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[The following is quotation; my summary and commentary is bracketed in red. Deleuze's commentary is found near the end. The Latin text comes last.]
Baruch Spinoza
Ethics
Part I "Concerning God"
Proposition XVI
Ethics
Part I "Concerning God"
Proposition XVI
Prop. XVI. From the necessity of the divine nature must follow an infinite number of things in infinite ways-that is, all things which can fall within the sphere of infinite intellect.
[It is necessary that God exists; and as a necessary consequence of his existence, he must produce an infinity of things in an infinity of ways, all of which he understands in his infinite intellect.]
Proof.-This proposition will be clear to everyone, who remembers that from the given definition of any thing the intellect infers several properties, which really necessarily follow therefrom (that is, from the actual essence of the thing defined) ; and it infers more properties in proportion as the definition of the thing expresses more reality, that is, in proportion as the essence of the thing defined involves more reality. Now, as the divine nature has absolutely infinite attributes (by Def. vi.), of which each expresses infinite essence after its kind, it follows that from the necessity of its nature an infinite number of things (that is, everything which can fall within the sphere of an infinite intellect) must necessarily follow. Q.E.D.
[We infer additional properties about a thing from its definition alone, for example, from the triangle's definition as having three angles, we can infer that these angles equal two right angles. And the more reality or essence the definition involves and expresses, the more we may infer from it.
We have defined God as possessing infinite attributes, with each attribute expressing an infinite essence. Moreover, within each attribute is an infinity of modifications. So, God's essence expresses an infinite number of things (modes) in an infinite number of ways (attributes). Hence God's essence is infinite, and thus we may infer an infinity of things from his definition or nature. And because God's intellect is infinite, he may conceive all of these things. So an infinity of things follow from God's nature in an infinity of ways, all of which are found in his intellect.]
Corollary I.-Hence it follows, that God is the efficient cause of all that can fall within the sphere of an infinite intellect.
[God causes all things that an infinite intellect can conceive.]
Corollary II.-It also follows that God is a cause in himself, and not through an accident of his nature.
[It follows from God's essence that he cause an infinity of things, so it is essential that he be a cause in himself.]
Corollary III.-It follows, thirdly, that God is the absolutely first cause.
[Although there is modal causation, God is absolutely the first cause.]
From Deleuze's Commentary:
Thus God produces an infinity of things because his essence is infinite; but having an infinity of attributes, he necessarily produces these things in an infinity of modes, each of which must be referred to an attribute to which it belongs. [ft.4, citation] (Deleuze, 14c)
En effet, Dieu produit une infinité de choses parce que son essence est infinité : mais parce qu’il a une infinité d’attributs, il produit nécessairement ces choses en une infinité de modes dont chacun renvoie à l’attribut dans lequel il est contenu [ft.4, citation]. (Deleuze, 10b)
That God understand himself should follow from the necessity of the divine nature. [ft.6:] This already appears in the Proof of II.3, which appeals to I.16. And the Scholium itself emphasized this reference (“It follows from the necessity of the divine nature... that God understands himself”). (Deleuze, 101c; 364b)
Que Dieu se comprenne lui-même, cela doit suivre de la nécessité de la nature divine. [ft.6:] C’est déjà ce qui apparaît dans la démonstration de II, 3, qui se réclame de I, 16. Et la scolie elle-même souligne cette référence (« Il suit de la nécessité de la nature divine …qui Dieu se comprenne lui-même. »). (Deleuze, 89bc ; d)
But as expressing the essence of substance, attributes are necessarily referred to an understanding that understands them objectively, that is, perceives what they express. Thus the idea of God is seen to be grounded in the divine nature itself: because God has as his nature an infinity of attributes, each of which “expresses” an infinite essence, it follows from this expressive nature that God understands himself and, understanding himself, produces all the things that “fall” within an infinite understanding. [ft.7, citation] Expressions are always explications. (Deleuze, 101-102, boldface mine)
Mais les attributs n’expriment pas l’essence de la substance sans se rapporter nécessairement à un entendement qui les comprend objectivement, c’est-à-dire qui perçoit ce qu’ils expriment. Ainsi l’idée de Dieu se trouve fondée dans la nature divine elle-même : parce que Dieu a pour nature une infinité d’attributs dont chacun « exprime » une essence infinie, il suit de cette nature expressive que Dieu se comprenne et, se comprenant, produise toutes les choses qui « tombent » sous un entendement infini. [ft.7, citation] Mais les expressions sont toujours des explications. (Deleuze, 89-90)
The power of existing we assert of God is an absolutely infinite power: God exists “absolutely,” and produces an infinity of things in the “absolute infinity” of his attributes (and so in an infinity of modes). [ft.9: Cf. Be I.16p: infinita absolute attribute] (Deleuze, 118bc; 365d)
La puissance d’exister que nous affirmons de Dieu est une puissance absolument infinie : Dieu existe « absolument », et produit une infinité de choses dans « l’infinité absolue » de ses attributs (donc en une infinité de modes). [ft.9 : Cf. E, I, 16, dem. : infinita absolute attributa] (Deleuze, 103d)
From the Latin text:
Ex necessitate divinæ naturæ, infinita infinitis modis (hoc est, omnia, quæ sub intellectum infinitum cadere possunt) sequi debent.
