22 Dec 2008

Spinoza's Ethics Part 1, Proposition 11, The Power of Existence, with Deleuze's commentary

[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 XI:

Prop. XI. God, or substance, consisting of infinite attributes, of which each expresses eternal and infinite essentiality, necessarily exists.

[God is substance and he necessarily exists. Also, he consist of infinite attributes, all of which express the eternity and infinity of his essence.]

Proof.-If this be denied, conceive, if possible, that God does not exist : then his essence does not involve existence. But this (Prop. vii.) is absurd. Therefore God necessarily exists.

[Because substance is self-caused, it necessarily exists. If we conceive God as not existing, we contradict his essence; thus God exists by necessity.]

Another proof.-Of everything whatsoever a cause or reason must be assigned, either for its existence, or for its non-existence-e.g. if a triangle exist, a reason or cause must be granted for its existence ; if, on the contrary, it does not exist, a cause must also be granted, which prevents it from existing, or annuls its existence. This reason or cause must either be contained in the nature of the thing in question, or be external to it. For instance, the reason for the non-existence of a square circle is indicated in its nature, namely, because it would involve a contradiction. On the other hand, the existence of substance follows also solely from its nature, inasmuch as its nature involves existence. (See Prop. vii.)

[If something exists, there must be a cause or reason for its existence, and if something does not exist, there must be a cause or reason for its non-existence.

Its reason or cause must either be contained in its nature, or be external to it. For example, it is in the nature of a squared circle that it not exist, because its existence would involve a contradiction. However, unlike the square circle, substance's cause or reason of existence lies within its nature.]

But the reason for the existence of a triangle or a circle does not follow from the nature of those figures, but from the order of universal nature in extension. From the latter it must follow, either that a triangle necessarily exists, or that it is impossible that it should exist. So much is self-evident. It follows therefrom that a thing necessarily exists, if no cause or reason be granted which prevents its existence.

[But the triangle's or circle's existence does not follow from their own nature; rather their existence follows from the nature of extensivity, which determines whether these shapes exist necessarily or are impossible to exist.

Something exists if nothing prevents it from existing.]

If, then, no cause or reason can be given, which prevents the existence of God, or which destroys his existence, we must certainly conclude that he necessarily does exist. If such a reason or cause should be given, it must either be drawn from the very nature of God, or be external to him-that is, drawn from another substance of another nature. For if it were of the same nature, God, by that very fact, would be admitted to exist. But substance of another nature could have nothing in common with God (by Prop. ii.), and therefore would be unable either to cause or to destroy his existence.

[Thus if there is nothing to prevent God from existing, he must necessarily exist.

But if we do somehow give a reason or cause for God not existing, that reason or cause must either be found in his nature or outside it. If it be exterior to him, then it would be drawn from another substance of another nature. For if that cause for his non-existence were drawn from something with the same nature, then God would have to exist, because something of the same nature exists. So the exterior cause of God's non-existence would have to come from something outside him.

But, we know that substances with different natures have nothing in common. For, if they had something in common, then conceiving one would involve conceiving something that characterizes the essence of another; but, substances by definition cannot be thought one through another. So if there were an exterior cause for God's non-existence, it would have to be from a substance with nothing in common with God. But we know that things with nothing in common cannot have a causal relationship, because by Proposition 3; we know that effects are understood through their causes, and things with nothing in common cannot be apprehended one from the other. So nothing exterior to God can cause him to not exist.

Thus neither something internal nor external to God can cause him to not exist; hence he necessarily exists.]

As, then, a reason or cause which would annul the divine existence cannot be drawn from anything external to the divine nature, such cause must perforce, if God does not exist, be drawn from God’s own nature, which would involve a contradiction. To make such an affirmation about a being absolutely infinite and supremely perfect is absurd ; therefore, neither in the nature of God, nor externally to his nature, can a cause or reason be assigned which would annul his existence. Therefore, God necessarily exists. Q.E.D.

[So we must say that God, the absolutely perfect and infinite substance, exists.]

Another proof.-The potentiality of non-existence is a negation of power, and contrariwise the potentiality of existence is a power, as is obvious. If, then, that which necessarily exists is nothing but finite beings, such finite beings are more powerful than a being absolutely infinite, which is obviously absurd ; therefore, either nothing exists, or else a being absolutely infinite necessarily exists also. Now we exist either in ourselves, or in something else which necessarily exists (see Axiom. i. and Prop. vii.). Therefore a being absolutely infinite-in other words, God (Def. vi.)-necessarily exists. Q.E.D.

