Lecture 13 — Matter, even as conceived by Platonists, cannot lack size and be the subject of growth.

But the same reasons also forbid us to regard the matter, out of which the body comes-to-be, as points or lines.

The matter is that of which points and lines are limits,

and it is something that can never exist without quality and without form.

Now it is no doubt true, as we have also established elsewhere, that one thing 'comes-to-be' (in the unqualified sense) out of another thing: and further it is true that the efficient cause of its coming-to-be is either (i) an actual thing (which is the same as the effect either generically—or the efficient cause of the coming-to-be of a hard thing is not a hard thing or specifically, as e.g. fire is the efficient cause of the coming-to-be of fire or one man of the birth of another), or (ii) an actuality.

Nevertheless, since there is also a matter out of which corporeal substance itself comes-to-be (corporeal substance, however, already characterized as such-and-such a determinate body, for there is no such thing as body in general), this same matter is also the matter of magnitude and quality—being separable from these matters by definition, but not separable in place unless Qualities are, in their turn, separable. It is evident, from the preceding development and discussion of difficulties, that growth is not a change out of something which, though potentially a magnitude, actually possesses no magnitude. For, if it were, the 'void' would exist in separation; but we have explained in a former work' that this is impossible.

Moreover, a change of that kind is not peculiarly distinctive of growth, but characterizes coming-to-be as such or in general. For growth is an increase, and diminution is a lessening, of the magnitude which is there already—that, indeed, is why the growing thing must possess some magnitude. Hence growth must not be regarded as a process from a matter without magnitude to an actuality of magnitude: for this would be a body's coming-to-be rather than its growth.

91. Above [in the previous lecture] the Philosopher showed that it is not possible for the subject of growth to be something having no quantity in act but only in potency as in the case of matter. And since some philosophers posited the matter of bodies to be something mathematical, the Philosopher therefore here shows that no such thing which lacks magnitude can be the subject of growth.

Now, in the genus of mathematical things, a point lacks quantity absolutely, a line does so according to the dimensions of width and depth, a surface according to depth. Body, however, has magnitude in every dimension: hence it is a perfect magnitude, as is said in On the Heavens I. He shows therefore that none of the things lacking magnitude in any whatsoever way can be assumed to be the matter which is the subject of growth, in three ways.

First of all, for the reasons given above. Whence he says (320b14) that neither should points, which entirely lack size, be posited as the matter of body which is, namely, the subject of growth, nor should lines, which lack size in some respect. And this for the same reasons, i.e., the reasons presented above—for points and lines either have to exist separately by themselves or be in some body. Consequently the same things as before would follow.

92. Second, at the matter is that of which (320b16), he disproves this by the very position of the Platonists, who asserted that mathematical things were the substance of natural bodies. And since points and lines are the termini of dimensions, as form is the terminus of matter, they posited that whatever was bounded by things of this sort would be the matter of bodies, while the termini themselves are more in the order of form. And this is what he says, namely, that that, namely, dimension or magnitude, of which these, namely, points and lines, are the extremes, was matter according to the Platonists.

93. Third, at and it is something (320b16), he shows in common that none of these can be the matter of bodies: namely, because according to them, mathematical things exist separated from natural forms and sensible passions—as they are according to the intellect, so they are according to reality. But matter cannot be separated from natural forms and sensible passions. Therefore it is impossible that any of those mathematical things be the matter of natural bodies.

First of all, therefore, he presents the middle term of his argument, when he says that it, namely, matter, cannot be without passion, i.e., passible quality, or without form, or morphe (which is the same thing), without which, however, according to the Platonists, mathematical things do exist.

94. Second, at now it is no doubt true (320b17), he proves what he had supposed.

first, that matter cannot be without form;

second, that it cannot be without passion, at nevertheless, since there is (320b22; [95]).

