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End towards which they are all tending, and the Per- fection which they^ are all striving to attain.

(3) Law ofComnuity. — From the description of the monads dven above, it is clear that all kinds and con- ditions of created things shade off by gradual differ- ences, the lower appearing to be merely an inferior degree of the higher. There are no " breaks " in the continuity of nature, no "gaps" between mineral, plant, animal, and man. The counter-view is the law of indiscernibles. There can be no meaningless duplication in nature. No two monads can be ex- actly alike. No two objects, no two events can be en- tirely similar, for, if they were, they would not, Leib- niz thinks, be two but one. The apphcation of these principles led Leibniz to adopt the view that, while every thing differs from every other thing, there are no true opposites. Rest, for instance, mav be con- sidered as mfinitely minute motion; the fluid is a solid with a lower degree of solidity;* animals are men with infinitelv small reason, and so forth. The application to the theory of the differential calculus is obvious.

(4) Optimism, — In the centre of the vast harmo- nious svstem of monads which we call the universe is God, the original, infinite monad. His power. His wisdom. His goodness are infinite. When, therefore. He created the system of monads. He created them as good as they could possibly be, and established among them the best possible kind of harmony. The world, therefore, is the best possible world, and the supreme law of finite being is the lex mdioris. The Will of God must realize what His understanding recognizes as more perfect. Leibniz represents the possible monads as present for all eternity in the mind of God; in them was the impulse towards actualization; and the more perfect the possible monad the more strongly did it possess this impulse.* There went on, therefore, so to speak, a competition before the throne of God, in which the best monads conauered, and, as God could not but see that they were the best, He could not but will their realization. Behind the lex melioris is, therefore, a more fundamental law, the law of suffi- cient reason, which is that '* things or events are real when there is a sufficient reason for their existence." This is a fundamental law of thought, as well as a primary law of being.

The four doctrines here outlined may be said to siun up Leibniz's metaphysical teaching. They find their principal application in his psychology and his the- odicy.

(5) Psychology. — In the " Nouveaux Essais ". which were written in refutation of Locke's " Essay, Leib- nix develops his doctrines regarding the human soul and the origin and nature of knowledge. The power of representation, which is common to all monads, makes its first appearance in souls as perception. Percep- tion, when it reaches the level of consciousness, b^ comes apperception. The Cartesians "have fallen into a serious error in that they treat as non-existent those perceptions of which we are not conscious." Perception is found in all monads; in those monads which we call souls there is apperception, but there is a large subconscious region of souls in which there are p«roeptions. Perceptions are the source of appercep- tions. They are the source also of volitions, because impulse, or appetite, is nothing but the tendency of one perception towards another. From percep- tion, therefore, which is found in everything, up to intelligenoe and volition, which are peculiar to man, there are imperceptibly small grades of differentiation.

Whence, then, come our ideas? The question is al- readv answered in Leibniz's general principles. Since intelligence is only a differentiation of that immanent action which all monads possess, our ideas must be the result of the self-activity of the monad called the human soul. The soul has "no doors or windows" towards the side facing the external world. No ideas come from that direction. All our ideas are in-

nate. The Aristotelian maxim, "there is nothing in the intellect that was not previously in the senses," must be amended by the aadition of the phrase, "ex- cept the intellect itself". The intellect is the source as well as the subject of all our ideas. These ideas, how- ever subjective tneir origin, have objective value, be- cause, by virtue of the harmony pre-estabUshed irom the beginning of the universe, the evolution of the psychic monad from virtual to actual knowledge is paralleled by the evolution in the outside world of the physical monad from virtual to actual activity.

Leibniz has no difiicultv in establishing the inmia- terialitv of the soul. All monads are immaterial, or rather, partlv immaterial and partly material. The human soul is no exception; its '^ immaterial- ity" is not absolute, but only relative, in the sense that in it the region of clear representation is so much greater than the re^on of ODScure representa- tion that the latter is practically a negligible quantity. Similarly, the immortality of the human soul is not, absolutely speaking, a unique privilege. All monads are immortal. Each monad being an independent, self-active, source of action, neither dependent on other monads nor influenced by them, it can continue acting without interference forever. The human soul is peculiar in this,' that its consciousness (appereep- tion) enables it to realize this independence, and therefore the soul's consciousness of its immortcdity is what makes human immortality to be different from every other immortality.

(6) Theodicy.— The work entitled "Th^dic^", a treatise on natural theology, was intended as a refuta- tion of the Encyclopaedist, Bayle, who had tried to show that reason and faith are incompatible. In it Leibniz takes up: (a) the existence of God (b) the problem of evil, and (c) the question of optimism.

(a) Existence of God. — Leibniz, true to his eclectic temperament, admits the validity of all the various argiiments for the existence of God. He adduces the argument from the contingency of finite being, recasts the ontological argument used by Descartes (see God), and adds the argument from the nature of the necessitv of our ideas. The third of these ar^- ments is really Platonic in its origin. Its validity de- pends on the fact that our ideas are necessary, not merely in a hypothetical, but in an absolute and cate- gorical sense, and on the further contention that a necessity of that kind cannot be explained unless we grant that an absolutely necessary Being exists.

(b) Problem of Evil. — This problem is mscussed at length in the "Th^odic^" and in many of Leibniz's letters. The law of continuity requires that there be no abrupt differences among monads. God, there- fore, although He wished to create the best possible world, and did, in fact, create the best world that was in se possible, could not create monads which were all perfect, each in its own kind. He was imder no ne- cessity of His own Nature, but He was obliged, as it were, by the terms of the problem, to lead up to per- fection oy passing through various degrees of imper- fection. Leibniz distinguishes metaphysical evil, which is mere finiteness, or imperfection in general, physical evilf which is suffering, and moral evil, which is sin. God permits these to exist, since the nature of the uni- verse demands varie^ and gradation, but He re- duces them to the minimum, and makes them to serve a higher purpose, the beauty and harmony of creation as a whwe. Leibniz faces resolutely the problem of reconciling the existence of evil with the goodness and omm'potence of God. He reminds us that we see only a part of God's creation, that part, namely, which is nearest to ourselves, and, for tnat reason, makes the largest demand on our sympathy. We should learn, he says, to look beyond our own immediate environ- ment, io observe the larger and more perfect world above us. Where our sympathies are involved, we should not allow the prevalence of evil to overpower