Bréhier (1.2) La théorie des incorporels dans l'ancien stoïcisme, “[The two planes of being: deep, real corporeality and surface incorporeality (predicates)]”, 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. So consult the original text. Also, I welcome corrections to my interpretations, because I am not good enough with French to make an accurate translation of the text.]

Summary of

 

Émile Bréhier

 

La théorie des incorporels dans l'ancien stoïcisme

 

 

Chapitre premier:

De l’incorporel en général

 

1.2

[The two planes of being: deep, real corporeality and surface incorporeality (predicates)]

 

 

 

 

 

 

Brief summary:

Only the beings that can act and be acted upon are real beings for the Stoics. These are the corporeal bodies. They are composed fundamentally of the element Fire, which under lesser degrees of tension constitutes Air, Water, and Earth. So the whole of the cosmos is fundamentally composed of Fire, and everything in the cosmos cyclically returns to a universal conflagration. As such, what we call bodies can also be understood as regions of the universal Fire-substrate that are unified according to principles of their elemental composition, namely, of their particular mixtures and internal arrangements  of elements (which again are no more than different tensions of the Fire substrate). When we say that one body acts upon another, we can also think of it as one organized region of the universal Fire interpenetrating with another region, creating a new mixture in that general region. So when we see one body interacting with another, we might want to think that the one body causes changes to the properties of the other one. But really, the one region of Fire has intermixed with another, and neither region changed the physical properties of the compositional Fire. It is still Fire at its various degrees of tension. What does change are the arrangements of the elemental parts, which correspond to alterations in the corporeal thing’s way of being (πώς ἔχον) and thus to a change in the thing’s predicates. So when a knife cuts flesh, the two interpenetrate to create a new mixture, and corresponding to the new arrangement within the flesh is a new predicate, “being cut”. [And to the knife’s new arrangement corresponds the predicate “cutting”.] So the action of bodies cause modifications not to other bodies but rather to their predicates. These predicates are entirely incorporeal and at best can additionally manifest in our minds when we conceive them. The Stoics were always sure to make the grammatical structures of their descriptions of corporeals and incorporeals match their physical differences: causes, which can only be corporeals, are always expressed with nouns, and effects, which can only be incorporeals, are always expressed with verbs in the form of predicates. This is the Stoics’ unique philosophical innovation, which, as we will see later, revolutionized logic. In sum, their innovation is that they fashioned the world into two planes: {1} There is the plane of real and profound being, in which there are corporeals (physical bodies) that act and are acted upon by other corporeals on account of physical forces driving their interaction. {2} There is the plane of surface [and unreal] being. It lies at the metaphysical limit of the corporeal plane, remaining directly related to the interactions of corporeals, but not existing as something physically real among those interacting bodies. Here facts (predicates) play at the surface of physical being.  These facts or predicates are the effects which are caused by the corporeal interactions. (In the case of the knife and flesh, the predicate, “being cut” is also “the fact of being cut.” So the action of the knife, in how it intermixes with the flesh, causes the fact-of-being-cut to arise upon the predicative/incorporeal “surface” of the flesh.) As such, the forces driving interaction on the deeper real plane are not exhausted by having produced effects on the incorporeal plane, since these effects are not matters of physical force.

 

 

 

 

 

 

Summary

 

 

1.2.1

[The only true beings recognized by the Stoics are the active cause (τὸ ποιοῦν) and the being that the cause acts upon (τό πάσχον). There are four elements of the world: Fire, Air, Water, and Earth. Fire and Air are active, and they act transformatively upon Water and Earth, which are passive. Fire is the primordial being and the seminal reason of the world, for two reasons: {1} the other elements are absorbed into the Fire (at cosmic cycles), and {2} the other elements are degrees of tension and relaxation of Fire.]