Demonstratio
Hæc Propositio unicuique manifesta esse debet, si modo ad hoc attendat, quod ex data cujuscunque rei definitione plures proprietates intellectus concludit, quæ revera ex eadem (hoc est, ipsa rei essentia) necessario sequuntur, & eo plures, quo plus realitatis rei definitio exprimit, hoc est, quo plus realitatis rei definitæ essentia involvit. Cum autem natura divina infinita absolute attributa habeat (per Defin. 6), quorum etiam unumquodque infinitam essentiam in suo genere exprimit, ex ejusdem ergo necessitate infinita infinitis modis (hoc est, omnia, quæ sub intellectum infinitum cadere possunt) necessario sequi debent. Q.E.D.
Corollarium I
Hinc sequitur, Iº. Deum omnium rerum, quæ sub intellectum infinitum cadere possunt, esse causam efficientem.
Corollarium II
Sequitur IIº. Deum causam esse per se, non vero per accidens.
Corollarium III
Sequitur IIIº. Deum esse absolute causam primam.
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
[It is necessary that God exists; and as a necessary consequence of his existence, he must produce an infinity of things in an infinity of ways, all of which he understands in his infinite intellect.]
Proof.-This proposition will be clear to everyone, who remembers that from the given definition of any thing the intellect infers several properties, which really necessarily follow therefrom (that is, from the actual essence of the thing defined) ; and it infers more properties in proportion as the definition of the thing expresses more reality, that is, in proportion as the essence of the thing defined involves more reality. Now, as the divine nature has absolutely infinite attributes (by Def. vi.), of which each expresses infinite essence after its kind, it follows that from the necessity of its nature an infinite number of things (that is, everything which can fall within the sphere of an infinite intellect) must necessarily follow. Q.E.D.
[We infer additional properties about a thing from its definition alone, for example, from the triangle's definition as having three angles, we can infer that these angles equal two right angles. And the more reality or essence the definition involves and expresses, the more we may infer from it.
We have defined God as possessing infinite attributes, with each attribute expressing an infinite essence. Moreover, within each attribute is an infinity of modifications. So, God's essence expresses an infinite number of things (modes) in an infinite number of ways (attributes). Hence God's essence is infinite, and thus we may infer an infinity of things from his definition or nature. And because God's intellect is infinite, he may conceive all of these things. So an infinity of things follow from God's nature in an infinity of ways, all of which are found in his intellect.]
Corollary I.-Hence it follows, that God is the efficient cause of all that can fall within the sphere of an infinite intellect.
[God causes all things that an infinite intellect can conceive.]
Corollary II.-It also follows that God is a cause in himself, and not through an accident of his nature.
[It follows from God's essence that he cause an infinity of things, so it is essential that he be a cause in himself.]
Corollary III.-It follows, thirdly, that God is the absolutely first cause.
[Although there is modal causation, God is absolutely the first cause.]
