1 Feb 2017

Bréhier (1.1) La théorie des incorporels dans l'ancien stoïcisme, “I. [on incorporeality and causality]”, summary


by Corry Shores


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[The following is summary. Bracketed commentary is my own, as is any boldface. Proofreading is incomplete, which means typos are present, especially in the quotation. Also, I request corrections to my interpretations, because I have probably misread the French text in some cases. So please always consult the original first.]




Summary of


Émile Bréhier


La théorie des incorporels dans l'ancien stoïcisme


Chapitre premier:

De l’incorporel en général



[on incorporeality and causality]




Brief summary:

The Stoics understood Platonic Ideas as being like geometrical definitions which set limits defining something, meaning that many individuals are generatable on that basis, all of which sharing some common formal structural feature. This view sees being as an incorporeal Ideal form which can serve as the cause of individuals, acting on bodies from the outside so to endow them with their formation. The Stoics held a view of causality and of being that goes directly against this Platonic sort of conception. Now, both views of cause and of being can be said to be matters of unity. The Platonic sort regards unity as what groups many individuals together under an Idea. The Stoic view sees unity as what gives coherence to an individual’s physical and temporal parts, and it is analogous to the vital force that gives unity to living things physically throughout their life. Being that is understood in this way is still like the Platonic Idea, in that it determines the thing’s limits, but it is different, in that these limits are the spatial boundaries that the thing grows toward but not beyond and the fixed set of latent capacities it will develop during its life. Thus a thing here is defined primarily by its principles of genesis. In an inanimate object it is called hexis, in plants, nature, and in animals, soul. This cause itself is something corporeal and is inherent to the corporeal thing it is the cause of. Corporeal things can act and undergo action, but incorporeal things cannot. This means that the Stoics regarded the soul as corporeal. They formulated syllogistic arguments against the incorporeality of the soul. There are three such arguments: {1} Since souls can resemble one another (as with child’s to parents’), and since incorporeal things are not matters of resemblance or non-resemblance, the soul is corporeal. {2} Since a body suffers when a soul does and vice versa, and since no incorporeal thing will suffer when a body does, the soul is corporeal. {3} Since the soul separates from the body, and since incorporeal things cannot separate from a body (as they never were a part of that body to begin with), the soul is corporeal. There are important principles underlying these arguments. The reason that incorporeals can be predicated neither of semblance nor non-semblance is because for the Stoics, properties are corporeal things, and semblance is a matter of sharing properties. Now, for Plato, a being’s property is the presence of an Idea in that being. But the Stoic notion of quality conceives it as being either something involved in a corporeal thing’s activity or as a final result of that activity. Thus properties under this Stoic conception make no appeal to an incorporeal Idea. Another important principle is that  the incorporeal has no causal efficacy on the corporeal. Although the Stoics consider the cause of beings as corporeal, that does not mean they make no place for the incorporeal. For, rather than placing the incorporeal on the side of the cause of beings, they instead place it on the side of the effects of beings.






[Mathematical and especially geometrical definitions can set limits that define a certain sort of entity, which enables an infinity of particular such entities to be generated. This is how the Stoics, like Chrysippus, understood Platonic Ideas.]


A mathematical definition allows us to generate a number of particular things fulfilling that definition by obeying the law it specifies. [Given that the specific things are generated on the basis of the definition, they in a sense can be said to be caused by them in a way. We might also here think of cause as reason or explanation, such that we say all the individuals have their formation on account of the fact they are endowed with the Idea forming them.] Thus we might say that between these generated beings and their model there is a causal relation of a sort, like that between a particular case and a law and between an imitation and its model. Whether or not Plato’s notion of the relation between the Idea and its proper sensible things is similar to this mathematical notion is not our concern here. For, this relation for Plato perhaps involves more activity and life than is found in the mathematical formulation. Nonetheless, it seems certain that the most prominent ancient Stoic, Chrysippus, understood this Platonic doctrine in the mathematical way. We know this from the first century B.C. mathematician Geminus of Rhodes. We first note Proposition 35 of Book 1 of Euclid’s Elements, which says that “parallelograms on the same base, and between the same parallels, are (in area) equal” (Euclid p.36).

On the basis of this theorem, we can construct an infinity of such equal figures, and this is how Chrysippus understands Ideas, namely, as involving the genesis of an indefinite number of beings within the given determinate limits. These limits set forth by the Idea only tell us what sort of thing will qualify [and thus what sorts of things do not qualify]; it does not, however, more precisely determine any of the beings falling within those limits. Thus the Idea determines not a particular thing but infinite multiplicity of them. [I am not certain, but the next idea might be that on the basis of Chrysippus’ interpretation, Proclus criticizes the Stoics for abandoning Platonic Ideas and for claiming that there is no reality outside the limits of given things.]

I. – Une définition mathématique est capable d’engendrer à elle seule une multiplicité indéfinie d’êtres, tous ceux qui obéissent à la loi exprimée dans la définition. Il y a entre ces êtres et leur modèle une espèce de rapport de causalité, celui du cas particulier à la loi, de l’imitation au modèle. Si c’est bien ainsi que Platon se représentait le lien entre l’Idée et les choses sensibles déterminées par elle, nous ne le recherchons pas ici. Il est possible qu’il ait cherché à introduire dans ses Idées plus d’activité et de vie qu’il n’y en a dans une formule mathématique. Mais ce qui est sûr, c’est que le représentant le plus considérable de l’ancien stoïcisme, Chrysippe, ne se représentait pas autrement la doctrine platonicienne. Nous avons sur ce point le témoignage de Geminus, un mathématicien du premier siècle avant J.-C. qui nous est connu par Proclus1. Suivant un théorème élémentaire, les parallélogrammes qui ont même base et dont les côtés sont compris entre les mêmes parallèles « sont égaux ». On peut, au moyen de ce théorème construire, dans des limites définies, une infinité de figures égales. De même, les Idées, suivant Chrysippe, « comprennent (περιλαμϐἀνουσιν) la genèse d’êtres indéfinis dans des limites déterminées ». La notion de limite est donc l’essentiel des êtres : l’Idée ne fait qu’indiquer les limites auxquelles doit satisfaire un être pour exister, sans déterminer de plus près la nature de cet être : il peut être ce qu’il veut dans ces limites, et par suite ce n’est pas un seul être qui est déterminé mais une multiplicité sans fin. On comprend par là que Proclus, reprochant aux Stoïciens d’avoir abandonné les Idées, leur fait sur- | tout d’avoir rejeté en dehors des réalités les limites des êtres1.

