Lecture 12 — The unity of the thing defined and of the definition

And now let us speak first of definition insofar as it has not been discussed in the Analytics, for the problem mentioned there constitutes a preamble to the arguments about substance. I speak about this problem: why is that thing one whose intelligible expression we call a definition? For example, two-footed animal is the definition of man (let this be his intelligible expression). Why, then, is this one thing and not many—namely, animal and two-footed?

For man and white are many since the latter is not present in the former; but they are one when the latter is present in the former, and the subject, man, is the recipient of some attribute. For then one thing is produced, and this is white man. But, in this case, one does not participate in the other, for a genus does not participate in its differences. Then the same thing would participate in contraries, for the differences by which a genus is distinguished are contraries.

And even if it does not participate in them, the same argument applies if the differences are many—for example, capable of walking, two-footed, and wingless. For why are all these one and not many? It is not because they are found in one thing, because then one thing will he composed of all differences.

But all the elements of a definition must be one, because a definition is one intelligible expression and one substance. Hence it must be the intelligible expression of some one particular thing, for substance signifies one thing and a particular thing, as we have said (1030a17).

Now it is necessary first to examine those definitions which are attained by the process of division. For there is nothing in a definition except the primary genus and the differences; and the other genera consist of the so-called primary genus and the differences along with this.

For example, the primary genus is animal, and the next is two-footed, and the next is two-footed animal without wings. And the same thing also applies if a definition is expressed by many terms. And, on the whole, it makes no difference whether it is expressed by many or by few, or whether it is expressed by few or by two.

Of the two, then, the one is the difference and the other the genus. For example, in the expression “two-footed animal,” animal is the genus and the other term is the difference.

Hence, if a genus in an unqualified sense does not exist apart from those things that are its species, or if it has the nature of matter (for the spoken word is both a genus and matter, and the differences make the species—the letters—out of this), it is clear that the definition is the intelligible expression composed of the differences.

Again, it is also necessary that a difference should be divided by a difference, as “having feet” is a difference of animal, and it is necessary also to know the difference of an animal having feet, inasmuch as it has feet.

Therefore, if someone is to speak correctly of something having feet, he must not say that one kind is winged and another wingless. If he does this, it will be because of incompetence.

But he will speak correctly only if he says that one kind has cloven feet and the other not, because these are the differences of the difference “having feet,” since a cloven foot is a certain kind of foot.

And one always wants to proceed in this way until he comes to the species which have no differences. Then there will be as many species of foot as there are differences, and the species of animals having feet will be equal in number to the differences.

If these things are so, then it is evident that the ultimate difference will be the substance and definition of the thing, if the same thing is not to be expressed many times over in definitive expressions, because this is superfluous.

However, this sometimes happens, for when one says, “two-footed animal having feet,” he has said nothing more than “animal having feet” and “having two feet.”

And if he divides this by its proper difference, he will express the same thing many times, and equal in number to the differences. If, then, a difference of a difference may be produced, the one which is the ultimate difference will be the specific form and substance.

But if the division is made according to what is accidental, as if one were to divide what has feet into what is white and what is black, there will be as many differences as there are divisions.

Hence, it is evident that the definition is an intelligible expression composed of differences, and that it is composed of the last of these if the definition is formed correctly.

Moreover, this will be evident if we change the order of the words in such definitions—for example, in the definition of man, by saying “two-footed animal having feet,” for “having feet” is superfluous when “two-footed” has been stated.

But there is no sequence of parts in substance, for how are we to understand that one part is subsequent and the other prior? Therefore, with regard to those definitions which are formed by the process of division, let this much be a preliminary statement of the kind of things they are.

1537. After having shown what parts are given in definitions, here the Philosopher inquires how a definition, being composed of parts, can be one thing. In regard to this, he does three things.

First (1037b8; [1537]), he raises a question.

Second (1037b14; [1538]), he argues on one side, at for man.

Third (1037b27; [1542]), he answers the question, at now it is necessary.

He accordingly says that, with regard to definition, we should speak now for the first time of the things about which a statement was not made in the Analytics, that is, in the Posterior Analytics. For in that work, a certain difficulty was raised about definition and left unsolved, and this must be answered here because it constitutes a preamble to the arguments about substance, that is, because the answer to this question is a prerequisite for establishing certain things about substance, which is the chief concern of this science.

This difficulty is why the thing whose intelligible expression (namely, the quiddity) is a definition is one thing. For a definition is an intelligible expression signifying a quiddity. For example, the definition of man is “two-footed animal” (for let us assume that this is his definition). Therefore, the question is, “Why is this thing which is called two-footed animal one thing and not many?”

1538. For man (1037b14). Then he raises arguments on both sides of the question.

He first does this (1037b14; [1538]) in order to show that one thing is not produced from them;

second (1037b24; [1540]), to show that the contrary is true, at but all the elements.

