21 Dec 2008

Spinoza's Ethics Part 1, Proposition 8, 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"

Prop. VIII. Every substance is necessarily infinite.

[Substances must be infinite.]

Proof.-There can only be one substance with an identical attribute, and existence follows from its nature (Prop. vii.) ; its nature, therefore, involves existence, either as finite or infinite. It does not exist as finite, for (by Def. ii.) it would then be limited by something else of the same kind, which would also necessarily exist (Prop. vii.) ; and there would be two substances with an identical attribute, which is absurd (Prop. v.). It therefore exists as infinite. Q.E.D.

[We know that we would contradict the definition of substance if there was more than one with the same attribute. Because if there were more than one with the same attribute, then one would share a characteristic with another, which means that thinking one involves thinking about another, which contradicts the definition of substance as self-conceivable. We know that substance must exist, because it is defined as self-caused.

There are two types of existences under consideration, finite and infinite. Because substance exists, its existence must be either infinite or finite.

And because there is not more than one substance, it cannot be finite, because finite things are limited by other things of the same nature. If it were of the same nature, it would be a substance, and we know that substances must exist, because they are defined as self-caused.

But also, if they were of the same nature, that means they share an attribute, which we contradicts the definition of substance.]

Note I.-As finite existence involves a partial negation, and infinite existence is the absolute affirmation of the given nature, it follows (solely from Prop. vii.) that every substance is necessarily infinite.

[Because substances exists on account of themselves alone, we know that there is no partial negation involved in their essence or definition, hence they must be infinite.]

Note II.-No doubt it will be difficult for those who think about things loosely, and have not been accustomed to know them by their primary causes, to comprehend the demonstration of Prop. vii. : for such persons make no distinction between the modifications of substances and the substances themselves, and are ignorant of the manner in which things are produced ; hence they may attribute to substances the beginning which they observe in natural objects. Those who are ignorant of true causes, make complete confusion-think that trees might talk just as well as men-that men might be formed from stones as well as from seed ; and imagine that any form might be changed into any other. So, also, those who confuse the two natures, divine and human, readily attribute human passions to the deity, especially so long as they do not know how passions originate in the mind.

[(Note that in the Improvement of the Understanding, Spinoza writes:

But, as we said above, the less men know of nature the more easily can they coin fictitious ideas, such as trees speaking, men instantly changed into stones, or into fountains, ghosts appearing in mirrors, something issuing from nothing, even gods changed into beasts and men and infinite other absurdities of the same kind.)

People who do not realize that there is a difference between substance and mode, that is, that there is a difference between existing in itself and existing in something else, will think that substance needs to be caused like modes do: our world is filled with modes each of which is caused by some other mode, so if one ascribes this necessity to substance, one will not be able to see that substance's existence is produced by its nature, and not by something exterior to it.

Spinoza offers an analogy: those who do not understand the true way modes are caused will attribute false causal relationships to the world, such as men being generated from stones or that any form may bring about any other form. On the contrary, each mode has a limited range in its power of affection, and those who realize this know that we cannot expect the stone to see, or in this example, to generate a man. We this as well when people confuse the divine nature with our nature, and attribute to God human passions and limitations.]

But, if people would consider the nature of substance, they would have no doubt about the truth of Prop. vii. In fact, this proposition would be a universal axiom, and accounted a truism. For, by substance, would be understood that which is in itself, and is conceived through itself-that is, something of which the conception requires not the conception of anything else ; whereas modifications exist in something external to themselves, and a conception of them is formed by means of a conception of the thing in which they exist.

[And just like those in the analogy who think falsehoods, because they do not understand how modes are caused, those who do not know the true way that substance is caused, that is, its being self-caused, will think that substance requires something else to conceive it or cause it (so they might wonder, who made God?).]

Therefore, we may have true ideas of non-existent modifications; for, although they may have no actual existence apart from the conceiving intellect, yet their essence is so involved in something external to themselves that they may through it be conceived.

[So because we can conceive modifications through that which they modify, and because that which they modify necessarily exists, we may conceive modifications through their substance even if the modes themselves do not actually exist but rather only exist in our minds. So in other words, there are certain truths regarding modifications that exist in the substance they modify, and may be conceived by thinking about substance.]

