“I am so sorry, Severn,” said Assunta after a pause in the conversation, “that Clara would not come to us to-day. I think a glimpse of quiet country life might be a pleasant change for her.”
“I fear,” replied her husband sadly, “that poor Clara has much to suffer yet. It is my opinion that Sinclair has no intention of returning from Europe at all. But who could have made her believe, in those sunshiny days, that she would ever live to be a deserted wife? Petite, the subject is a very painful one. I am going to change it for one of which I am never weary. Augustine, it is not the custom, I believe, for a man to toast his wife on such an occasion, but I am going to be an exception to the rule [pg 487] to-day. Lord Lytton has in that grand work of his, My Novel, two types of women—the one who exalts, and the one who consoles. He probably had never seen the combination of the two types in one person. I now propose—and, my darling, you must drink and not blush—‘Assunta Carlisle: blessed be the woman who both exalts and consoles!’ And let me add that a happy man was I—unworthy—when, ten years ago, that woman became my wife.”
Matter. V.
Although continuous matter cannot be proved to exist, yet its existence, as every one knows, is still very commonly believed, even by philosophers, on the ground that it was believed for centuries by all great men, and has never been conclusively refuted. From some hints which we have given in our previous article about the difficulties of this ancient doctrine, the intelligent reader may have already satisfied himself that material continuity is not merely “a philosophical mystery,” as Goudin confesses, but a metaphysical absurdity. As, however, this last conclusion, owing to its paramount importance in metaphysics and in natural philosophy, deserves a more explicit and complete demonstration than we have yet given, we propose to develop in the present article a series of arguments, drawn from different sources, to show the absolute and intrinsic impossibility of continuous matter. The prejudices of our infancy may at first resist the demonstration, but it is to be hoped that they will finally yield to reason.
First argument.—We know, and it is conceded by the advocates of continuous matter, that a finite being cannot involve in its composition an infinite multitude of distinct terms; for evidently the infinite cannot be the constituent of the finite. Now, we have shown in our preceding article that, if there were a piece of continuous matter, it should involve in its continuous constitution an infinite multitude of distinct terms, every one of which should have its own distinct existence independently of the others. Therefore continuous matter cannot exist.
Second argument.—A primitive substance cannot absolutely be made up of other substances. But if there were any continuous matter, a primitive substance would be made up of other substances. Therefore no continuous matter can exist. The major of this syllogism is quite evident; for a primitive substance, if made up of other substances, would be primitive and non-primitive at the same time. The minor can be easily proved. For it is plain that continuous matter, if any such existed, would necessarily consist of continuous parts, substantially distinct from one another, and therefore having their own distinct matter and their own [pg 488] distinct substantial act, and ranking as distinct, complete, and separable substances, as we have shown in our last article. Now, assuming that either of these parts is a primitive substance, it is evident that the primitive substance would be made up of other substances; for such a part, being continuous, is itself made up of other parts, which are likewise distinct and complete substances, as we have just remarked. And since a continuum cannot be resolved into any but continuous parts, the conclusion cannot be avoided that the primitive material substance would always be made up of other substances. To elude this argument, the advocates of continuous matter are compelled to deny that there is any primitive material substance mathematically continuous. But, even so, their position is not improved. For if there is no primitive material substance mathematically continuous, the combination of such primitive substances will never give rise to continuous matter, it being obvious that all the elementary constituents of continuum must be continuous, as all philosophers agree. Whence we again conclude that no continuous matter is possible.
Third argument.—No continuum can be made up of unextended constituents, as we have just observed, and as our opponents not only concede, but also demonstrate most irrefragably in their own treatises. Now, continuous matter, if any such existed, would be made up of unextended constituents—that is, of mere mathematical points. Therefore continuous matter would be a formal contradiction. The minor of our syllogism is proved thus. All the points which can be designated within the dimensions of the continuum are immediately united with one another, and therefore no room is to be found between any two consecutive points; which shows that in the constitution of the continuum we would have nothing but mere points. For let there be a continuous plane and a continuous sphere. The sphere, if perfect, cannot touch the plane, except in a single indivisible point, as is proved in geometry; nevertheless, the sphere may move along the plane, and, always touching the plane in a single point, may measure a linear extension of matter, which, accordingly, would contain nothing but mathematical points immediately following one another. In other terms, the extended matter would be made up of indivisible points; and since all admit that this is impossible, it follows that continuous matter is impossible. Against this argument the objection is made that it proves too much; as it would prove the impossibility of measuring space by continuous movement. But this objection has no good foundation, as we shall show after concluding the series of our arguments.
Fourth argument.—All the points that can be designated in a material continuum would necessarily touch one another in such a manner as to form a continuous extension; hence their contact would necessarily be extensive. But an extensive contact of indivisible points is intrinsically impossible. Therefore material continuity is intrinsically impossible. The major of this syllogism is a mere corollary from the definition of continuum; for, if there be no contact, the continuum will be broken, and if the contact be not extensive—that is, such as to allow each point to extend beyond its neighbor—no continuous extension will result. The minor of our [pg 489] syllogism can be proved as follows:
The contact of a point with a point is the contact of an indivisible with another indivisible; and, since the indivisible has no parts, such a contact cannot be partial, but must needs be total. Accordingly, the second point, by its contact with the first, will be totally in the first; the third, by its contact with the second, will be totally in the second, and consequently in the first; the fourth, by its contact with the third, will be totally in the third, and consequently in the second and in the first, and so on. Therefore all the points which are in mathematical contact will necessarily correspond to the same point in space. Now, to be all in the same point, and to form a continuous extension, are contradictories. And thus it is manifest that material continuity is a mere contradiction.