Propositions: 9-15, The existence of God

Proposition 9: The more reality or being a thing has, the greater the number of its attributes (Def. 4). Proposition 10: Each particular attribute of the one substance must be conceived through itself. Proof: An attribute is that which the intellect perceives of substance, as constituting its essence (Def. 4), and, therefore, must be conceived through itself (Def. 3). Q.E.D. Note: It is obvious that though two attributes are, in fact, conceived as distinct—that is, one without the help of the other—yet we cannot, therefore, conclude that they constitute two entities, or two different substances. Proposition 11: God, or substance, consisting of infinite attributes, of which each expresses eternal and infinite essentiality, necessarily exists. Proof: If this be denied, conceive, if possible, that God does not exist: then his essence does not involve existence. But this (Prop. 7) is absurd. Another proof: Of everything whatsoever a cause or reason must be assigned, either for its existence, or for its non-existence. e.g. if a triangle exist, a reason or cause must be granted for its existence. Another proof: The potentiality of non-existence is a negation of power, and contrariwise the potentiality of existence is a power, as is obvious. Note: In this last proof, I have purposely shown God's existence à posteriori, so that the proof might be more easily followed, not because, from the same premises, God's existence does not follow à priori. Proposition 12: No attribute of substance can be conceived from which it would follow that substance can be divided. Proof: The parts into which substance as thus conceived would be divided either will retain the nature of substance, or they will not. Proposition 13. Substance absolutely infinite is indivisible. Proof: If it could be divided, the parts into which it was divided would either retain the nature of absolutely infinite substance, or they would not. Corollary: It follows that no substance, and consequently no extended substance, in so far as it is substance, is divisible. Note: The indivisibility of substance may be more easily understood as follows. Proposition 14. Besides God, no substance can be granted or conceived. Proof: God is a being absolutely infinite. Corollary 1: Clearly, therefore: 1. God is one, that is (by Def. 6) only one substance can be granted in the universe, and that substance is absolutely infinite, as we have already indicated (in the note to Prop. 10). Corollary 2: It follows: 2. That extension and thought are either attributes of God or (by Axiom 1) accidents (affectiones) of the attributes of God.

Proposition 15: Whatsoever is, is in God, and without God nothing can be, or be conceived.

Proof: Besides God, no substance is granted or can be conceived (by Prop. 14), that is (by Def. 3) nothing which is in itself and is conceived through itself. Note: Some assert that God, like a man, consists of body and mind, and is susceptible of passions.