space, we correct our opinion and say the thing is real. But the spatial or primary qualities of a thing, although they may seem more permanent and more essential to the reality of the thing than the secondary qualities, are nevertheless only qualities. They are not the thing itself, but ways in which it affects us. It seems to us that these qualities must inhere in or belong to the thing, and so we try to form the idea of the real thing as a substance or substratum which has the qualities. This was a generally accepted notion until Berkeley (1685-1763) showed how contradictory it is. So {33} simple and convincing was his criticism of the notion, that never since has material 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 {34} 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