At an early period Herbart had become impressed with the necessity of applying mathematics to psychology(29). To the usual objection, that psychical facts do not admit of measurement, he had a ready reply. We can calculate even on hypothetical assumptions: indeed, could we measure, we should scarcely take the trouble to calculate(30). To calculate (i.e. to deduce mathematically) is to perform a general experiment, and to perform it in the medium where there is least likelihood of error or disturbance. There may be anomalies enough apparent in the mental life: there may be the great anomalies of Genius and of Freedom of Will; but the Newton and the Kepler of psychology will show by calculation on assumed conditions of psychic nature that these aberrations can be explained by mechanical laws. “The human Soul is no puppet-theatre: our wishes and resolutions are no marionettes: no juggler stands behind; but our true and proper life lies in our volition, and this life has its rule not outside, but in itself: it has its own purely mental rule, by no means borrowed from the material world. But this rule is in it sure and fixed; and on account of this its fixed quality it has more similarity to (what is otherwise heterogeneous) the laws of impact and pressure than to the marvels of an alleged inexplicable freedom(31).” Psychology then deals with a real, which exhibits phenomena analogous in several respects to those discussed by statics and mechanics. Its foundation is a statics and mechanics of the Soul,—as this real is called. We begin by presupposing as the ultimate reality, underlying the factitious and generally imperfect unity of self-consciousness and mind, an essential and primary unity—the unity of an absolutely simple or individual point of being—a real point which amongst other points asserts itself, maintains itself. It has a character of its own, but that character it only shows in and through a development conditioned by external influences. The specific nature of the soul-reality is to be representative, to produce, or manifest itself in, ideas (_Vorstellungen_). But the character only emerges into actuality in the conflict of the soul-atom with other ultimate realities in the congregation of things. A soul _per se_ or isolated is not possessed of ideas. It is merely blank, undeveloped, formal unity, of which nothing can be said. But like other realities it defines and characterises itself by antithesis, by resistance: it shows what it is by its behaviour in the struggle for existence. It acts in self-defence: and its peculiar style or weapon of self-defence is an idea or representation. The way the Soul maintains itself is by turning the assailant into an idea(32): and each idea is therefore a _Selbsterhaltung_ of the Soul. The Soul is thus enriched—to appearance or incidentally: and the assailant is annexed. In this way the one Soul may develop or evolve or express an innumerable