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By Root 3099 0

as regards the relation of mind and matter, and as regards the number of substances. Descartes allowed three substances, God and mind and matter; Spinoza admitted God alone. For Descartes, extension is the essence of matter; for Spinoza, both extension and thought are attributes of God. Leibniz held that extension cannot be an attribute of a substance. His reason was that extension involves plurality, and can therefore only belong to an aggregate of substances; each single substance must be unextended. He believed, consequently, in an infinite number of substances, which he called 'monads'. Each of these would have some of the properties of a physical point, but only when viewed abstractly; in fact, each monad is a soul. This follows naturally from the rejection of extension as an attribute of substance; the only remaining possible essential attribute seemed to be thought. Thus Leibniz was led to deny the reality of matter, and to substitute an infinite family of souls.

The doctrine that substances cannot interact, which had been developed by Descartes' followers, was retained by Leibniz, and led to curious consequences. No two monads, he held, can ever have any causal relation to each other; when it seems as if they had, appearances are deceptive. Monads, as he expressed it, are 'windowless'. This led to two difficulties: one in dynamics, where bodies seem to affect each other, especially in impact; the other in relation to perception, which seems to be an effect of the perceived object upon the percipient. We will ignore the dynamical difficulty for the present, and consider only the question of perception. Leibniz held that every monad mirrors the universe, not because the universe affects it, but because God has given it a nature which spontaneously produces this result. There is a 'pre-established harmony' between the changes in one monad and those in another, which produces the semblance of interaction. This is obviously an extension of the two clocks, which strike at the same moment because each keeps perfect time. Leibniz has an infinite number of clocks, all arranged by the Creator to strike at the same instant, not because they affect each other, but because each is a perfectly accurate mechanism. To those who thought the pre-established harmony odd, Leibniz pointed out what admirable evidence is afforded of the existence of God.

Monads form a hierarchy, in which some are superior to others in the clearness and distinctness with which they mirror the universe. In all there is some degree of confusion in perception, but the amount of confusion varies according to the dignity of the monad concerned. A human body is entirely composed of monads, each of which is a soul, and each of which is immortal, but there is one dominant monad which is what is called the soul of the man of whose body it forms part. This monad is dominant, not only in the sense of having clearer perceptions than the others, but also in another sense. The changes in a human body (in ordinary circumstances) happen for the sake of the dominant monad: when my arm moves, the purpose served by the movement is in the dominant monad, i.e. my mind, not in the monads that compose my arm. This is the truth of what appears to common sense as the control of my will over my arm.

Space, as it appears to the senses, and as it is assumed in physics, is not real, but it has a real counterpart, namely the arrangement of the monads in a three-dimensional order according to the point of view from which they mirror the world. Each monad sees the world in a certain perspective peculiar to itself; in this sense we can speak, somewhat loosely, of the monad as having a spatial position.

Allowing ourselves this way of speaking, we can say that there is no such thing as a vacuum; every possible point of view is filled by one actual monad, and by only one. No two monads are exactly alike; this is Leibniz's principle of the 'identity of indiscernibles'.

In contrasting himself with Spinoza, Leibniz made much of the free will allowed in his system. He had a 'principle of