1. In Euclid. 35, 25 (Arnim. S. V. F. II 123, I. 39).

1. In Euclid. def. I, p. 89 (S. V. F. II, 159, 26).





[One view on being is concerned with the conceptualizable permanent structures that can characterize a being, with the thing’s variations from the ideal form being understood as degradations. This view the Stoics were against. Another view sees being as the coherence that unifies a being throughout its entire existence, during which it undergoes continual variation.]


[So one sense of causality is that a concept or definition can prescribe the limits for what constitutes something, thereby opening the generation of an infinity of things. The thinking here might be more or less similar to Spinoza’s notion of the definition generating its things by being formulated such that its things can be generated on its basis. What is important is that this should be seen as a notion of causality. It is not causality in the sense of efficient causality like one physical body striking another and causing it to move. But how to conceive this sort of causality is not so obvious to me. It could perhaps be something like the following. The Idea would be something like a productive mechanism. It might not guarantee the production of any particulars. However, any particulars that do come into existence would have been made possible by the Idea which prescribed their constitution in advance. Perhaps more simply cause is just to be understood as the reason or explanation for the particular formation of individuals, but I am not sure. We further need to consider what notion of being would be derived from this concept of causality. The beings here are the Idea and the particulars. But perhaps we are to think especially of the Ideas, as they are the causes and thus are more primary, meaning that the more primary mode of being is the Ideal sort.] The Stoics attacked this notion of causality and the conception of being that is derived from it. The nature of a cause is determined by the nature of the things or facts that the cause is supposed to explain. The Stoics, however, did not intend to explain the same things as Plato and Aristotle, who were concerned with the permanent and stable element of things which as well forms a basis for conceptual thought. This means that the Idea for them has the sort of permanence found in geometrical concepts. [It seems the next idea is something like the following. We are talking about permanence. What about movement, becoming, and the “corruption” of beings? We might think that the change involved in them would require some additional cause to put them in motion. However, from this idealistic sort of view, these factors found in particulars are like what escapes the causal hold of the ideas. The idea of a circle would cause instances of that circle, meaning that they should be perfectly round. However, any actual circle will have variations either initially in its production or over time from deterioration. So we cannot under this view say that the variations are caused by the Ideas but rather are escapes or breakdowns from those Ideas. Let me just add something, but it might not be part of the thinking here. We might be inclined to say that we are only able to conceive things using such conceptual forms which are Ideal. So when we see an actual circle in the world, we can conceptualize only its circularity. But that in it which veers from any sort of concept, the imperfections that are aberrations, are not things we can conceive. We must instead see them as subtractions from the ideal form implied in the concept.] What can attract attention in a being is, first of all, the element by which it resembles other beings and enables one to classify it. But another point of view on the matter considers the history and evolution of the being from its appearance until its disappearance. Being would then be considered not as part of a higher unity, but as the unity and center of all the parts that substantially constitute the being and of all the events which temporally constitute its life. It will be the deployment in time and space of this life, with its continuous changes. So, one way of understanding some being is in terms of how it resembles another in accordance with their common classification [thus in terms of the Idea they share]. However, another way is to consider a being in terms of its full development throughout its entire existence. Here being is not understood as being found in something higher that the particular thing but rather in the unity that coheres its parts and moments together as it continually varies over time.

C’est bien en effet à cette conception même de la causalité que les Stoïciens s’attaquent, et à la notion de l’être qui en dérive. La nature d’une cause est déterminée par la nature des choses ou des faits que cette cause a pour mission d’expliquer. Or les Stoïciens veulent expliquer autre chose, se placent à un point de vue autre que Platon et Aristote. Pour ceux-ci, le problème était d’expliquer dans les êtres le permanent, le stable, ce qui pouvait offrir un point d’appui solide à la pensée par concepts. Aussi la cause, qu’elle soit l’Idée ou le moteur immobile, est permanente comme une notion géométrique. Pour le mouvement, le devenir, la corruption des êtres, dans ce qu’ils ont de perpétuellement instable, ils sont dus non pas à une cause active, mais à une limitation de cette cause, échappant par sa nature à toute détermination et à toute pensée. Ce qui peut attirer l’attention dans un être, c’est d’abord l’élément par lequel il ressemble à d’autres êtres et qui permet de le classer. Mais un autre point de vue consiste à considérer dans cet être lui-même son histoire et son évolution depuis son apparition jusqu’à sa disparition. L’être sera alors considéré lui-même non pas comme partie d’une unité plus haute, mais comme étant l’unité et le centre de toutes les parties qui constituent sa substance, et de tous les événements qui constituent sa vie. Il sera le déploiement dans le temps et dans l’espace de cette vie, avec ses changements continuels.





[The Stoics saw being as a matter of the cohering composition found in living beings along with the development living beings undergo.]


For the issue of the problem of causes, the Stoics then did not look to the permanent features of things but rather to the changing ones. Hence Sextus Empiricus concludes that there are causes on the basis of certain facts relating to change and development, namely, growth from a seed or germ, the development of a plant, life and death, becoming and corruption, and the generation of like from like. As we can see, these facts in most cases involve living things, and the other cases were conceptually related to living things in the Stoics’ time. The whole world itself from their perspective is seen as a living being, given how it develops between its beginning and end and given the way its parts cohere like that of a living being. Even rocks are composed of cohered parts analogous to how those of living beings are. Thus the change of being itself is always analogous to the development of a living being.

