substance been put forward as an explanation of the reality of the things we perceive. All that he did was to show how impossible and contradictory it is to think that the reality of that which we perceive is something in its nature imperceptible, for such must material substance be apart from its sense qualities. How can that which we perceive be something imperceptible? And if we reflect on it, we shall surely agree that it is so—by the thing we mean its qualities, and apart from the qualities there is no thing. We must try, then, in some other way to reach the reality.

What, we shall now ask, can it be that binds together these sense qualities so that we speak of them as a thing? There are two elements that seem to enter into everything whatever that comes into our experience, and which it seems to us would remain if everything in the universe were annihilated. These are space and time. Are they reality? Here we are met with a new kind of difficulty. It was possible to dismiss material substance as a false idea, an idea of something whose existence is impossible; but space and time are certainly not false ideas. The difficulty about them is that we cannot make our thought of them consistent—they are ideas that contain a self-contradiction, or at least that lead to a self-contradiction when we affirm them of reality. With the ideas of space and time are closely linked the ideas of change, of movement, of causation, of quality and quantity, and all of these exhibit this same puzzling characteristic, that they seem to make us affirm what we deny and deny what we affirm. I might fill this little book with illustrations of the paradoxes that are involved in these ordinary working ideas. Everyone is familiar with the difficulty involved in the idea of time. We must think there was a beginning, and we cannot think that there was any moment to which there was no before. So also with space, it is an infinite extension which we can only think of as a beyond to every limit. This receding limit of the infinitely extensible space involves the character of infinite divisibility, for if there are an infinite number of points from which straight lines can be drawn without intersecting one another to any fixed point there is therefore no smallest space that cannot be further divided. The contradictions that follow from these demonstrable contents of the idea of space are endless. The relation of time to space is another source of contradictory ideas. I shall perhaps, however, best make the meaning of this self-contradictory character of our ordinary ideas clear by following out a definite illustration. What is known as the antinomy of motion is probably familiar to everyone from the well-known paradox of the Greek philosopher Zeno. The flying arrow, he said, does not move, because if it did it would be in two places at one and the same time, and that is impossible. I will now put this same paradox of movement in a form which, so far as I know, it has not been presented before. My illustration will involve the idea of causation as well as that of movement. If we suppose a space to be fully occupied, we shall agree that nothing within that space can move without thereby displacing whatever occupies the position into which it moves. That is to say, the movement of any occupant of one position must cause the displacement of the occupant of the new position into which he moves. But on the other hand it is equally clear that the displacement of the occupant of the new position is a prior condition of the possibility of the movement of the mover, for nothing can move unless there is an unoccupied place for it to move into, and there is no unoccupied place unless it has been vacated by its occupant before the movement begins. We have therefore the clear contradiction that a thing can only move when something else which it causes to move has already moved. Now if we reflect on it we shall see that this is exactly the position we occupy in our three-dimensional space. The space which surrounds us is occupied, and therefore we cannot move until a way is made clear for us, and nothing makes way for us unless we move. We cannot move through stone walls because we cannot displace solid matter, but we can move through air and water because we are able to displace these. The problem is the same. My movement displaces the air, but there is no movement until the air is displaced. Can we escape the contradiction by supposing the displacement is the cause and the movement the effect. Are we, like people in a theatre queue, only able to move from behind forward as the place is vacated for us in front? In that case we should be driven to the incredible supposition that the original cause or condition of our movement is the previous movement of something at the outskirts of our occupied space, that this somewhat moving into the void made possible the movement of the occupant of the space next adjoining, and so on until after a lapse of time which may be ages, which may indeed be infinite, the possibility of movement is opened to us. In fact we must believe that the effect of our movement—namely, the displacement of the previous occupants from the positions we occupy in moving—happened before it was caused. Now it is impossible for us to believe either of the only two alternatives—either that we do not really move but only appear to do so, or that the displacement our movement causes really precedes the movement. When we meet with a direct self-contradiction in our thoughts about anything, we can only suppose that that about which we are thinking is in its nature nonsensical, or else that our ideas about it are wrong.

It may perhaps be thought that the whole difficulty arises simply because what we are trying to think consistently about is a reality that is external to us. Space and time, movement, cause and effect are ideas that apply to a world outside and independent of the mind that tries to think it. May not this be the reason of our failure and the whole explanation of the seeming contradiction? If we turn our thoughts inward upon our own being and think of the self, the I, the real subject of experience, then surely where thought is at home and its object is mental not physical, we shall know reality. It is not so. The same self-contradiction characterises our ideas when we try to present the real object of inner perception as when we try to present the real object of external perception. Not, of course, that it is possible to doubt the reality of our own existence, but that we fail altogether to express the meaning of the self we so surely know to exist in any idea which does not fall into self-contradiction. As in the case of the thing and its qualities, we think that there is something distinct from the qualities in which they inhere and yet find ourselves unable to present to the mind any consistent idea of such thing, so we think that there must be some substance or basis of personal identity, some real self which has the successive changing conscious states, which has the character which distinguishes our actions as personal but which nevertheless is not itself these things. The self-contradiction in the idea of self, or I, or subject, is that it both cannot change and is always changing. As unchanging, we distinguish it from our body, which is an external object among other objects and is different from other objects only in the more direct and intimate relation in which it stands to us. The body is always changing; never for two successive moments is it exactly the same combination of chemical elements. We distinguish also ourself from that consciousness which is memory, the awareness of past experience, from present feelings, desires, thoughts, and strivings—these, we say, belong to the self but are not it. The self must have qualities and dwell in the body, guiding, directing, and controlling it, yet