Spinoza's Ethics, Part 1, Proposition 5, 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 V:

Prop. V. There cannot exist in the universe two or more substances having the same nature or attribute.

[Any attribute that one substance has cannot be found in any other substance, so if one substance has an attribute, there cannot be another substance with that same attribute.]

Proof.-If several distinct substances be granted, they must be distinguished one from the other, either by the difference of their attributes, or by the difference of their modifications (Prop. iv.). If only by the difference of their attributes, it will be granted that there cannot be more than one with an identical attribute. If by the difference of their modifications-as substance is naturally prior to its modifications (Prop. i.),-it follows that setting the modifications aside, and considering substance in itself, that is truly, (Deff. iii. and [*] Axiom vi.), there cannot be conceived one substance different from another,-that is (by Prop. iv.), there cannot be granted several substances, but one substance only. Q.E.D.

[We know that there are only two ways to distinguish substances, by their modifications or their attributes. For, because

1) something exists either in itself or in something else, and because

2) what exists in itself is substance and that which exists in something else is a mode, then we know that one way to distinguish substances is by means of their having different modifications. Also, because the different ways we conceive the essential qualities of substance are its attributes, we know that we can distinguish substances by means of their having different attributes.

Although Spinoza does not cite Proposition 2, it will help us understand his claim that "If only by the difference of their attributes, it will be granted that there cannot be more than one with an identical attribute."

We would contradict the definition of substance if we said that there were more than one substance sharing a common attribute.

Substances are conceived by themselves alone, and attributes are the essential qualities that our mind conceives a substance to have. If a substance shared an attribute with another substance, then whenever we conceive that substance, we thereby conceive along with it the characteristics of another substance. But substances can only be conceived alone, so they cannot share attributes, for if they did, the conception of one would relate to the conception of another, hence we could conceive one by means of the other, which contradicts the definition of substance.

So if we were to distinguish substances by means of their having different attributes, we would have to first acknowledge, by Proposition 2 that there cannot be more than one substance with the same attribute.

From this, Spinoza will want to conclude that we cannot then distinguish substances according to their attributes. To understand this claim, we will look also at passages he does not cite here. We know that even if there are more than one substance, they cannot have the same attribute. If in this case we were to want to distinguish one from the other solely on account of their attributes, then we would be observing that one substance lacks an attribute that the other one has. But to do this means that we are conceiving one substance in relation to another. But we know that by Axiom 5 that when things have nothing in common, our conception of one cannot involve the conception of the other. But we see that if we agree that

a) substances share no same attributes, then we acknowledging that we cannot conceive one in terms of the other, but if we are

b) distinguishing one substance from another because it is lacking an attribute another has, or that it has an attribute that another is lacking, then we thereby are conceiving one in terms of the other.

But we said this cannot be, so we cannot distinguishing substances by means of their having different attributes.

This would seem then to draw his conclusion that, "There cannot exist in the universe two or more substances having the same nature or attribute," but Spinoza addresses another possibility, that different substances could be distinguished on account of their having different modifications.

To eliminate this possibility, Spinoza draws from Axiom vi., which says that a true idea agrees with what it is an idea of. So the true idea of substance would be an idea of substance as it is defined, as something self-conceivable. We need not also consider that it can be modified in order to conceive it, so if we were to consider substance as it truly is, would not consider what depends on it, namely modifications.

So we cannot distinguish substances according to their modifications, because then we would not be considering substance as it truly is, and we also cannot distinguish substances according to their attributes, because then we would be conceiving one substance in terms of another, which is contrary to its definition.

Thus we have no means to distinguish substances.

That which is indistinguishable from something else is no different from it. Hence even if we presuppose that there are more than one substance, we still come to conclude that there is only one substance.]

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 V

In rerum natura non possunt dari duæ, aut plures substantiæ ejusdem naturæ, sive attributi.

Demonstratio

Si darentur plures distinctæ, deberent inter se distingui, vel ex diversitate attributorum, vel ex diversitate affectionum (per Prop. præced.). Si tantum ex diversitate attributorum, concedetur ergo, non dari, nisi unam ejusdem attributi. At si ex diversitate affectionum, cum substantia sit prior natura suis affectionibus (per Prop. 1), depositis ergo affectionibus, & in se considerata, hoc est (per Defin. 3 & Axiom. 6) vere considerata, non poterit concipi ab alia distingui, hoc est (per Prop. præced.) non poterunt dari plures, sed tantum una. Q.E.D.

( [*] Note that this adelaide version implies that Definition 3 is meant instead of Axiom 6, but according to other versions and according to what one would expect given his reasoning in this demonstration, Axiom 6 seems to be the proper reference. So, I have made the correction in the quotation above.)

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