From Deleuze's Commentary:
Thus God produces an infinity of things because his essence is infinite; but having an infinity of attributes, he necessarily produces these things in an infinity of modes, each of which must be referred to an attribute to which it belongs. [ft.4, citation] (Deleuze, 14c)
En effet, Dieu produit une infinité de choses parce que son essence est infinité : mais parce qu’il a une infinité d’attributs, il produit nécessairement ces choses en une infinité de modes dont chacun renvoie à l’attribut dans lequel il est contenu [ft.4, citation]. (Deleuze, 10b)
That God understand himself should follow from the necessity of the divine nature. [ft.6:] This already appears in the Proof of II.3, which appeals to I.16. And the Scholium itself emphasized this reference (“It follows from the necessity of the divine nature... that God understands himself”). (Deleuze, 101c; 364b)
Que Dieu se comprenne lui-même, cela doit suivre de la nécessité de la nature divine. [ft.6:] C’est déjà ce qui apparaît dans la démonstration de II, 3, qui se réclame de I, 16. Et la scolie elle-même souligne cette référence (« Il suit de la nécessité de la nature divine …qui Dieu se comprenne lui-même. »). (Deleuze, 89bc ; d)
But as expressing the essence of substance, attributes are necessarily referred to an understanding that understands them objectively, that is, perceives what they express. Thus the idea of God is seen to be grounded in the divine nature itself: because God has as his nature an infinity of attributes, each of which “expresses” an infinite essence, it follows from this expressive nature that God understands himself and, understanding himself, produces all the things that “fall” within an infinite understanding. [ft.7, citation] Expressions are always explications. (Deleuze, 101-102, boldface mine)
Mais les attributs n’expriment pas l’essence de la substance sans se rapporter nécessairement à un entendement qui les comprend objectivement, c’est-à-dire qui perçoit ce qu’ils expriment. Ainsi l’idée de Dieu se trouve fondée dans la nature divine elle-même : parce que Dieu a pour nature une infinité d’attributs dont chacun « exprime » une essence infinie, il suit de cette nature expressive que Dieu se comprenne et, se comprenant, produise toutes les choses qui « tombent » sous un entendement infini. [ft.7, citation] Mais les expressions sont toujours des explications. (Deleuze, 89-90)
The power of existing we assert of God is an absolutely infinite power: God exists “absolutely,” and produces an infinity of things in the “absolute infinity” of his attributes (and so in an infinity of modes). [ft.9: Cf. Be I.16p: infinita absolute attribute] (Deleuze, 118bc; 365d)
La puissance d’exister que nous affirmons de Dieu est une puissance absolument infinie : Dieu existe « absolument », et produit une infinité de choses dans « l’infinité absolue » de ses attributs (donc en une infinité de modes). [ft.9 : Cf. E, I, 16, dem. : infinita absolute attributa] (Deleuze, 103d)
From the Latin text:
PROPOSITIO XVI
Ex necessitate divinæ naturæ, infinita infinitis modis (hoc est, omnia, quæ sub intellectum infinitum cadere possunt) sequi debent.
Demonstratio
Hæc Propositio unicuique manifesta esse debet, si modo ad hoc attendat, quod ex data cujuscunque rei definitione plures proprietates intellectus concludit, quæ revera ex eadem (hoc est, ipsa rei essentia) necessario sequuntur, & eo plures, quo plus realitatis rei definitio exprimit, hoc est, quo plus realitatis rei definitæ essentia involvit. Cum autem natura divina infinita absolute attributa habeat (per Defin. 6), quorum etiam unumquodque infinitam essentiam in suo genere exprimit, ex ejusdem ergo necessitate infinita infinitis modis (hoc est, omnia, quæ sub intellectum infinitum cadere possunt) necessario sequi debent. Q.E.D.
Corollarium I
Hinc sequitur, Iº. Deum omnium rerum, quæ sub intellectum infinitum cadere possunt, esse causam efficientem.
Corollarium II
Sequitur IIº. Deum causam esse per se, non vero per accidens.
Corollarium III
Sequitur IIIº. Deum esse absolute causam primam.
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
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