Spinoza's Ethics Part 1, Proposition 6, with Deleuze's commentary

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

Spinoza, Ethics

Part I "Concerning God"

Proposition VI:

Prop. VI. One substance cannot be produced by another substance.

[One substance cannot bring about another one.]

Proof.-It is impossible that there should be in the universe two substances with an identical attribute, i.e. which have anything common to them both (Prop. ii.), and, therefore (Prop. iii.), one cannot be the cause of the other, neither can one be produced by the other. Q.E.D.

[We know that it contradicts the definition of substance as being self-conceivable that there be two substances sharing something in common, because that means we would conceive one in terms of an extrinsic property (shared between the two substances) and hence we would conceive one along with the other. So there are no two substances with something in common, but that means also that we cannot account for one by considering the other, because they do not relate to each other. So one cannot be the cause of the other (that is, provide an account for the other). And if one does not account for the other or cause it, then it cannot be said to produce it either.]

Corollary.-Hence it follows that a substance cannot be produced by anything external to itself. For in the universe nothing is granted, save substances and their modifications (as appears from Ax. i. and Deff. iii. and v.). Now (by the last Prop.) substance cannot be produced by another substance, therefore it cannot be produced by anything external to itself. Q.E.D.

[We know that everything which exists does so either in itself or in something else, and that substances exist in themselves and modes exist in something else. Thus there are only substances and modifications in the universe. Also, we know that there is only one substance, because there are only two ways to distinguish things, by their modes or by their attributes. If we distinguish according to their attributes, then we are saying that one lacks an attribute that the other has, which is to conceive one substance by means of another, which is contrary to substance's definition as self-conceivable. If we distinguish them in terms of modes, we are not distinguishing substances as they truly are, because we do not define substances in terms of their modes. Thus there is only one substance, because there is no means to distinguish multiple substances.

So if there is only one substance, no substance can be produced by anything external to it.]

This is shown still more readily by the absurdity of the contradictory. For, if substance be produced by an external cause, the knowledge of it would depend on the knowledge of its cause (Ax. iv.), and (byDef. iii.) it would itself not be substance.

[Also, if one substance were produced by another, then one is the cause of the other. We understand effects by knowing their causes, so we would understand the caused substance by means of what causes it. But this contradicts the definition of substances as being self-conceivable.]

Deleuze's Commentary

Propositions 1-8: The first stage in the proof of the reality of the definition: numerical distinction not being real, every really distinct attribute is infinitely perfect, and every qualified substance is unique, necessary and infinite. This sequence obviously relies only upon the first five definitions.

(75d)

Propositions 1-8, première étape de la démonstration de la réalité de la définition : la distinction numérique n'étant pas réelle, chaque attribut réellement distinct est infiniment parfait, chaque substance qualifiée est unique, nécessaire et infinie. Cette série, évidemment, doit s'appuyer seulement sur les cinq premières définitions.

(65bc)

From the Latin:

PROPOSITIO VI

Una substantia non potest produci ab alia substantia.

Demonstratio

In rerum natura non possunt dari duæ substantiæ ejusdem attributi (per Prop. præced.), hoc est (per Prop. 2), quæ aliquid inter se commune habent. Adeoque (per Prop. 3) una alterius causa esse nequit, sive ab alia non potest produci. Q.E.D.

Corollarium

Hinc sequitur substantiam ab alio produci non posse. Nam in rerum natura nihil datur præter substantias, earumque affectiones, ut patet ex Axiom. 1 & Defin. 3 & 5. Atqui a substantia produci non potest (per Prop. præced.). Ergo substantia absolute ab alio produci non potest. Q.E.D.

Aliter

Demonstratur hoc etiam facilius ex absurdo contradictorio. Nam si substantia ab alio posset produci, ejus cognitio a cognitione suæ causæ deberet pendere (per Axiom. 4); adeoque (per Defin. 3) non esset substantia.

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