Whereas the only truth substances can have, external to the intellect, must consist in their existence, because they are conceived through themselves. Therefore, for a person to say that he has a clear and distinct-that is, a true-idea of a substance, but that he is not sure whether such substance exists, would be the same as if he said that he had a true idea, but was not sure whether or not it was false (a little consideration will make this plain); or if anyone affirmed that substance is created, it would be the same as saying that a false idea was true-in short, the height of absurdity.

[It follows from substance's definition that it exist, because it is self-caused. So it is in its essence that it exists. Thus if we think a truth about substance, we are thinking of its essence, but because its essence is its existence, when we think about substance's essence, we are conceiving it through its existence. So when we have a clear and distinct (thus a true) idea of substance, we would have to know that it exists, because its truths regard what is essential to substance, and what is essential to it is that it exists. And because substance is self-caused, we cannot say of it that something else caused it.]

It must, then, necessarily be admitted that thText Coloure existence of substance as its essence is an eternal truth. And we can hence conclude by another process of reasoning-that there is but one such substance. I think that this may profitably be done at once; and, in order to proceed regularly with the demonstration, we must premise :— 1. The true definition of a thing neither involves nor expresses anything beyond the nature of the thing defined.

[True definitions only give what is essential to what it defines. (See the demonstration to Proposition 5 where Spinoza uses this idea to distinguish the truth of modes from that of substance to say that there must be one substance).]

From this it follows that-2. No definition implies or expresses a certain number of individuals, inasmuch as it expresses nothing beyond the nature of the thing defined. For instance, the definition of a triangle expresses nothing beyond the actual nature of a triangle : it does not imply any fixed number of triangles.

[The definition for something does not stipulate how many things fall under this definition; it merely tells us how those things are defined, regardless of their number.]

3. There is necessarily for each individual existent thing a cause why it should exist.

[If something exists, there must be something that accounts for it; that is, it must have some cause or reason.]

4. This cause of existence must either be contained in the nature and definition of the thing defined, or must be postulated apart from such definition.

[What accounts for something must be found either within its definition and nature, or without it. See Axiom 1.]

It therefore follows that, if a given number of individual things exist in nature, there must be some cause for the existence of exactly that number, neither more nor less. For example, if twenty men exist in the universe (for simplicity’s sake, I will suppose them existing simultaneously, and to have had no predecessors), and we want to account for the existence of these twenty men, it will not be enough to show the cause of human existence in general ; we must also show why there are exactly twenty men, neither more nor less : for a cause must be assigned for the existence of each individual.

[Because according to 3 every individual must have a cause, to every member of any given number of individuals must correspond some cause.]

Now this cause cannot be contained in the actual nature of man, for the true definition of man does not involve any consideration of the number twenty. Consequently, the cause for the existence of these twenty men, and, consequently, of each of them, must necessarily be sought externally to each individual.

[Men are not substance, hence they are not self-caused, so their cause must be found externally to them.]

Hence we may lay down the absolute rule, that everything which may consist of several individuals must have an external cause.

[Because there is only one substance, if we have more than one individual, we must have something more than substance, and anything other than substance has an external cause; so if we have any plurality of individuals, there must exist an external cause for at least part of that group's membership.]

And, as it has been shown already that existence appertains to the nature of substance, existence must necessarily be included in its definition ; and from its definition alone existence must be deducible. But from its definition (as we have shown, notes ii., iii.), we cannot infer the existence of several substances; therefore it follows that there is only one substance of the same nature. Q.E.D.

[In 2 we said that a definition does not tells us how many members fall under that definition, and in 3 we said that there must be a cause for all existing things. So because we cannot infer the existence of a group from the definition of substance, we can only infer the existence of one thing, substance. That one thing must have a cause, in this case itself. So we know that the one substance which can be deduced from the definition of substance must necessarily exist and at least be unitary; and because we cannot deduce anything else from the definition of substance, we cannot have more than one substance. For, if we had two substances, each would have their account in themselves and not in relation to anything else. But if each substance bears no essential relation to anything else but itself, then the supposed other substance would not be of the same nature. Hence there can only be one substance of the same nature.]

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.

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.

The positive demonstration [for the uniqueness of substance] comes further on, in a scholium to Proposition 8: two substances with the same attribute would be only numerically distinct - and the character of numerical distinction is such as to exclude the possibility of making of it a real or substantial distinction.