In regard to the first, he does two things.

First, he shows that one thing is not produced from a genus and a difference.

Second (1037b21; [1539]), he shows that one thing is not produced from many differences, at and even if.

He accordingly first says (1037b14) that these two things, man and white, are many when one of them is not present in the other. For if white does not belong to man, then man and white are one in no way. But they are one when one of them is present in the other, and when the subject, man, is the recipient of some attribute, that is, when it receives the modification, white; then something accidentally one is produced from these two things—a white man. Now, from these remarks, it is understood that one thing is not produced from two things when one does not exist in the other.

But in this case, namely, when one speaks of two-footed animal, one, the animal, does not participate in the other, in two-footed, as white man participates in white. And this is so because animal is a genus and two-footed is a difference. But a genus does not seem to participate in differences, for it would follow that the same thing would participate in contraries at the same time. For differences are the contraries by which a genus is distinguished (that is, by which a genus is divided), and for the same reason that it participates in one, it will participate in the other. But if it is impossible for the same thing to participate in contraries, it will be impossible for one thing to be produced from a genus and a difference.

1539. And even if (1037b21). Then he shows that one thing cannot be produced from many differences. He says that, even if it is admitted that a genus participates in some way in a difference (as, for example, animal is not taken under its common aspect but insofar as it is restricted to a species by a difference, and then one thing is produced from a genus and a difference), the same argument can still be used to show that a definition does not signify one thing, if many differences are given in the definition.

For example, in the definition of man these three differences are given: first, capable of walking or having feet; second, two-footed; and third, wingless. But it cannot be said why these things are one and not many.

1540. For to explain this, it is not enough to give as a reason that they exist in one thing (as in the animal, man), for in this way it would follow that all accidents which inhere in any subject would be per se one thing; for we do speak of one accident in relation to another accident as well as to the subject. And since those things that are accidents of one subject may also be accidents of another subject, it would follow that those two subjects would be one—for example, snow and a swan, in both of which whiteness is found. And thus, by inference, it would follow that all things would be one. Thus it cannot be said that one thing is produced from many differences, even though one thing is produced from a genus and a difference. Hence it seems that a definition does not signify one thing composed of two parts.

1541. But all the elements (1037b24). Here he argues one side of the question, showing that a definition does signify one thing. He says that all the attributes which are given in a definition must be one. And this is so because a definition is one intelligible expression, and what it signifies is the substance of a thing. Hence, a definition must be an intelligible expression signifying one thing, because the substance of a thing, which the definition signifies, is one quiddity. And it was also stated above (1030a17; [1330]), where definition was shown to belong properly to substances, that a definition signifies a particular thing.

1542. Now it is necessary (1037b27). He answers the foregoing question by showing that a definition signifies one thing, and in regard to this, he does two things.

First (1037b27), he shows how one thing is produced from a genus and a difference;

second (1038a9; [1551]), how one thing is produced from many differences, at again, it is.

He accordingly first says (1037b27) that, in order to investigate the unity of definitions, it is first necessary to examine definitions which are based on the division of genus into differences. For those are true definitions which contain nothing but the primary genus and differences, because some definitions are based on certain accidents, properties, or extrinsic causes which do not signify the substance of a thing. Hence such definitions are not to the point, since here he is treating of definitions with a view to investigating the substances of things.

1543. Therefore, I say that, in a definition, there is a primary genus with differences, because, even if one sometimes gives in definitions certain intermediate genera between the primary genus, which is the most general, and the last species which are defined, those intermediate genera are nevertheless nothing but the primary genus and the differences included in the understanding of the intermediate genus along with this, that is, along with the primary genus.

For instance, when animal, which is an intermediate genus, is given in the definition of man, it is evident that animal is nothing but substance (which is the primary genus) along with certain differences, for an animal is a living sensible substance. And the case is the same when we understand the primary genus to be animal, two-footed; and again when we understand the third genus to be two-footed animal without wings. And the same thing is true when any genus is limited by many differences, for a subsequent genus always includes a prior genus along with some difference. Hence it is evident that every definition is dissolved into a primary genus and certain differences.

1544. And in general it makes no difference whether the thing defined is defined by many terms or by few. Hence, it makes no difference whether it is defined by few or by two, so long as one of these is a genus and the other a difference, for animal is the genus of two-footed animal, and the other term (two-footed) is the difference. Therefore, it must first be shown how one thing is produced from these. This becomes clear as follows.

1545. A genus does not exist apart from those things that are its species, for no animal is found that is not a man or an ox or some other animal of this kind. Or if there is something which is a genus apart from its species, taken in the sense that it exists apart from its species, it is not a genus, but matter, because it is possible for something to be both the genus and matter of certain things, as the vocal sound is both the genus of letters and their matter. That it is a genus is evident from the fact that differences added to the vocal sound make the species of articulate sounds. That it is matter is evident because the differences make the elements, or the letters, out of this, namely, out of the vocal sound, as something is made out of matter.

