syllogism was, so far as it went, a process of this very kind; it brought a certain thought-law into contact with the special premises of each argument; and, by means of that general law, extracted the conclusion. To make Logic a more powerful instrument than it had hitherto been, what was needed was not, as Gratry seems to suggest, to import into it a new process, the process of faith; but to extend and make freer and more vigorous our use of that process; seeing that every syllogism is, so far as it goes, an act of faith in the general Laws of the Creative Logos. The Aristotelian Logic was, in fact, an Arithmetic of reasoning, analogous to such an Arithmetic of number as might be evolved by a race whose general knowledge of the Laws of Number amounted to familiarity with the "twice" column of the multiplication-table.
We may say then that what logicians had been seeking, though without quite knowing what they sought, was a Logic made wide and vigorous by using all attainable knowledge of the Laws of Thought as freely as, in working sums, we use our knowledge of the Laws of Number. Such a Logic, it need hardly be added, is yet to be created; though George Boole did a little towards laying its foundations. He brought to light three great principles of mental action:—
First, that all sound thinking treats the Universe of Thought as a Unity; and classes of things as fractions of Unity; and that Unity itself as a fraction of a larger Unity.
Secondly, that we cannot deal logically with any statement except by comparing it impartially with the opposite statement.
