This incontrovertible fact maybe confirmed à priori by reflecting that the active principle, or the substantial form, of a primitive element, is not exposed to the influence of any natural agent capable of impairing it. Everything that is impaired is impaired by its contrary. Now, the active principle has no contrary. The only thing which might be imagined to be contrary to a motive power would be a motive power of an opposite nature, such as the repulsive against the attractive. Motive powers, however, do not act on one another, but on their matter only, as matter alone is passive. On the other hand, even if one power could act on another, its motive action would only produce an accidental determination to local movement, which determination surely would not alter in the least the substance of a primitive being. Hence, although two opposite actions, when terminated to the same subject, can neutralize each other, yet two opposite motive powers can never exercise any influence on each other by their natural actions; and therefore, in spite of their finite entity, they are never impaired or weakened, and are applicable to the production of an unlimited number of actions.
A fifth objection.—An action of infinite intensity cannot but proceed from a power of infinite intensity. But, according to the Newtonian law, two elements, when their distance has become infinitely small, act on one another with an intensity infinitely great. Therefore, if the Newtonian law hold good even to the very centre of the element, the [pg 011] elementary power possesses infinite intensity.
To this we reply that the mathematical expression of the intensity of the action, in the case of infinitesimal distances, does not become infinite, except when the action is supposed to last for a finite unit of time. But the action continued for a finite unit of time is not the actual action of an element; it is the integral of all the actions exerted in the infinite series of infinitesimal instants which makes up the finite unit of time. To judge of the true intensity of the actual exertion, it is necessary to exclude from the calculation the whole of the past or future actions, and to take into account the only action which corresponds to the infinitesimal present. In other terms, the actual action is expressed, not by an integral, but by a differential. In fact, the elements act when they are, not when they have been, or when they will be; they act in their present, not in their future or in their past; and the present, the now, is only an instant, which, though connecting the past with the future, has in itself neither past nor future, and therefore has a rigorously infinitesimal duration. It is this instant, and not the finite unit of time, that measures the actual effort of the elements. Accordingly, the action as actually proceeding from the elements, when at infinitesimal distance, is infinitely less than the integral calculated for a finite unit of time; which shows that the argument proposed has no foundation.
This answer serves also to complete our solution of the preceding objection. It was there objected that the active power of an element can be applied to the production of an infinite multitude of finite effects; to which we answered that a finite power was competent to do this by being applied simultaneously to an infinite multitude of terms. But now we add that none of those effects acquire a finite intensity, except by the continuation of the action during a finite unit of time, and therefore that the true effect produced in every instant of time is infinitesimal. Hence the infinite multitude of such effects, as related to the instant of their actual production, is an infinite multitude of infinitesimals, and the total effort of a primitive element in every instant of time is therefore finite, not infinite.
A sixth objection.—If we admit that a material element has an indefinite sphere of power, we must also admit that the element has a kind of immensity. For the active power must evidently be present entitatively in all the parts of space where it is ready to act. Accordingly, as by the hypothesis it is ready to act everywhere, its sphere being unlimited, it must be present everywhere and extend without limit. In other words, the elementary power would share with God the attribute of immensity—which is impossible.
This objection, which, in spite of its apparent strength, contains only an appeal to imagination instead of intellect, might be answered from S. Thomas in two different ways. The first answer is suggested by the following passage: “The phrase, A thing is everywhere and in all times, can be understood in two manners: First, as meaning that the thing possesses in its entity the reason of its extending to every place and to every time; and in this manner it is proper of God to be everywhere and for ever. Secondly, as meaning that the thing has nothing in itself by which it be [pg 012] determined to a certain place or time.”[7] According to this doctrine, a thing can be conceived to be everywhere, either by a positive intrinsic determination to fill all space, or by the absence of any determination implying a special relation to place. We might therefore admit that the elementary power is everywhere in this second manner; for although the matter of an element marks out a point in space, we have seen that its power, as such, has no determination by which it can be confined to a limited space. And yet nothing would oblige us to concede that the active power of an element, by its manner of being everywhere, “shares in God's immensity”; for it is evident that an absence of determination has nothing common with a positive determination, and is not a share of it.
The second answer is suggested by a passage in which the holy doctor inquires “whether to be everywhere be an attribute of God alone,” and in which he proposes to himself the objection that “universals are everywhere; so also the first matter, as existing in all bodies, is everywhere; and therefore something is everywhere besides God.” To which he very briefly replies: “Universals and the first matter are indeed everywhere, but they have not everywhere the same being.”[8] This answer can be applied to the active power of primitive elements with as much reason, to say the least, as it is to the first matter. The active power may therefore be admitted to be everywhere, not indeed like God, who is everywhere formally, and “has everywhere the same being,” but in a quite different manner—that is, by extending everywhere virtually, and by possessing everywhere a different degree of virtual being. We know, in fact, that this is the case, as the exertions of such a power become weaker and weaker in proportion as the object acted on is more and more distant from the centre of activity.
Yet a third answer, which may prove to be the best, can be drawn from the direct comparison of the pretended immensity of the elementary power with the real immensity of the divine substance. God's immensity is an infinite attribute, which contains in itself the formal reason of the existence of space, and therefore eminently contains in itself all possible ubications. By his immensity God is essentially everywhere with his whole substance, and is as infinite and entire in any one point of space as he is in the whole of the universe and outside of it. On the other hand, what is the pretended immensity of the elementary power? It is unnecessary to remark that an indefinite sphere of power does not give existence to space, as it presupposes it; but it is important to notice that, however great may be the expansion of that virtual sphere, the essence and the substance of the element are absolutely confined to that single point, where its form is terminated to its matter. Both matter and form are included in the essence of an element; hence there only can the element be with its essence and substance where its matter and its form are together. [pg 013] But they are not together, except in a single point. Therefore the element, however great may be the virtual expansion of its sphere of power, is essentially and substantially present only in a single point.
From this every one will see that there is no danger of confounding the virtual ubiquity of created power with God's immensity. Divine immensity has been ingeniously, though somewhat strangely, defined by a philosopher to be “a sphere of which the centre is everywhere.” The power of an element, on the contrary, is “a sphere of which the centre is ubicated in a single point.” If this does not preclude the notion that the element “shares in God's immensity,” we fail to see why every creature should not share also in God's eternity, by its existence in each successive moment of time. The objection is therefore insignificant. As to the virtual sphere itself, we must bear in mind that its power loses continually in intensity as the virtual expansion is increased, till millions of millions of elements are required to produce the least appreciable effect. Hence the virtuality of elementary powers tends continually towards zero as its limit, although it never reaches it. And as a decreasing series, though implying an infinity of terms, may have a finite value, as mathematicians know, so the virtuality of the elementary powers, although extending after its own manner beyond any finite limit, represents only a finite property of a finite being.
From what we have said in these pages the intelligent reader will realize, we hope, that the much-maligned actio in distans, as explained by us according to Faraday's conception, can bear any amount of philosophical scrutiny. The principles which have formed the basis of our preceding answers are the three following: