Lecture 4 — The analogous character of definition

Or another solution is that definition, like the whatness of a thing, is used in many senses. For, in one sense, whatness signifies the substance and this particular thing, and in another sense, it signifies any of the categories, such as quantity, quality, and others such as these. For just as being is found in all things, although not in the same way, but in one thing primarily and in the others secondarily, so too whatness is found in an unqualified sense in substance, but in another sense, in the other categories.

For we might even speak of the whatness of quality, so that quality is also one of those things that have whatness. This is not in an unqualified sense, however; but just as some say, in a logical sense, that non-being “is” (not in an unqualified sense, but insofar as it is nonbeing), so is this is also the case with quality.

Therefore, it is also necessary to consider how we must say it of each particular thing, yet not more than the condition of each warrants. Hence, too, since what is said is evident, essence (or whatness) will also be found in like manner primarily and unqualifiedly in substance, and then in the other categories, not as essence in an unqualified sense, but as the essence of quality and quantity. For these things must be said to be beings either equivocally or by adding or removing something, just as it is said that the unknowable is known.

For the truth of the matter is that this word is used neither equivocally nor according to the same meaning, but just as the word “medical” is used in reference to one and the same thing, although not according to one and the same meaning or equivocally. For a body, an operation, and an instrument are called “medical” neither equivocally nor according to one meaning, but in reference to one thing. It makes no difference, then, as to the way in which one wishes to express this.

Now it is evident that definition and essence belong to substances in the primary and unqualified sense. And they belong not only to these but also to other things as well, although not in the primary sense.

For if we maintain this, it is not necessary that there be a definition of any word which means the same thing as any concept, but it must mean the same thing as any determinate concept.

And this will be the case if it is the concept of some one thing not because it is continuous, like the Iliad, or one of the things that are one by being linked together, but if it is one according to one of the many meanings of that term.

But the word “one” is used in the same number of senses as “being” is. In one sense, “being” signifies a particular thing, and in another, quantity, and in another, quality. And for this reason there will be a definition and concept of “white man,” but in a different sense from that of whiteness and of substance.

Now if one denies that a concept which involves the addition of something else is a definition, the problem arises as to how there can be a definition of things that are not simple but compound, for this must come about by way of addition.

I mean, for example, that there is “nose” and “concavity” and snubness” (which is a word compounded of the two) because the one is found in the other; and neither concavity nor snubness is an accidental attribute of nose, but an essential one. Nor do they belong to nose as white belongs to Callias or to man (because Callias, who happens to be a man, is white), but as male belongs to animal and equal to quantity, and as all those attributes which are said to belong to something else essentially.

Now these attributes are those in which is found either the concept or name of the subject to which each one belongs, and which cannot be explained apart from it. For example, it is possible to explain white apart from man, but not female apart from animal. Hence, there is either no essence and definition of any of these things or, if there is, it is in the way we have described (1030a17–1030b4).

And there is also a second difficulty about them. For if “snub nose” and “concave nose” are the same, “snub” and “concave” will be the same. If they are not, then, since it is impossible to use the word “snub” without the thing of which it is a proper attribute (because snub is concavity in a nose), either it is impossible to speak of a snub nose or the same term is used twice—a concave nose nose. For a snub nose will be a concave nose nose. Hence it is absurd that such things should have an essence.

And if they have, there will be an infinite regression, because some other nose will be found in the nose of snub-nose. It is clear, then, that there is definition of substance alone; if the other categories also had a definition, this would have to be a result of adding something, just as there is no definition of “equal” and “odd” without “number” or of “female” without “animal.”

And, by “adding something,” I mean those expressions in which the same thing happens to be said twice. And if this is true, there will not be any definition of those things that are compounded—for example, “odd number.”

But this is hidden from us, because the concepts of these things are not expressed exactly. But if these things also have formulae, either they have such in a different way—or, as we have said (1030a17–1030b4), “definition” and “essence” must be used in many senses.

Hence, in one sense, there will be no definition of anything, and definition and essence will be found only in substance; and in another sense, the other things will have a definition and essence. It is evident, then, that a definition is a concept of the essence of a thing, and that essence belongs to substances either alone, or chiefly, primarily, and without qualification.

1331. Here he gives the second solution to the question which was raised, and in regard to this, he does three things.

First (1030a17; [1331]), he gives the solution.

Second (1030b4; [1339]), he proves it, at now it is evident.

Third (1030b14; [1342]), he dispels certain difficulties which could arise from the previous discussion, at now if one denies.

In regard to the first, he does two things.

First (1030a17; [1331]), he shows how the definition and whatness are found in substance and accidents.

Second (1030a27; [1335]), how it is predicated of both, at therefore, it is also.

