LESSON 4

The Existence of a First in Final and Formal Causes

Chapter 2: 994b 9-994b 31

             160. Again, that for the sake of which something comes to be is an end. Now such a thing is not for the sake of something else, but other things are for its sake. Therefore, if there is such a thing as an ultimate end, there will not be an infinite regress; but if there is no ultimate end, there will be no reason for which things come to be.

             161. Now those who posit infinity do away with the nature of the good without realizing it.

             162. But no one will attempt to do anything unless he thinks he can carry it through to its term.

             163. Nor will there be any intelligence in such matters, because one who has intelligence always acts for the sake of something since this limit is the end of a thing.

             164. Nor can the quiddity be reduced to a definition which adds to the defining notes.

             165. For a prior definition is always more of a definition, whereas a subsequent one is not; and where the first note does not apply, neither does a later one.

             166. Again, those who speak in this way do away with science, because it is impossible to have science until we reach what is undivided.

             167. Nor will knowledge itself exist; for how can one understand things which are infinite in this way?

             168. This case is not like that of a line, whose divisibility has no limit, for it would be impossible to understand a line if it had no limits. This is why no one will count the sections, which proceed to infinity.

             169. But it is necessary to understand that there is matter in everything that is moved, and that the infinite involves nothingness, but essence does not. But if there is no infinite, what essence [i.e., definition] does the infinite have?

             170. Again, if the classes of causes were infinite in number, it would also be impossible to know anything; for we think that we have scientific knowledge when we know the causes themselves of things; but what is infinite by addition cannot be traversed in a finite period of time.

COMMENTARY

             316. Having shown that there is no infinite regress either among the causes of motion or among material causes, the Philosopher now shows that the same thing is true of the final cause, which is called "that for the sake of which" something comes to be (160).

             He proves this by four arguments. The first is as follows. That for the sake of which something comes to be has the character of an end. But an end does not exist for the sake of other things, but others exist for its sake. Now such a thing either exists or not. If there is something of such a kind that all things exist for its sake and not it for the sake of something else, it will be the last thing in this order; and thus there will not be an infinite regress. However, if no such thing exists, no end will exist; and thus the class of cause called "that for the sake of which" will be eliminated.

             317. Now those who posit infinity (161).

             He gives the second argument, which is derived from the foregoing one; for from the first argument he concluded that those who posit an infinite regress in final causes do away with the final cause. Now when the final cause is removed, so also is the nature and notion of the good; because good and end have the same meaning, since the good is that which all desire, as is said in Book I of the Ethics. Therefore those who hold that there is an infinite regress in final causes do away completely with the nature of the good, although they do not realize this.

             318. But no one will attempt (162).

             He gives the third argument, which is as follows. If there were an infinite number of final causes, no one could reach a last terminus, because there is no last terminus in an infinite series. But no one will attempt to do anything unless he thinks he is able to accomplish something as a final goal. Therefore, those who hold that final causes proceed to infinity do away with every attempt to operate and even with the activities of natural bodies; for a thing's natural movement is only toward something which it is naturally disposed to attain.

             319. Nor will there be (163).

             He states the fourth argument, which is as follows. One who posits an infinite number of final causes does away with a limit, and therefore with the end for the sake of which a cause acts. But every intelligent agent acts for the sake of some end. Therefore it would follow that there is no intellect among causes which are productive; and thus the practical intellect is eliminated. But since these things are absurd, we must reject the first position, from which they follow, i.e., that there is an infinite number of final causes.

             320. Nor can the quiddity (164).

             He shows that there is not an infinite number of formal causes. In regard to this he does two things. First (164:C 320), he states what he intends to prove. Second (165:C 322), he proves it ("For a prior definition").

             Regarding the first we must understand that each thing derives its particular species from its proper form, and this is why the definition of a species signifies chiefly a thing's form. Therefore we must understand that a procession of forms is consequent upon a procession of definitions; for one part of a definition is prior to another just as genus is prior to difference and one difference is prior to another. Therefore an infinite regress in forms and in the parts of a definition is one and the same thing. Now since Aristotle wishes to show that it is impossible to proceed to infinity in the case of formal causes, he holds that it is impossible to proceed to infinity in the parts of a definition. Hence he says that it is impossible for a thing's quiddity to be reduced to another definition, and so on to infinity, so that the defining notes are always increased in number. For example, one who defines man gives animal in his definition, and therefore the definition of man is reduced to that of animal, and this in turn to the definition of something else, thereby increasing the defining notes. But to proceed to infinity in this way is absurd.

             321. Now we do not mean by this that there are the same number of forms in each individual as there are genera and differences, so that in man there is one form by which he is man, another by which he is animal, and so on; but we mean that there must be as many grades of forms in reality as there are orders of genera and differences [in knowledge]. For we find in reality one form which is not the form of a body, another which is the form of a body but not of an animated body, and so on.

