"Arithmetic is the science of the Evaluation of Functions, Algebra is the science of the Transformation of Functions."

““Either, then, we must carry out our modern moral conception of God's nature and government into a conception of creation that matches it — a conception based on that eternity of man which alone can mean moral freedom — or else, in all honesty and good logic, we ought to travel penitently back to a Calvinism, a Scotism, an Augustinianism, of the so-called "highest" type. Then we would view man as a "creature" indeed. We should have to accept him as a being belonging to time only, with a definite date of beginning, though lasting through unceasing ages, if that could indeed then be. We should have to surrender all freedom for him as a delusion. In effect, with this conception of creation, we must return to an unmitigated Predestinationism. Nor may this stop short of foreordination to Reprobation as well as to Election — a foreordination not simply "supralapsarian," but precedent to creation itself. The separation of the Sheep from the Goats must be from "before the foundation of the world," and the Elect must be created "unto life everlasting," while the reprobate are created "unto shame and everlasting contempt.”

““Idealism is constituted by the metaphysical value it sets upon ideals, not by the aesthetic or the ethical, and rather by its method of putting them on the throne of things than by the mere intent to have them there. It is always distinct from mysticism , and still more so from voluntarism. Its method is, at bottom, to vindicate the human ideals by showing them to be not merely ideals but realities, and to effect this by exhibiting conscious being as the only absolute reality;”

““When we say that the mind is a function of the brain, we are therefore to understand that in exact scientific truth we can mean nothing more than this: That physical and physiological changes go on, seriatim, side by side with changes in psychic experience; or vice versa, that psychic changes run parallel, pari passu, with physiological changes in the brain and the other neural tissues.”

““For the ultimate and real meaning of the argument is, that a soul or mind or person, purely as such, is itself the fountain of its percipient experience, and so possesses what has been happily named "life in itself." Proof of the presence in us of a priori or spontaneous cognition, then, is proof of just this self-causative life.”

““So far from holding God to be finite, I hold, and in the book clearly teach, that all minds are infinite , and God preeminently so. . Eternity, self-existence, self-activity, freedom, and infinity are to me all interchangeable terms, and are so treated wherever they turn up in the course of the book. My reviewer falls into a non sequitur when he concludes that I make God finite because I make him one of a community of spirits, each absolutely real; not God's finitude, but his definiteness, is what follows from that. This confusion of the definite with the finite is very common, and is the explanation of two tendencies in sceptical thinking — the tendency to deny the personality of God, whose infinity is supposed to mean his utter indefiniteness, and the tendency, in recoil from the former, to assert God's finitude in order to save his personality, which of course must be definite. But the true infinite, as distinguished from the pseudo-infinite, the infinite of quality in contrast to the infinite of quantity, is entirely definite; more definite, indeed, than any finite can be.”

““Natural science must therefore, in truth, be declared silent on this question of pantheism; as indeed it is, and from the nature of the case must be, upon all theories of the supersensible alike — theistic, deistic, atheistic, pantheistic. Natural science has no proper concern with such theories.”