SPACE AND TIME (Mathematics). We do not here propose to enter into any discussion of the doctrines of psychologists as to the idea of space, or as to whether it be innate or acquired. Space and time are essential to thought, and are, come by the notions how we may, necessary attendants on our own consciousness of existence. It is possible for imagination to picture the annihilation of all things, itself included, or to fancy that it can form such a picture, which is the same thing ; but what then would remain (in the thoughts) ? Infinitely extended empty space, lasting through infinitely extended time. Exist ence of space and successions of existence we may defy the speculator to deprive himself of for one moment. The greatest proof we have of our ignorance of the Creator of all things is the absolute impossibility which we find of making •the necessity of his existence as real a con ception of our minds as that of space or time. The most religious man will read with pleasure a work on natural theology tending to prove that there must be a God ; but who would bear ten pages of a serious attempt to demonstrate the existence of space and time I In these ideas we have the foundation of the mathematical sciences ; for from space follows form, which is the conception of the manner in which one part of space is separated from the rest, and from the investi gation of forms arises geometry. Again, time is only apprehended by succession of events or ideas, and succession or repetition gives the notion of numbering. And though collection is sometimes stated to be the leading idea in number, yet it may be asserted that number in the last sense is not the object of arithmetic, except as furnishing the sub ject of numbering. The leading phrases of arithmetic suggest the idea of time, and are derived from it. How often is 2 contained in 12 ? Six times. The 2 presented to the thoughts at six different times is the mode in which the collection of 12 is counted by twos.
From both space and time we get the notion of direction, but in very different manners. The extremities of a portion of length give the idea of a point of space, a fundamental notion of an indivisible index of com mencement or termination. The extremities of time give the notion of points of time, or indivisible portions of duration. No point of space con tains any apace; no point of time lasts any time. If we choose a point of space or a point of time, we can in bur thoughts set out from the former iu an infinite number Of different ways; • from the latter, in only two.
This is the law of thought, upon which it is useless to speculate ; but it is followed by important consequences. So long as algebra, the science of reasoning by symbols, was founded only on notions of arith metic or succession, its ideas were not competent to furnish explanation to all the results of its mechanical processes. As soon as the same rules were transferred to ideas of space, or made to spring from geo metrical explanations, the mysteries of that science gradually vanished.
From space and time, also, we get the idea of infinity, a subject which has been already treated [INFINITE]; but only in such a point of view as would meet the objections of those who cannot reason clearly on absolute infinity. That space and time are unbounded, is the simple consequence of their being necessary to our notion of the existence of anything: we speak of our conceptions of them. For if it could be imseintal that spare eeaseri at a certain boundary, it would be as easy to make it cease in our own neighbourhood; and if duration could be .imagined to have an end, it would not be difficult to place.ourselves in thought within five minutes of that end. The denial of the possibility of our approaching the boundary of space or time in our thoughts, is the same thing as the denial of the existence of such a boundary ; and the notion of infinity becomes a relief from the incongruity of the attempt to conceive existence stripped of its essential conditions. But it might be asked why not, as to space at least, consider real existing extension, not as the object of our thoughts, but as it would exist if we were not alive to think t Is it, or is it not, physically possible to go on for ever in space t If a person could provide himself with an unlimited supply of motive-power, air, heat, food. ezc., must we, or must we not, say that there is anything to hinder his travelling to all eternity f For ourselves, we should say there is clearly nothing to hinder ; but of course we cannot appeal to experiment, and it may be only the impossibility of destroying our own conception of space which dictates an answer as to that external reality which, let metaphysicians nay what they please, can always be established by a wave of the hand.