It is only when we confuse the single experience with the real line that we fall into absurdities.  What the mathematician tells us about real points and real lines has no bearing on the constitution of the single experience and its parts.  Thus, when he tells us that between any two points on a line there are an infinite number of other points, he only means that we may expand the line indefinitely by the system of substitutions described above.  We do this for ourselves within limits every time that we approach from a distance a line drawn on a blackboard.  The mathematician has generalized our experience for us, and that is all he has done.  We should try to get at his real meaning, and not quote him as supporting an absurdity.

[1] “Seeing and Thinking,” p. 149.

CHAPTER VII

OF TIME

27.  TIME AS NECESSARY, INFINITE, AND INFINITELY DIVISIBLE.—­Of course, we all know something about time; we know it as past, present, and future; we know it as divisible into parts, all of which are successive; we know that whatever happens must happen in time.  Those who have thought a good deal about the matter are apt to tell us that time is a necessity of thought, we cannot but think it; that time is and must be infinite; and that it is infinitely divisible.

These are the same statements that were made regarding space, and, as they have to be criticised in just the same way, it is not necessary to dwell upon them at great length.  However, we must not pass them over altogether.

As to the statement that time is a necessary idea, we may freely admit that we cannot in thought annihilate time, or think it away.  It does not seem to mean anything to attempt such a task.  Whatever time may be, it does not appear to be a something of such a nature that we can demolish it or clear it away from something else.  But is it necessarily absurd to speak of a system of things—­not, of course, a system of things in which there is change, succession, an earlier and a later, but still a system of things of some sort—­in which there obtain no time relations?  The problem is, to be sure, one of theoretical interest merely, for such a system of things is not the world we know.

And as for the infinity of time, may we not ask on what ground any one ventures to assert that time is infinite?  No man can say that infinite time is directly given in his experience.  If one does not directly perceive it to be infinite, must one not seek for some proof of the fact?  The only proof which appears to be offered us is contained in the statement that we cannot conceive of a time before which there was no time, nor of a time after which there will be no time; a proof which is no proof, for written out at length it reads as follows:  we cannot conceive of a time in the time before which there was no time, nor of a time in the time after which there will be no time.  As well say:  We cannot conceive of a number the number before which was no number, nor of a number the number after which will be no number.  Whatever may be said for the conclusion arrived at, the argument is a very poor one.