Commentary Aristotle Physics
He first says that, granting that it seems absurd to say that there is such a disposition in natural things because of the matter, it also appears absurd to say that this is true of artificial things, an example of which has already been given. However, such a disposition is not produced in natural things and in artificial things unless the material principles have an aptitude for such a disposition. For a house would not stand well unless the heavier materials were placed in the foundation and the lighter materials above.
However, it must not be said because of these that the house is so disposed that one part of it is below and another above. I say because of these, meaning because of the heaviness or lightness of certain parts (except insofar as the term because of refers to the material cause, which is for the sake of the form).
Rather, the parts of a house are so disposed for the sake of an end, which is to shelter and protect men from the heat and the rain. And, just as it is with a house, so it is with all other things in which something happens to act for the sake of something. For in all things of this sort, the dispositions of what is generated or made do not follow without material principles, which have a necessary matter by which they are apt to be so disposed.
However, the things made or generated are not so disposed because the material principles are such, unless the term because refers to the material cause. Rather, they are so disposed because of the end. And the material principles seek to be apt for this disposition that the end requires, as is clear in a saw. For a saw is this way, that is, has a certain disposition or form. And, for this reason, it must have such a matter. And it has this disposition or form because of some end.
However, this end, which is cutting, could not be achieved unless the saw were of iron. Therefore, it is necessary that a saw be iron if there must be a saw and if it must be for this end, which is its operation. Thus, it is clear that there is a necessity by supposition in natural things, just as there is such a necessity in artificial things, but not such that what is necessary is the end. For that which is necessary is posited on the part of the matter, but the reason for the necessity is posited on the part of the end. For we do not say that there must be such an end because the matter is such. Rather we say that, since the end and the future form are such, the matter must be such. And, so, the necessity is placed in the matter, but the reason for the necessity is placed in the end.
273. Next, at “necessity in mathematics” (200a15), he compares the necessity that is in the generation of natural things to the necessity that is in the demonstrative sciences.
He does this first with reference to the order of necessity, and second with reference to that which is the principle of the necessity, at “and the end” (200a34; [274]).
He says first (200a15) that, in a certain respect, necessity is found in the demonstrative sciences in the same way that it is found in things that are generated according to nature. For a priori necessity is found in the demonstrative sciences, as when we say that, since the definition of a right angle is such, it is necessary that a triangle be such and such—namely, that it have three angles equal to two right angles. Therefore, from that which is first assumed as a principle, the conclusion arises by necessity. But the converse does not follow, that, if the conclusion is true, then the principle is. For sometimes a true conclusion can be drawn from false propositions.
But it does follow that, if the conclusion is not true, then neither is the given premise true. For a false conclusion is drawn only from a false premise.
But, in things that are made for the sake of something, either according to art or according to nature, this converse does obtain.
For if the end either will be or is, then it is necessary that what is prior to the end either will have been or is.
If, however, that which is prior to the end is not, then the end will not be, just as, in demonstrative sciences, if the conclusion is not true, then the premise will not be true.
Thus, it is clear that, in things that come to be for the sake of an end, the end holds the same order that the premise holds in demonstrative sciences. This is so because the end also is a principle, not indeed of action, but of reasoning. For from the end, we begin to reason about those things that are the means to the end.
In demonstrative sciences, however, a principle of action is not considered, but only a principle of reasoning, because there are no actions in demonstrative sciences, but only reasonings.
Hence, in things that are done for the sake of an end, the end properly holds the place that the premise holds in demonstrative sciences. Hence, there is a similarity on both sides, even though they seem to be related conversely because of the fact that the end is last in action, which does not pertain to demonstration.
Therefore, he concludes that, if a house, which is the end of a generation, is to come to be, it is necessary that the matter that is for the sake of this end come to be and preexist. Thus, tiles and stones must exist first if a house is to come to be. This does not mean that the end is for the sake of the matter, but rather that the end will not be if the matter does not exist.
Thus, there will be no house if there are no stones, and there will be no saw if there is no iron. For just as, in demonstrative sciences, the premises are not true if the conclusion, which is similar to things that are for an end, is not true, so also is the beginning related to the end, as was said.
Thus it is clear that, in natural things, that is said to be necessary that is material or is a material motion. And the reason for this necessity is taken from the end, for it is necessary for the sake of the end that the matter be such. And one ought to determine both causes of a natural thing—that is, both the material and the final cause—but especially the final cause, because the end is the cause of the matter, but not conversely. For the end is not such as it is because the matter is such, but rather the matter is such as it is because the end is such, as was said above.
274. Next, at “and the end” (200a34), he compares the necessity of natural generation to the necessity of the demonstrative sciences with respect to that which is the principle of the necessity. It is clear that, in demonstrative sciences, the definition is the principle of the demonstration.
And in like manner the end, which is the principle and reason for necessity in things that come to be according to nature, is a sort of principle taken by reason and by definition. For the end of generation is the form of the species that the definition signifies.
This also is clear in artificial things. For as the demonstrator in demonstrating takes the definition as a principle, so also does the builder in building and the physician in curing.
Thus, because the definition of a house is such, this must come to be and exist in order that a house might come to be; because this is the definition of health, this must come to be in order for someone to be cured. And if this and that are to be, then we must accomplish those things that must come to be.
However, in demonstrative sciences, definition is threefold.
One of these is a principle of demonstration, for example, thunder is the extinguishing of fire in a cloud.
The second is the conclusion of a demonstration, for example, thunder is a continuous sound in the clouds.
The third is a combination of these two, for example, thunder is a continuous sound in the clouds caused by the extinguishing of fire in a cloud. This definition embraces within itself the whole demonstration without the order of demonstration. Hence, it is said in Posterior Analytics 1.8 that definition is a demonstration differing by position.
Since, therefore, in things that come to be for the sake of an end, the end is like a principle in demonstrative science, and since those things that are for the sake of the end are like the conclusion, there is also found in the definition of natural things that which is necessary because of the end.
For if one wishes to define the operation of a saw (which is a division of a certain sort that will not occur unless the saw has teeth, and these teeth are not suitable for cutting unless they are of iron), it will be necessary to place iron in the definition of saw.
For nothing prevents us from placing certain parts of matter in the definition—not individual parts, such as this flesh and these bones, but common parts, such as flesh and bones. And this is necessary in the definition of all natural things.
Therefore, the definition that comprises in itself the principle of the demonstration and the conclusion is the whole demonstration. Thus, the definition that draws together the end, the form, and the matter comprises the whole process of natural generation.