CONCEIVABILITY AND THE INFINITE. 187 act by which such a conception is formed is, in fact, one of our most common mental operations. Those who have maintained the existence of the qualitative infinite as a real conception have been neither few nor far between ; but they have not been able to make their doctrine clear to others, nor obtain for it general vogue, partly because they have usually failed to keep the notion free from admixture with other elements quite foreign to it, and partly because they have not made a careful analysis of the actual psychical elements present in the conception, and shown the essential identity of thinking it with other acts which receive general recognition. The question is simply one of psychological analysis, and it is quite possible to discuss it clearly and simply, remembering that our aim is only to find out what is in mind when we habitually use a certain very common word. The word ' infinite ' means endless ; and surely it will not be denied that we make a mental distinction between an object thought as having no end at all and one thought as having an end at an indefinite distance. We at least know what we mean by the word ' endless ' ; and if the word presents any meaning to the mind at all, that to which it is applied must present itself as really distinguished from the merely indefinite. If then, when we speak of the infinite, we mean to say that it is really endless, we cannot know it by a continued addition of parts which may serve to bring us to a limit at some indefinite distance there is no such limit, definite or indefinite, by the very conditions of the pro- blem ; but that which is in mind when we think an infinite must be distinctly different from what is in mind when we add to our previous thought the notion of a limit, and think the indefinite. Now, when we analyse the mental state in which we have reference to an infinite, let us say, in this case, an infinite straight line, we find the following elements : in the first place, there are present the usual qualities of a line, for the fact of our conceiving it as without limits need not alter any of its usual qualities, any more than the fact of our being unable to see the ends of a telegraph-wire need force us to deny that it is a wire of a certain diameter, material or colour ; and, in the second place, there is present the notion that, however far we may go in thought, we shall find a continuation of the line ; in other words, there is the notion of unlimited possibility of quantity a notion which, be it marked, is strictly qualitative. Quantity in general, not this or that determined quantity, is as much a qualitative