He accordingly first says (1030a17) that it is necessary to say, as was stated in the foregoing solution (1029b28; [1325]), that there is no definition and whatness of accidents but only of substances. Or, according to another solution, it is necessary to say that the terms “definition” and “whatness” are used in many senses. For, in one sense, “whatness” signifies substance and this particular thing, and in another sense, it signifies each of the other categories, such as quantity, quality, and the like.

Moreover, just as “being” is said to belong to all the other categories, although not in the same way, but primarily to substance and secondarily to the others, in a similar fashion, “whatness” belongs in an unqualified sense to substance, but in another sense, that is, in a qualified sense, to the other categories.

1332. For the fact that it belongs to the others in another sense, that is, in a qualified sense, is clear from the fact that, in each of the other categories, some reply may be made to the question “What is it?” For we ask of what sort a thing is, or what its quality is, as “What is whiteness?” And we answer, “Color.” Hence it is evident that quality is one of the many things in which whatness is found.

1333. However, quality does not have whatness in an unqualified sense, but the whatness of quality. For when I ask what “man” is and one answers “animal,” the term “animal,” since it belongs in the genus of substance, not only designates what man is but also designates a what—that is, a substance—in an unqualified sense. But when one asks what whiteness is, and someone answers, “color,” this word, even though it signifies what whiteness is, does not signify what something is in an unqualified sense, but of what sort it is. Hence, quality does not have whatness in an unqualified sense, but with some qualification. For this kind of whatness is found in quality, as when we say that color is the whatness of whiteness. And this kind of whatness is substantial rather than substance.

1334. For by reason of the fact that all the other categories get the notion of being from substance, the mode of being of substance—that is, being a “what”—is therefore participated in by all the other categories according to a certain proportional likeness. For example, we say that just as animal is the whatness of man, in a similar fashion color is the whatness of whiteness, and number the whatness of double.

And, in this way, we say that quality has whatness—not in an unqualified sense, but of this particular kind, just as some say, for example, in speaking of non-being from a logical point of view, that non-being exists, not because non-being is in an unqualified sense, but because non-being is non-being. And in a similar way quality does not have whatness in an unqualified sense, but the whatness of quality.

1335. Therefore, it is also (1030a27). He now shows that whatness and definition are predicated of the nature found in substance and in accidents. He says that, since definition and whatness are found in some way both in substance and in accidents, therefore one must try to consider how we must say it (that is, predicate the definition) of each thing, yet no more than its condition warrants, namely, so that we do not say that those predicates are applied univocally which do not have one essential character in reality.

1336. And for this reason the things that have been said about definition and whatness in regard to substance and accidents is clear—namely, that whatness will belong primarily and unqualifiedly to substance, and secondarily to the other categories, not, of course, so as to be whatness in an unqualified sense, but the whatness of this or that particular category (namely, of quantity or quality). For it is evident that definition and whatness must be predicated of substance and accidents either equivocally or by adding or removing something to a greater or lesser degree. Or, in a primary or secondary way, as being is predicated of substance and accident, and as we say that the unknowable is known in a qualified sense, that is, secondarily, because, so far as the unknowable is concerned, we can know that it is not an object of knowledge. Thus we can also say of non-being that it is not.

1337. For the truth is that whatness and definition are not predicated of substance and accidents either equivocally or unqualifiedly and according to the same meaning (or univocally), but as the term “medical” is predicated of different particulars in reference to one and the same thing, although it does not signify one and the same thing in the case of all the things of which it is predicated, nor is it also predicated equivocally. For a body is said to be medical because it is the subject of the art of medicine, and an activity is said to be medical because it is performed by the art of medicine, like purging; and an instrument, such as a syringe, is said to be medical because it is used by the art of medicine. Thus, it is clear that the term “medical” is not used in a purely equivocal sense of these three things, since equivocal things have no relationship to some one thing.

Nor again is it used univocally according to the same meaning, for the term “medical” is not predicated in the same sense of one who uses the art of medicine and of something that assists the art of medicine to produce its effect, but it is predicated analogically in reference to one thing (namely, to the art of medicine).

And similarly, whatness and definition are predicated of substance and accident neither equivocally nor univocally, but in reference to one thing. For they are predicated of an accident in relation to substance, as has been explained.

1338. And since he had given two solutions, he adds that it makes no difference which way one wishes to answer the above question—that is, whether one says that accidents do not have a definition, or that they have one in a secondary and qualified sense. However, the statement made in the first solution, to the effect that accidents do not have a definition, is to be understood in a primary and unqualified sense.

1339. Now it is evident (1030b4). Second, he proves the solution which was given. He says that it is evident that definition and essence belong primarily and unqualifiedly to substances, yet not to substances alone, since, in a sense, accidents also have a definition and essence, though not in the first way.

This is made clear as follows. Not every concept by which a word is explained is the same as a definition, nor is the word explained by each concept always something defined; but it is proper that there should be a definition of any determinate concept, namely, of one that signifies one thing. For if I say that Socrates is white and musical and curly-haired, this concept does not signify one thing, except perhaps accidentally, but signifies many. Therefore, such a concept is not a definition.

1340. However, it is not enough for there to be a definition of a concept that the thing signified by it should be one thing from the viewpoint of continuity, for then the Iliad—the poem about the Trojan war—would be a definition, because that war was waged over a continuous period of time.

Nor again is it enough that the thing should be one by connection. For example, if I were to say that a house is stones and mortar and wood, this concept would not be a definition of a house.

But a concept that signifies one thing will be a definition if it signifies in some one of those senses in which the term “one” is predicated per se; for the term “one” is used in as many senses as “being” is. And in one sense, being signifies this particular thing, and in another, quantity, and in another, quality, and so on for the other categories. Yet it is predicated primarily of substance and secondarily of the other categories. Therefore, the term “one” in an unqualified sense will apply primarily to substance and secondarily to the other categories.

1341. If, then, it is characteristic of the notion of definition that it should signify one thing, it follows that there will be a definition of “white man,” because “white man” is in a sense one thing. But the concept of white will be a definition in a different sense than the concept of substance, because the concept of “substance” will be a definition in a primary sense, and the concept of “white” will be a definition in a secondary sense, just as the term “one” is predicated of each in a primary and in a secondary sense.

1342. Now if one denies (1030b14). He clears up some of the difficulties pertaining to the point established above, and this is divided into two parts corresponding to the two difficulties which he removes.

The second (1030b28; [1347]) begins where he says, and there is also.

Now there are two things that have to be noted first of all in order to make the first part of this division evident.

The first is that some said that no definition comes about by way of addition; that is, no definition contains anything extrinsic to the essence of the thing defined. And they seemed to have in mind the fact that the definition signifies the essence of a thing. Hence it would seem that whatever is extrinsic to the essence of a thing should not be given in its definition.

1343. The second thing which has to be noted is that some accidents are simple and some compound. Those are said to be simple which have no determinate subject included in their definition (for example, “curved” and “concave” and other mathematical entities); those are said to be compound which have a determinate subject without which they cannot be defined.

1344. Hence a problem arises if someone wants to say that a concept which is formed by addition is not a definition of those accidents which are simple, but of those which are compound; for it seems that none of these can have a definition. It is clear, then, that, if compound accidents are defined, their definition must be formed by addition, since they cannot be defined without their proper subject. For example, if we take the following three things—nose, concavity, and snubness—then concavity is an accident in an unqualified sense, especially in relation to nose, since nose is not contained in the concept of concavity. And snubness is a compound accident, since nose is a part of its concept. Thus, snubness will be an expression of both, inasmuch as it signifies that the one is found in the other—that is, a definite accident in a definite subject—and neither concavity nor snubness is an attribute of nose in an accidental way, as white belongs accidentally to Callias and to man, inasmuch as Callias, who happens to be a man, is white. But snubness is an essential quality of nose, for it is proper to nose as such to be snub.

Another translation has “aquiline” in place of “concave,” and its meaning is more evident, because nose is given in the definition of aquiline just as it is in the definition of snub.

Concavity or snubness, then, belongs to nose per se, just as male belongs to animal per se, and equality to quantity, and all other things that are said to be present per se in something else, because the concept of all is the same; and these attributes are those in which, that is, in the concepts of which, there is found either the name of the thing to which this attribute belongs, namely, substance, or its concept. For in definitions, the concept can always be given in place of the name. For example, when we say that man is a mortal rational animal, the definition can be given in place of the term animal, just as it may be said that man is a mortal rational sensory animated substance. And similarly, if I say that a male is an animal capable of generating in another, I can also say that a male is a sensory animated substance capable of generating in another.

1345. Clearly then, it cannot be explained apart from it, that is, knowledge cannot be conveyed of one of the accidents mentioned above, which we called compound, apart from its subject, as, for example, it is possible to convey knowledge of whiteness without giving man in its definition or concept. But it is not possible to convey knowledge of female without mentioning animal, because animal must be given in the definition of female, just as it must be given in the definition of male. Hence it is evident that none of the compound accidents mentioned above have a whatness and real definition if there is no definition by way of addition, as happens in the definitions of substances.