According to the Scholium, a distinction would not be numerical if the things distinguished did not have the same concept or definition; but in that case the things would not be distinct, were there not an external cause, beside the definition, which determined that they exist in such a number. So that two or more numerically distinct things presuppose something outside their concept. Thus substances could only be numerically distinct through the operation of some external causality that could produce them. But only by holding conjointly a number of confused ideas can we claim that substances are produced. We say they have a cause, but that we do not know how this cause operates; we imagine that we have a true idea of these substances, since they are conceived in themselves, but we are unsure of the truth of this idea, because we do not know, from the substances themselves, whether they exist. This amounts to a criticism of the odd Cartesian formula "what can exist by itself." External causality does not make sense, but only in relation to the existence of finite modes: every existing mode may be referred to another, precisely because it cannot exist by itself. To apply such causality to substance is to make it operate outside the terms that legitimate and define it - to propose its operation in a sort of void, and quite indeterminately. In short, external causality and numerical distinction share the same fate of applying to modes, and to modes alone.

The argument of Scholium 8 has, then, the following form: (1) Numerical distinction requires an external cause to which it may be referred; (2) But a substance cannot be referred to an external cause, because of the contradiction implied in such a use of causal principles; (3) So two or more substances cannot be distinguished in numero, and there cannot be two substances with the same attribute. The structure of the argument here differs from that of the first eight proofs, which runs: (1) Two or more substances cannot share the same attribute, for they would then have to be distinguished by the modes, which is absurd; (2) So that a substance cannot have a cause external to it, for to be produced or limited by another substance it would have to share the same nature or the same attribute; (3) So that there cannot be numerical distinction in any substance, of whatever attribute, and "Every substance must be infinite."

On the one hand, one deduces from the nature of numerical distinction that it is inapplicable to substance; on the other, one deduces from the nature of substance its infinity, and thus the impossibility of applying to it numerical distinctions. In either case, numerical distinction can never distinguish substances, but only modes that involve the same attribute. For number expresses in its own way the character of existing modes: the composite nature of their parts, their limitation by other things of the same nature, their determination from outside themselves. Number thus goes on ad infinitum. But the question is, can it ever reach infinity itself? Or, as Spinoza puts it: even in the case of modes, is it from the multitude of parts that we infer their infinity? When we make of numerical distinction a real or substantial distinction, we carry it to infinity, if only to ensure the convertibility that then becomes necessary between the attribute as such and the infinity of finite parts which we distinguish in it. Great absurdities then follow: "If an infinite quantity is measured by parts equal to a foot, it will consist of an infinitely many such parts, as it will also, if it is measured by parts equal to an inch. And therefore, one infinite number will be twelve times greater than another." The absurdity does not, as Descartes thought, lie in hypostatizing extension as an attribute but rather in conceiving it as measurable and composed of finite parts into which one supposes it convertible. Physics here intervenes to support the principles of logic: the absence of a vacuum in nature means simply that division into parts is not real distinction. Numerical distinction is division, but division takes place only in modes, only modes are divisible.

Mais la démonstration positive apparaît plus loin, dans un scolie de 8 : deux substances de même attribut seraient seulement distinctes in numero ; or les caractères de la distinction numérique excluent la possibilité d'en faire une distinction réelle ou substantielle.

D'après ce scolie, une distinction ne serait pas numérique si les choses n'avaient pas le même concept ou la même définition ; mais ces choses ne seraient pas distinctes s'il n'y avait hors de la définition une cause extérieure par laquelle elles existent en tel nombre. Deux ou plusieurs choses numériquement distinctes supposent donc autre chose que leur concept. C'est pourquoi des substances ne pourraient être numériquement distinctes qu'en renvoyant à une causalité externe capable de les produire. Or, quand nous affirmons que des substances sont produites, nous avons beaucoup d'idées confuses à la fois. Nous disons qu'elles ont une cause, mais que nous ne savons pas comment cette cause procède ; nous prétendons avoir de ces substances une idée vraie, puisqu'elles sont conçues par elles-mêmes, mais nous doutons que cette idée soit braie, puisque nous ne savons pas par elles-mêmes si elles existent. On retrouve ici la critique de l'étrange formule cartésienne: ce qui peut exister par soi. La causalité externe a un sens, mais seulement à l'égard des modes existants finis : chaque mode existant renvoie à un autre mode, précisément parce qu'il ne peut pas exister par soi. Quand nous appliquons cette causalité aux substances, nous la faisons jouer hors des conditions qui la légitiment et la déterminent. Nous l'affirmons, mais dans le vide, en lui retirant toute détermination. Bref, la causalité externe et la distinction numérique ont un sort commun : elles s'appliquent aux modes, et seulement aux modes.

