Page:Russell - The Problems of Philosophy, 1912.djvu/154

150 white thing. As an account of our actual mental processes, this is no doubt largely true. In geometry, for example, when we wish to prove something about all triangles, we draw a particular triangle and reason about it, taking care not to use any characteristic which it does not share with other triangles. The beginner, in order to avoid error, often finds it useful to draw several triangles, as unlike each other as possible, in order to make sure that his reasoning is equally applicable to all of them. But a difficulty emerges as soon as we ask ourselves how we know that a thing is white or a triangle. If we wish to avoid the universals whiteness and triangularity, we shall choose some particular patch of white or some particular triangle, and say that anything is white or a triangle if it has the right sort of resemblance to our chosen particular. But then the resemblance required will have to be a universal. Since there are many white things, the resemblance must hold between many pairs of particular white things; and this is the characteristic of a universal. It will be useless to say that