Or c’est bien là qu’est situé pour les Stoïciens le problème des causes. Voici, d’après Sextus2, quelques-uns, des faits d’où il ils concluaient qu’il y avait des causes : la semence et le développement d’une germe, le développement d’une plante, la vie et la mort, le gouvernement du monde, le devenir et la corruption, la génération du semblable par le semblable. Les exemples sont presque tous, on le voit, empruntés aux êtres vivants. Même dans le cas contraire, les autres êtres sont, d’ans la pensée intime des Stoïciens, assimilés à des vivants. La chose est trop connue pour y insister longuement : le monde entier avec son organisation et la hiérarchie de ses parties, son évolution qui va d’une conflagration à une autre est un être vivant. Le minéral lui- | même, avec la cohésion de ses parties, possède une unité analogue à celle d’un vivant. Ainsi la donnée à expliquer, le changement de l’être est toujours analogue à l’évolution d’un vivant.

2. Sextus. Math. IX 196 (Arnim S. V. F. II 118, 8).





[Being as what unifies the thing’s physical and temporal parts is like the Platonic idea, in that it determines the thing’s limits, but it is different, in that these limits are those of the spatial extent to which the thing’s forms grow and of the capacities it will attain during its development. A thing then is defined primarily by its principles of genesis. In an inanimate object it is called hexis, in plants, nature, and in animals, soul.]


We now wonder what the nature is of this sort of being that unifies the temporal variability and constituent multiplicity of living formations. In a living thing it is the force that holds it together. In minerals this force is called hexis (ἕξις, “a relatively stable arrangement or disposition;” wiki), in plants it is called nature, and in animals it is called soul. It is always linked to whatever being it is the cause of. It determines the external form and limits of the thing it causes, not in the way that a sculptor crafts her statue, but rather in the way that a germ develops the outer form of the living thing up to a certain spatial limit and also only to a certain extent develops its latent capacities. This unity of cause and principle is expressed in the unity of the body it produces. According to Chrysippus, this holds also for the whole world itself as one entire thing. [The next idea might be the following, but check the quotation. Mathematics and geometry seemed to be the triumph of Platonism, on account of their purified formalism. But, with this other view of being, these forms are instead to be understood in terms of their genesis. The Stoics saw the Ideal forms as they are expressed in mathematics as being matters of definitions allowing for things’ construction. But now under this Stoic view, we would not even see them as predefined limits but rather as principles of genesis; for example, a straight line is one that stretches out to its end.] This means that the essence of being is not some ideal model that beings aim to imitate but is rather the productive cause that lives in the thing and gives it life.

Quelle est la nature de cette unité du vivant, unité sans cesse mobile, unité d’un contenant? Comment les parties de l’être sont-elles jointes de façon à persister? Ce sera, comme chez le vivant, par une force interne qui les retient, qu’on appelle cette force ἕξις dans les minéraux, nature dans les plantes, ou âme dans les animaux. Dans tous les cas, il est indispensable qu’elle soit liée à l’être même dont elle constitue la cause, comme la vie ne peut être que dans le vivant. Elle détermine la forme extérieure de l’être, ses limites, non pas à la façon d’un sculpteur qui fait une statue, mais comme un germe qui développe jusqu’à un certain point de l’espace, et jusqu’à ce point seulement, ses capacités latentes. L’unité de la cause et du principe se traduit dans l’unité du corps qu’elle produit. Ce principe est aussi vrai pour le monde dont l’unité se prouvait, selon Chrysippe, par l’unité de son principe1, que pour le moindre des êtres particuliers. Dans les mathématiques même, qui paraissaient être le triomphe du platonisme, les figures sont considérées non plus comme provenant d’une définition qui permet de les construire, mais comme l’extension dans l’espace d’une force interne qui se déploie : la droite est la ligne « tendue jusqu’à l’extrémité »2. La cause est donc véritablement l’essence de l’être, non pas un modèle idéal que l’être s’efforce d’imiter, mais la cause productrice qui agit en lui, vit en lui et le fait vivre, plus semblable, suivant une comparaison d’Hamelin3 à l’essentia particularis affirmativa dé Spinoza qu’à l’Idée platonicienne.

1. Plut. de defectu orac. ch. 29 (Arnim S. V. F. II 13).

2. Simpl. in Airst. cat. f. 68 e (S. V. F. II 149, 25).

3. Sur la Logique des Stoïciens (Ann. philos. 1901, p. 25).





[The Stoics’ return to dynamism and their tracing all causes to something analogous to a vital force is remarkable given the mechanistic trend at that time.]


Plato and Aristotle held a mechanistic view of life. The scholar Alfred Espinas has shown this development of mechanism in classic Greek philosophy. Given this strong trend, it is remarkable that the Stoics went against this current and returned to principles of dynamism and also traced all causes in the universe to something akin to a vital force.

L’on sait que Platon et Aristote admettaient assez volontiers une explication mécaniste de la vie. Espinas a montré dans les inventions mécaniques qui se poursuivent en Grèce depuis le VIe siècle, la raison de cette représentation de la vie4. Il est d’autant plus remarquable que, malgré cet te impulsion, les Stoïciens soient revenus au dynamisme, et qu’ils aient conçus, suivant l’analogie de la force vitale, toutes les causes de l’univers.

4. Revue de Métaph. 1905.





[For the Stoics, this causal principle of bodies is itself something bodily, given the intimate mixture between a things cause and the body that develops and manifests that cause.]


