empirical instances,—if, I say, this explanation, which I hold to be false, were correct, all the more would it be plain that what causes an idea is not, as such, the object of the idea, for it is not of broken china, nor of spilled milk, nor even of lost youth that one thinks in announcing the view that the past is irrevocable,—but of what one supposes to be an universal law of all time, which one applies as well to the repeated sequence of the monotonous beats of the pendulum, or to the waves that break over and over upon the beach, as to youth, or even to death. For even of the monotonously repeated series of events, one asserts that each individual case of the repetition is irrevocable when past. Even if one's view as to this matter were false, one's object would here be a character of the whole of time, and a character which is certainly no cause of present ideas.
It is hopeless, then, to persist in the hypothesis that the object of an idea is as such the cause of the idea. Were one to persist in such a view, what would he say about all the mathematical objects? Does the binomial theorem act as a seal, or any other sort of cause, impressing its image on the wax of a mathematician's mind? Do the properties of equations do anything to the mathematician when he thinks of them? Is not all the fresh creative activity in this case his own?
VI
Nearer to our desired definition we may come if we next observe the reason for the plausibility of the usual appeal to the objects of vision and touch as the typical cases of objects of ideas. For, in fact, nobody can doubt
