Pirates & Revolutionaries: Spinoza's Ethics Part 1, Definition 4, 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"

Definition IV:

IV. By attribute, I mean that which the intellect perceives as constituting the essence of substance.

[Substance is infinite, and it expresses its infinity in every way, so there are an infinity of qualitative ways by which it may be conceived. Each of these attributes expresses one of the infinity of substance's essences. We have access to two, Extension and Thought. So one quality of substance is Extension, which means that one of its essential characteristics is Extension, hence one of its essences is Extension. So one of the ways our intellect perceives the essential constitution of substance is as it being infinitely extensive.]

Deleuze's Commentary:

The opening scheme of the Ethics is thus as follows: 1. Definitions 1-5: Merely nominal definitions, needed in the mechanism of subsequent proofs.
(75c)

Le plan du début de l'Ethique est donc le suivant: 1) Définitions 1-5: ce sont de simples définitions nominales, nécessaires au mécanisme des démonstrations futures.
(65a)

The idea of expression is neither defined nor deduced by Spinoza, nor could it be. It appears as early as the sixth Definition, but is there no more defined than it serves to define anything. It defines neither substance nor attribute, since these are already defined (Definitions 3 and 4).
...
It would be wrong to invoke Definitions 3 and 4 in order to deduce directly from them the relation between substance and attribute in God, because God himself "transforms" their relation, rendering it absolute. Definition 3 and 4 are merely nominal, the sixth Definition alone is a real one, with real consequences for substance, attribute and essence.
(19d) (20b)

Sans doute y a-t-il une raison à cette situation du commentaire. C'est que l'idée d'expression chez Spinoza n'est objet ni de définition ni de démonstration, et ne peut pas l'être. Elle apparaît dans la définition 6 ; mais elle n'est pas plus définie qu'elle ne sert à définir. Elle ne définit ni la substance ni l'attribut, puisque ceux-ci le sont déjà (3 et 4).
...
Il serait inexact d'invoquer les définitions 3 et 4 pour en déduire aussitôt la nature du rapport entre la substance et l'attribut tel qu'il doit être en Dieu, puisque Dieu suffit à « transformer » ce rapport, l'élevant à l'absolu. Les définitions 3 et 4 sont seulement nominales ; seule la définition 6 est réelle et nous dit ce qui s'ensuit pour la substance, l'attribut et l'essence.
(15c) (16a)