LESSON 19

The Senses of Limit, of "According to Which," of "In Itself," and of Disposition

Chapters 17 & 18: 1022a 4-1022a 36

             503. The term limit (boundary or terminus) means the extremity of anything, i.e., that beyond which nothing of that being can be found, and that within which everything belonging to it is contained.

             504. And limit means the form, whatever it may be, of a continuous quantity or of something having continuous quantity; and it also means the goal or end of each thing. And such too is that toward which motion and action proceed, and not that from which they proceed. And sometimes it is both, not only that from which, but also that to which. And it means the reason for which something is done; and also the substance or essence of each. For this is the limit or terminus of knowledge; and if of knowledge, also of the thing.

             505. Hence it is clear that the term limit has as many meanings as the term principle has, and even more. For a principle is a limit, but not every limit is a principle.

Chapter 18

             506. The phrase according to which (secundum quod) has several meanings. In one sense it means the species or substance of each thing; for example, that according to which a thing is good is goodness itself. And in another sense it means the first subject in which an attribute is naturally disposed to come into being, as color in surface. Therefore, in its primary sense, "that according to which" is the form; and in its secondary sense it is the matter of each thing and the first subject of each. And in general that according to which is used in the same way as a reason. For we speak of that according to which he comes, or the reason of his coming; and that according to which he has reasoned incorrectly or simply reasoned, or the reason why he has reasoned or reasoned incorrectly. Further, that according to which is used in reference to place, as according [i.e., next] to which he stands, or according to [i.e., along] which he walks; for in general these signify position and place.

             507. Hence the phrase in itself (secundum se) must be used in many senses. For in one sense it means the quiddity of each thing, as Callias and the quiddity of Callias. And in another sense it means everything that is found in the quiddity of a thing. For example, Callias is an animal in himself, because animal belongs to his definition; for Callias is an animal. Again, it is used of a thing when something has been manifested in it as its first subject or in some part of it; for example, a surface is white in itself, and a man is alive in himself. For the soul is a part of man in which life is first present. Again, it means a thing which has no other cause. For there are many causes of man, namely, animal and two-footed, yet man is man in himself. Further, it means any attributes that belong to a thing alone and inasmuch as they belong to it alone, because whatever is separate is in itself.

COMMENTARY

             1044. Here Aristotle proceeds to examine the terms which signify the conditions necessary for perfection. Now what is perfect or complete, as is clear from the above, is what is determinate and absolute, independent of anything else, and not deprived of anything but having whatever befits it in its own line. Therefore, first (503:C 1044), he deals with the term limit (boundary or terminus); second (506:C 1050), with the phrase in itself ("The phrase according to which"); and third (509:C 1062), with the term having ("Having means").

             In regard to the first he does three things. First (503), he gives the meaning of limit. He says that limit means the last part of anything, such that no part of what is first limited lies outside this limit; and all things which belong to it are contained within it. He says "first" because the last part of a first thing may be the starting point of a second thing; for example, the now of time, which is the last point of the past, is the beginning of the future.

             1045. And limit means the form (504).

             Second, he gives four senses in which the term limit is used. The first of these applies to any kind of continuous quantity insofar as the terminus of a continuous quantity, or of a thing having continuous quantity, is called a limit; for example, a point is called the limit of a line, and a surface the limit of a body, or also of a stone, which has quantity.

             1046. The second sense of limit is similar to the first inasmuch as one extreme of a motion or activity is called a limit, i.e., that toward which there is motion, and not that from which there is motion, as the limit of generation is being and not non-being. Sometimes, however, both extremes of motion are called limits in a broad sense, i.e., both that from which as well as that to which, inasmuch as we say that every motion is between two limits or extremes.

             1047. In a third sense limit means that for the sake of which something comes to be, for this is the terminus of an intention, just as limit in the second sense meant the terminus of a motion or an operation.

             1048. In a fourth sense limit means the substance of a thing, i.e., the essence of a thing or the definition signifying what a thing is. For this is the limit or terminus of knowledge, because knowledge of a thing begins with certain external signs from which we come to know a thing's definition, and when we have arrived at it we have complete knowledge of the thing. Or the definition is called the limit or terminus of knowledge because under it are contained the notes by which the thing is known. And if one difference is changed, added, or subtracted, the definition will not remain the same. Now if it [i.e., the definition] is the limit of knowledge, it must also be the limit of the thing, because knowledge is had through the assimilation of the knower to the thing known.