So for the Stoics, there is an intimate mixture between a thing’s cause and the body that develops and manifests it. [To follow the reasoning, we might say the following. Since the unifying cause of things is so bound up with bodies, we would not turn to another incorporeal realm outside the one where the cause manifests to explain what goes on there.] This intimacy of the cause within the corporeal leads to the negation of any sort of incorporeal action, and it also leads us to ask if the only existing things are bodies. To understand the Stoics’ sort of materialism, we should note that they did not have the notion of inertia that for us now serves as the fundamental postulate of materialism. According to this postulate, any force in a body comes from outside it and is endowed to it. This leads us to regard force as something immaterial, because it is not of the essence of the material. [But Stoics see force as something bodily.] This makes the Stoics spiritualist in a sense, and it is similar to Leibniz’s notion of dynamism. [I am not following so well. Perhaps they are spiritualist in the sense that force which is normally considered incorporeal is given a bodily form, or perhaps I am misreading the text, and the Stoics actually see force as outside the body.] [I am not certain, but perhaps the Leibniz idea is similar to the notion of conatus as the beginning and end of motion; see part 10 from Leibniz’ “Studies in Physics and the Nature of Body”.] This notion of the basic force that is endowed to all the parts of the universe and that gives them their unity could lead to a sort of mysticism. In fact, all the ancients saw the body as active by its essence and in itself. So we now can better see what is meant by “all is body.” Given the way we conceive of body [that is, as something whose uniting principle and source of activity is a physical part of it], the cause of the body is itself a body, and also that which undergoes this causal action is also a body. Thus this position does not claim that there is no principle of spontaneous activity in the world.

C’est ce mélange intime de la cause avec le corps qui la développe et la manifeste qui aboutit à la négation de toute espèce | d’action incorporelle, et à l’affirmation que nous devons maintenant examiner : « Tout ce qui existe est corps ». Pour comprendre cette espèce de « matérialisme », il faut se rappeler que les Stoïciens, non plus qu’aucun Stoïcien, n’ont possédé la notion de l’inertie de la matière, postulat fondamental du matérialisme de notre époque. D’après ce postulat, toute force ne réside dans la matière que par emprunt, parce qu’elle lui a été donnée de l’extérieur. Pour cette raison aussi nous avons peine à ne pas nous représenter la force comme quelque chose d’immatériel, puisqu’elle n’est pas de l’essence de la matière. En ce sens le stoïcisme serait aussi « spiritualiste » que le dynamisme leibnitzien sur lequel il n’a d’ailleurs pas été sans influence. Dans la longue carrière qu’il a fournie, il est d’ailleurs un moment où le stoïcisme, même dans sa physique, a présenté un aspect éminemment spirituel et favorable à l’éclosion du mysticisme : on trouva le moyen, par le recueillement sur cette force interne qui constitue le fond de notre être, de se rattacher à la forme compréhensive de l’univers, et de se sentir vivre en elle. Aussi bien, pour tous les anciens, le corps, comme tel, est actif par essence et en lui-même. Aussi l’affirmation que tout est corps veut dire seulement que la cause telle que nous venons de la définir est un corps, et que ce qui subit l’action de cette cause (τὸ πάσχον) est aussi un corps1; ce n’est nullement le refus de reconnaître qu’il y ait dans l’univers un principe spontané d’activité.

1. Πᾶν τὸ δοῶν ἢ χαι ποιοῦν σῶμα. Aèt. Plac. IV 20, 2(V. S. F. II 128).

(5-6. Note: the above Greek formulation is not legible in my copy and probably contains mistakes. It appears as:






[The incorporeal by nature can neither act nor undergo action. These properties for the Stoics are corporeal.]


The incorporeal by nature can neither act nor undergo action. These properties for the Stoics are corporeal, given the way that they use a more biological conception of cause instead of a mathematical one and also given that they have endowed the body with an internal activity.

L’incorporel par nature ne peut en effet agir ni pâtir2, au sens où les Stoïciens prennent l’activité et au sens où ils parlent du corps, c’est-a-dire en substituant une conception biologique de la cause à une conception mathématique, et en douant le corps d’une activité interne.

2. Sextus, Math. VIII 263 (V. S. F. II 123, 31).





[The Stoics, following Antisthenes, went against Plato’s notion of the activity of the Ideas and instead saw activity as corporeal in nature.]


The Stoics criticized the notion of the incorporeal activity. For example, Cleanthes and Chrysippus argue that the soul is a body. We know this from Nemesius, who argued against the Stoic position and in favor of the incorporeal action. The Stoics made many arguments that all quality is body, but we need not examine them, as they assume already that body is the sole acting agent. But also, in Plato’s time, Antisthenes, who was a precursor to the Stoics, was critical of the activity of Ideas, and he also claimed that every being is a body.

Il y a eu certainement chez les Stoïciens une critique de l’activité des incorporels. On en trouve certains principes dans l’argumentation de Cléanthe et de Chrysippe pour montrer que l’âme est un corps ; elle nous a été conservée par Némésius qui s’efforce : de réhabiliter contre elle l’action de l’incorporel. Nous n’avons rien à tirer, pour la compléter des arguments conservés en assez grande abondance, par lesquels les Stoïciens cherchaient à démontrer que « toute qualité est corps » ; car ils supposent tous précisément que le corps est le seul agent. Mais il faut se souve-| nir que, dès l’époque de Platon, une vigoureuse critique de l’activité, des Idées se trouve chez Antisthènes, le véritable précurseur des Stoïciens aussi bien dans la théorie de la connaissance que dans la morale. Antisthènes aussi affirmait, au scandale de Platon, que tout être était corps, et les Stoïciens ne font que soutenir jusqu’au bout le principe de ce philosophe, lorsqu’au défi de Platon : « ils n’oseraient soutenir que la prudence et les vertus ne sont rien ou sont des corps »1, ils répondent précisément que les vertus sont corps2.

