Ethics — Part 1

by Benedictus de Spinoza

XII. 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. If the former, then (by Prop. viii.) each part will necessarily be infinite, and (by Prop vi.) self-caused, and (by Prop. v.) will perforce consist of a different attribute, so that, in that case, several substances could be formed out of one substance, which (by Prop. vi.) is absurd. Moreover, the parts (by Prop. ii.) would have nothing in common with their whole, and the whole (by Def. iv. and Prop. X) could both exist and be conceived without its parts, which everyone will admit to be absurd. If we adopt the second alternative—namely, that the parts will not retain the nature of substance—then, if the whole substance were divided into equal parts, it would lose the nature of substance, and would cease to exist, which (by Prop. vii.) is absurd.

XIII. 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. If the former, we should have several substances of the same nature, which (by Prop. v.) is absurd. If the latter, then (by Prop. vii.) substance absolutely infinite could cease to exist, which (by Prop. xi.) is also absurd.

<<<<<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. 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.

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. 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. That extension and thought are either attributes of God or (by Ax. i.) accidents ("affectiones") of the attributes of God.