The fundamental defect in Professor Royce’s reasoning seems to me to lie in the tacit transition from the notion of an infinite _series_ to that of an infinite completed _sum_. Thus he speaks of the series of prime numbers as a “whole” being present at once to the mind of God. But are the prime numbers, or any other infinite series, an actual sum at all? They are surely not proved to be so by the existence of general truths about any prime number. Footnote 95: See, _e.g._, Dedekind, _op. cit._, § 2: “It frequently happens that different things _a_, _b_, _c_ ... are apprehended upon whatsoever occasion under a common point of view, mentally put together, and it is then said that they form a _system_; the things _a_, _b_, _c_ ... are named the _elements_ of the system”; and § 3 (definitions of _whole_ and _part_). Footnote 96: _Ante_, Bk. II. chap. 2, § 5. Footnote 97: It is no answer to this view to urge that as soon as the intellect undertakes to reflect upon and describe Reality it unavoidably does so in relational terms. For it is our contention that the same intellect which uses these relational methods sees _why_ they are inadequate, and to some extent at least how they are ultimately merged in a higher type of experience. Thus the systematic use of the intellect in Metaphysics itself leads to the conviction that the mere intellect is not the whole of Reality. Or, in still more paradoxical language, the highest truth for the mere intellect is the thought of Reality as an ordered system. But all such order is based in the end on the number-series with its category of whole and part, and cannot, therefore, be a perfectly adequate representation of a supra-relational Reality. Hence Truth, from its own nature, can never be quite the same thing as Reality. Footnote 98: Or does Dr. Stout merely mean that there may be a hat and a head, and also a relation of on and under (_e.g._, between the _hat_ and the _peg_), and yet my hat not be on my head? If this is his meaning, I reply we have not really got the _relation_ and its _terms_; if the hat is not on the head, hat and head are not terms in the relation at all. I do not see why, on his own principles, Dr. Stout should not add a fourth factor to his analysis, namely, qualified_ness_, or the fact that the qualities are there, and so on indefinitely. Footnote 99: