Page:Mind (New Series) Volume 12.djvu/214

 200 B. RUSSELL: similar, and corresponding terms are called simultaneous. (This is in fact the meaning of simultaneity.) Not only do the various series correspond term for term, but also all the parts of corresponding terms (each term being infinitely complex) correspond in the way required for interpreting the dictum that each monad mirrors the universe. Each term is what is called a momentary state of the monad ; the monad itself is the generating relation of the series. 1 Each state of a monad is composed of perception and appetition. The latter is an embodiment, in a confused manner suggested by the Calculus and the subject-predicate logic, of the generating relation of the series. The former is a belief in the existence of what are called phenomena the world of matter in time and space which however do not exist. Such in outline is the philosophy attributed to Leibniz. Except as regards appetition, there is, I think, no logical contradiction in this system. There is, however, an empirical fact which, unluckily for themselves, the supporters of the system cannot deny which is logically inconsistent with it ; and that is the fact that parts, at least, of the system have been believed. For the subjective theory of phenomena leads, with the doctrine of the correspondence of monads, to the conclusion that whatever has been or will be believed is false ; and a philosophy leading to this conclusion can only be true if no one advocates it. The conclusion will, of course, be denied by supporters of the theory ; but the conse- quence follows inevitably from the doctrine that " only indivisible substances and their various states are absolutely real " (Gerh., ii., 119), together with Dr. Cassirer's opinion that monads are not objects of either clear or confused perception. For it cannot be maintained that there is another sort of knowledge besides perception, unless at most in regard to God and the eternal truths. To distinguish other knowledge of what exists from perception, it would be necessary to define perception as causally related to its object a course which is inadmissible in a Leibnizian system. But innumerable grounds concur in making it improbable that the above were Leibniz's opinions. In the first place, the attempt to infer Monadism from Dynamics, which Dr. Cassirer attributes to Leibniz, would surely be absurd, if the phenomena with which Dynamics deals are not appearances of monads, but are a mere phantasmagoria in each monad. Solipsism is the legitimate out- come of such a theory. The plurality of monads must have either been deduced from phenomena, or assumed quite arbitrarily. 1 Dr. Cassirer sometimes speaks of the monad, as Leibniz himself does, as the law of the series ; sometimes (p. 538) as the general term of the series. But neither of these notions has the necessary precision : a law is merely a confused way of describing a relation, and as for the general term of a series, there is properly no such entity. When the general term is expressed mathematically as a function of a variable number, the expression indicates that the^ series is denned by a certain relation correlating its terms respectively with the various numbers.