrated by a demonstration, be the 'quia est', unless perchance someone would want to say that the 'quia est' itself is the substance of a thing. However, this is impossible. For the to be is not the substance or essence of anything existing in a genus; otherwise it would be required that 'being' be a genus, because a genus is something predicated in quod quia. But, as it is proved in Metaphysics III, being is not a genus. For this reason God Who is His own essence is not in a genus. Furthermore, if the 'quia est' were the substance of any thing, then in the same breath that one shows the 'quia est' he would be showing the 'quid est'; consequently, the whole which a demonstrator manifests would not be the 'quia est'. But this is false. Therefore, it is clear that demonstration manifests only the 'quia est', for it demonstrates some enunciation which signifies that something is or is not. This is apparent also in the way a science proceeds. For geometry assumes what the name 'triangle' signifies, and demonstrates quod sit, as when it demonstrates that an equilateral triangle has been formed on a given straight line. Therefore, if one demonstrated merely what a triangle is apart from the method of demonstrating which the sciences employ, he would not be demonstrating this whole which is that a triangle exists, but only what I call triangle. For just as, owing to the fact that to be is not the substance of a thing, one who demonstrates to be demonstrates that and nothing more, so if someone demonstrates the 'quid est', that is all he demonstrates. It would follow, therefore, that someone who knew the quid est in virtue of a definition would not know an est—which is impossible in view of what has been established above.
Then, at: moreover it is clear (93b18) he presents the third reason. Now, this reason uses ordinary definitions as examples to manifest the same fact that was concluded in the previous reason, namely, that one who demonstrates the 'quid est' is not demonstrating the 'quia est'. Wherefore he says that it is clear not only in the light of the foregoing but also in view of the modes of terms, that is, of definitions, which are now in use, that those who define do not manifest the 'quia est'. For example, one who defines a circle as something all the lines from whose center to the circumference are equal, is still left with the question why there must be such a thing as he has defined, such as why it is required to posit that there is a circle which is defined in the way mentioned. For it is acceptable to give a like description of a brass mountain by saying, for example, that it is a brass body which is lofty and extensive; but the task would still remain to establish whether there is such a thing in nature. And this is because terms, that is, defining notions, do not state that their counterpart either exists or is capable of existing; rather, whenever such a notion is formulated, it is legitimate to ask why such a thing should exist. Clearly then, it is impossible to demonstrate quid est and quia est simultaneously.
Then, at: since, therefore, to define (93b26), by leading to something absurd, he shows that the 'quod quid' cannot be shown by demonstration.
First, therefore, he shows what would follow from this.
Second, he shows that what does follow is unacceptable, at: but that were a strange consequence (93b28).
He says therefore (93b26) that since a definer might show either the quid est or merely what a name signifies, it follows that a definition does not necessarily manifest the 'quod quid', which belongs to definition in the proper sense; otherwise, it will follow that a definition signifying 'quod quid' is nothing more than a statement signifying in the same way that a name does: for the only thing that a definition adds to such a notion is that it signifies the essence of some thing. Hence, if there is no thing whose essence the definition signifies, it will be no different from a statement explaining the signification of some name.
Then, at: but that were a strange consequence (93b28) he shows that it is unacceptable for a definition to be nothing more than a statement explaining the signification of a name.
This is for three reasons.
The first of these is that it happens that even things which are neither substances nor beings in a universal sense can be signified by a name. Now, a name can be explained by some interpretation. Consequently, if a definition were nothing more than a statement interpreting a name, it would follow that a definition could be given of non-substances and of things that do not exist at all. But this is clearly false, for as it is shown in Metaphysics VII, definition bears principally on substance and on other things insofar as they are related to substance.
Then, at: all sets of words (93b30) he gives the second reason and it is this: To any notion, that is, to any statement signifying something, it is possible to apply a corresponding name which is explained by that notion. Therefore, if a definition is nothing more than a notion explaining a name, it would follow that all notions were definitions. As a consequence, it would follow that when we dispute or converse with anyone, the disputations or our discussions are definitions; similarly, it would follow that the Iliad, that is, Homer’s poem about the Trojan War, is a definition.
Then, at: no demonstration can prove (93b32) he gives the third reason and it is this: No science demonstrates that a given name signifies a given thing. For names are arbitrary signs; hence they must be used according to the will of the one inventing them. But it is obvious that definitions are given in every science. Therefore, it is obvious that definitions do not signify this, that is, a mere interpretation of a name.
Then, at: it appears then (93b35) he sums up what has been so far discussed disputatively.
And he says that from the foregoing it is seen to follow that definition and syllogism are neither the same nor concerned with the same; and furthermore that a definition demonstrates nothing, since it is not concerned with the same thing as a demonstration. In like manner, it seems to have been shown that it is not possible to know quod quid either by a definition or a demonstration, because a definition merely shows the what and a demonstration the 'quia'. But to know the 'quod quid' a knowledge of 'quia' est is required, as has been shown.