Note (return) — Chapter V

The introduction of the idea of "the mathematical infinite" into metaphysical speculation, especially by Kant and Hamilton, with the design, it would seem, of transforming the idea of infinity into a sensuous conception, has generated innumerable paralogisms which disfigure the pages of their philosophical writings. This procedure is grounded in the common fallacy of supposing that infinity and quantity are compatible attributes, and susceptible of mathematical synthesis. This insidious and plausible error is ably refuted by a writer in the "North American Review." 219 We can not do better than transfer his argument to our pages in an abridged form.