For a full reply, given by implication, I must refer Prof. Bain to § 56 of _The Principles of Psychology_, where I have contended that “while, under its objective aspect, Psychology is to be classed as one of the Concrete Sciences which successively decrease in scope as they increase in speciality; under its subjective aspect, Psychology is a totally unique science, independent of, and antithetically opposed to, all other sciences whatever.” A pure idealist will not, I suppose, recognize this distinction; but to every one else it must, I should think, be obvious that the science of subjective existences is the correlative of all the sciences of objective existences; and is as absolutely marked off from them as subject is from object. Objective Psychology, which I class among the Concrete Sciences, is purely synthetic, so long as it is limited, like the other sciences, to objective data; though great aid in the interpretation of these data is derived from the observed correspondence between the phenomena of Objective Psychology as presented in other beings and the phenomena of Subjective Psychology as presented in one’s own consciousness. Now it is Subjective Psychology only which is analytic, and which affords aid in the {106} development of Logic. This being explained, the apparent incongruity disappears. A difficulty raised respecting the manner in which I have expressed the nature of Mathematics, may next be dealt with. Prof. Bain writes:― “In the first place, objection may be taken to his language, in discussing the extreme Abstract Sciences, when he speaks of the _empty_ _forms_ therein considered. To call Space and Time empty forms, must mean that they can be thought of without any concrete embodiment whatsoever; that one can think of Time, as a pure abstraction, without having in one’s mind any concrete succession. Now, this doctrine is in the last degree questionable.”