Some will say that the contact is indeed made in the points, but that the parts, which touch one another in a common point, are quite distinct. But this appeal to the parts of the continuum, though much insisted upon by many ancient philosophers, is of no avail against our argument. For the existence of these parts cannot be assumed, without presupposing the continuity of matter. Such parts are, in fact, assumed to be continuous; and therefore, before we admit their existence, we must inquire whether and how they can have intrinsic extension and continuity. And dividing these parts into other parts, and these again into others without end, of all these parts of parts the same question must be asked—that is, whether and how they can have intrinsic extension and continuity. Hence one of two things will follow: either we shall never find the intrinsic reason of material continuity, or we shall find it only after having exhausted an infinite division—that is, after having reached, if possible, a term incapable of further division, viz., a mathematical point. But in the mathematical point it is impossible to find the intrinsic reason of material continuity, as we have just shown. And therefore the material continuity of the parts has no formal reason of its constitution, or, in other terms, the parts themselves are intrinsically impossible.
Moreover, the very distinction made by our opponents between the points of contact and the parts which touch one another in those points, is altogether irrational. For a parte rei—that is, considering the continuum as it is in itself—there is no foundation for the said distinction, it being evident that in a homogeneous continuum no place is to be found where we cannot mark out a point. Hence it is irrational to limit the designability of the points in order to make room for the parts. In other words, the parts themselves cannot be conceived as continuous without supposing that all the neighboring points which can be designated in them form by their contact a continuous extension, which we have proved to be inadmissible. The aforesaid distinction is therefore one of the subterfuges resorted to by the advocates of material continuity, to evade the unanswerable difficulties arising from their sentence; for it is true indeed, as Goudin remarks, that material continuity is “a philosophic mystery, against which reason objects more than it can answer,” though not because in this question “reason proves more than it can understand,” but because continuous matter is shown to be an absolute impossibility.
Fifth argument.—It is a known metaphysical principle that “nothing can possibly become actual, except by the intervention of an act”—Impossibile est aliquid fieri in actu nisi per aliquem actum (S. Thomas passim). But no act can be imagined by which matter would become actually continuous. Therefore no actually continuous matter can possibly exist. The minor of our syllogism is proved thus. Acts are either substantial or accidental; hence if any act could be conceived as giving actual continuity to matter, such an act would be either substantial or accidental—that is, it would give to its matter either its first being or a mere mode of being. Now, neither the substantial nor the accidental act can make matter actually continuous. For, first, no substantial act can give to its matter a being for which the matter has no disposition. But actuable matter has no disposition for actual continuity, for where there are no distinct terms requiring continuation, there is no disposition to actual continuity, as is evident; and it is not less evident that the matter which is to be actuated by a substantial act involves no distinct terms, and does not even connote them, but merely implies the privation of the act giving it its first being, which act is one, not many, and gives one being, not many, and consequently is incapable of constituting a number of actual terms actually distinct, as would be required for actual continuity. To say the contrary would be to deny one of the most fundamental and universal principles of metaphysics, viz., Actus est qui distinguit, which means that there cannot be distinct terms where there are no distinct acts.
Moreover, continuity presupposes quantity; hence, if the substantial act gives actual continuity to its matter, it must be conceded that a certain quantity exists potentially in the actuable matter, and is reduced to act by the first actuation of matter. This quantity would therefore rank among the essentials of the substance, and could not possibly be considered as an accident; for the immediate result of the first actuation of a term by its substantial act is not a mere accident, but the very actuality of the essence of which that act and that term are the principles. Whence it follows that so long as quantity remains an accident, it is impossible to make it arise from the substantial act; and, accordingly, no substantial act can make matter actually continuous.
That actual continuity cannot arise from any accidental act is no less evident. For the only accidental act which could be supposed to play a part in the constitution of a material continuum would be some actual composition. But as composition without components is impossible, and the components of continuous matter, before such a composition, are not continuous (since we must now consider continuity as a result of the composition), our continuous matter would be made up of components destitute of continuous extension—that is, of mere mathematical points. But, as this is avowedly impossible, it follows that it is as impossible to admit that matter becomes actually continuous by the reception of an accidental act.