1. Soph. 247 b c.

2. Sen. Ep. 117, 2.





[The Stoics formulated three syllogistic arguments against the incorporeality of the soul. {1} Since souls can resemble one another (as with child’s to parents), and since incorporeal things are not matters of resemblance or non-resemblance, the soul is corporeal. {2} Since a body suffers when a soul does and vice versa, and since no incorporeal thing will suffer when a body does, the soul is corporeal. {3} Since the soul separates from the body, and since incorporeal things cannot separate from a body (as they never were a part of that body to begin with), the soul is corporeal.]


Cleanthes argues against the incorporeality of the soul. The first argument is the following. The child resembles its parents both in body and in soul. Now, semblance and non-semblance are matters of the body and not of incorporeal things. Thus the soul is bodily. The second argument is the following. No incorporeal will suffer when a body does, nor will a body suffer when an incorporeal does. Now, the soul suffers when the body does, as for example when the body is sick or is injured. Similarly, the body suffers when the soul does, as for example when the body turns red when the soul suffers shame or when the body turns white when the soul is afraid. Chrysippus adds the following third argument. Death is the separation of the soul and the body. But no incorporeal is separated from a body. For, the incorporeal does not touch the body. [I did not follow that argument.] Thus the incorporeal can be neither agent nor patient with respect to the body.

On connaît les arguments de Cléanthe contre l’incorporéité de l’âme ; d’abord l’enfant ressemble à ses parents non seulement par le corps, mais par l’âme; or le semblable et le dissemblable appartiennent au corps, non aux incorporels : l’âme est donc un corps. Le second est le suivant : « Aucun incorporel ne pâtit avec un corps, ni un corps avec un incorporel ; or l’âme pâtit avec le corps, lorsqu’il est malade ou lésé; et le corps avec l’âme, dans la rougeur de la honte ou la pâleur de la crainte »3. A ces deux arguments, Chrysippe ajoute le suivant : « La mort est la séparation de l’âme et du corps ; mais aucun incorporel n’est séparé d’un corps; car l’incorporel ne touche pas le corps »4. Evidemment les trois principes de ces trois arguments dépassent la question de la nature de l’âme : ils sont destinés à montrer qu’en général l’incorporel ne peut être agent ni patient à l’égard du corps.

3. Tert. de an. 5 et Nemes. de nat. hom. p. 32 (S. V. F. I 116, 32).

4. Nemes. ib. p. 53 (S. V. F. 219, 25).





[We might be confused by the principle behind the first argument above, namely, that the incorporeal is a matter neither of resemblance nor dissimilarity. For, we would think that if it takes not one designation, it should take the other. However, incorporeality is of such a nature that neither designation applies. This is analogous to how the smallest circular conic sections of a cone are incorporeal and thus it is not absurd to say that adjacent ones are neither equal nor unequal in diameter.]


There were three principles involved in the above three arguments. The first is the most obscure: the soul is body because it is subject to resemblance and dissimilarity. To better grasp the difficulty with the principle, we consider an example Chrysippus gives with regard to a particular incorporeal, namely, the geometric surface. Democritus describes a geometrical problem that Chrysippus provides a solution for [for details, see this entry on Plutarch’s text, which discusses Democritus’ problem and Chrysippus’ solution. Here is a moving diagram from that summary.


(Moving diagram by Corry Shores, made with Open Office Draw and Unfreez)

The basic idea is the following. We think of a cone being built up from its base of horizontal layers. We are to think of each very smallest possible layer. If all the smallest possible layers were of different diameters (if they are “uneven” or “unequal”), then you would not get a smooth surface for the cone, but rather it would have many tiny ridges, like a staircase on the smallest scale. This of course goes against our notion that the sides are perfectly smooth, as a straight line should be found when going from the edge of the base to the peak, following along the surface. But if all the thinnest layers are of the same size, the figure would not incline to a peak like a cone but rather rise up like a cylinder. Chrysippus’ solution is thus to say that the layers are neither even nor uneven, which Plutarch takes to be an absurdity. In that summary, our purpose was to consider Chrysippus’ concept as an early sort of notion of the calculus infinitesimal, which would say that each layer is a tiny variation in size rather than a tiny complete size.] Democritus was examining the problem of the spatial continuum, and he posed it with the example of a cone. If we conceive of all its adjacent circular conical sections as being unequal, then they would not be smooth but rather will have asperities. If however we conceive them as equal, then the figure will have the properties of a cylinder and not a cone. According to Plutarch, Chrysippus’ solution was to claim that the conic circles were neither equal nor unequal. Plutarch says this is an absurdity, since it is impossible to conceive of something being both equal and not equal at the same time. However, if Chrysippus means by this that the surfaces do not exist, then his solution avoids the absurdity and also is based on very profound insight. This interpretation is based on Chrysippus’ other claims that he has made regarding continua. For instance, he demonstrates that the division of space admits of no limit, thus we cannot speak of some determinate number of parts contained in a magnitude, as they are infinite. He similarly demonstrates the non-being of the Universe as a whole, and he also shows that the universe is neither corporeal, incorporeal, at motion, nor at rest. [Regarding the cone at least, perhaps we can conceive of the incorporeality of the conic sections in the following way. If we see them as infinitesimal, they are not nothing, but at the same time, they still have a magnitude. Were we to see them as “vanishing”, then they would not be incorporeal, as they have a quantitative property that only bodies can have (magnitude), but they are not corporeal, as they have vanished from the realm of extension.] [We need now relate this reasoning to the principle behind the first argument that the soul is corporeal because it admits of semblance and non-semblance. I am going to make a guess, but please consult the quotation below to find your own better interpretation. Let us draw an analogy. The conic sections are neither equal nor unequal. They are neither, because they are incorporeal. Likewise, the incorporeal is a matter neither of semblance nor of non-semblance. The idea might simply be that certain designations apply to the corporeal and not to the incorporeal. The problem with conceiving them might be that we would think that the incorporeal would have to be a matter either of resemblance or of non-resemblance, because to not be one is to be the other. But maybe Chrysippus’ point is that neither designation applies to it. Please see for yourself.] Thus perhaps by saying that neither semblance nor non-semblance are predicates of incorporeality, Cleanthes is claiming that it is not a being.

