one thing from another, hence what it is not, expresses a limitation of it.  Consequently God, who is free from every negation and limitation, is to be conceived as the absolutely indeterminate.  The results thus far reached run:  Substantia una infinita—­Deus sive natura—­causa sui (aeterna) et rerum (immanens)—­libera necessitas—­non determinata.  Or more briefly:  Substance = God = nature.  The equation of God and substance had been announced by Descartes, but not adhered to, while Bruno had approached the equation of God and nature—­Spinoza decisively completes both and combines them.

A further remark may be added concerning the relation of God and the world.  In calling the infinite at once the permanent essence of things and their producing cause, Spinoza raises a demand which it is not easy to fulfill, 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 theorems 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 characterized as a confusion of ratio and causa, of logical ground and real cause,—­but it is just as certain that Spinoza committed it.  He not only compares the dependence of the effect on its cause to the dependence of a derivative principle on that from which it is derived, but fully equates the two; he thinks that in logico-mathematical “consequences” 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 mathematical 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 mathematics because of the clearness and certainty which distinguish 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 certitude, but, forgetting the diversity of the two fields, strove to imitate other qualities which are not transferable; instead of learning from mathematics she became subservient 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 perceives of substance as constituting the essence of it” (quod intellectus de substantia percipit, tanquam ejusdem essentiam constituens).  The more reality a substance contains, the more attributes it has; consequently infinite substance possesses an