 

The only true beings recognized by the Stoics are in the first place the active cause (τὸ ποιοῦν) and then secondly the beings that the cause acts upon (τό πάσχον). [Recall from Sambursky’s Physics of the Stoics section 1.1 that the Stoics held that the cosmos is a continuous whole surrounded by a void. The continuity of the whole is a dynamic continuity resulting from a cohering activity of a very rarified substrate called pneuma. Pneuma is composed of a mixture of the active elements, Air and Fire, while Water and Earth are the other two passive elements that pneuma serves to bind.] The active elements of the world, fire and air, act transformatively upon the passive elements [Water and Earth]. Air, Water, and Earth are consumed in the universal conflagration. Thus Fire is the primordial being and the seminal reason of the world. The other beings [presumably Air, Water, and Earth, or if not, perhaps any individual object composed of the elements] are produced by a relaxation of the tension of the primordial fire. [I may not get this last point right, so see the final sentence of the quotation below. It might be the following. Air, Water, and Earth are not the effects or the parts of Fires (êtres primitifs), but are rather different states of tension of Fire.]

Les seuls êtres véritables que reconnaissent les Stoïciens, c’est d’abord la cause active (τὸ ποιοῦν), puis l’être sur lequel agit cette cause (τό πάσχον).³ Encore faut-il ajouter que les éléments actifs du monde, le feu et l’air, donnent naissance par transformation aux éléments passifs ; les trois derniers, dans la conflagration universelle, se résorbent eux-mêmes | dans le feu, si bien que l’être primordial est le feu, la raison séminale du monde. Les autres êtres sont produits par une tension moindre, un relâchement du feu primordial. Ils ne sont ni les effets ni les parties des êtres primitifs, mais plutôt des états de tension différents de cet être.

3. Philon du mund. op. 8 (V.S.F. II 111, 18).

(11-12, note, the footnote reads V.S.F rather than S.V.F. in my version)

 

 

 

1.2.2

[The active beings are the pneumata (πνεύματα) or “breaths,” whose actions are evinced through their effects. Through these effects, they can serve as qualities of bodies, namely primary ones: being hot, being cold, being dry, and being wet, and secondary ones like colors and sounds.]

 

Among these active beings are the qualities of bodies. The active beings are the pneumata (πνεύματα) or “breaths” whose actions are evinced through their effects. The active beings as qualities are in the first place the primarily qualities that can belong to the elements, namely, being hot, being cold, being dry, and being wet. And secondly they are such sensible [secondary] qualities as colors and sounds.

Parmi ces êtres actifs se trouvent les qualités des corps ; ce sont des souffles (πνεύματα) dont l’action se montre par leurs effets. Il y a d’abord les premières qualités qui appartiennent aux éléments, le chaud, le froid, le sec, l’humide, puis les autres qualités sensibles comme les couleurs et les sons.

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1.2.3

[We should not understand the Stoic notion of the world as being composed of distinct corporeal things that can be said to be the causes or effects of one another. Rather, beings are spontaneous principles that are different moments or aspects of one same universal being, the Fire.]

 

Bréhier notes that the world is composed not just of material beings made of the elements [Fire primarily, whose lesser degrees of tension are the other elements]. There are as well causes and principles. [I may not get the rest right, so please consult the text below. Given the Stoic cosmology of the universal fire, it is best not to think of the things in the world as being like substantial objects that can cause one another. Rather, beings should be seen as spontaneous “principles” (or let us say for now, “events”) that happen within the one same being, the Fire. But otherwise, in their doctrine of causality, one (corporeal) being cannot be said to be the effect of another (corporeal) being. (See for example the selective summary of Clement’s Stromata section 8.9.)]

Il faut remarquer que l’énumération de ces êtres, qui sont tous les êtres de la nature, ne nous fait pas sortir des causes et des principes. Le monde des Stoïciens est composé de principes spontanés, puisant en eux-mêmes vie et activité, et aucun d’eux ne peut être dit proprement l’effet d’un autre. La relation de cause à effet entre deux êtres est tout à fait absente de leur doctrine. S’il y a relation, elle est d’un tout autre genre : ces principes sont plutôt comme les moments ou les aspects de l’existence d’un seul et même être, le feu dont l’histoire est l’histoire même du monde.