Le premier de ces principes est le plus obscur : Σώματος τὸ ὅμοιον και τὸ ἀνόμοιον, οὐχὶ δὲ ἀσωμάτου, ou comme dit Tertullien: « l’âme est corps parce qu’elle est sujette à la ressemblance et à la dissemblance ». Un exemple de Chrysippe à propos d’un incorporel particulier, la surface géométrique, pourra au moins préciser la difficulté : Démocrite avait posé de la façon suivante le problème du continu spatial : Si nous considérons, dans un cône, des sections coniques circulaires voisines les unes des autres, ou bien ces surfaces seront inégales, et alors la surface du cône ne sera pas lisse, mais présentera des aspérités, ou bien elles seront égales, et la figure aura alors la propriété d’un cylindre : ce ne sera plus un cône. D’après Plutarque, Chrysippe résolvait la difficulté en disant que les cercles n’étaient ni égaux | ni inégaux1. C’est à l’avis de Plutarque, une absurdité, puisqu’il est impossible de concevoir ce qui n’est ni égal ni inégal. L’absurdité n’existerait plus (et la réponse serait même singulièrement profonde) si Chrysippe avait voulu faire entendre par là que ces surfaces n’existent pas. Or c’est bien cette réponse qui ressort de toutes ses autres considérations sur le continu : il y montre qu’aucune limite n’existe à la division de l’espace et que l’on ne peut par suite parler du nombre des parties contenues dans des grandeurs différentes, comme le monde et le doigt d’un homme, puisqu’il n’y a pas de plus ou de moins dans l’infini2. C’est sous la même forme qu’il montre le non-être de l’Univers comme tout (τὸ πᾶν : c’est-à-dire à la fois le monde et le vide qui l’entoure), en montrant qu’il n’est ni corporel, ni incorporel, ni mû, ni en repos, etc.3. Il est donc probable qu’en refusant à l’incorporel en général à la fois le prédicat de semblable et de dissemblable, Cléanthe veut dire qu’il n’est pas un être.

1. Plut. de comm. not. ch. 39 (S. V. F. II 159, 34).

2. Ib. chap. 38 (S. V. F. II 159, 1).

3. Ib. chap. 3o (S. V. F. II 167, 19).





[The reason that incorporeals can be predicated neither of semblance nor non-semblance is because for the Stoics, properties are corporeal things, and semblance is a matter of sharing properties.]


We still need to determine in what sense Cleanthes understands this double negation [that the incorporeal is a matter neither of semblance nor of non-semblance.] Plato thought he could resolve the difficulties regarding subject and predicate raised by the Megarian philosophers by introducing the notions of semblance and non-semblance into the Ideas. In fact, in Stoic logic there are traces of Megarian doctrines that were imported through Antisthenes. But Aristotle defines semblance in the Metaphysics in the following way: Things are said to resemble when they have an identical property or when they have more identical properties than different ones. [“Things are called ‘like’ which have the same attributes in all respects; or more of those attributes the same than different.” I found this passage in Aristotle’s Metaphysics under Book 5, Δ, line 1018a. See Perseus and Loeb.] For the Stoics, properties are bodies, and as such they cannot be seen as belonging to incorporeals. For this reason, we cannot think of incorporeals as being alike or not alike. [Since incorporeals cannot have properties, they cannot share any to begin with, and thus they cannot be said to be resembling or non-resembling]. [Check the quote, but the next idea might be that incorporeals for the Stoics take the form of beings deprived of all action and differentiation.]

Reste à chercher en quel sens il entend cette double négation. On sait que c’est en introduisant dans les Idées le semblable et le dissemblable, le même et l’autre que Platon, pensait pouvoir résoudre les difficultés sur le rapport du sujet au prédicat, qui avaient été soulevées par les philosophes de Mégare. Il y a dans la logique stoïcienne des traces nombreuses des doctrines mégariques qui lui sont parvenues par l’intermédiaire d’Antisthènes. D’autre part Aristote avait donné du semblable la définition suivante au chapitre IX du livre IV de la Métaphysique : « Sont dites semblables les choses qui ont une propriété identique (ταὐτὸ πεπονθότα) ou qui ont plus de propriétés identiques que de différentes ». Or les propriétés (ποιότητες) sont pour les Stoïciens des corps4 ; il est donc impossible de penser qu’une propriété en général appartienne aux incorporels, et par conséquent de parler de leur ressemblance ou de leur dissemblance. Si nulle part nous ne rencontrons cette preuve nous en voyons au moins les conséquences dans le stoïcisme. Le seul incorporel qui subsistera sera non plus comme chez Platon l’Idée remplacée par la qualité corporelle, mais le vide, la forme des êtres, privée de toute action et de toute différence.

4. Gal. de qual. inc. 1 (S. V. F. II 126, 16).





[A Platonic approach to the notion of quality would say that a thing has a certain property because it is qualified (or shaped) by some Idea. Such quality exists as a form and not as something active or corporeal. But the Stoic notion of quality instead conceives it as being either something involved in a corporeal thing’s activity or as a final result of that activity. Thus properties under this conception make no appeal to an incorporeal Idea.]