He says therefore first (320b17) that as was determined in other books, for example, in Physics I, one thing is generated absolutely out of some other things. For each thing comes to be from a subject which is matter. Morover, that which is generated has to be generated by some agent in act which is either homogeneos, i.e., of one form or species (and he gives the example that fire is generated by fire as by an agent of one species, and as man is generated by man). Or else it is required at least that something be generated by something existing in act, or by the action of something existing in act, even though the agent be not akin to the thing generated in genus or species, as when something hard is generated by something not hard—for example, when milk is solidified by fire.

Now, it comes about that something produced is not akin to the agent in respect of form, in one way, because the thing produced does not primarily and per se correspond to the agent, but per accidens, or subsequently. One has per accidens generation, for example, when the musician causes health, not in so far as he is a musician but in so far as he is a doctor—for the likeness of health does not belong to musician as musician, but in so far as he is a doctor, who, through the form of health which he has in his mind, produces health in a body.

One has "subsequent" generation, for example, when the quality produced is consequent upon one of the primary qualities, as when health is caused by some hot medication, through the heat it produces in the body, although the form of health is not in the medication itself.

In a second way this [absence of likeness] occurs because the agent acts through instruments. For an instrument does not act in virtue of its own form but in so far as it is moved by the principal agent, which acts through its own form. Hence the effect is akin in form not, indeed, to the instrument, but to the principal agent—as a house which is produced in matter is assimilated to the house in the mind of the builder and not to the axe or hatchet, and as a man who is generated is assimilated in species to the father generating and not to the seed.

One has a third way, when the matter of the patient is not proportionate to receiving the form of the agent, because of its excellence, but receives something less, as is evident in the case of animals generated without seed by the power of the sun. Hence it is also that the effect is not assimilated in species to the remote, but to the proximate, agent, as man is assimilated to man but not to the sun, although man is begotten by man and by the sun as well, as is said in Physics II.

Now, just as each thing is generated by an agent in some way similar as to form, so something is corrupted by an agent that is contrary. And because a thing is generated from what has been corrupted, as was said above, the matter from which something is generated and into which something is corrupted, must always have some form through which it is similar or contrary to that which generates or corrupts.

95. Then, at nevertheless, since there is (320b22), he shows that matter is not without some passion. For matter belongs only to corporeal substance, incorporeal substances being immaterial. Hence it follows that all matter belongs to such a body, i.e., an individual body; for there cannot be a common body which is not determined to some species and to some individual. But every such body must have some passion, either following on its specific form, as in the case of a proper passion, or occurring in any other way, as in the case of individual accidents. Therefore, the same matter that is the subject of magnitude must also be the subject of passion, in such a way, indeed, that the matter which is the subject of magnitude is conceptually distinct from the passion (as the notion of "man" differs from that of "white"), while they are not distinct locally, i.e., as to subject—unless one were to maintain that passions are separable from substances, which is impossible.

And because the Philosopher appeared to have somewhat digressed from his proposition, he collects it from all the foregoing and says that it is plain from everything investigated that growth is not a change produced out of something which is in potency to magnitude, in such a way as to have no magnitude in act. For it would follow that the common subject, namely, first matter, would be separated per se, existing without any form. And this is something which has been proved impossible both now, and also previously in other books, as, for example, in Physics I.

96. Then, at moreover, a change of that kind (320b28), he shows his proposition with an argument based on growth. And he says that such a change, one, namely, that would be produced out of that which was solely in potency to magnitude would not properly pertain to growth, but more to generation. For it is of the very nature of growth that addition be made to pre-existing magnitude: for a thing is said to grow, because it acquires greater magnitude, which would not be the case if it did not first have magnitude. On the other hand, it is the nature of diminution that a lessening of a pre-existing magnitude occur. Hence it is plain that what grows must have some magnitude. Consequently, when growth takes place, it cannot be in such a way that matter having previously no magnitude in act now arrives at having magnitude in act—for that would be not growth of a body, but generation, to whose notion it pertains that something be produced in act which previously was in potency.