Fourth difficulty.—The notions of space and of ubication above given imply a sort of vicious circle. For space is explained by the possibility of ubications, whilst ubications are said to be modes of being in space. Therefore neither space nor ubication is sufficiently defined.
We answer, that then only is a sort of vicious circle committed in defining or explaining things, when an unknown entity is defined or explained by means of another equally unknown. When, on the contrary, we explain the common notions of such things as are immediately known and understood before any definition or explanation of them is given, there is no danger of a vicious circle. In such a case, things are sufficiently explained if our definition or description of them agrees with the notion we have acquired of them by immediate apprehension. We say that Being is that which is, and we explain the extension of time by referring to movement, while we also explain movement by referring to time and velocity, and again we explain velocity by referring to the extension of time and movement. This is no vicious circle; for every one knows these entities before hearing their formal definition. Now, the same is true with respect to space and ubication; for the notion of space is intuitive, and before we hear its philosophical definition, we know already that it is the region of all possible ubications and movements.
Moreover, such things as have a mutual connection, or as connote one another, can be explained and defined by one another without a vicious circle. Thus we say that a father is one who has a son, and a son is one who has a father. In the same manner we define the matter as the essential term of a form, and the form as the essential act of the matter. Accordingly, since ubications are extrinsic terms of absolute space, and space is the formal reason of their extrinsic possibility, it is plain that we can, without any fear of a vicious circle, define and explain the former by the latter, and vice versa.
Finally, no philosopher has ever defined space or explained it otherwise than by reference to possible or actual ubications, nor was ubication ever described otherwise than as a mode of being in absolute or in relative space. This shows that it is in the very nature of things that the one should be explained by reference to the other. Hence it is that even our own definition of absolute space, which does not explicitly refer to contingent ubications, refers to them implicitly. For when we say that “absolute space is the virtuality, or extrinsic terminability, of divine immensity,” we implicitly affirm the possibility of extrinsic terms, viz., of ubications.
And here we will end our discussion on the entity of relative space; for we do not think that there are other difficulties worthy of a special solution. We have seen that relative space is entitatively identical with absolute space, since it does not differ from it by any intrinsic reality, but only by an extrinsic denomination. We have shown that space is relative in an active, not in a passive sense, that is, as the formal reason, not as a result of extrinsic relations. We have also seen that these extrinsic relations are usually called “relative spaces,” and that this phrase should not be used in philosophy without some restrictive epithet, as it is calculated to mislead.
Let us conclude with a remark on the known division of space into real and imaginary. This division cannot regard the entity of space, which is unquestionably real. It regards the reality or unreality of the extrinsic terms conceived as having a relation in space. The true notion of real, as contrasted with imaginary space, is the following: Space is called real, when it is really relative, viz., when it is extrinsically terminated by real terms, between which it founds a real relation; on the contrary, it is called imaginary, when the extrinsic terms do not exist in nature, but only in our imagination; for, in such a case, space is not really terminated, and does not found real relations, but both the terminations and the relations are simply a fiction of our imagination. Thus it appears that void space, as containing none but imaginary relations, may justly be called “imaginary,” though in an absolute sense it is intrinsically real.
Hence we infer that the indefinite space, which we imagine, when we carry our thoughts beyond the limits of the material world, and which philosophers have called “imaginary,” is not absolute, but relative space, and is not imaginary in itself, but only as to its denomination of relative, because where real terms do not exist there are only imaginary relations, notwithstanding the reality of the entity through which we refer the imaginary terms to one another.
That absolute space, considered in itself, cannot be called “imaginary” is evident, because absolute space is not an object of imagination. Imagination cannot conceive space except in connection with imaginary terms so related as to offer the image of sensible dimensions. It is, therefore, a blunder to confound imaginary and indefinite space with absolute and infinite space. Indeed, our intellectual conception of absolute and infinite space is always accompanied in our minds by a representation of indefinite space; but this depends on the well-known connection of our imaginative and intellectual operations: Proprium est hominis intelligere cum phantasmate; and we must be careful not to attribute to the object what has the reason of its being in the natural condition of the subject. It was by this confusion of the objective notion of space with our subjective manner of imagining it, that Kant formed his false theory of subjective space. He mistook, as we have already remarked, with Balmes, the product of imagination for a conception of the intellect, and confounded his phantasma of the indefinite with the objectivity of the infinite. It was owing to this same confusion that other philosophers made the reality of space dependent on real occupation, and denied the reality of vacuum. In vacuum, of course, they could find no real terms and no real relations, but they could imagine terms and relations. Hence they concluded that, since vacuum supplied nothing but imaginary relations, void space was an imaginary, not a real, entity. This was a paralogism; for the reason why those relations are imaginary is not the lack of real entity in absolute space, but the absence of the real terms to which absolute space has to impart relativity that the relation may ensue. It was not superfluous, then, to warn our readers, as we did in our introduction to this article, against the incursions of imagination upon our intellectual field.