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1.2.4

[Although corporeals cannot be causes or effects of one another (that is to say, they cannot change the corporeal properties of one another), they can still interpenetrate to form new mixtures, which is what really happens when we say that one body is causally influencing another body. Since everything is made of Fire, and since Fire never changes its physical nature (except for its degrees of tension, which is more a matter of distribution rather than composition), that means when one body mixes into another, neither one changes the physical properties of the other. For, their fundamental components of Fire retain their same physical Fire properties. What does change however as a result of the mixture are the arrangements and tensions of their component parts, corresponding to which are changed predicates (attributs) of the mixing bodies. Now, a predicate is not a quality. It is rather a way of being of the corporeal. So when a knife cuts flesh, the knife’s action causes the flesh’s way of being to change and to take on the predicate “being cut,” (and in the same stroke, the flesh’s passion causes the knife to take on the predicate “is cutting”). Predicates, then, are always expressed by verbs. And since they are not corporeal changes but rather correspond to them as incorporeal “events”, that places them at the “limit” or “surface” of the corporeal bodies they are predicates of.]

 

[But even though beings cannot be causes and effects of one another,] real beings can, however, enter into relations with one another, and by means of these relations, they in some sense modify one another. Clement of Alexandria says that real beings are not causes of one another but are rather causes of certain things for one another. [See especially subsection 12.1 of Stromata section 8.9.] These modifications are not themselves realities. They are neither substances nor qualities. One body cannot give new properties (propriétés) to another body. When bodies interact such that causation can be said to occur, what is really happening is that the two bodies interpenetrate and form a mixture (μῐξις or κρᾶσις). So when fire heats iron until it reddens, the fire has not given the iron a new quality (qualité) [redness or heat]; rather, the fire has penetrated into the iron and the fire’s parts now coexist among the iron’s parts. These modifications (modifications) however are not on this level of mixtures. They are not new realities (réalités), as properties (propriétés) of the things; rather, they are only attributes (attributs) (κατηγορήματα) [predicates] of the things. When the scalpel cuts the flesh, the first body (scalpel) produces upon the second body (flesh) not a new property (propriété) but a new attribute (attribut) [predicate], namely, that of being cut. [As we see, we must make some critical terminological distinctions. A property is a physical trait produced by a physical modification. One body cannot cause another body to have a property, because one body can only form a mixture with another. This mixture does not cause the mixed bodies to change their physical traits, that is, their properties; it only changes one another’s attributes or predicates. To continue this account, let me draw from an overall interpretation I gave in my commentary to Luhtala’s On the Origin of Syntactical Description in Stoic Logic section 5.6.2.4; but I will modify it to fit what Bréhier said in section 1.2.3 above. We have Fire primarily, and its various degrees of relaxation are the other elements. But overall, there is just one element, Fire. The parts of fire never change their properties. They only change their mixture arrangements. Different mixture arrangements will correspond to different predicates (here, ‘attributs’). So one thing, which as a corporeal is madee fundamentally of Fire, does not change the properties of another thing, which is also fundamentally Fire. Rather, the two sets of organized Fire particles, like the sets composing the knife and the sets composing the flesh, both enter into mixtures when they interpenetrate. But since all is just one Fire, we can think of their interpenetration as one region of the Fire moving through another region. So the region we call ‘knife’, when it is penetrated by the region we call ‘flesh’, does not thereby involve any physical change to its fundamental Fire particles. Rather, that region we call ‘knife’ now takes on the new incorporeal predicate ‘is cutting’, in accordance with its new compositional mixture. And similarly for the region we call ‘flesh’, the only change to it through this mixture is its new predicate ‘being cut’. I am not sure how to define “quality” yet. We know at least that a quality is not an attribute, because attributes are expressible by verbs. But attribute is defined as an incorporeal predicate, which is of such a physical nature that it is best expressed as a verb.] An attribute does not indicate a real quality. White and black for example [may be qualities, but they] are not attributes. For, an attribute is always expressed by a verb. This means that it is not a being, rather, it is a way of being. [It is not a thing itself, but rather] it is a category of being, πώς ἔχον. [See Luhtala On the Origin section 5.5.3.7 and Sambursky Physics section 1.4. Luhtala calls it “disposition” and Sambursky, “state”.] This way of being is somehow found at the limit of the being, that is to say, at the surface of the being. And this way of being cannot change its nature [Or, maybe, this way of being cannot change the nature of the thing it is affixed to.] Also, a way of being is neither active nor passive. For, in order for something to be passive, that would require that it be a corporeal that is suffering some action. Yet, some specific way of being, like “being cut”, is not itself suffering some action. Rather, it purely and simply is a result or effect of some interaction/interpenetration of bodies, and thus it should not itself be considered among the class of beings.

