Key Arguments

• Being absolutely infinite, God has no attribute of substance denied to him (Def. vi) and necessarily exists (Prop. xi); if another substance existed, it would be explained by some attribute of God, yielding two substances with the same attribute (contrary to Prop. v).
• If any other substance could be conceived, it would have to be conceived as existent, which the proof shows to be absurd.
• Corollary I: Only one substance can be granted in the universe, and that is absolutely infinite (God).
• Corollary II: Extension and thought are either attributes of God or accidents (affectiones) of his attributes.

Source Quotes

The nature of substance can only be conceived as infinite, and by a part of substance, nothing else can be understood than finite substance, which (by Prop. viii) involves a manifest contradiction. PROP. XIV. Besides God no substance can be granted or conceived. Proof.—As God is a being absolutely infinite, of whom no attribute that expresses the essence of substance can be denied (by Def. vi.), and he necessarily exists (by Prop. xi.); if any substance besides God were granted, it would have to be explained by some attribute of God, and thus two substances with the same attribute would exist, which (by Prop. v.) is absurd; therefore, besides God no substance can be granted, or, consequently, be conceived.

Besides God no substance can be granted or conceived. Proof.—As God is a being absolutely infinite, of whom no attribute that expresses the essence of substance can be denied (by Def. vi.), and he necessarily exists (by Prop. xi.); if any substance besides God were granted, it would have to be explained by some attribute of God, and thus two substances with the same attribute would exist, which (by Prop. v.) is absurd; therefore, besides God no substance can be granted, or, consequently, be conceived. If it could be conceived, it would necessarily have to be conceived as existent; but this (by the first part of this proof) is absurd.

Therefore, besides God no substance can be granted or conceived. Q.E.D. Corollary I.—Clearly, therefore: 1. God is one, that is (by Def. vi.) 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. x.). Corollary II.—It follows: 2.

God is one, that is (by Def. vi.) 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. x.). Corollary II.—It follows: 2. That extension and thought are either attributes of God or (by Ax. i.) accidents (affectiones) of the attributes of God. PROP.

Key Concepts

• PROP. XIV. Besides God no substance can be granted or conceived.
• if any substance besides God were granted, it would have to be explained by some attribute of God, and thus two substances with the same attribute would exist, which (by Prop. v.) is absurd;
• Corollary I.—Clearly, therefore: 1. God is one, that is (by Def. vi.) 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. x.).
• Corollary II.—It follows: 2. That extension and thought are either attributes of God or (by Ax. i.) accidents (affectiones) of the attributes of God.

Context

Ethics I, Prop. XIV with proof and Corollaries I–II (lines 170–303)