Our answer to this objection is that time and movement are not engendered by a formal contact of a real instant with the instant following, or of a real point with the point following. Duration is not a sum of indivisible instants formally touching one another, nor is the length of space a sum of indivisible points touching one another. We may have points in space, but not points of space; and in like manner we have instants in succession, not instants of succession, though in common language we usually confound the latter with the former. Yet, when we talk of a point of space, our meaning is not that space is made up of points, but simply that a point of matter existing in space marks out its own ubication, thus lending to the space occupied the name of point. Hence no movement in space can be conceived to extend by successive contacts of points, or by the flowing of a point towards other points immediately following; for these points immediately following exist only in our imagination. Nor does a flowing point engender a line of space, but only a line of movement; and even this latter is not properly engendered, but merely marked out in space; for all possible lines are already virtually contained in space, and therefore they need no engendering, but simply marking out by continuous motion.
The same is to be said of the origin of time. Time is not a formal sum of instants touching one another. The instant just past is no more, hence it cannot touch the instant which is now; and the instant which is to follow is not yet, hence it cannot be touched by the instant which is now. Accordingly, as the movement of a single point marks out a continuous line in absolute space, so also the flowing of a single instant extends a line in absolute duration. For, as S. Thomas teaches, in the whole length of time there is but a single instant in re, though this same instant becomes virtually manifold in ratione prioris et posterioris by shifting from “before” to “after.” And in the same manner, in the whole length of a line measured in space by continuous movement, there is but a single point in re actually shifting its ubication from “here” to “there,” and thus becoming virtually manifold in its successive positions. And for this reason both movement and time are always and essentially developing (in fieri), and never exist as developed (in facto esse); since of the former nothing is actual but a point, and of the latter nothing is actual but an instant.
It is scarcely necessary to repeat that, if there were any continuous matter, its parts would all be actual and simultaneous. Its continuous extension would therefore be properly engendered by the contact of indivisible points, not by the shifting of a point from one end of its dimensions to another. This sufficiently shows that from the continuity of movement and of [pg 499] time nothing can be concluded in favor of continuous matter.
Fifth objection.—Between two given points in space infinite other points can be placed. Now, what is possible can be conceived to be done; and thus we can conceive an infinite multitude between the two points. Accordingly, an infinite multitude can be contained within limits; and if so, continuous matter is not impossible, and our first argument has no weight.
We answer that, although an infinite multitude of points can be placed between any two given points, yet nothing can be inferred therefrom in favor of continuous matter. For those innumerable points either will touch one another or not. If they do not touch, they will not make a continuum; and if they touch, they will, as we have shown, entirely coincide, instead of forming a continuous extension. It is plain, therefore, that the distance between the two given points cannot be filled continuously, even by an infinite multitude of other points. And therefore the objection has no force.
Nor is it true that by the creation of an infinite multitude of points between two given points such a multitude would be an infinity within limits. For the two given points are limits, or rather terms, of a local relation, but they are no limits of the multitude, or discrete quantity, which can be placed between them; for, without altering the position of those two points, we can increase without end the number of the intervening points. As volume is not a limit of density, so the distance of two points is not the limit of the multitude that can be condensed between them.
Sixth objection.—All the arguments above given against the continuity of matter are grounded on a false supposition; for they all take for granted that a continuum must be made up of parts—an assumption which can be shown to be false. For, first, in the geometric continuum there are no actual parts; for such a continuum is not made up by composition, but is created, such as it is, all in one piece. Whence it must be inferred that the primitive elements of matter, though exempt, as primitive, from composition of parts, and really simple, may yet possess extension. Secondly, who can deny that God has the power to create a solid body as perfectly continuous as a geometric volume? Such a body, though divisible into any number of parts, would not be a compound; for its parts would be merely possible, not actual; and therefore it would be simple, and yet continuous. Thirdly, those who deny the possibility of continuous matter admit a vacuum existing between simple points of matter. Such a vacuum is a continuous extension intercepted between real terms, and is nothing else than the possibility of real extension. But the real extension, which is possible between real terms, is not, of course, a series of points touching one another, for such a series, as all admit, is impossible. It is, therefore, an extension really continuous, not made up of parts, but only divisible into parts. Hence matter may be continuous and simple at the same time.[111]
This objection tends to establish the possibility of simple-extended matter. Yet that simplicity and material extension exclude one another [pg 500] is an evident truth; in other terms, material continuity, without composition of parts, is utterly inconceivable. If, therefore, we persist in taking for granted that a material continuum must be made up of actual parts, we do not make a gratuitous supposition.
The three reasons adduced in the objection are far from satisfactory. The first makes an unlawful transition from the geometric extension of volumes to the physical extension of masses. Such a transition, we say, is unlawful; for the geometrical extension is only virtually continuous, and therefore involves no actual multitude of parts; whereas the physical extension of the mass of matter would be formally and materially continuous, thus involving a formal multitude of actual parts perfectly distinct from one another, though united to form one continuous piece. The geometric extension is measured by three linear dimensions, and has no density. Now, a geometric line is nothing else than the trace of the movement of a point; and accordingly its continuity arises from the continuity of the movement itself, which alone is formally continuous; for the space measured by such a movement has no formal continuity of its own, as we have already explained, but is styled “continuous” only inasmuch as it is the region of continuous movement. There is no doubt, therefore, that geometric extension is merely virtual in its continuity; and for this reason it is not made up of parts of its own, but simply corresponds to the parts of the movement by which it can be measured. Material extension, on the contrary, would be densely filled with actual matter, and therefore would be made up of actual parts perfectly distinct, though not separated. To apply, as the objection does, to material extension, what geometry teaches of the extension of volumes, is therefore a mere paralogism. It amounts to saying: Vacuum is free from composition; therefore the matter also which would fill it is free from composition.
We may add that even geometric extension, if real, involves composition. For, evidently, we cannot conceive a geometric cube without its eight vertices, nor can we pretend that a figure requiring eight distinct points as the terms of its dimensions is free from composition. Now, if an empty geometric volume cannot be simple, what shall we say of a volume full of matter? Wherever there is real extension, there are real dimensions, of which the beginning, and the end, and all the intermediate terms are really distinct from one another. Hence in a material extension there should be as many distinct material terms as there are geometric points within its limits. And if this is simplicity, we may well ask what is composition?