susceptible of explanation at all—is at length seen to be at every point thoroughly explicable, provided we only yield our assent to what? To an hypothesis? Why if an hypothesis—if the merest hypothesis—if an hypothesis for whose assumption—as in the case of that pure hypothesis the Newtonian law itself—no shadow of à priori reason could be assigned—if an hypothesis, even so absolute as all this implies, would enable us to perceive a principle for the Newtonian law—would enable us to understand as satisfied, conditions so miraculously—so ineffably complex and seemingly irreconcileable as those involved in the relations of which Gravity tells us,—what rational being could so expose his fatuity as to call even this absolute hypothesis an hypothesis any longer—unless, indeed, he were to persist in so calling it, with the understanding that he did so, simply for the sake of consistency in words?
But what is the true state of our present case? What is the fact? Not only that is not an hypothesis which we are required to adopt, in order to admit the principle at issue explained, but that it is a logical conclusion which we are requested not to adopt if we can avoid it—which we are simply invited to deny if we can:—a conclusion of so accurate a logicality that to dispute it would be the effort—to doubt its validity, beyond our power:—a conclusion from which we see no mode of escape, turn as we will; a result which confronts us either at the end of an inductive journey from the phænomena of the very Law discussed, or at the close of a deductive career from the most rigorously simple of all conceivable assumptions—the assumption, in a word, of Simplicity itself.
And if here, for the mere sake of cavilling, it be urged, that although my starting-point is, as I assert, the assumption of absolute Simplicity, yet Simplicity, considered merely in itself, is no axiom; and that only deductions from axioms are indisputable—it is thus that I reply:—
Every other science than Logic is the science of certain concrete relations. Arithmetic, for example, is the science of the relations of number—Geometry, of the relations of form—Mathematics in general, of the relations of quantity in general—of whatever can be increased or diminished. Logic, however, is the science of
