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12 6 DE VELOPMENT OF CAR TESIANISM. the demand to think the existence of things in substance as a following from substance, and their procession from God as a remaining in him. He refers us to mathematics : the things which make up the world are related to God as the properties of a geometrical figure to its concepts, as theo- rems to the axiom, as the deduction to the principle, which from eternity contains all that follows from it and retains this even while putting it forth. It cannot be doubted that such a view of causality contains error, — it has been char- acterized as a confusion of ratio and causa, of logical ground, and real cause, — but it is just as certain that Spinoza com-j mitted it. He not only compares the dependence of the effect on its cause to the dependence of a derivative prin- ciple on that from which it is derived, but fully equates the two; he thinks that in logico-mathematical "con- sequences" he has grasped the essence of real "effects": for him the type of all legality, as also of real becoming, was the necessity which governs the sequence of mathe- matical truths, and which, on the one hand, is even and still, needing no special exertion of volitional energy, while, on the other, it is rigid and unyielding, exalted above all choice. Philosophy had sought the assistance of mathe- matics because of the clearness and certainty which dis- tinguish the conclusions of the latter, and which she wished to obtain for her own. In excess of zeal she was not content with striving after this ideal of indefectible certi- tude, but, forgetting the diversity of the two fields, strove to imitate other qualities which are not transferable ; instead of learning from mathematics she became sub- servient to it. Substance does not affect us by its mere existence, but through an Attribute. By attribute is meant, according to the fourth definition, " that which the understanding per- ceives of substance as constituting the essence of it " {quod intellectus de substantia percipit, tanquani ejusdem essentiam constituens). The more reality a substance contains, the more attributes it has ; consequently infinite substance possesses an infinite number, each of which gives expres- sion to its essence, but of which two only fall within our knowledge. Among the innumerable divine attributes the