2014 年 2014 巻 65 号 p. 56-72_L6
The infinite was a common metaphysical concern of Spinoza and Leibniz. According to the Aristotelian definition the infinite that always has “something outside it” has only potential existence while the infinite that has “nothing outside it”could have no actual existence, since something that has nothing outside it must be complete and a limited whole. Both Spinoza and Leibniz made an attempt to conceive the former actually infinite in virtue of the latter Eleatic infinite, though in quite different manners. Leibnizian solution to the problem consists in integrating the infinite series of details of the world into a perspectival view from a “metaphysical point”, a Monad. Each Monad, a simple substance unique, is complete and whole yet infinite in that it expresses the infinite details of the whole universe in its spacial and temporal perspective. Godʼs perspective is like a overhead view that integrates the infinitely many Monadʼs views. Spinozaʼs solution on the other hand consists in making infinite causal chains of individuals into the infinite mode of a substance, God or Nature, which is infinite itself in that it has nothing outside it. The contrast is striking. Like infinite series in mathematics leibnizian series converge at the point at infinity so as to make up a consistent whole （the sufficient reason which is outside the series） while spinozan infinite series stand by themselves and have no need for outside, for the actual infinite series of individuals are produced in such a way that an individual is determined to exist and produce an effect by another, which again is determined to exist and produce an effect by another, ... et sic in infinitum. Spinoza identifies as Godʼs actually infinite intellect the actual infinite series of ideas strictly identical to the series of individuals. Spinozan God has no overhead view nor memory in producing by its necessity infinite sequences, whose actual necessary existence Spinoza calls aeternitas. This was surely a disconcerting system for Leibniz who held God as the warrant for the identity of the actual world as the best possible world He had chosen.