Page:Mind (Old Series) Volume 11.djvu/199

 188 G. S. FULLEETON : notion as colour or form ; and in thus denning the second element present in our notion of an infinite line, I have used the word advisedly to bring out what is a distinctive charac- teristic of the conception. The word infinite does not denote a quantity, but it has reference to quantity ; and it cannot, in accordance with its derivation and true significa- tion, be rightly applied to what is incapable of being quanti- tatively considered. My objection to the usage of the word ' infinite ' by some who yet recognise that the conception for which it stands is qualitative, is that they overlook the distinctive characteristic of this conception, which marks it out from other qualitative conceptions ; that is, its necessary reference to quantity, though not itself quantitative. If, by that process of abstraction which takes place when I com- pare objects similar in some of their qualities, I fix my attention upon the other qualities of any finite line, disre- garding its length and leaving out of view for the time being its limits, my conception is qualitative ; and yet it is not the conception of an infinite line. In this case, so far from affirming infinite length, I do not think of length at all. But in the case of an infinite line, I add to the former com- plex of qualities a new quality, possibility of quantity in general, not this or that quantity. When I try to bring before my mind the notion of an infinite line, what I am conscious of is this : I represent in imagination a line of indefinite length, and then run mentally along the line representing additional line-portions which proceeding would give so far, of course, only the finite ; but what makes my conception distinctively of the infinite is, that, in this progression, I proceed to fix my attention upon the progression itself, and eliminate by abstraction the limits to which such a progression is subject. I do not, be it marked, merely fix my attention upon other qualities of a line, abstracting from the notion of limits ; but I have in mind a progression, a possibility of ever-increasing quantity, and I abstract from the limits of this progression. The i conceptions are distinctly different, although both are quali- tative, and they should not be confounded with one another. The question, therefore, whether I can conceive an infinite line is identical with the question whether I can mentally grasp the usual qualities of a line and the notion of a con- tinuous increase in length, without including the notion of limits : and it will be seen that this question is simply one of the phases of the broader question which is concerned with the possibility of the concept or general notion. A certain complex of qualities being necessary to the existence