L'argument du scolie 8 se présente donc sous la forme suivante : 1) la distinction numérique exige une cause extérieure à laquelle elle renvoie ; 2) or il est impossible d'appliquer une cause extérieure à une substance, en raison de la contradiction contenue dans un tel usage du principe de causalité : 3) deux ou plusieurs substances ne peuvent donc pas se distinguer in numero, il n'y a pas deux substances de même attribut. L'argument des huit premières démonstrations n'a pas la même structure : 1) deux ou plusieurs substances ne peuvent pas avoir le même attribut, parce qu'elles devraient se distinguer par les modes, ce qui est absurde ; 2) une substance ne peut donc pas avoir une cause externe, elle ne peut pas être produite ou limitée par une autre substance, car toutes deux devraient avoir la même nature ou le même attribut ; 3) il n'y a donc pas de distinction numérique dans une substance de quelque attribute, « toute substance est nécessairement infinite ».

Tout à l'heure, de la nature de la distinction numérique, on concluait son impuissance à s'appliquer à la substance. Maintenant, de la nature de la substance, nous concluons son infinité, donc l'impossibilité de lui appliquer des distinctions numériques. De toutes façons, la distinction numérique ne distingue jamais des substances, mais seulement des modes enveloppant le même attribut. Car le nombre exprime à sa façon les caractères du mode existant : la composition des parties, la limitation par autre chose de même nature, la détermination externe. En ce sens il peut aller à l'infini. Mais la question est : peut-il être porté dans l'infini lui-même ? Ou, comme dit Spinoza : même dans le cas des modes, est-ce de la multitude des parties que nous concluons qu'elles sont une infinité ? Quand nous faisons de la distinction numérique une distinction réelle ou substantielle, nous la portons dans l'infinie, ne serait-ce que pour assurer la conversion devenue nécessaire entre l'attribut comme tel et l'; infinité des parties finies que nous y distinguons. En sortent de grandes absurdités : « Si une quantité infinie est mesurée en parties égales à un pied, elle devra, consister en une infinité de telles parties ; et de même si elle est mesurée en parties égales à un doigt ; et par suite un nombre infini sera douze fois plus grand qu'un autre nombre infini. » L'absurdité ne consiste pas, ainsi que le croyait Descartes, à hypostasier l'étendue comme attribut, mais au contraire à la concevoir comme mesurable et composée de parties finies avec lesquelles on prétend la convertir. La physique, ici, vient confirmer les droits de la logique : qu'il n'y ait pas de vide dans la nature signifie seulement que la division des parties n'est pas une distinction réelle. La distinction numérique est une division, mais la division n'a lieu que dans le mode, seul le mode est divisé.

From the Latin:

