Moreover, it is obvious that there is some first principle, and that the causes of things are not infinitely many either in a direct sequence or in kind. For the material generation of one thing from another cannot go on in an infinite progression (e.g. flesh from earth, earth from air, air from fire, and so on without a stop); nor can the source of motion (e.g. man be moved by air, air by the sun, the sun by Strife, Footnote 1Aristotle is evidently thinking of Empedocles’ system. with no limit to the series).
In the same way neither can the Final Cause recede to infinity—walking having health for its object, and health happiness, and happiness something else: one thing always being done for the sake of another.
And it is just the same with the Formal Cause. For in the case of all intermediate terms of a series which are contained between a first and last term, the prior term is necessarily the cause of those which follow it; because if we had to say which of the three is the cause, we should say the first.
At any rate it is not the last term, because what comes at the end is not the cause of anything. Neither, again, is the intermediate term, which is only the cause of one
(and it makes no difference whether there is one intermediate term or several, nor whether they are infinite or limited in number). But of series which are infinite in this way, and in general of the infinite, all the parts are equally intermediate, down to the present moment. Thus if there is no first term, there is no cause at all.
On the other hand there can be no infinite progression downwards (where there is a beginning in the upper direction) such that from fire comes water, and from water earth, and in this way some other kind of thing is always being produced. There are two senses in which one thing comes from
another—apart from that in which one thing is said to come after another, e.g. the Olympian from
Footnote 2ἐκ means not only from
but after
; Aristotle dismisses this latter meaning. The Isthmian fell alternatively in the same year as the Olympian festival; when this happened the former was held in the spring and the latter in the summer. Cf. Aristot. Met. 5.24.5. the Isthmian games—either as a man comes from a child as it develops, or as air comes from water.
Now we say that a man comes from
a child in the sense that that which has become something comes from that which is becoming: i.e. the perfect from the imperfect. (For just as becoming
is always intermediate between being and not-being, so is that which is becoming between what is and what is not. The learner is becoming informed, and that is the meaning of the statement that the informed person comes from
the learner.)
On the other hand A comes from B in the sense that water comes from air by the destruction of B. Hence the former class of process is not reversible (e.g. a child cannot come from a man, for the result of the process of becoming is not the thing which is becoming, but that which exists after the process is complete. So day comes from early dawn, because it is after dawn; and hence dawn does not come from day). But the other class is reversible.
In both cases progression to infinity is impossible; for in the former the intermediate terms must have an end, and in the second the process is reversible, for the destruction of one member of a pair is the generation of the other. At the same time the first cause, being eternal, cannot be destroyed; because, since the process of generation is not infinite in the upper direction, that cause which first, on its destruction, became something else, cannot possibly be eternal. Footnote 3The argument is elliptical and confused. The meaning is this: Since there is an upward limit, there is a first cause which is eternal, being independent of any other cause. Therefore this cause cannot cause other things by its destruction, in the manner just described.
Further, the Final cause of a thing is an end , and is such that it does not happen for the sake of some thing else, but all other things happen for its sake. So if there is to be a last term of this kind, the series will not be infinite; and if there is no such term, there will be no Final cause. Those who introduce infinity do not realize that they are abolishing the nature of the Good (although no one would attempt to do anything if he were not likely to reach some limit);
nor would there be any intelligence in the world, because the man who has intelligence always acts for the sake of something, and this is a limit, because the end is a limit.
Nor again can the Formal cause be referred back to another fuller definition;
for the prior definition is always closer, and the posterior is not; and where the original definition does not apply, neither does the subsequent one. Further, those who hold such a view do away with scientific knowledge, for on this view it is impossible to know anything until one comes to terms which cannot be analyzed.
Understanding, too, is impossible; for how can one conceive of things which are infinite in this way? It is different in the case of the line, which, although in respect of divisibility it never stops, yet cannot be conceived of unless we make a stop (which is why, in examining an infinite Footnote 4i.e. infinitely divisible. line, one cannot count the sections). Footnote 5It does not follow that we can apprehend that which is infinite because we can apprehend a line which is infinitely divisible. We can only really apprehend the line by setting a limit to its divisibility and regarding it simply as divisible into a very great (but not infinite) number of sections. An infinite number of sections can neither be apprehended nor counted.
Even matter has to be conceived under the form of something which changes, Footnote 6Matter too, which is infinite in its varieties, can only be apprehended in the form of concrete sensible objects which are liable to change. This seems to be the meaning of the text, but Ross’s reading and interpretation may be right: see his note ad loc. and there can be nothing which is infinite. Footnote 7i.e. not actually, but only potentially. In any case the concept of infinity is not infinite. Footnote 8Cf. the third note above.
Again, if the kinds of causes were infinite in number it would still be impossible to acquire knowledge; for it is only when we have become acquainted with the causes that we assume that we know a thing; and we cannot, in a finite time, go completely through what is additively infinite.