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21 Dec 2008

Spinoza's Ethics Part 1, Proposition 14

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 XIV:




Prop. XIV. Besides God no substance can be granted or conceived.

[There is only one substance, which is God.]

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.

[We have defined God as having infinite attributes.

And, if we were to consider the possibility that there was some substance other than God, it would have to have one of God's attributes, because his are infinite and thus include every possible one. But then we would have two substances with the same attribute, which contradicts the definition of substance; for, if we were to conceive two substances with the same attribute, we would be considering them with characteristics that allow one to be conceived through the other, but substances are self-conceivable, so it cannot be that there are two substances with the same attribute. Hence, we cannot conceive another substance besides God, nor grant that one exists.]

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.).

[God is both singular and infinite. He is singular, because there is nothing other to him. And he is infinite, because nothing can be denied of him.

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.

[There is only one substance, God. That means Thought and Extension cannot also be substances. There are only two other options. They could be attributes of God. Or, they can be modifications of attributes.]



From the Latin:


PROPOSITIO XIV

Præter Deum nulla dari, neque concipi potest substantia.

Demonstratio

Cum Deus sit ens absolute infinitum, de quo nullum attributum, quod essentiam substantiæ exprimit, negari potest (per Defin. 6), isque necessario existat (per Prop. 11), si aliqua substantia præter Deum daretur, ea explicari deberet per aliquod attributum Dei, sicque duæ substantiæ ejusdem attributi existerent, quod (per Prop. 5) est absurdum; adeoque nulla substantia extra Deum dari potest, & consequenter non etiam concipi. Nam si posset concipi, deberet necessario concipi, ut existens; atqui hoc (per primam partem hujus Demonstrat.) est absurdum. Ergo extra Deum nulla dari, neque concipi potest substantia. Q.E.D.

Corollarium I

Hinc clarissime sequitur Iº. Deum esse unicum, hoc est (per Defin. 6) in rerum natura non, nisi unam substantiam, dari, eamque absolute infinitam esse, ut in Scholio Prop. 10 jam innuimus.

Corollarium II

Sequitur IIº. rem extensam, & rem cogitantem, vel Dei attributa esse, vel (per Axiom. 1) affectiones attributorum Dei.



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