“For years I have used my nose for smelling. Have I, then, actually a right to it that can be proved?” Indeed it seems to me that the logical method is hereby reduced to absurdity. Yet it is just through the controversies about this, together with the vain attempts to prove what is _directly_ certain as merely _indirectly_ certain, that the self-sufficingness and clearness of intuitive evidence appears in contrast with the uselessness and difficulty of logical proof—a contrast which is no less instructive than amusing. The direct certainty is not allowed to be valid here, because it is no mere logical certainty following from the conceptions, thus resting only upon the relation of the predicate to the subject, according to the principle of contradiction. That axiom, however, is a synthetical proposition _a priori_, and as such has the guarantee of pure, not empirical, perception, which is just as immediate and certain as the principle of contradiction itself, from which all demonstrations first derive their certainty. Ultimately this holds good of every geometrical theorem, and it is quite arbitrary where we draw the line between what is directly certain and what has first to be demonstrated. It surprises me that the eighth axiom is not rather attacked. “Figures which coincide with each other are equal to each other.” For “coinciding with each other” is either a mere tautology or something purely empirical which does not belong to pure perception but to external sensuous experience. It presupposes that the figures may be moved; but only matter is movable in space. Therefore this appeal to coincidence leaves pure space—the one element of geometry—in order to pass over to what is material and empirical.