On the psychological processes by which meaning is acquired, see Stout, _Manual of Psychology_^3, bk. i. chap. 3; and on the apprehension of form, the same author’s _Analytic Psychology_, bk. i. chap. 3. Much interesting discussion of the difference between “external” and “internal” meaning will be found in Royce, _The World and the Individual_, First Series. Footnote 24: For some good observations on the fallacy of assuming that mathematical symbolism must always be interpretable, see B. Russell, _Foundations of Geometry_, p. 45-46; or Whitehead, _Universal Algebra_, vol. i p. 10 ff. For a further elaboration of the argument of the foregoing section I may refer to my _Problem of Conduct_, pp. 14-21. I need hardly warn the reader against confusing a “symbolic” concept in my sense of the word, _i.e._ one which cannot be fully interpreted in terms of direct experience, with a “symbolic” idea in Mr. Spencer’s sense, _i.e._ one which is not, psychologically, a copy of the presentations for which it stands. Our use of the word is, of course, purely logical, and has nothing to do with the psychological character of mental images, but only with their meaning. Footnote 25: Compare my _Problem of Conduct_, pp. 22-39. Footnote 26: The fundamental peculiarity of “inductive” procedure, in fact, is that, while its object is the internal analysis of its data, which, if completed, would permit of a universal conclusion being drawn from the single case, it is never able to effect the analysis, and is driven to reinforce it by external comparison with “similar” cases. Footnote 27: On the confusion between the metaphysical and psychological standpoint in Kant’s own treatment of the _a priori_, see B. Russell, _Foundations of Geometry_, pp. 1-4, and Adamson, _Development of Modern Philosophy_, bk. i. pp. 244-247. ----- CHAPTER III THE SUB-DIVISIONS OF METAPHYSICS § 1. The traditional sub-division of Metaphysics into _Ontology_, _Cosmology_, _Rational Psychology_, common to all the great modern constructive systems. § 2. Precise sense in which we adopt these divisions for the purposes of our own treatment of the subject. § 3. Relation of _Cosmology_ and _Rational Psychology_ to the empirical sciences.