Those who make this objection suppose that the activity of a material element is entitatively enclosed, embedded, and merged in the matter as in a physical recipient by which it must be circumscribed. This supposition is a gross philosophical blunder. The matter of a primitive element is not a physical recipient of the substantial form; for it is nothing physically before it is actuated. The substantial form gives to the matter its first being; and therefore it cannot be related to it as the enclosed to the encloser or the supported to the supporter, but only as the determiner to the determinable. This is an obvious metaphysical truth that cannot be questioned. Moreover, the form can determine the existence of a material point in space without being itself confined to that point. This is very clearly inferred from the fact already established, viz., that a material point acts all around itself in accordance with the Newtonian law; for this fact compels the conception of a material element as a virtual sphere, of which the matter is the central point, while its virtual sphericity must be traced to the special character of the form. Now, although the centre of a sphere borrows all its centric reality from the sphericity of which it is the intrinsic term, yet the sphericity itself cannot be confined within its own centre; which shows that, although the matter of an element borrows all its reality from the substantial form of which it is the essential term, yet the substantial form itself, on account of its known spherical character, must virtually extend all around its matter, and constitute, so to say, an atmosphere of power expanding as far, at least, from the central point as is necessary for the production of the phenomena of universal gravitation.
Nor can this be a sufficient ground for inferring, as the objection does, that in such a case the form would be distant from its matter as much as the sun is from the planets. The form, as such, cannot be considered as a term of the relation of distance; for, as we have already remarked, there is no distance without two formal ubications. Now, the form, as such, has no formal ubication, but is reduced to the predicament ubi only by the ubication of its own matter. Hence it is impossible rationally to conceive a distance between the matter and its form, however great may be the sphere of activity of the material element. When the substantial form is regarded as a principle of accidental actions, we may indeed consider it, if not as composed of, at least as equivalent to, a continuous series of concentric spherical forms overlying one another throughout the whole range of activity; and we may thus conceive every one of them as virtually distant from the material centre, its virtual distance being measured by its radius. But, strictly speaking, the radius measures the distance between the agent and the [pg 008] patient, not between the agent and its own power; and, on the other hand, as the imagined series of concentric sphericities continues uninterruptedly up to the very centre of the sphere, we can easily perceive that the substantial form, even as a principle of action, is immediately and intrinsically terminated to its own matter.
A third objection.—What conception can we form of an indefinite sphere? For a sphere without a spherical surface is inconceivable. But an indefinite sphere is a sphere without a spherical surface; for if there were a surface, there would be a limit; and if there were a limit, the sphere would not extend indefinitely. It is therefore impossible to conceive an indefinite sphere of activity.
This objection is easily answered. A sphere without a spherical form is indeed inconceivable; but it is not necessary that the spherical form should be a limiting surface, as the objection assumes. We may imagine an indefinite sphere of matter; that is, a body having a density continually decreasing in the inverse ratio of the squared distances from a central point. Its sphericity would consist in the spherical decrease of its density; which means that the body would be a sphere, not on account of an exterior spherical limit, but on account of its interior constitution. Now, what we say of an indefinite sphere of matter applies, by strict analogy, to an indefinite sphere of power. Only, in passing from the former to the latter, the word density should be replaced by intensity; for intensity is to power what density is to matter. And thus an indefinite sphere of power may have its spherical character within itself without borrowing it from a limiting surface. We may, therefore, consider this third objection as solved.
Let us add that in our sphere of power not only all the conditions are fulfilled which the law of gravitation requires, but, what is still more satisfactory, all the conditions also which befit the metaphysical constitution of a primitive substance. We have a centre (matter), the existence of which essentially depends on the existence of a principle of activity (form) constituting a virtual sphere. Take away the substantial form, and the matter will cease to have existence. Take away the virtual sphericity, and the centre will be no more. But let the spherical form be created; the centre will immediately be called into existence as the essential and intrinsic term of sphericity, it being impossible for a real sphericity not to give existence to a real centre. And although this spherical form possesses an intensity of power decreasing in proportion as the sphere expands, still it has everywhere the same property of giving existence to its centre, since it has everywhere an intrinsic spherical character essentially connected with a central point as its indispensable term. Whence we see that the substantial form, though virtually extending into an indefinite sphere, is everywhere terminated to its own matter. Thus the Newtonian law and the actio in distans, far from being opposed to the known metaphysical law of the constitution of things, serve rather to make it more evident by affording us the means of representing to ourselves in an intelligible and almost tangible manner the ontologic relation of matter and form in the primitive substance.