             1049. Hence it is clear (505).

             Here he concludes by comparing a limit with a principle, saying that limit has as many meanings as principle has, and even more, because every principle is a limit but not every limit is a principle. For that toward which there is motion is a limit, but it is not in any way a principle, whereas that from which there is motion is both a principle and a limit, as is clear from what was said above (504:C 1046).

             1050. The phrase "according to which" (506).

             Here he deals with the phrase in itself; and in regard to this he does three things. First (506), he lays down the meaning of the phrase according to which, which is more common than the phrase in itself. Second (507:C 1054), he draws his conclusion as to the ways in which the phrase in itself is used ("Hence the phrase"). Third (508:C 1058), he establishes the meaning of the term disposition ("Disposition means"), because each of the senses in which we use the phrases mentioned above somehow signifies disposition.

             In regard to the first (506), he gives four senses in which the phrase according to which is used. The first has to do with the "species," i.e., the form, or "the substance of each thing," or its essence, inasmuch as this is that according to which something is said to be; for example, according to the Platonists "the good itself," i.e., the Idea of the Good, is that according to which something is said to be good.

             1051. This phrase has a second meaning insofar as the subject in which some attribute is naturally disposed to first come into being is termed "that according to which," as color first comes into being in surface; and therefore it is said that a body is colored according to its surface. Now this sense differs from the preceding one, because the preceding sense pertains to form, but this last sense pertains to matter.

             1052. There is a third sense in which this phrase is used, inasmuch as any cause or reason in general is said to be "that according to which." Hence the phrase "according to which" is used in the same number of senses as the term reason. For it is the same thing to ask, "According to what does he come?" and "For what reason does he come?" And in like manner it is the same to ask, "According to what has he reasoned incorrectly or simply reasoned, and, for what reason has he reasoned?"

             1053. This phrase according to which is used in a fourth sense inasmuch as it signifies position and place; as in the statement, "according to which he stands," i.e., next to which, and, "according to which he walks," i.e., along which he walks; and both of these signify place and position. This appears more clearly in the Greek idiom.

             1054. Hence the phrase (507).

             From what has been said above he draws four senses in which the phrase in itself or of itself is used. The first of these is found when the definition, which signifies the quiddity of each thing, is said to belong to each in itself, as Callias "and the quiddity of Callias," i.e., the essence of the thing, are such that one belongs to the other "in itself." And not only the whole definition is predicated of the thing defined in itself, but so too in a way everything which belongs to the definition, which expresses the quiddity, is predicated of the thing defined in itself. For example, Callias is an animal in himself. For animal belongs in the definition of Callias, because Callias is an individual animal, and this would be given in his definition if individual things could have a definition. And these two senses are included under one, because both the definition and a part of the definition are predicated of each thing in itself for the same reason. For this is the first type of essential predication given in the Posterior Analytics; and it corresponds to the first sense given above (506:C 1050) in which we use the phrase according to which.

             1055. This phrase is used in a second sense when something is shown to be in something else as in a first subject, when it belongs to it of itself. This can happen in two ways: for either the first subject of an accident is the whole subject itself of which the accident is predicated (as a surface is said to be colored or white in itself; for the first subject of color is surface, and therefore a body is said to be colored by reason of its surface); or also the subject of the accident is some part of the subject, just as a man is said to be alive in himself, because part of him, namely, the soul, is the first subject of life. This is the second type of essential predication given in the Posterior Analytics, namely, that in which the subject is given in the definition of the predicate. For the first and proper subject is given in the definition of a proper accident.

             1056. This phrase is used in a third sense when something having no cause is spoken of as in itself; as all immediate propositions, i.e., those which are not proved by a middle term. For in a priori demonstrations the middle term is the cause of the predicate's belonging to the subject. Hence, although man has many causes, for example, animal and two-footed, which are his formal cause, still nothing is the cause of the proposition "Man is man," since it is an immediate one; and for this reason man is man in himself. And to this sense is reduced the fourth type of essential predication given in the Posterior Analytics, the case in which an effect is predicated of a cause; as when it is said that the slain man perished by slaying, or that the thing cooled was made cold or chilled by cooling.

             1057. This phrase is used in a fourth sense inasmuch as those things are said to belong to something in themselves which belong to it alone and precisely as belonging to it alone. He says this in order to differentiate this sense of in itself from the preceding senses, in which it was not said that a thing belongs to something in itself because it belongs to it alone; although in that sense too something would belong to it alone, as the definition to the thing defined. But here something is said to be in itself by reason of its exclusiveness. For in itself signifies something separate, as a man is said to be by himself when he is alone. And to this sense is reduced the third sense given in the Posterior Analytics, and the fourth sense of the phrase according to which, which implies position.