In Prop. XI, where he attempts to prove the existence of only one substance of infinite attributes, he really proves only the existence of an infinite number of substances, or of an infinite number of attributes. The subsumption of these latter under unity is entirely unjustified by anything in the proposition. In scholium of Prop. X he seems to realize the difficulty of having an infinity of attributes belonging to one and the same substance, but attempts to escape from it by saying that nothing could be clearer than that the more reality or being anything has, the more attributes it must have, and hence a being absolutely infinite must have an infinity of attributes. This would be true if he had before proved that for substance, as he defines it, to have such a number was possible, or implied no contradiction. But he has not done this, and it may be shown in the following that he cannot. An attribute is that which constitutes the essence of substance. Hence, if there are two or more attributes (a fortiori, if an infinity) in the same substance, they must either constitute different essences, which is absurd, or the same essence, in which case they will be one and the same attribute. Two things only are possible to Spinoza. He may have either an infinite number of attributes existing in entire independence of each other, hence constituting an infinite number of substances ; or one infinite substance, with one infinite attribute. But to unite the two conceptions involves contradiction, as before shown. Yet this is what he does practically, using either, as the exigencies of the case require.
We now see Spinoza as a magician, supplied with his conjuring material. With two infinites — one the very negation of the finite, the other existing only in relation to the finite; with two substances — one with a number of attributes, the other with but one — he can proceed by dexterous substitutions to produce any required results before our astonished eyes.
This concludes our examination of Part First. We hope that our original statement regarding the existence of contradictions in the premises, and the introduction of new conceptions from without, will be seen to be justified. The contradiction is now seen to be this: In definitions three and four a substance is posited which can be conceived only, and, consequently, can exist only in itself, constituted by attributes necessarily existing in the same manner. But in the fifth we have the idea of something which can exist in
