This passage has been quoted at length, because it lends the weighty authority of St. Thomas to three important propositions. For it is therein declared, not only that Primordial Matter is indivisible, but also that it is one and the same in all sublunary bodies; and, finally, that one and the same portion of Matter cannot at the same time receive opposite and disparate forms. To this last may be added, that, (as will be seen later), the same portion of Matter cannot at the same time be actuated by two substantial forms even of the same species; otherwise, either Matter would cease to be the principle of individuation in the sense explained in the third Book, or, there could be two essences in the same individual. That the being of Matter is essentially dependent on the form, is categorically affirmed by St. Thomas. Form gives being to Matter 1,' are his words. So, again, 'You must also know that, though Primordial Matter does not include in its essential concept any form; nevertheless, it is never stripped of form; because of itself it can never exist. For, seeing that it includes no form in its essential concept, it cannot be in act; since to be in act, can result only from the form. It is, therefore, only in potentiality 2.'

§ 4. DIFFICULTIES.

As the difficulties and objections urged against the doctrine contained in this Article are of more than ordinary interest and importance, and as they are also not a little heterogeneous; it has seemed good, (as we have already forewarned the reader), to collect them in one under a separate Section. Some there are, which directly or indirectly impugn the entire Scholastic teaching touching the existence and nature of Primordial Matter; while others are directed against one or other of the Propositions in particular. The whole doctrine is indirectly attacked, by the proposal and advocacy of other theories in preference to that which has universally obtained in the School; directly, by arguments that impugn

separata quantitate a substantia, remanet indivisibilis, ut in 1 Physic. Philosophus dicit.' 2 d. iii, Q. I, a. 4, c.

1.

Simpliciter loquendo, forma dat esse materiae.' Opusc. XXXI, (aliter XXVII), init. See the whole of this treatise.

2 Sciendum etiam, quod licet materia prima non habeat in sua ratione aliquam formam, . . . materia tamen nunquam denudatur a forma. . . . Per se autem nunquam potest esse; quia, cum in ratione sua non habeat aliquam formam, non potest esse in actu, cum esse actu non sit nisi a forma; sed est solum in potentia.' Ibidem, v. med.

the existence or nature of Primordial Matter as understood and taught by the Scholastics. Accordingly, there are three classes of difficulties, which shall be taken in the order just given.

A. THE FIRST CLASS includes the principal rival theories which have been proposed in place of the Scholastic doctrine. Now, there are two ways in which such proposals may be made. A theory touching the ultimate constituents of bodily substance may be advocated, simply on the ground that it satisfies the needs of physical inquiry and corresponds most nearly with the experience of sensile phenomena; quite irrespectively of ulterior metaphysical examination into the essences of such entities. Thus presented, it cannot be justly treated as antagonistic to the teaching of the School, or as a difficulty to be confronted; and the sole duty of metaphysics in such case will be to see, whether it satisfies those universal principles of human thought and of ontological truth, to which all knowledge, scientific or other, must conform. But again, the same theory may be proposed as a professed solution of the metaphysical problem, and be avowedly set up in opposition to the Scholastic theory; and then it confronts us as a stumbling-block to be removed out of the way. These theories, therefore, as they are presented in succession before the reader, will be submitted to this twofold. treatment. It will concern us to know whether and how far they are tenable in themselves as physical theories, and whether they afford a satisfactory answer to the metaphysical problem. It is hardly necessary to repeat, that the present examination is metaphysical. Of course, every theory concerning the ultimate constitution of bodies should fit in with the latest discoveries of physical science. On the other hand, physical theories, (so to term them), must answer to another and higher requirement. They must harmonize with those universal laws of thought, from which no dispensation is possible. It is most necessary to insist again and again on this important condition.

I. The theory which is among the earliest,—and has been, under one form or another, the most persistent,-is the purely ATOMIC; according to which, the ultimate constituents of all bodies are supposed to be atoms, that is, indivisible substances. Hence the name. There are two separate questions which are essentially included under this, as under every other, theory concerning the constitution of material substances. These concern, the one that which

may be called the matter, the other the form, of corporal consistence. The former regards the atoms themselves; the latter, the principle of atomic union. Let us consider the two apart; for as to each there has been, during the progress of the ages, considerable variety of opinion. i. Touching the atoms themselves, some maintain that they are only mechanically or physically indivisible. Such would seem to have been the idea of Democritus, of Epicurus, and in our own day, of Sir William Thomson. According to others,-Boscovich, for instance, and Leibnitz,-they are mathematically indivisible. The former would consonantly admit, that the atoms might have integrating parts; and would certainly have extension, dimensions, shape. The latter, on the contrary, maintain, that these atoms are mathematical points, without extension either intrinsic or extrinsic, without dimensions, without shape. According to one theory, the number of these atoms is finite; according to another, -that, for instance, of Anaxagoras,-their number is finite in each separate body, but infinite in nature as a whole; while, according to a third, of which Leibnitz (not to mention others) is an advocate, the number is infinite in each body,-nay, as Leibnitz maintains, in each particle of a body. Again: Some, for instance, Democritus,-teach that these atoms, or corpuscles, are all homogeneous; others, as Anaxagoras, that they are partly homogeneous, partly heterogeneous, while Leibnitz asserts that each atom is different from its neighbour. Lastly, according to one theory, the atoms have only extrinsic motion in space. Such would seem to have been the idea of the ancient atomists, and certainly was the idea of Boscovich. According to another theory, the atoms have only intrinsic motion, such as Leibnitz attributes to his Monads; according to a third, they have both local and intrinsic motion, as in the vortex rings of Helmholtz, assumed by Sir William Thomson to be the true form and nature of the atom. ii. As the atomic physicists differ respectively in their account of the atoms themselves; so they likewise differ in the principle of their union, by virtue of which they coalesce to form a particular body. Democritus attributes it to a fortuitous concourse; Anaxagoras, to commixture and separation; Leibnitz, to a pre-established harmony; Sir William Thomson, to the varied vibrations, 'knottedness,' and 'linkedness' of the vortex rings.

