knowledge of mathematics; each has within himself as absolute a personal conviction of the validity of the processes by which he works out his results, as if those processes were purely syllogistic. None the less is that conviction arrived at by a mode of mental action essentially of the same nature as that far more vigorous and sustained mental exercise by which we arrive at a sound and rational faith in God.
"Reasoning is not one process only, it contains two processes, equally valid ; but the second is by far the most powerful and most fertile. The syllogistic process deduces, passing from like to like. It never leaves its original stand-point; it never rises above that stand-point. It develops what it originally possessed. The other process, the dialectic, rises above its own starting-point; it does not merely develop the material which it originally possessed, it acquires fresh material. . . . This process passes from the finite to the Infinite. . . . This is the process of prayer. . . .Whence it follows that the human mind is capable of a process which, when it is taught as a part of Logic, will give wings to Logic which before had only feet. . . . The Logic of the highest philosophers, both practical and theoretical, has always had wings. But the class of average thinkers exerts itself chiefly in trying to cut those wings, and seems to have succeeded. They must learn to recognize their error, or rather their crime." The author then quotes the following passage from Cournot:—"The process by which the mind seizes new truths is often quite distinct from that by which it connects known truths together; and most important truths have been first seen by the help of that philosophic sense which precedes rigorous
