pied with the realistic assumptions which lie had unconsciously derived from previous systems. In a similar way we may demonstrate that the hypothesis regarding determination to action or change must be false if we admit the previous conclusions. For they show that no attribute can change, or produce change, since it is eternal and immutable (Cor. 2, Prop. XX). And if a mode can change, the change must depend upon a change in some other mode, and so on in an infinite regression. That is, God could not produce the first change, which is absurd. Therefore, the hypothesis of change is absurd.
Prop. 5. One attribute cannot be produced by another.
Dem. For since they have nothing in common (Cor. 3, Prop, 3) they cannot be conceived through each other (Ax. 5), and, accordingly, one cannot be the cause of another (Ax. 4). Q. E. D.
Prop. 6. It belongs to the nature of attributes to exist.
For since one cannot be the cause of another (preceding Prop.), it must be its own cause — i. e. (Def. 1), it belongs to its nature to exist.
Cor. Attributes are eternal (preceding Prop, and Def. 8).
Prop. 7. An infinite number of attributes exist.
Dem. If you deny it, imagine, if you can, that there is not an infinite number. Then the essence of each will not include existence, which is absurd (Prop. 6). Therefore, the hypothesis is absurd, and an infinite number, etc.
Scholium. The reader will observe that this is precisely the argument of Spinoza in Prop. XXI regarding the existence of God.
Prop. 8. An infinite number of substances exist.
Dem. Proved like the previous proposition, or
Aliter. Since an infinite number of attributes exist, each of which constitutes the essence of substance (Def. 4), an infinite number of substances must exist.
Cor. God, or one substance with an infinite number of attributes, does not exist.
Scholium. The reader who may have been prepared for the demonstration that the existence of finite things was contradictory to the remainder of Spinoza's philosophy, will perhaps be surprised to see this denial of God's existence, and think that it may depend upon some trickery of words, and not be logically involved in Spinoza's premises. But that it is, may be shown, I think.