1546. Moreover, it must be understood that, while genus and matter can be the same in name, they nevertheless do not mean the same thing, for matter is an integral part of a thing, and thus cannot be predicated of a thing (for it cannot be said that man is flesh and bones). But a genus is predicated of its species, and therefore it must in some way signify the whole thing, just as matter along with its privation is sometimes designated by the simple name of the matter, in view of the namelessness of privations. Thus it was said above (1033a5; [1416]) that bronze is taken for formless bronze when we say that a statue is made of bronze. In a similar fashion, when the form is nameless, the composite of matter and form is designated by the simple name of the matter—not common matter, but some determinate matter. And in this way, it is taken as a genus, for just as a species is a composite of matter and a determinate form, so too a genus is a composite of matter and a common form.

1547. This becomes evident in many ways. For body can be taken both as the matter and as the genus of animal, for if we understand in the notion of body a substance completed by its ultimate form, having in itself three dimensions, then body is a genus and its species are the complete substances determined by these ultimate forms, as that of gold, of silver, of olive, or of man. But if one considers in the notion of body only that it is a thing having three dimensions with an aptitude for an ultimate form, then body is matter.

1548. And the same thing applies in the case of a vocal sound; for if, in the intelligible expression of vocal sound, one includes the formation of sound in common according to the form which is subdivided into the different forms of the letters and syllables, then vocal sound is a genus. But if, in the intelligible expression of vocal sound, one understands only the substance of sound, to which the foregoing formation can accrue, then vocal sound will be the matter of the letters. From this, it is also evident that vocal sound, which is a genus, cannot exist without species, for a sound can be formed only if it has the definite form of this or that letter. But if it lacked altogether the form of a letter insofar as it is matter, then it would be found without letters, just as bronze is found without the things that are produced from it.

1549. If the foregoing statements are true, then it is evident that a definition is an intelligible expression having unity from its differences in such a way that the whole essence of the definition is included in a certain way in the difference. For animal, which is a genus, cannot exist without species, because the forms of the species, the differences, are not different forms from the form of the genus, but are the forms of the genus lacking determination. For example, it is evident that an animal is a thing having a sentient soul, that man is one having such and such a sentient soul (one with reason), and that a lion is one having such and such a soul, namely, with an abundance of daring. And it is the same in other cases.

Hence, when a difference is added to a genus, it is not added as though it were an essence distinct from the genus, but as though it were contained implicitly in the genus, as the determinate is contained in the indeterminate (for example, white in the thing colored).

1550. And in the light of this, the problem raised above (1037b8; [1537]) is solved, since nothing prevents one and the same genus from containing within itself various differences, as the indeterminate contains within itself various determinate things. Additionally, it is solved by the fact that a difference does not accrue to a genus as constituting an essence distinct from it, as white accrues to man.

1551. Again, it is (1038a9). He next shows that a multitude of differences does not prevent a definition from being one. In regard to this, he does two things.

First, he shows in what way a multitude of differences should be taken in a definition.

Second (1038a18; [1555]), he shows that, if differences are taken in the right way, a multitude of differences does not prevent a definition from being one, at if these things.

He accordingly first says (1038a9) that, in the case of those definitions which include many differences, not only should the genus be divided by a difference, but the first difference should also be divided by the second difference. For example, footed is the difference of animal according to which animal is said to have feet or to be capable of walking. But, since this difference is also found to have many forms, it is again necessary to know the difference of such an animal—that is, what its difference is—inasmuch as it has feet, that is, inasmuch as it is considered per se and not accidentally.

1552. Therefore, since it is accidental to a thing having feet to have wings, in dividing the difference, it must not be said that, among those things that have feet, one kind is winged and another wingless, if a man wants to express correctly the division of the differences. Yet when someone, in dividing differences, does this, namely, divides it by means of those attributes that are accidental, this is why he cannot find proper and essential differences. For sometimes necessity compels us to use accidental differences in place of essential differences inasmuch as accidental differences are the signs of certain essential differences unknown to us.

1553. But this difference of having feet must be divided so that, among animals of this kind, one kind has cloven feet and another has not. For these—cloven and uncloven—are the differences of the difference “having feet.” Therefore, having cloven feet divides per se the difference of having feet, for a cloven foot is a certain kind of foot, that is, the difference of having cloven feet is something contained under the difference of having feet. And they are related to each other as the determinate to the indeterminate, as we said of genus and difference.

1554. And it is always necessary to proceed in this way in the division of differences until the one making the division comes to the species which have no differences, that is, to ultimate differences, which are not divided further into other differences. Then there will be as many species of foot as there are differences, and the species of animals having feet will be equal in number to the differences, for any individual difference constitutes one ultimate species.

