Key Arguments

• Besides God no substance is or can be conceived (Prop. xiv); nothing exists which is in itself and conceived through itself apart from God (Def. iii).
• Modes cannot be or be conceived without substance (Def. v); therefore they can only be in and conceived through the divine nature.
• Since substances and modes exhaust what exists (Ax. i), it follows that without God nothing can be, or be conceived.

Source Quotes

That extension and thought are either attributes of God or (by Ax. i.) accidents (affectiones) of the attributes of God. PROP. XV. 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. xiv.), that is (by Def. iii.) nothing which is in itself and is conceived through itself.

Proof.—Besides God, no substance is granted or can be conceived (by Prop. xiv.), that is (by Def. iii.) nothing which is in itself and is conceived through itself. But modes (by Def. v.) can neither be, nor be conceived without substance; wherefore they can only be in the divine nature, and can only through it be conceived. But substances and modes form the sum total of existence (by Ax. i.), therefore, without God nothing can be, or be conceived.

But modes (by Def. v.) can neither be, nor be conceived without substance; wherefore they can only be in the divine nature, and can only through it be conceived. But substances and modes form the sum total of existence (by Ax. i.), therefore, without God nothing can be, or be conceived. Q.E.D. Note.—Some assert that God, like a man, consists of body and mind, and is susceptible of passions.

Key Concepts

• PROP. XV. Whatsoever is, is in God, and without God nothing can be, or be conceived.
• But modes (by Def. v.) can neither be, nor be conceived without substance; wherefore they can only be in the divine nature, and can only through it be conceived.
• substances and modes form the sum total of existence (by Ax. i.), therefore, without God nothing can be, or be conceived.

Context

Ethics I, Prop. XV with proof (lines 170–303)