Spinoza's Ethics Part 1, Proposition 13

by Corry Shores
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[the following is quotation; my summary and commentary is in brackets. The Latin text comes last.]

Baruch Spinoza

Ethics

Part I "Concerning God"

Proposition XIII:

Prop. XIII. Substance absolutely infinite is indivisible.

[A substance that is absolutely infinite cannot be divided.]

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. xii.) substance absolutely infinite could cease to exist, which (by Prop. xi.) is also absurd.

[If we could divide substance, its parts would either retain the nature of absolutely infinite substance or they would not retain its nature.

If they did retain its nature, then we would have many substances of the same nature, which is absurd. For, if they shared the same nature, conceiving one would be conceiving some essential characteristic of the other, but substances cannot be conceived through one another.

If however when we divide substance, its parts do not retain its nature, then substance might cease to exist, because if by dividing it up it loses its nature, and if it is in its nature to exist, then dividing it up causes substance not to exist, which is absurd, because God necessarily exists.]

Corollary.-It follows, that no substance, and consequently no extended substance, in so far as it is substance, is divisible.

[Because no substance is divisible, extended substance cannot be 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.

[Substance is infinite because nothing limits it. When we think of a part of substance, we are considering some finite part of it. And if it is a finite part of substance, then a finite substance results from the division. But we know that substances cannot be finite, because finite things are limited by other things, and nothing can limit substance, so we cannot divide infinite substance into finite parts.

So substance must be infinite, because it cannot be divided.]

From the original Latin:

PROPOSITIO XIII

Substantia absolute infinita est indivisibilis.

Demonstratio

Si enim divisibilis esset, partes, in quas divideretur, vel naturam substantiæ absolute infinitæ retinebunt, vel non. Si primum, dabuntur ergo plures substantiæ ejusdem naturæ, quod (per Prop. 5) est absurdum. Si secundum ponatur, ergo (ut supra) poterit substantia absolute infinita desinere esse, quod (per Prop. 11) est etiam absurdum.

Corollarium

Ex his sequitur, nullam substantiam, & consequenter nullam substantiam corpoream, quatenus substantia est, esse divisibilem.

Scholium

Quod substantia sit indivisibilis, simplicius ex hoc solo intelligitur, quod natura substantiæ non potest concipi, nisi infinita, & quod per partem substantiæ nihil aliud intelligi potest, quam substantia finita, quod (per Prop. 8) manifestam contradictionem implicat.

[*] Note: The text on this adelaide site says Prop.vii instead of Prop.xii, so I made the correction in the text above. The Latin says "ut supra", or, "as above." G.H.R. Partkinson adds in a footnote to his translation that this refers to the last sentence of proposition 12: "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." But as we see, this last sentence is based more fundamentally on Prop. vii, so the adelaide rendition works as well.]

From:

Deleuze, Gilles. Spinoza et le problème de l'expression. Paris: Les Éditions de Minuit, 1968.

Deleuze, Gilles. Expressionism in Philosophy: Spinoza. Trans. Martin Joughin. New York: Zone Books, 1990.

Spinoza. Ethics. Transl. Elwes. available online at:

http://ebooks.adelaide.edu.au/s/spinoza/benedict/ethics/index.html

Spinoza. Ethica. available online at:

http://www.hs-augsburg.de/~harsch/Chronologia/Lspost17/Spinoza/spi_eth