Setting aside, for the moment, the specific differences in these multiform theories and assuming the atomic theory, under its

generic form, as teaching that the ultimate constituents of bodily substance are atoms, or physically indivisible entities, this theory seems to commend itself by its correspondence with the experience of the senses and the phenomena of nature. For it is plain to sense that every body, potentially at least, consists of integrating parts which, up to a certain point, are capable of actual mechanical separation. Those mechanically separated parts admit of further subdivision; and these subdivided parts can be further subdivided, till we reach the limit of division. The result are atoms; that isto say, elements in capable of ulterior physical division. We are told, that the smallest organized particle under the microscope contains about two million molecules of organic matter 1.' There are about five million red corpuscles in a cubic millimetre of blood. Both these calculations are conclusions based on certain facts of experience. If these molecules are not the last, (which chemically they cannot be, because themselves composed of atoms), they must at all events contain the ultimates. Further, the science of chemistry is founded upon the supposition, that the ultimates in the constitution of bodily substance are atoms; and long-continued experiments in every direction and of every kind only add fresh force to the truth of the hypothesis. Finally, it is perhaps the oldest-known theory; nevertheless, it has managed to hold its own to the present hour.

ANSWER. It cannot be denied that there must be some element of truth in the atomic theory; otherwise, it would be impossible to account for its persistent hold on the minds of men, subsequently even to all the modern advances in physical discovery. But, though true perhaps as far as it goes, it is not satisfactory. Let us begin our examination, by reducing the number of its divergent systems. We must at once eliminate all such as ascribe infinite number to these atoms, either collectively, or in each separate body. For these atoms, infinite in number, are indivisible either physically only or mathematically also. But, in either case, the world would necessarily assume an infinite magnitude; which is repugnant to reason. Therefore, etc. The Minor is thus proved in either hypothesis. If the atoms are only physically indivisible; they have, each of them, a certain extension and therefore a certain magnitude. The number being infinite, as is supposed; that magnitude must be multiplied to infinity. If, on the other hand, they are also mathematically indivisible, in order to be able to conceive of

Encyclop. Brit. (9th ed.) under the word, 'Atomic.'

extension, it is necessary to admit certain intervals of space between them. But these intervals of space must be infinitely multiplied, in order to correspond with the infinite number of atoms; and would thus necessitate an infinite magnitude in the whole collection. It will, further, be necessary to eliminate all such systems as suppose the said atoms to be mathematical points. For mathematical points can have no independent physical existence. In so far as they are accounted real entities at all, (for about this there is a controversy in the Schools), they belong to the Category of Quantity and, save by an act of the Divine Omnipotence, could not be separated from the line which is their immediate, nor from the material substance which is their ultimate, Subject. The mathematical point must, therefore, be accompanied by the material substance which it presupposes. Thus we are not only landed in a composite; but we find an accident, that is to say, a quantitative element,-proposed as sole ultimate of a substance. If, however, it should be objected that this argument is of little account, since it is based on the Peripatetic metaphysics and thus amounts in some sort to a begging of the question; let us, by way of reply, gauge our mathematical point, or atom, by a more modern measurement. In our recent systems of philosophy, quantity is not considered to be an accident really distinct from material substance; nor are points, lines, superficies, and other geometrical entities, treated as other than intellectual abstractions,-derived from the dimensions and shapes of bodies, having no real existence, or possibility of real existence, apart from those bodies. Judged, then, by this standard, these mathematical points would fare worse than under the old philosophy. For they would be denuded of all reality in themselves; accordingly, the visible or material world would be made up of an aggregate of abstract concepts. Thus this form of materialism resolves itself into a species of mathematical idealism. Betaking ourselves now to the formal principle of union, it will be necessary to eliminate the Democritan dream of a fortuitous concourse, as being in direct contravention of the principle of causality. We must likewise reject the Leibnitzian theory of a pre-established harmony. For it is unphilosophical to attribute all the mutations, transformations, generations, and corruptions of bodies to the immediate operation of an external law Divinely pre-established, rather than to that of natural causes and of a constant order intrinsic in the material entities themselves.