An ultimate principle has been defined as one which is presupposed in every attempt to account for it. The functional finalities of which I speak bear the test of this definition. The upshot of it all is that the constitutive principles of the human mind cannot be explained or understood, but can nevertheless be verified. And verification, in the last analysis, means exemplification. If we look at these ultimate truths, whether in geometry, in physics, or, as we shall later see, in ethics and æsthetics, as enunciated abstractly, baldly, we confront them blankly, we are as it were dumbfounded in their presence. They seem arbitrarily imposed upon us. And why? Because we are endeavoring to understand them. We have acquired the habit of trying to get hold of truth by referring back to some antecedent. And therefore we are uneasy and disconcerted. But the moment we see them exemplified, as in the constructions of the geometer, in the laws or uniformities established by the physicist, etc., we are convinced. The subject-matter of ethics is different. The kind of exemplification is likewise different. But verification is exemplification in ethics as elsewhere; and this will be found to mean that the life, the ethical experience, must lead to the certainty. And now we have reached the point where a brief discussion of the ethical manifold and its mode of unification comes up in proper order. FOOTNOTES: [26] To rate anyone as an end _per se_ means that in a world conceived as perfect his existence would be indispensable. The world we know may not be perfect, is not perfect, but we do conceive of an ideal world that is. And to ascribe to anyone the quality of worth, to denominate him an end _per se_, is to place him into that world, to regard him as potentially a member of it. [27] For a creature endowed with different senses, and having a mind unlike our own, the world would be a totally different world. [28] To deny such _a priori_ knowledge of the object called God is not to deny that the production of this object is due to constructive principles of human thinking; while, in turn, to assert the functional derivation of the God-idea is not to validate that idea itself as permanent and inexpugnable. It may have owed its origin to a permanent disposition of the mind, and yet be fallible because of the historical conditions under which it arose and the defective data in which it was expressed. By way of illustration we might apply the same reflection to the Ptolemaic astronomy. The mathematical processes by which this astronomy was constructed may be traced to permanent singularities of human thinking, yet the astronomical theory of Ptolemy is not on that account _a priori_ true.