For Plato, a being’s property is the presence of an Idea in that being. [The Stoics however aimed to define property in such a way that it is understood as arising from within the thing and not as resulting from the exterior intervention of a form.] From this notion some Stoics derive the distinction that Simplicius notes between ποιόν and ποιότης. [For a translation of these terms: “First, Simplicius addresses the subtitle he has received for this section, Περὶ ποιοῦ καὶ ποιότητος (On what sort and | quality), which he explains as an error: if such a distinction were recognized, he says, Aristotle’s categories would need to be doubled from ten to twenty, for each category would be subdivided into the general quality that is shared by an individual particular (the ποιότης) and the particular property contained in the individual (τὸ ποιόν)” (Antisthenes / Prince, Susan: pp.437-438, italics mine).] There are three kinds of ποιά [qualities / properties] [or three senses of the term]: {1} both transient properties, like running, walking, and as well stable properties; {2} states, like prudence; and {3} ποιότης: properties that have arrived at a permanent state of perfection. We see here something more than a simple distinction between essential and accidental properties. Rather, there is the difference of nature between the sorts of quality {a} that have an active and corporeal reality and that need nothing else to explicate them but which are confined to a unique notion, and {b} the first type of ποιόν, which are a result without corporeal reality. It is by means of this theory that the Stoics deprived the incorporeal Idea of any efficacy or property. [The idea here might be the following, but please check to be sure. If we take the Platonic approach, we would say that a thing has a certain property because it is qualified (or shaped) by some idea. The quality thus is something existing as a form and therefore is not active or corporeal, and such qualities in things need the form to explain them. But the Stoic way of understanding quality instead sees it as being either something involved in a corporeal thing’s activity or as a final result of that activity. Thus properties under this conception make no appeal to an incorporeal Idea.]

La propriété d’un être était chez Platon la présence d’une | Idée dans l’être. Les Stoïciens se sont efforcés de définir la propriété de façon à la faire naître de la qualité fondamentale de l’état, sans l’intervention extérieure d’une forme1. De là est dérivée, chez certains d’entre eux, cette distinction que nous fait connaître Simplicius2, entre le et la ποιόν et la ποιότης. Il y a trois sortes de ποιά : dans le premier sens, le mot indique aussi bien les propriétés passagères (courir, marcher) que les propriétés stables. Dans le second sens, il indique seulement les états (σχέσεις, comme le prudent). Dans le troisième enfin qui coïncide entièrement avec celui du mot ποιότης, il indique seulement les propriétés arrivées à leur état de perfection et tout à fait permanentes (ἀπαρτίζοντας χαὶ ἐμμόνους ὄντας). Il y a l’à bien en autre chose que la simple distinction des propriétés essentielles et accidentelles : c’est la différence intime de nature entre la qualité qui est une réalité corporelle et active qui n’a pas besoin d’autre chose pour être expliquée, mais « qui se borne à une notion unique », et le ποιόν du premier genre, qui n’est dans le premier de ses sens, qu’un résultat sans réalité corporelle. C’est par cette théorie dont nous n’avons pas à suivre ici le développement qu’ils privaient l’Idée incorporelle de toute efficacité et de toute propriété, n’y rencontrant plus que le vide absolu de pensée et d’être.

1: Simpl. in Ar. cat. f. 57 E (S. V. F. II 126, 21).

2. Simpl. in Ar. cat. f. 55 A (S. V. F. II 128, 31).

(8-9. Note. There is a third footnote, but I do not see a superscript 3 for it in the text, in my copy. It may apply either to this or to the prior paragraph. I will place it below, along with an image of the quotation in Greek, because it is not legible for me.)

3. Id., in. Ar. cat. fr. f. 57 E (S. V. F. II, 126, 21) εὶς ἓν νόημα ἀπολῄγο ουσαν.





[The second argument was that the soul is corporeal, because it suffers when the body does, and vice versa. The principle at work here is that the incorporeal has no causal efficacy on the corporeal. The third principle is that the incorporeal does not touch the body, which is why it has no causal effect on it. At work here is a new concept of causality. The cause of something’s form is not some exterior Idea that explains the formation of many individuals. Rather, it is something inherent to every individual, explaining the particular unity it has among its physical and temporal parts. In order for the soul, then, to have such a unifying force on the body that we know it to have, it would need to be a corporeal cause of this sort.]

[Recall the second argument. No incorporeal will suffer when a body does, nor will a body suffer when an incorporeal does. Now, the soul suffers when the body does, as for example when the body is sick or is injured. Similarly, the body suffers when the soul does, as for example when the body turns red when the soul suffers shame or when the body turns white when the soul is afraid.] The second principle is the following: Οὐδέν ἀσώματον συμπάσχει σώματι, ούδὲ ἀσωματῳ σῶμα, ἀλλὰ σῶμα σώματι. [I do not know how that translates. I found this passage in Nemesius’ On the Nature of Man. In the 1565 edition on page 33, lines 18-20. In the 1987 edition on page 21 lines 6-7. And in the 2008 translation on p.58 (lines corresponding to the 1987 edition). Supposing I have the lines right, there the translation is: “nothing incorporeal shares affections with a body, nor any body with the incorporeal”.] This principle excludes any reciprocal action between the realm of bodies and the realm of the intelligible. By doing so, it eliminates the necessity of the incorporeal. [I am not sure why the incorporeal is made unnecessary, but perhaps since it has no effect on the corporeal, and since all qualities and actions are corporeal, we do not need the incorporeal.] [Recall that the third argument is: Death is the separation of the soul and the body. But no incorporeal is separated from a body. For, the incorporeal does not touch the body.] The third principle, from Chrysippus, explains what sorts of conditions would be needed were the incorporeal to be able to act on the body. According to him, the incorporeal does not touch the body. So if the only way the incorporeal could affect the body is by contact, then this deprives the soul, which is incorporeal, of any power of action on the body. Here the Stoics seem to have anticipated a problem with the mind-body relation that is later dealt with by the Cartesian school. The Stoic solution is simply to claim that the soul is corporeal. What is at play here is their notion of causality, which makes an ideal causality impossible. There are two conditions for this. {1} The causes are of the same substance as the effects, with effects here being the effectuated thing. {2} Cause itself must then be conceptualized in a different way than in the Platonic sense. The first condition is needed in order to explain the interpenetration of force and body that constitutes biological causality. The second condition’s necessity was indicated actually in Simplicius’ critique of it. He was thinking really of Aristotle’s analysis of cause into different elements that are reassembled in order to produce its effect. According to Aristotle’s theory, the incorporeal cause, being the action of the form, can coincide with the material cause. But the Stoics instead argued that there was only one type of cause. Their concern was not to explain the comprehensive unity of a plurality of individual with a single generality but rather simply to explain the unity of an individual itself, which includes the unity of the world as well as any rock or animal in it. Since the cause is something interior to the individual, that means it cannot be traced to the exterior action of an immaterial being.

