Its boundaries are surfaces. How we become acquainted with surfaces; in other words, what are the sensations, the copies of which form our complex idea of surface, has been already explained. They are certain sensations of touch, and certain sensations of muscular action. This complex idea is easily distinguished into two parts; first, a certain idea of resistance; secondly, the idea of extension. The sides 108 of a box I call resisting, and I call them extended; and I call them by both names on account of certain sensations. Let us conceive the box without a lid; each of the sides is extended and resisting. What is the top without a lid? Extended, and non-resisting. The idea of the top is that of extension without resistance; extension, in a particular direction, that of a plane surface. What is the idea of the inside of the box without its contents? That of extension in all directions without resistance. This is emptiness.
So far is plain, and not doubtful. There are still, however, some things which require explanation. What are we distinctly to understand by extension without resistance? Whenever we use the concrete extended, we mean something extended; and by that something we always mean something that resists. What do we mean when we use the abstract extension? It will be easily recollected that all this is a case of association, which has been already fully explained.
Concrete Terms are Connotative Terms; Abstract Terms are Non-connotative Terms. Concrete terms, along with a certain quality or qualities, which is their principal meaning, or notation, connote the object to which the quality belongs. Thus the concrete red, always means, that is, connotes, something red, as a rose. We have already, by sufficient examples, seen, that the Abstract, formed from the Concrete, notes precisely that which is noted by the Concrete, leaving out the connotation. Thus, take away the connotation from red, and you have redness; from hot, take away the connotation, and you have heat.
109 The very same is the distinction between the concrete extended, and the abstract extension. What extended is with its connotation, extension is without that connotation. We have then to explain, wherein the connotation consists.
When we say extended, meaning something extended, we mean one or other of three things, a line, a surface, or bulk. We have already explained sufficiently in what manner we come by the ideas of line, surface, and bulk. We have certain sensations of touch, and of muscular action, conjoined, and the ideas of those sensations, in conjunction, form our ideas of line, surface, and bulk. The sensation, or sensations, which we mark by the word resisting, seem to be those alone which are connoted by the word extending; for it is most important to observe, that what we call extending in the parts of our own body, by the operation of its own muscles, is that which we call extended in all other things; and thus the essential connotation of the concrete, extended, is, resisting, and nothing else. In other concrete terms the connotation is greater. Thus red, connotes a surface, that is, something extended; and extended connotes resisting. And thus red connotes both extended and resisting, while extended connotes resisting alone. It is true, that persons enjoying the faculty of seeing cannot conceive any thing extended, without conceiving it coloured; because in them the idea of something extended includes, by association, the visual, as well as the tactual, and muscular, ideas; and the visual being accustomed to predominate, the tactual, and muscular, are faintly observed. This, however, cannot be the case in persons born blind, 110 who have the tactual, and muscular, feelings, and not the visual at all.
Now, then, we can easily understand what extension is in all its cases. Linear extension is the idea of a line, the connotation dropped, that is, the idea of resisting, dropped; superficial extension is the idea of a surface, the same connotation dropped; and solid extension, or bulk, is merely the idea of bulk, the connotation, or resisting, dropped. But bulk, the connotation (i.e. resistance) dropped, is what? The place for bulk: Position. But place is, what? A portion of SPACE; or, more correctly speaking. SPACE itself, with limitation.
We thus seem to have arrived, without any difficulty, at an exact knowledge of what is noted or marked by the word SPACE; a phenomenon of the human mind hitherto regarded as singularly mysterious. The difficulty which has been found in explaining the term, even, by those philosophers who have approached the nearest to its meaning, seems to have arisen, from their not perceiving the mode of signification of Abstract Terms; and from the obscurity of that class of sensations, a portion of which we employ the word “extended” to mark. The word “space” is an abstract, differing from its concrete, like other abstracts, by dropping the connotation. Much of the mystery, in which the idea has seemed to be involved, is owing to this single circumstance, that the abstract term, space, has not had an appropriate concrete. We have observed, that, in all cases, abstract terms can be explained only through their concretes; because they note or name a part of what the concrete names, leaving out the rest. If we were 111 to make a concrete term, corresponding to the abstract term space, it must be a word equivalent to the terms “infinitely extended.” From the ideas included under the name “infinitely extended,” leave out resisting, and you have all that is marked by the abstract Space.[26]
[26] There is great originality as well as perspicacity in the explanation here given of Space, as a privative term, expressing when analysed, the absence of the feeling of resistance in the circumstances in which resistance is frequently felt, namely, after the sensations of muscular action and motion. The only part of the exposition to which I demur is the classing of Space among abstract terms. I have [already] objected to calling the word line, when used in the geometrical sense, an abstract term. I hold it to be the concrete name of an ideal object possessing length but not breadth. In like manner a Space may be said to be the concrete name of an ideal object, extended but not resisting. The sensations connoted by this concrete name, are those which accompany the motion of our limbs or of our body in all directions: and along with these sensations is connoted the absence of certain others, viz. of the muscular sensations which accompany the arrest of that motion by a resisting substance. This being the meaning of a Space, Space in general must be a name equally concrete. It denotes the aggregate of all Space.—Ed.
In the idea of SPACE, the idea of Infinity is included. What the idea of Infinity is, needs therefore to be explained. When the word Infinite is not used metaphorically, as it is when we speak of the infinite perfections of God, in which case it is not a name for ideas, but for the want of them, it is applied only to Number, Extension, and Duration.
We increase numbers by adding one to one, one to two, and so on, without limit, giving a name to 112 each aggregate. The association of ideas which constitutes the process has been already explained. With each number, one, two, three, four, as we go on, the idea of one more is so strongly associated, that we cannot help its existing in immediate conjunction. However high, therefore, we go in numbering, the idea of one more always forces itself upon us; and hence we say that number is infinite. That this, literally, is not true; that, indeed, it is a verbal contradiction, is obvious. Number, is something numbered; but if numbered, limited; that is, not infinite. Number is the negation of infinite; as black is the negation of white. The name infinite, in this case, is, in reality, nothing but a mark for that state of consciousness, in which the idea of one more is closely associated with every succeeding number. And Infinity, the abstract term, is the peculiar idea, without the connotation.