             322. For a prior definition (165).

             He proves his premise by four arguments. The first is this. Wherever there are a number of forms or defining notes, a prior definition is always "more of a definition." This does not mean that a prior form is more complete (for specific forms are complete), but that a prior form belongs to more things than a subsequent form, which is not found wherever a prior form is found; e.g., the definition of man is not found wherever that of animal is found. From this he argues that if the first note [of a series] does not fit the thing defined, "neither does a later one." But if there were an infinite regress in definitions and forms, there would be no first definition or definitive form. Hence all subsequent definitions and forms would be eliminated.

             323. Again, those who speak (166).

             He gives the second argument, which is as follows. It is impossible to have scientific knowledge of anything until we come to what is undivided. Now in this place "undivided" cannot mean the singular, because there is no science of the singular. However, it can be understood in two other ways. First, it can mean the definition itself of the last species, which is not further divided by essential differences. In this sense his statement can mean that we do not have complete knowledge of a thing until we reach its last species; for one who knows the genus to which a thing belongs does not yet have a complete knowledge of that thing. According to this interpretation we must say that, just as the first argument concluded that it is impossible to have an infinite regress in an upward direction among formal causes, in a similar fashion this second argument concludes that it is impossible to have an infinite regress in a downward direction, otherwise it would be impossible to reach a last species. Therefore this position destroys any complete knowledge.

             324. Now a formal division exists not only when a genus is divided by differences (and when such division is no longer possible the last species can be said to be undivided), but also when the thing defined is divided into its definitive parts, as is evident in Book I of the Physics. Therefore in this place "undivided" can also mean a thing whose definition cannot be resolved into any definitive parts. Now according to this the supreme genus is undivided; and from this point of view his statement can mean that we cannot have scientific knowledge of a thing by definition unless we reach its supreme genera; because when these remain unknown it is impossible to know its subsequent genera. And according to this the second argument concludes, as the former one did, that it is impossible to proceed to infinity in an upward direction among formal causes.

             325. Or, in order to reach the same conclusion, "undivided" can be explained in another way, i.e., in the sense that an immediate proposition is undivided. For if it were possible to proceed to infinity in an upward direction in the case of definitions, there would be no immediate proposition, and thus science as such, which is about conclusions derived from immediate principles, would be destroyed.

             326. Nor will knowledge (167).

             He gives the third argument, which proceeds to [show that such an infinite regress would] destroy not only science but any kind of human knowing whatsoever. In regard to this argument he does two things. First (167:C 326), he gives his argument. Second (168:C 327), he refutes an objection raised against it ("This case is not like").

             The argument is as follows. We know each thing by understanding its form. But if there were an infinite regress in forms, these forms could not be understood, because the intellect is incapable of understanding the infinite as infinite. Therefore this position destroys knowing in its entirety.

             327. This case is not like (168).

             He disposes of an objection; for someone could say that a thing having an infinite number of forms can be understood in the same way as a line which is divided to infinity. But he denies this. He says that this case is not the same as that of a line, whose divisions do not stop but go on to infinity. For it is impossible to understand anything unless some limit is set to it. Therefore a line can be understood inasmuch as some actual limit is given to it by reason of its extremes. However, it cannot be understood insofar as its division does not terminate. Hence no one can count the divisions of a line insofar as they are infinite. But as applied to forms "infinite" means actually infinite, and not potentially infinite as it does when applied to the division of a line. Therefore, if there were an infinite number of forms, there would be no way in which a thing could be known either scientifically or in any way at all.

             328. But it is necessary (169).

             He gives the fourth argument, which runs thus. Matter must be understood to exist in everything that is moved; for whatever is moved is in potentiality, and what is in potentiality is matter. But matter itself has the character of the infinite, and nothingness belongs to the infinite in the sense of matter, because matter taken in itself is understood without any of kind of form. And since nothingness belongs to the infinite, it follows contrariwise that the principle by which the infinite is a being is itself not infinite, and that it does not belong "to the infinite," i.e., to matter, to be infinite in being. But things are by virtue of their form. Hence there is no infinite regress among forms.

             329. However, it must be noted that in this place Aristotle holds that the infinite involves the notion of nothingness, not because matter involves the notion of privation (as Plato claimed when he failed to distinguish between privation and matter), but because the infinite involves the notion of privation. For a potential being contains the notion of the infinite only insofar as it comes under the nature of privation, as is evident in Book III of the Physics.

             330. Again, if the classes (170).

             He shows that the classes of causes are not infinite in number, and he uses the following argument. We think that we have scientific knowledge of each thing when we know all its causes. But if there were an infinite number of causes in the sense that one class of cause may be added to another continuously, it would be impossible to traverse this infinity in such a way that all causes could be known. Hence in this way too the knowing of things would be destroyed.