Le deuxième principe est le suivant : Οὐδέν ἀσώματον συμπάσχει σώματι, ούδὲ ἀσωματῳ σῶμα, ἀλλὰ σῶμα σώματι. Ce principe, en supprimant toute action réciproque entre le monde des corps et l’intelligible, supprime la nécessité de l’incorporel. Nous sommes aussi peu renseignés d’une façon directe sur sa démonstration que sur celle du premier principe. Mais le troisième principe, celui de Chrysippe, l’éclaircit un peu en montrant à quelles conditions on pourrait concevoir l’action de l’incorporel sur le corps. «L’incorporel, dit Chrysippe, ne touche pas (οὐχ ἐφάπτεται) le corps». Se figurer que l’action de l’âme sur le corps n’a lieu que par le contact, c’est en effet rendre tout à fait impossible l’action de l’âme, supposée incorporelle de nature. Les Stoïciens semblent avoir entrevu ici la difficulté des rapports de l’âme et du corps qui constituera un problème pour les écoles cartésiennes. Ils la résolvent d’une façon simple en admettant la corporéité de l’âme. C’est en effet leur conception même de la causa- | lité qui est en jeu. Pour qu’elle subsiste, il faut deux conditions qui rendent impossible toute causalité idéale1 : d’abord que les causes soient de même substance que les effets (ὁμοούσια τοῖς ἀποτελουμένοις) en entendant ici par effet la chose effectuée ; ensuite qu’il y ait une conception unique de la cause. La première condition est nécessaire, puisque sans elle on ne conçoit pas cette pénétration intime de la force et du corps qui constitue la causalité biologique. La seconde ne l’est pas moins : Simplicius en l’indiquant en fait un reproche aux Stoïciens. Il songe sans doute à l’analyse aristotélicienne de la cause, qui avait brisé pour ainsi dire celle-ci en différents éléments qui se rassemblaient pour concourir à la production de l’effet. Dans cette théorie la cause incorporelle, comme action de la forme, pouvait subsister à côté de la cause matérielle. Qu’il n’y ait qu’une seule espèce de cause, c’est au contraire la théorie soutenue avec insistance par les Stoïciens2. C’est qu’il s’agissait pour eux d’expliquer l’unité de l’individu, aussi bien l’unité du monde que l’unité d’une pierre ou d’un animal, et non plus cette unité compréhensive de plusieurs individus qui est le général. Aussi la cause doit être une dans l’intimité de l’individu. Cette force intérieure ne peut nullement se concilier avec l’action extérieure d’un être immatériel.

1. Simplic. in Arist. cat. f. 56 Δ (S. V. F. II 626, 18).

2. Cf. surtout Sen. Ep. 65, 4 (S. V. F. II 120, 9).

(9-10. Note: the 6 in 626 of footnote one is blotted in my copy. I note this in case it was struck-out.





[Although the Stoics consider the cause of beings as corporeal, that does not mean they make no place for the incorporeal. For, rather than placing the incorporeal on the side of the cause of beings, they instead place it on the side of the effect.]


The Stoics’ nominalism arises more from their physics than from their logic. The reason they see the real and being in the individual alone is because for them, the cause and vital center of a being is found only in the individual itself. Nonetheless, from a very different point of view, we could say that in both their physics and in their general theory of causes they provide a substantial place for the incorporeal. But rather than placing the incorporeal on the side of the cause of beings, they instead place it on the side of the effect. We turn now to elaborate on this notion.

Le nominalisme des Stoïciens se trouve être moins un postulat de la logique, qu’un résultat de la physique. S’ils voient le réel et l’être dans l’individu seul, c’est parce qu’en lui seulement se trouve la cause et le centre vital de l’être. Pourtant à un tout autre point de vue, ils ont fait dans leur physique même et dans leur théorie générale des causes une large place à l’incorporel. Seulement au lieu de mettre l’incorporel dans la cause des êtres, ils le mettent dans l’effet. C’est ce point que nous allons maintenant expliquer.







Bréhier, Émile. 1962. La théorie des incorporels dans l'ancien stoïcisme. 3rd Edn. Paris: Vrin. PDF of a microfilm version available at:




Or if otherwise noted:


Antisthenes / Prince, Susan. 2015. Antisthenes of Athens: Texts, Translations, and Commentary. Ann Arbor: University of Michigan.


Aristotle. Metaphysics. Book 5, Δ, line 1018a.




Euclid; Oliver Byrne. The First Six Books of The Elements of Euclid, in which Coloured Diagrams and Symbols are Used Instead of Letters for the Greater Ease of Learners. London: William Pikering, 1847. Available at:




Nemesius. 1565. Nemesii episcopi et philosophi De natvra hominis: liber unus. Antverpiae: Christophori Plantini [Antwerp: C. Plantin]. Available online at:



Nemesius. 1987. Nemesii Emeseni. De natvra hominis, ed. Moreno Morani. Leipzig: Teubner. Available online at:



Nemesius. 2008. On the Nature of Man. English trans. by R.W. Sharples and P.J. van der Eijk. Liverpool: Liverpool University.




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