A fourth objection.—A power [pg 009] which virtually extends throughout an indefinite sphere must possess an infinite intensity. But no material element possesses a power of infinite intensity. Therefore no element extends its power throughout an indefinite sphere. The major of this syllogism is proved thus: In an indefinite sphere we can conceive an infinite multitude of concentric spherical surfaces, to every one of which the active power of the element can be applied for the production of a finite effect. But the finite taken an infinite number of times gives infinity. Therefore the total action of an element in its sphere will be infinite; which requires a power of infinite intensity.
The answer to this objection is not difficult. From the fact that the active powers virtually extend through an indefinite sphere and act everywhere in accordance with the Newtonian law, it is impossible to prove that material elements possess a power of infinite intensity. We concede, of course, that in an indefinite sphere “an infinite multitude of concentric spherical surfaces can be conceived, to every one of which the active power of the element can be applied for the production of a finite effect.” We also concede that “the finite taken an infinite number of times gives infinity.” But when it is argued that therefore “the total action of an element in its sphere will be infinite,” we must distinguish. The total action will be infinite in this sense: that it would reach an infinite multitude of terms, if they existed in its sphere, and produce in each of them a determinate effect, according to their distance—this we concede. The total action will be infinite—that is, the total effort of the element will be infinitely intense; this we deny. The schoolmen would briefly answer that the action will be infinite terminative, but not intensive. This distinction, which entirely upsets the objection, needs a few words of explanation.
In the action of one element upon another the power of the agent, while exerted on the patient, is not prevented from exerting itself at the very same time upon any other element existing in its sphere of activity. This is a well-known physical law. Hence the same element can emit a thousand actions simultaneously, without possessing a thousand powers or a thousandfold power, by the simultaneous application of its single power to a thousand different terms. The actions of an agent are therefore indefinitely multiplied by the mere multiplication of the terms, with no multiplication of the active power; and accordingly an active power of finite intensity may have an infinite applicability. This is true of all created powers. Our intellect, for instance, is substantially finite, and yet it can investigate and understand any number of intelligible objects. This amounts to saying that, if there is no limit to possible intellectual conceptions, there is no limit to the number of intelligible terms; but from this fact it would be absurd to infer that a created intellect has a power of infinite intensity. In like manner, the motive power of a material element is substantially finite, and yet it can be applied to the production of a number of movements which has no limit but the number of the terms capable of receiving the motion. The infinity of the total action is therefore grounded on an assumed infinity of terms, not on an infinite intensity of the power.
Nor can this be a matter of surprise. For, as the motive power is not transmitted from the agent to the patient, it remains whole and entire in the agent, however much it may be exerted in all directions. It is not absorbed, or exhausted, or weakened by its exertions, and, while acting on any number of terms, is yet ready to act on any number of other terms as intensely as it would on each of them separately. If ten new planets were now created, the sun would need no increase of power to attract them all; its actual power would suffice to govern their course without the least interference with the gravitation of the other existing planets. And the reason of this is that the power of all material elements is naturally determined to act, and therefore needs no other condition for its exertion than the presence of the movable terms within the reach of its activity. The number of such terms is therefore at every instant the measure of the number of the real actions.
We have said that the active power is not weakened by its exertions. In fact, a cause is never weakened by the mere production of its connatural effects, but only because, while producing its effects, it is subjected to the action of other agents which tends to alter and break up its natural constitution. Now, to be altered and impaired may be the lot of those causes whose causality arises from the conspiration of many active principles, as is the case with all the physical compounds. But primitive causes, such as the first elements of matter, are altogether unalterable and incorruptible with respect to their substantial being, and can never be impaired. When we burn a piece of paper, the paper with its composition is destroyed, but we know that its first components remain unaltered, and preserve still the same active powers which they possessed when they were all united in the piece of paper.