1555. If these things (1038a18). He shows here, from the things that have been set down, that a multitude of differences does not prevent a definition from being one. And in regard to this, he does two things.

First (1038a18; [1555]), he proves his thesis.

Second (1038a28; [1561]), he draws the conclusion at which he aims, at hence, it is evident.

In regard to the first, he does two things.

First, he proves how one thing is produced from many differences, if differences are understood per se.

Second (1038a26; [1560]), he shows that this cannot be the case if the differences are understood accidentally, at but if the division.

He accordingly first says (1038a18) that, if the differences taken in a definition are such as has been indicated—namely, so that differences are always taken per se and not accidentally—it is obvious that the ultimate difference will constitute the whole substance of the thing and its entire definition, for it includes in itself all preceding parts.

1556. For on the grounds that a genus does not exist without differences, it has been shown that a genus is included in its differences. But that the ultimate difference includes all preceding differences is evident from the fact that, unless this were affirmed to be so, it would follow that, in definitive expressions, that is, in their definitions, the same thing would have to be expressed many times. This would be superfluous and meaningless.

1557. And this absurd conclusion follows because, if someone were to define an animal by saying two-footed animal having feet (as he must do if two-footed is a difference distinct from having feet and does not include it), when he defines it in this way he has said nothing but “animal having feet having two feet.” For two-footed is nothing but having two feet, in which the difference of having feet is obviously included. Hence it is evident that, if both are used, we get nonsense.

1558. Moreover, if someone divides two-footed by its proper difference—namely, by those things that are per se and not accidental—it follows further that the same thing is expressed many times, and as many times is the number of differences used. Thus, if I say that one kind of two-footed animal is one which has a foot divided into five toes, and another kind is one which has a foot divided into four toes, anyone wishing to give all intermediate differences in defining man would express the same thing many times, and as often as he added differences. For he would say that man is an animal having feet, having two feet, having feet divided into five toes.

1559. Now since these things are unacceptable, it is evident that, if differences are taken in a definition, there will be one ultimate difference, namely, the one which will be the specific form and substance, or which comprises the substance and specific form of the thing defined. As a result of the unity of this difference, the definition will be one.

1560. But if the division (1038a26). Here he shows that the definition cannot be said to be one if the differences which are taken are accidental. He says that, if someone, in dividing and defining, were to take an accidental difference (for example, if things having feet were divided into black and white), there would be as many ultimate differences as the divisions which have been made, because one of them would not include another. And concerning differences taken in this way, the argument introduced above was directed against the unity of the definition. For differences of this kind taken accidentally in this way would be one only in their subject, and this is not enough to account for the unity of the definition.

1561. Hence, it is evident (1038a28). He now concludes to his thesis, and in regard to this, he does two things.

First, he gives his conclusion. He says that it is evident from the above discussions that, even though a genus and a difference are given in a definition, still a definition is an intelligible expression composed only of differences, because a genus is not something apart from its differences, as was stated above (1037b27; [1549]). And even though many differences are given in a definition, still the entire definition depends on and is constituted by the ultimate difference, when the division is made correctly, that is, by descending from more common to less common essential differences, and not by bringing in accidental differences from the side, so to speak.

1562. Moreover, this will be evident (1038a30). Second, he clarifies by means of an example the conclusion which was drawn, saying, moreover this will be evident—namely, that the entire definition consists in the ultimate difference—on the grounds that, if anyone changes the parts of such definitions, an absurdity results. Thus someone might say that the definition of man is a two-footed animal having feet. But as soon as two-footed has been expressed, it is superfluous to add having feet. But if one were to say first “having feet,” it would still be necessary to ask whether it was two-footed, by dividing the difference of having feet.

1563. From this it is evident that, insofar as those differences are many, they have a definite order among themselves. But this cannot mean that there is any order in the substance of a thing, for it cannot be said that this part of a substance is prior and another subsequent, because substance is complete all at once and not successively, except in the case of those things that are deficient in being, such as motion and time.

1564. Hence it is evident that a multiplicity of parts in a definition does not signify a multiplicity of essential parts of which the essence is constituted as if they were distinct things, but all signify one thing which is made determinate by an ultimate difference. It is also evident from this that there is one substantial form for every species. Thus there is one form of lion by which it is a substance, a body, a living body, an animal, and a lion. For if there were many forms corresponding to all the differences mentioned above, all could not be included under one difference, nor could one thing be composed of them.

1565. Lastly, he brings his discussion to a close with a summary. He says that, with regard to definitions which are based on the divisions of genera into differences and of difference into differences, these points should constitute a preliminary statement of the kinds of things they are: they are composed of essential predicates, they contain in themselves the parts of the specific form, and each is also a unity. He says preliminary because, in the following discussions, certain points are established about definitions and quiddities.