Page:Mind (Old Series) Volume 11.djvu/197

III. CONCEIVABILITY AND THE INFINITE. By Professor GEORGE S. FULLERTON. IN an examination of the mathematical antinomies printed in the Journal of Speculative Philosophy for January, 1884, I found a solution of those much-mooted problems in the elimination of a contradictory element the quantitative which had been inadvertently introduced into our notion of infinity. It was shown that the antinomies arise from the attempt to know the infinite as a whole ; that the word ' whole ' has necessary reference to limits beyond which there is no more of any object ; and that, consequently, the attempt to know all of an infinite is simply an attempt to find the limits of the limitless. It follows, of course, that the infinite is not to be known by a successive synthesis of parts, i.e., by exhausting a quantity ; but that, if it is to be known at all, it must be known in some other way. The mathematical antinomies of Kant and Hamilton, reasserted more lately by Mr. Herbert Spencer, when regarded from this stand-point, are disposed of very satisfactorily, and simply disappear ; but the question may still be raised whether our notion of infinity does not disappear with them, that is, whether proving the contradictory nature of the quantitative infinite does not simply prove that we have no notion of the infinite whatever, and that our supposed dis- cussions as to infinites are really concerned only with more or less disguised indefinites. This position is not a very sensible one to take, to be sure : for, when a man says of any given object that it is not infinite but indefinite, we usually expect him to know what ' infinite ' means, which would intimate that he brought the conception of the infinite before his mind in some way thought it ; and the negative quality of his proposition would imply a true distinction between the conception thus thought and that of the inde- finite. But the frequency with which this position is taken, and the confidence with which it is asserted that, the quan- titative infinite being proved self-contradictory and the qualitative being inconceivable, we can have no knowledge of the infinite at all, make it desirable that the exact elements of the conception be carefully separated and exhibited, and that it be shown as it can be that the conception of an infinite is qualitative, is perfectly conceivable, and that the