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 infinite number, each of which gives expression to its essence, but of which two only fall within our knowledge. Among the innumerable divine attributes the human mind knows those only which it finds in itself, thought and extension. Although man beholds God only as thinking and extended substance, he yet has a clear and complete; an adequate--idea of God. Since each of the two attributes is conceived without the other, hence in itself (_per se_), they are distinct from each other _realiter_, and independent. God is absolutely infinite, the attributes only in their kind (_in suo genere_). How can the indeterminate possess properties? Are the attributes merely ascribed to substance by the understanding, or do they possess reality apart from the knowing subject? This question has given rise to much debate. According to Hegel and Ed. Erdmann the attributes are something external to substance, something brought into it by the understanding, forms of knowledge present in the beholder alone; substance itself is neither extended nor cogitative, but merely appears to the understanding under these determinations, without which the latter would be unable to cognize it. This "formalistic" interpretation, which, relying on a passage in a letter to De Vries (_Epist_. 27), explains the attributes as mere modes of intellectual apprehension, numbers Kuno Fischer among its opponents. As the one party holds to the first half of the definition, the other places the emphasis on the second half ("that which the _understanding_ perceives--as constituting the _essence_ of substance"). The attributes are more than mere modes of representation--they are real properties, which substance possesses even apart from an observer, nay, in which it consists; in Spinoza, moreover, "must be conceived" is the equivalent of "to be." Although this latter "realistic" party undoubtedly has the advantage over the former, which reads into Spinoza a subjectivism foreign to his system, they ought not to forget that the difference in interpretation has for its basis a conflict among the motives which control Spinoza's thinking. The reference of the attributes to the understanding, given in the definition, is not without significance. It sprang from the