Secondly, we may ask, Can the intrinsic extension and continuity of matter be proved from the essence of material substance?
The answer must again be negative. For nothing can in any manner be involved in, or result from, the essence of material substance, unless it be required either by the matter, or by the substantial form, or by the relation and proportion which must exist between the form and the matter. But neither the matter, nor the substantial form, nor their mutual relation requires [pg 274] material continuity or material extension. Therefore the essence of material substance cannot supply us with any valid argument in favor of the extension and continuity of matter.
In this syllogism the major proposition needs no proof, as it is evident that material substance, like all other created things, essentially consists of act and potency; and it is known that its act is called the substantial form, while its potency is called the matter.[74] It is therefore manifest that, if anything has a necessary connection with the essence of material substance, it must be of such a nature as to be needed either by the matter or by the substantial form, or by both together.
The minor proposition can be demonstrated as follows: In the first place, continuous quantity is not needed by the matter, whether actuated or actuable. For, as actuable, the matter is a “mere potency” (pura potentia) which has yet to receive its “first actuality” (primum esse), as philosophers agree; and accordingly it has no actual quantity or continuous extension, nor is it potential with respect to it, as its potency regards only existence (primum esse), and evidently existence is not dimensive quantity. Hence the schoolmen unanimously maintain with Aristotle that the first matter has “no quiddity, no quality, and no quantity” (nec quid, nec quale, nec quantum)—a truth which we hope fully to explain in some future article. As actuated, the matter is nothing else than a substantial term susceptible of local motion; for we know from physics that material substance receives no other determination than to local movement, and for this reason, as we remarked in another place, it has been defined Ens mobile, or a movable thing. Now, a term, to be susceptible of local motion, needs no dimensions, as is evident. And therefore the matter, whether actuated or not, has nothing in its nature which requires continuous extension.
In the second place, material continuity is not required by the nature of the substantial form. This form may, in fact, be considered either as a principle of being or as a principle of operation. As a principle of being, it gives the first existence to its matter; and it is plain that to give the first existence is not to give bulk. Our adversaries teach that what gives bulk to the bodies is quantity; and yet, surely, they will not pretend that quantity is the substantial form. On the other hand, it is evident that to be and to have bulk are not the same thing; and since the substantial form merely causes the matter to be, it would be absurd to infer that it must also cause it to be extended. As a principle of operation, the form needs matter only as a centre from which its exertions are directed. Now, the direction [pg 275] of the exertion, as well as that of the movement, must be taken from a point to a point, not from a bulk to a bulk; and therefore the form, as a principle of operation, needs only one point of matter. Thus it is clear that no material extension is required to suit the wants of the substantial form.
In the third place, material extension is not required to make the matter proportionate to its substantial form. We shall see later that no form which requires a determinate quantity of mass can be a substantial form in the strict sense of the expression; at present it will suffice to keep in mind that the substantial form must give the first being to its matter, and that the matter is therefore perfectly proportioned to its substantial form by merely being in potency to receive its first being. Now, such a potency implies no extension; for if it did, the accident would precede the substance. Besides, the matter before its first actuation is a nonentity, and, as such, is incapable of any positive disposition, as we shall more fully explain in the sequel. But a determinate bulk would be a positive disposition. Hence the matter which receives its first actuation is proportionate to its form independently of material extension. We can therefore safely conclude that the essence of material substance supplies no proof whatever of the continuity of matter.
Thirdly, we ask, Can the continuity of matter be proved from mechanics?
Here also our answer must be negative. For the theorems of mechanics are each and all demonstrated quite independently of the question of material continuity. The old writers of mechanical works (or rather the old metaphysicians, from whom these writers borrowed their notion of matter) admitted the continuity of matter on two grounds: first, because they thought that nature abhorred a vacuum; and, secondly, because they rejected the actio in distans as impossible. But we have already shown that no action of matter upon matter is possible, except on the condition that the matter of the agent be distant from the matter of the patient; which implies that all the material particles, to act on their immediate neighbors, must be separately ubicated, with intervening vacuum. And thus the only reasons by which the ancients could plausibly support the continuity of matter have lost all weight in the light of modern mechanics.
Fourthly: Can the continuity of matter be inferred from geometrical considerations?
We reply that it cannot. For geometric quantity is not a quantity of matter, but a quantity of volume—that is, the quantity of space mensurable within certain limits. Hence it is evident that the continuity of the geometric quantity has nothing to do with the continuity of matter, and is not dependent on it, but wholly depends on the possibility of a continuous movement within the limits of the geometric space. In fact, we have in geometry three dimensions—length, breadth, and depth, which are simple lines. Now, a line is not conceived as made up of material points touching and continuing one another, but as the track of a point moving between certain limits; so that the continuity of the geometric dimensions is not grounded on any extension or continuation of material particles, but on the possibility of continuous movement, on which the continuity of time also depends. [pg 276] We must therefore remain satisfied that no geometrical consideration can lend the least support to the hypothesis of material continuity.