Omnis substantia est necessario infinita.
Substantia unius attributi non, nisi unica, existit (per Prop. 5), & ad ipsius naturam pertinet existere (per Prop. 7). Erit ergo de ipsius natura, vel finita, vel infinita existere. At non finita. Nam (per Defin. 2) deberet terminari ab alia ejusdem naturæ, quæ etiam necessario deberet existere (per Prop. 7); adeoque darentur duæ substantiæ ejusdem attributi, quod est absurdum (per Prop. 5). Existit ergo infinita. Q.E.D.
Scholium I
Cum finitum esse revera sit ex parte negatio, & infinitum absoluta affirmatio existentiæ alicujus naturæ, sequitur ergo ex sola Prop. 7 omnem substantiam debere esse infinitam.
Scholium II
Non dubito, quin omnibus, qui de rebus confuse judicant, nec res per primas suas causas noscere consueverunt, difficile sit, demonstrationem Prop. 7 concipere; nimirum quia non distinguunt inter modificationes substantiarum, & ipsas substantias, neque sciunt, quomodo res producuntur. Unde fit, ut principium, quod res naturales habere vident, substantiis affingant; qui enim veras rerum causas ignorant, omnia confundunt, & sine ulla mentis repugnantia tam arbores, quam homines, loquentes fingunt, & homines tam ex lapidibus, quam ex semine, formari, &, quascunque formas in alias quascunque mutari, imaginantur. Sic etiam, qui naturam divinam cum humana confundunt, facile Deo affectus humanos tribuunt, præsertim quamdiu etiam ignorant, quomodo affectus in mente producuntur. Si autem homines ad naturam substantiæ attenderent, minime de veritate Prop. 7 dubitarent; imo hæc Prop. omnibus axioma esset, & inter notiones communes numeraretur. Nam per substantiam intelligerent id, quod in se est, & per se concipitur, hoc est, id, cujus cognitio non indiget cognitione alterius rei. Per modificationes autem id, quod in alio est, & quarum conceptus a conceptu rei, in qua sunt, formatur: quocirca modificationum non existentium veras ideas possumus habere; quandoquidem, quamvis non existant actu extra intellectum, earum tamen essentia ita in alio comprehenditur, ut per idem concipi possint. Verum substantiarum veritas extra intellectum non est, nisi in se ipsis, quia per se concipiuntur. Si quis ergo diceret, se claram, & distinctam, hoc est, veram ideam substantiæ habere, & nihilominus dubitare, num talis substantia existat, idem hercle esset, ac si diceret, se veram habere ideam, & nihilominus dubitare, num falsa sit (ut satis attendenti fit manifestum); vel, si quis statuat, substantiam creari, simul statuit, ideam falsam factam esse veram, quo sane nihil absurdius concipi potest; adeoque fatendum necessario est, substantiæ existentiam, sicut ejus essentiam, æternam esse veritatem. Atque hinc alio modo concludere possumus, non dari, nisi unicam, ejusdem naturæ, quod hic ostendere, operæ pretium esse duxi. Ut autem hoc ordine faciam, notandum est, I. veram uniuscujusque rei definitionem nihil involvere, neque exprimere præter rei definitæ naturam. Ex quo sequitur hoc II., nempe nullam definitionem certum aliquem numerum individuorum involvere, neque exprimere, quandoquidem nihil aliud exprimit, quam naturam rei definitæ. Ex. gr. definitio trianguli nihil aliud exprimit, quam simplicem naturam trianguli; at non certum aliquem triangulorum numerum. III. Notandum, dari necessario uniuscujusque rei existentis certam aliquam causam, propter quam existit. IV. Denique notandum, hanc causam, propter quam aliqua res existit, vel debere contineri in ipsa natura, & definitione rei existentis (nimirum quod ad ipsius naturam pertinet existere), vel debere extra ipsam dari. His positis sequitur, quod, si in natura certus aliquis numerus individuorum existat, debeat necessario dari causa, cur illa individua, & cur non plura, nec pauciora existunt. Si ex. gr. in rerum natura 20 homines existant (quos, majoris perspicuitatis causa, suppono simul existere, nec alios antea in natura exstitisse), non satis erit (ut scilicet rationem reddamus, cur 20 homines existant) causam naturæ humanæ in genere ostendere; sed insuper necesse erit, causam ostendere, cur non plures, nec pauciores, quam 20 existant; quandoquidem (per Notam III) uniuscujusque debet necessario dari causa, cur existat. At hæc causa (per Notam II & III) non potest in ipsa natura humana contineri, quandoquidem vera hominis definitio numerum vicenarium non involvit; adeoque (per Notam IV) causa, cur hi viginti homines existunt, & consequenter cur unusquisque existit, debet necessario extra unumquemque dari, & propterea absolute concludendum, omne id, cujus naturæ plura individua existere possunt, debere necessario, ut existant, causam externam habere. Jam quoniam ad naturam substantiæ (per jam ostensa in hoc Schol.) pertinet existere, debet ejus definitio necessariam existentiam involvere, & consequenter ex sola ejus definitione debet ipsius existentia concludi. At ex ipsius definitione (ut jam ex Nota II & III ostendimus) non potest sequi plurium substantiarum existentia; sequitur ergo ex ea necessario, unicam tantum ejusdem naturæ existere, ut proponebatur.


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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