Spinoza's Ethics Part 1, Proposition 3, 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 III:

Prop. III. Things which have nothing in common cannot be one the cause of the other.

[For one thing to cause another, it must have something in common with it.]

Proof.-If they have nothing in common, it follows that one cannot be apprehended by means of the other (Ax. v.), and, therefore, one cannot be the cause of the other (Ax. iv.). Q.E.D.

[We cannot understand one thing through another unless they have something in common. Yet if they have nothing in common, then knowledge of one would not depend on knowledge of the other. But the knowledge of an effect depends on knowledge of the cause. So things which have nothing in common cannot be causally related.]

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 III

Quæ res nihil commune inter se habent, earum una alterius causa esse non potest.

Demonstratio

Si nihil commune cum se invicem habent, ergo (per Axiom. 5) nec per se invicem possunt intelligi; adeoque (per Axiom. 4) una alterius causa esse non potest. Q.E.D.

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_eth0.html