Lecture 15 — How necessity is found in natural things

As regards what is “of necessity,” we must ask whether the necessity is hypothetical, or simple as well.

The current view places what is of necessity in the process of production, just as if one were to suppose that the wall of a house necessarily comes to be because what is heavy is naturally carried downward and what is light to the top; thus, the stones and foundations take the lowest place, with earth above because it is lighter, and wood at the top of all as being the lightest.

Nevertheless, though the wall does not come to be without these, it is not because of these except as its material cause: it comes to be for the sake of sheltering and guarding certain things.

It is the same in all other things that involve production for an end: the product cannot come to be without things that have a necessary nature, but it is not due to these except as its material; it comes to be for an end. For instance, why is a saw this way? To effect such-and-such and for the sake of such-and-such.

This end, however, cannot be realized unless the saw is made of iron. It is therefore necessary for it to be of iron if we are to have a saw and perform the operation of sawing.

What is necessary, then, is necessary on a hypothesis; it is not a result necessarily determined by antecedents. Necessity is in the matter, while “that for the sake of which” is in the definition.

Necessity in mathematics is similar in a way to necessity in things that come to be through the operation of nature.

Since a straight line is what it is, it is necessary that the angles of a triangle should equal two right angles, but not conversely—though, if the angles are not equal to two right angles, then the straight line is not what it is either.

But, in things that come to be for an end, the reverse is true. If the end is to exist or does exist, that also that precedes it will exist or does exist; otherwise, just as the premise will not be true if the conclusion is not true, so here the end or “that for the sake of which” will not exist.

For this too is itself a starting-point, but of the reasoning, not of the action; while the starting-point in mathematics is the starting-point of the reasoning only, as there is no action.

If, then, there is to be a house, such-and-such things must be made or be there already or exist, or generally the matter relative to the end (bricks and stones if it is a house). But the end is not due to these except as the matter, nor will it come to exist because of them.

Yet, if they do not exist at all, neither will the house or the saw—the former in the absence of stones, the latter in the absence of iron—just as, in the other case, the premises will not be true if the angles of the triangle are not equal to two right angles.

The necessary in nature, then, is plainly what we call by the name of matter, and the changes in it. Both causes must be stated by the physicist, but especially the end, for that is the cause of the matter, not vice versa.

And the end is “that for the sake of which,” and the beginning starts from the definition or essence.

This is just as in artificial products: since a house is of such-and-such a kind, certain things must necessarily come to be or be there already; or, since health is this, these things must necessarily come to be or be there already.

Similarly if man is this, then these [must necessarily come to be or be there already]; if these, then those.

Perhaps the necessary is present also in the definition.

For if one defines the operation of sawing as being a certain kind of dividing, then this cannot come about unless the saw has teeth of a certain kind, and these cannot be unless they are of iron. For in the definition too there are some parts that are, as it were, its matter.

269. Having shown that nature acts for an end, the Philosopher here proceeds to inquire into the second question, that is, how necessity is found in natural things.

Concerning this, he makes three points.

First, he raises the question.

Second, at the current view (199b35; [271]), he sets forth the opinion of others.

Third, at nevertheless, though the wall (200a5; [272]), he determines the truth.

270. Thus, he asks (199b34) whether, in natural things, there is a simple necessity—that is, an absolute necessity—or a necessary by condition or by supposition. In order to understand this, it must be noted that the necessity that depends upon prior causes is an absolute necessity, as is clear from the necessity that depends upon matter. That an animal is corruptible is absolutely necessary. For to be composed of contraries is a consequence of being an animal.

In like manner, that which has necessity from the formal cause is also absolutely necessary. For example, man is rational, or a triangle has three angles equal to two right angles, which is reduced to the definition of triangle.

Similarly, that which has necessity from the efficient cause is absolutely necessary. Thus, because of the motion of the sun, it is necessary that day and night alternate. But that which has necessity from that which is posterior in existence is necessary upon condition, or by supposition.

For example, it might be said that it is necessary that this be if this ought to come to be. Necessity of this kind is from the end and from the form insofar as it is the end of generation. Therefore, to ask whether, in natural things, there is a simple necessity or a necessity by supposition is nothing else than to ask whether necessity is found in natural things from the end or from the matter.

271. Next, at the current view (199b35), he gives the opinion of others. He says that some are of the opinion that the generation of natural things arises from an absolute necessity of matter. For example, one might say that a wall or a house is such as it is by the necessity of matter, because heavy things are disposed to move downward and light things to rise above. And, because of this, the heavy and hard stones remain in the foundation, while earth, being lighter, rises above the stones, as is clear in walls constructed of tiles that are made of earth. But the timbers, which are the lightest, are placed at the highest point, at the roof. Thus, they thought that the dispositions of natural things have come to be such as they are from the necessity of matter. For example, it might be said that a man has feet below and hands above because of the heaviness or lightness of humors.

272. Next, at nevertheless, though the wall (200a5), he determines the truth.

Concerning this, he makes two points.

First, he shows what sort of necessity there is in natural things;

second, at necessity in mathematics (200a15; [273]), he compares the necessity of natural things to the necessity that is in the demonstrative sciences.

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. (Cf. St. Thomas, Commentary on Posterior Analytics, bk. 1, lect. 16, nn. 138–39; lect. 26, n. 215.)

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. (Cf. lect. 5, n. 179.)

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.