22 Dec 2008

Spinoza's Ethics Part 1, Proposition 12

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


Part I "Concerning God"

Proposition XII:

Prop. XII. No attribute of substance can be conceived from which it would follow that substance can be divided.

[It follows from none of substance's attributes that substance is divisible.]

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.

[If we divided substance, its parts would either retain or not retain its nature.

Substance exists by definition, and there can only be one substance, because if there were more than one, they would share in common that they are all self-caused. But if substances have something in common, then to think one is to conceive what characterizes the other, which contradicts substance's definition as being self-conceivable. So there is only one substance.

That one substance is either finite or infinite. Since there is nothing else of its kind, nothing else limits it, hence it is unlimited and infinite.

So it is in the nature of substance to be infinite. So if one of its divided parts shares in its nature, that part must be infinite as well.

Also, it is in substance's nature to be self-caused; for, if there is nothing else of its kind, nothing else could cause it. And it exists by necessity. So it must be its own cause of existence. Hence any divided part of substance which retains its nature will also be self-caused.

But we also said that there cannot be more than one substance with the same attribute, so if substance is divided into parts sharing in its nature, they must have different attributes. Thus there would be more than one substance. But that is absurd.

Furthermore, if the divided parts of substance shared in substance's nature, they could not share the same attributes as their whole, for they all would be substances; and this is absurd. Also, if they had different attributes which are solely self-conceivable, then we could conceive the whole without conceiving its parts, which is also absurd.

Thus it cannot be that if we divide substance its parts retain its nature.

But if we supposed that when we divide substance that its parts do not retain its nature, then that means the substance which was divided ceased to exist, which contradicts its necessity of existence.

So substance cannot be divided.]

From the Latin:

Nullum substantiæ attributum potest vere concipi, ex quo sequatur, substantiam posse dividi.
Partes enim, in quas substantia, sic concepta, divideretur, vel naturam substantiæ retinebunt, vel non. Si primum, tum (per Prop. 8) unaquæque pars debebit esse infinita, & (per Prop. 6) causa sui, & (per Prop. 5) constare debebit ex diverso attributo, adeoque ex una substantia plures constitui poterunt, quod (per Prop. 6) est absurdum. Adde, quod partes (per Prop. 2) nihil commune cum suo toto haberent, & totum (per Defin. 4 & Prop. 10) absque suis partibus, & esse, & concipi posset, quod absurdum esse, nemo dubitare poterit. Si autem secundum ponatur, quod scilicet partes naturam substantiæ non retinebunt; ergo, cum tota substantia in æquales partes esset divisa, naturam substantiæ amitteret, & esse desineret, quod (per Prop. 7) est absurdum.


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