[The potential for something to exist affirms its power; something that is more able, likely, capable, etc. of existing has more power. The potential for something not to exist is a negation of its power. Something that has a low potential for existing has little power.

Some finite being that exists necessarily has an enormous power to exist. And as existing it would have more power to exist than something that is absolutely infinite, but which might not necessarily exist. But it is absurd to think that something finite could have more potential to exist, that is more power, then something that is absolutely infinite. Thus either nothing exists, for in that case we would not reach this contradiction, or an absolutely infinite being necessarily exists. For if there is not just nothing, then there is either or both infinite and finite things. It cannot be just that the finite things have more power to exist than the infinite ones, so the infinite ones must necessarily exist.

So if even one thing exists, this would mean something infinite must exist. We know that we exist, hence God must exist.]

Note.-In this last proof, I have purposely shown God’s existence a posteriori, so that the proof might be more easily followed, not because, from the same premises, God’s existence does not follow a priori. For, as the potentiality of existence is a power, it follows that, in proportion as reality increases in the nature of a thing, so also will it increase its strength for existence. Therefore a being absolutely infinite, such as God, has from himself an absolutely infinite power of existence, and hence he does absolutely exist.

[The above is an a posteriori proof of God, because one of the premises involves knowledge of our own existence. But from the same premises (minus the knowledge of our own existence) we may still conclude a priori that God exists; for power is the strength of existence, and as infinite, God has absolutely infinite power of existence, hence he absolutely exists.]

Perhaps there will be many who will be unable to see the force of this proof, inasmuch as they are accustomed only to consider those things which flow from external causes. Of such things, they see that those which quickly come to pass-that is, quickly come into existence-quickly also disappear ; whereas they regard as more difficult of accomplishment-that is, not so easily brought into existence-those things which they conceive as more complicated.
However, to do away with this misconception, I need not here show the measure of truth in the proverb, “What comes quickly, goes quickly,” nor discuss whether, from the point of view of universal nature, all things are equally easy, or otherwise : I need only remark that I am not here speaking of things, which come to pass through causes external to themselves, but only of substances which (by Prop. vi.) cannot be produced by any external cause. Things which are produced by external causes, whether they consist of many parts or few, owe whatsoever perfection or reality they possess solely to the efficacy of their external cause ; and therefore their existence arises solely from the perfection of their external cause, not from their own. Contrariwise, whatsoever perfection is possessed by substance is due to no external cause ; wherefore the existence of substance must arise solely from its own nature, which is nothing else but its essence. Thus, the perfection of a thing does not annul its existence, but, on the contrary, asserts it. Imperfection, on the other hand, does annul it ; therefore we cannot be more certain of the existence of anything, than of the existence of a being absolutely infinite or perfect-that is, of God. For inasmuch as his essence excludes all imperfection, and involves absolute perfection, all cause for doubt concerning his existence is done away, and the utmost certainty on the question is given. This, I think, will be evident to every moderately attentive reader.

[Those who do not see the force of this proof are probably too accustomed to think that all causes come from external sources. But Spinoza is talking about substance, whose cause is itself. But those things which are caused by external sources owe their perfection or reality to those external causes. Substance's reality or perfection, however, arises from its its own nature, as does its existence, which is nothing but its essence. We see that God's perfection makes his nature such that his existence is necessary, because a thing's perfection asserts its existence rather than nullifies it. However, imperfection does negate existence. So the only being whose existence we cannot doubt is God, because he has not imperfection but rather is absolutely perfect.]

Deleuze's Commentary:

Proposition 11: The absolutely infinite necessarily exists; otherwise it could not be a substance, and could not have as a property infinite perfection.

Proposition 11 : l'absolument infini existe nécessairement ; sinon il ne pourrait pas être une substance, il ne pourrait pas avoir comme propriété l'infiniment parfait.

From the Latin:

