Page:Russell - The Problems of Philosophy, 1912.djvu/124

120 of seeing two things and two other things, and finding that altogether they made four things, we were led by induction to the conclusion that two things and two other things would always make four things altogether. If, however, this were the source of our knowledge that two and two are four, we should proceed differently, in persuading ourselves of its truth, from the way in which we do actually proceed. In fact, a certain number of instances are needed to make us think of two abstractly, rather than of two coins or two books or two people, or two of any other specified kind. But as soon as we are able to divest our thoughts of irrelevant particularity, we become able to see the general principle that two and two are four; any one instance is seen to be typical, and the examination of other instances becomes unnecessary.

The same thing is exemplified in geometry. If we want to prove some property of all triangles, we draw some one triangle and