1346. Or if they have some kind of definition, since they can be defined only by way of addition, they will have a definition in a way different from substances, as we said in the second solution. Hence, in this conclusion, he states the solution to the foregoing difficulty, for the statement which he made there—namely, that there is no definition by way of addition—is true of definition insofar as it applies to substances. Hence, the accidents mentioned above do not have a definition in this way, but differently, that is, in a secondary sense.

1347. And there is (1030b28). Here he states the second difficulty; and in regard to this, he does two things.

First, he raises the difficulty;

second (1031a7; [1351]), he gives its solution, at but this is hidden.

He accordingly first says (1030b28) that there is another problem concerning the points discussed above. For to say “snub nose” and “concave nose” is either to say the same thing or not. If it is the same, it follows that “snub” and “concave” are the same; but this is clearly false, since the definition of each is different.

1348. But if it is not the same thing to say “snub nose” and “concave nose,” because “snub” cannot be understood without the thing of which it is a per se attribute—that is, without nose, since snubness is concavity in a nose (although concave can be spoken of without nose being involved)—and if what I call snub involves more than concave, then it follows that this thing which I call nose either cannot be called a snub nose, or if it is called such, the word will be used twice, namely, inasmuch as we might say that a snub nose is “a concave nose nose.” For the definition of a word can always be given in place of that word. Hence, when the word “snub nose” is used, the word “snub” can be removed and the definition of snub, which is a concave nose, can be added to the definition of nose. Thus it would seem that to speak of a snub nose is merely to speak of a concave nose nose, which is absurd. And, for this reason, it would seem absurd to say that such accidents have an essence.

1349. For if it is not true that they do not have an essence, the same word may be repeated an infinite number of times when the definition of the word is put in place of that word. For it is obvious that, when I say “concave nose,” the word “snub” can be understood in place of concave, because snubness is merely concavity in a nose; and the term “concave nose” can also be understood in place of “snub”; and so on to infinity.

1350. Hence it would seem to be evident that only substance has a definition; for, if the other categories also had a definition, this would have to be a result of adding something to their subject, as the definition of equal and that of odd must be derived from the definition of their subjects. For there is no definition of “odd” without number, or of “female” (which signifies a certain quality of animal) without animal. Therefore, if some things are defined by way of addition, it follows that the same words may be used twice, as was shown in the example given above. Hence if it is true that this absurd conclusion would result, it follows that compound accidents do not have a definition.

1351. But this is hidden (1031a7). He solves the problem raised above. He says that anyone who raises the above question is ignorant of the fact that these concepts are not expressed exactly (that is, with exactness), as those which are used univocally, but are employed in a primary and secondary way, as was stated above (1030a17; [1331]). But if the compound accidents mentioned above have a formula, or conceptual expression, they must have such in a different way from definitions, or “definition” and “essence,” which is signified by definition, must be used in different senses.

1352. Hence in one sense, that is, primarily and without qualification, only substance will have a definition, and only substance will have an essence. And in another sense, that is, secondarily and with some qualification, the other categories will also have a definition. For substance, which has a quiddity in the absolute sense, does not depend on something else so far as its quiddity is concerned. An accident depends on its subject, however, although a subject does not belong to the essence of its accident (in much the same way as a creature depends on the creator, yet the creator does not belong to the essence of the creature), so that an extrinsic essence must be placed in its definition. In fact, accidents have being only by reason of the fact that they inhere in a subject, and therefore their quiddity depends on their subject. Hence a subject must be given in the definition of an accident at one time directly and at another, indirectly.

1353. Now, a subject is given directly in the definition of an accident when an accident is signified concretely as an accident fused with a subject, as when I say that snubness is a concave nose. For “nose” is given in the definition of “snub” as a genus in order to signify that accidents subsist only in a subject. But when an accident is signified in the abstract, after the manner of a substance, then the subject is given in its definition indirectly, as a difference, as it is said that snubness is the concavity of a nose.

1354. Hence it is clear that, when I say “snub nose,” it is not necessary to understand “concave nose” in place of “snub”; because nose is not included in the definition of “snub” as though it were part of its essence, but as something added to its essence. Hence snub and concave are essentially the same. But snub adds over and above concave a relation to a determinate subject. Thus, in this determinate subject, “nose,” snub differs in no way from concave, nor is it necessary that any word should be put in place of snub except the word concave. Thus it will not be necessary to use “concave nose” in place of “snub,” but only “concave.”

1355. In bringing his discussion to a close he draws the conclusion which follows as obvious—namely, that a definition, which is the concept of a thing’s essence and the essence itself, belongs to substances alone, just as the first solution maintained. Or substances are defined in a primary and unqualified sense, and accidents in a secondary and qualified sense, as has been stated in the second solution.