Deus, sive substantia constans infinitis attributis, quorum unum quodque æternam, & infinitam essentiam exprimit, necessario existit.
Si negas, concipe, si fieri potest, Deum non existere. Ergo (per Axiom. 7) ejus essentia non involvit existentiam. Atqui hoc (per Prop. 7) est absurdum: Ergo Deus necessario existit. Q.E.D.
Cujuscunque rei assignari debet causa, seu ratio, tam cur existit, quam cur non existit. Ex. gr. si triangulus existit, ratio, seu causa dari debet, cur existit; si autem non existit, ratio etiam, seu causa dari debet, quæ impedit, quominus existat, sive quæ ejus existentiam tollat. Hæc vero ratio, seu causa, vel in natura rei contineri debet, vel extra ipsam. Ex. gr. rationem, cur circulus quadratus non existat, ipsa ejus natura indicat; nimirum, quia contradictionem involvit. Cur autem contra substantia existat, ex sola etiam ejus natura sequitur, quia scilicet existentiam involvit (vide Prop. 7). At ratio, cur circulus, vel triangulus existit, vel cur non existit, ex eorum natura non sequitur, sed ex ordine universæ naturæ corporeæ; ex eo enim sequi debet, vel jam triangulum necessario existere, vel impossibile esse, ut jam existat. Atque hæc per se manifesta sunt. Ex quibus sequitur, id necessario existere, cujus nulla ratio, nec causa datur, quæ impedit, quominus existat. Si itaque nulla ratio, nec causa dari possit, quæ impedit, quominus Deus existat, vel quæ ejus existentiam tollat, omnino concludendum est, eundem necessario existere. At si talis ratio, seu causa daretur, ea, vel in ipsa Dei natura, vel extra ipsam dari deberet, hoc est, in alia substantia alterius naturæ. Nam si ejusdem naturæ esset, eo ipso concederetur dari Deum. At substantia, quæ alterius esset naturæ, nihil cum Deo commune habere (per Prop. 2), adeoque neque ejus existentiam ponere, neque tollere posset. Cum igitur ratio, seu causa, quæ divinam existentiam tollat, extra divinam naturam dari non possit, debebit necessario dari, siquidem non existit, in ipsa ejus natura, quæ propterea contradictionem involveret. Atqui hoc de Ente absolute infinito, & summe perfecto affirmare, absurdum est; ergo nec in Deo, nec extra Deum ulla causa, seu ratio datur, quæ ejus existentiam tollat, ac proinde Deus necessario existit. Q.E.D.
Posse non existere impotentia est, & contra posse existere potentia est (ut per se notum). Si itaque id, quod jam necessario existit, non nisi entia finita sunt, sunt ergo entia finita potentiora Ente absolute infinito: atque hoc (ut per se notum) absurdum est; ergo vel nihil existit, vel Ens absolute infinitum necessario etiam existit. Atqui nos, vel in nobis, vel in alio, quod necessario existit, existimus (vide Axiom. 1 & Prop. 7). Ergo Ens absolute infinitum, hoc est (per Defin. 6), Deus necessario existit. Q.E.D.
In hac ultima Demonstratione Dei existentiam a posteriori ostendere volui, ut Demonstratio facilius perciperetur; non autem propterea, quod ex hoc eodem fundamento Dei existentia a priori non sequatur. Nam, cum posse existere potentia sit, sequitur, quo plus realitatis alicujus rei naturæ competit, eo plus virium a se habere, ut existat; adeoque Ens absolute infinitum, sive Deum infinitam absolute potentiam existendi a se habere, qui propterea absolute existit. Multi tamen forsan non facile hujus demonstrationis evidentiam videre poterunt, quia assueti sunt, eas solummodo res contemplari, quæ a causis externis fluunt; & ex his, quæ cito fiunt, hoc est, quæ facile existunt, eas etiam facile perire vident, & contra eas res factu difficiliores judicant, hoc est, ad existendum non adeo faciles, ad quas plura pertinere concipiunt. Verum, ut ab his præjudiciis liberentur, non opus habeo hic ostendere, qua ratione hoc enunciatum, quod cito fit, cito perit, verum sit, nec etiam, an respectu totius naturæ omnia æque facilia sint, an secus. Sed hoc tantum notare sufficit, me hic non loqui de rebus, quæ a causis externis fiunt, sed de solis substantiis, quæ (per Prop. 6) a nulla causa externa produci possunt. Res enim, quæ a causis externis fiunt, sive eæ multis partibus constent, sive paucis, quicquid perfectionis, sive realitatis habent, id omne virtuti causæ externæ debetur, adeoque earum existentia ex sola perfectione causæ externæ, non autem suæ oritur. Contra, quicquid substantia perfectionis habet, nulli causæ externæ debetur; quare ejus etiam existentia ex sola ejus natura sequi debet, quæ proinde nihil aliud est, quam ejus essentia. Perfectio igitur rei existentiam non tollit, sed contra ponit; imperfectio autem contra eandem tollit, adeoque de nullius rei existentia certiores esse possumus, quam de existentia Entis absolute infiniti, seu perfecti, hoc est, Dei. Nam quandoquidem ejus essentia omnem imperfectionem secludit, absolutamque perfectionem involvit, eo ipso omnem causam dubitandi de ipsius existentia tollit, summamque de eadem certitudinem dat, quod mediocriter attendenti perspicuum fore credo.


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:


Spinoza. Ethica. available online at:


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