Sixth argument.—In a philosophico-mathematical work published in England a few years ago,[108] from [pg 491] which we have already borrowed some plain arguments concerning other questions on matter, the impossibility of continuous matter is proved by the following argument: “A compound which has no first components is a sheer impossibility. Continuous matter, if admitted, would be a compound which has no first components. Therefore continuous matter is a sheer impossibility. In this argument the first proposition is self-evident; for the components are the material constituents of the compound; and therefore a compound which has no first components is a thing which is constituted without its first constituents, or a pure contradiction. The second proposition also is undeniable. And, first, there can be no doubt that continuous matter would be a compound; for continuous matter would be extended, and would have, accordingly, parts distinct from parts; which is the exclusive property of compounds. Now, that this compound would be without first components, can be proved as follows: If continuous matter has any first components, these components will either be extended or unextended. If they are supposed to be extended, then they are by no means the first components; since it is clear that in this case they have distinct parts, and therefore are themselves made up of other components. If they are supposed to be unextended, then they are by no means the components of continuum; since all know and admit that no continuum can be made up of unextended points. And, indeed, unextended points have no parts, and therefore cannot touch one another partially; whence it follows that either they touch each other totally, or they do not touch at all. If they do not touch at all, they do not make a continuum, as is evident. If they touch totally, the one will occupy exactly the same place which is occupied by the other, and no material extension will arise. And for this reason geometrical writers consider that a mathematical line cannot be conceived as made up of points, but only as the track of a single point in motion. We see, then, that a material continuum is a compound, of which the first components cannot be extended, and cannot be unextended. And since it is impossible to think of a third sort of first components which would be neither extended nor unextended, we must needs conclude that continuous matter is a compound which has no first components. And therefore continuous matter is a mere absurdity” (p. 30).
This argument is, in our opinion, altogether unanswerable. Those philosophers, in fact, who still venture to fight in favor of continuous matter, have never been able to solve it. When we urge them to declare whether they hold the first components of continuous matter to be extended or unextended, they constantly ignore and elude the question. They simply answer that the components of material substance are “the matter” and “the form.” But if the matter which lies under the form has no distinct parts, it is evident that the substance cannot be continuous. The composition of matter and form does not, therefore, entail continuity, unless the matter which is under the form has its own material composition of parts; and it is with reference to the composition of these parts of matter, not to the composition of matter and form, that we inquire whether the first components of continuous matter [pg 492] be extended or unextended. To ignore the gist of the argument is, on the part of our opponents, an implicit confession of their inability to cope with it.
Seventh argument.—Material substance, as consisting of act and potency, like everything else in creation, is both active and passive, its activity and passivity being essentially confined, as we have already explained,[109] to the production and the reception of local movement. Hence, so long as material substance preserves its essential constitution, it is impossible to admit that matter is incapable of receiving movement from natural causes. But continuous matter would be incapable of receiving movement from natural causes. Therefore it is impossible to admit continuous matter. To prove the minor of this syllogism, let there be two little globes of continuous matter, and let them act on one another. Since no finite velocity can be communicated by an immediate contact of matter with matter, as shown in a preceding article, it follows that the velocity must be communicated by virtual contact in accordance with the law of the inverse squared distances. Hence, since some points of the two globes are nearer to one another, and others are farther, different points must acquire different velocities. Now, one and the same piece of matter cannot move onward with different velocities, as is evident; it will therefore be unable to move so long as such different velocities are not reduced to a mean one, which shall be common to the whole mass. Such a reduction of unequal velocities to a mean one would meet with no difficulty, if the globes in question were made up of free and independent points of matter; for in such a case the globes would be compressed, and each point of matter would act and react according to known mechanical laws, and thus soon equalize their respective velocities. But in the case of material continuity the reduction of different velocities to a mean one is by no means possible. For “in a piece of continuous matter,” to quote again from the above-mentioned work of molecular mechanics, “any point which can be designated is so invariably united with the other points that no impact and no mutual reaction are conceivable; the obvious consequence of which is that no work can be done within the continuous particle in order to equalize the unequal velocities impressed from without. Moreover, in our case the reduction ought to be rigorously instantaneous; which is another impossibility. In fact, if distinct points of a continuous piece of matter were for any short duration of time animated by different velocities, the continuum would evidently undergo immediate and unavoidable resolution; which is against the hypothesis. Since, then, the said reduction cannot be made instantaneously, as we have proved above, nor, indeed, in any other way, and, on the other hand, our continuous particle cannot move onward before the different velocities are reduced to one of mean intensity, it is quite evident that the same continuous particle will never be capable of moving, whatever be the conditions of the impact. And since what is true of one particle on account of its supposed continuity is true also of each of the other particles equally continuous, we must conclude that bodies made up of particles materially continuous are totally incapable [pg 493] of receiving any communication of motion.”[110]
This argument, though seemingly proving only the non-existence of continuous matter in nature, proves in fact, also, the impossibility of its existence. For, if a substance could be created possessing intrinsic extension and continuity, that substance would essentially differ from the existing matter, and would therefore be anything but matter. Hence not even in this supposition would continuous matter exist.
Eighth argument.—The inertia of matter, and its property of acting in a sphere, might furnish us with a new argument against material continuity. But we prefer to conclude with a mathematical demonstration drawn from the weight of matter. The weight of a mass of matter depends on the number of material terms to which the action of gravity is applied, and it increases exactly in the same ratio as the number of the elementary terms contained in the mass. This being the case, let us assume that there is somewhere an atom of continuous matter. The action of gravity will find in it an infinite multitude of points of application; for it is of the nature of continuum to supply matter for an endless division. Hence if we call g the action of gravity on the unit of mass in the unit of time, the action of the same gravity on any of those infinite points of application will be