Les êtres réels peuvent cependant entrer en relation les uns avec les autres, et au moyen de ces relations, se modifier. « Ils ne sont pas, dit Clément d’Alexandrie exposant la théorie stoïcienne, causes les uns des autres, mais causes les uns pour les autres de certaines choses »¹. Ces modifications sont-elles des réalités? des substances ou des qualités? Nullement : un corps ne peut pas donner à un autre des propriétés nouvelles. On sait de quelle façon paradoxale les Stoïciens sont obligés de se représenter les relations entre les corps, pour éviter cette production des qualités les unes par les autres : ils admettaient un mélange (μῐξις ou κρᾶσις) des corps qui se pénétraient dans leur intimité, et prenaient une extension commune. Lorsque le feu échauffe le fer au rouge par exemple, il ne faut pas dire que le feu a donné au fer une nouvelle qualité, mais que le feu a pénétré dans le fer pour coexister avec lui dans toutes ses parties ². Les modifications dont nous parlons sont bien différentes : ce ne sont pas des réalités nouvelles, des propriétés, mais seulement des attributs (κατηγορήματα). Ainsi lorsque le scalpel tranche la chair, le pre- | mier corps produit sur le second non pas une propriété nouvelle mais un attribut nouveau, celui d’être coupé ¹. L’attribut, à proprement parler, ne désigne aucune qualité réelle ; blanc et noir par exemple ne sont pas des attributs, ni en général aucune épithète. L’attribut est toujours au contraire exprimé par un verbe, ce qui veut dire qu’il est non un être, mais une manière d’être, ce que les Stoïciens appellent dans leur classement des catégories un πώς ἔχον. Cette manière d’être se trouve en quelque sorte à la limite, à la superficie de l’être, et elle ne peut en changer la nature : elle n’est à vrai dire ni active ni passive, car la passivité supposerait une nature corporelle qui subit une action. Elle est purement et simplement un résultat, un effet qui n’est pas à classer parmi les êtres.

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1. Strom. VIII 9 (V.S.F. II 121, 4).

2. Stob. Ecl. I, p. 154 (S.V.F. II 153, 9).

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|

1. Sextus Math. IX 211 (S.V.F. II 119, 21) ; cf. les idées d’Archédème (S.V.F. III 262, 31).

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[Note, regarding Bréhier’s Stob. Ecl. I, p. 154 (S.V.F. II 153, 9). There is no English translation that I can find, but there is a similar passage by Alexander (On mixture 216, 14-218,6 / SVF 2.473): “Moreover they say that fire as a whole passes through iron as a whole while each of them preserves its own substance” (Long & Sedley 291).]

 

Some of these passages above are translated by Mark Lester and Charles Stivale in The Logic of Sense:

When the scalpel cuts through the flesh, the first body produces upon the second not a new property but a new attribute, that of being cut. The attribute does not designate any real quality

 

it is, to the contrary, always expressed by the verb, which means that it is not a being, but a way of being.

 

This way of being finds itself somehow at the limit, at the surface of being, the nature of which it is not able to change: in fact, neither active nor passive, for passivity would presuppose a corporeal nature which undergoes an action. It is purely and simply a result, or an effect which is not to be classified among beings.

(Deleuze 1969: 14; Deleuze 1990: 5; Deleuze 2004: 8)

 

 

 

1.2.5

[These predicate-effects are what we today call facts (faits) or events (événements). Predicates are incorporeals, and they are what is said or affirmed of corporeals. As such, they have no bodily existence but can enter to some extent into the mind. Causes, which are corporeals, are always expressed using nouns, and effects, which are predicates, are always expressed using verbs.]

 

The predicates, being results of the actions of corporeals, are what we today call facts (faits [and not ‘états de choses’]) or events (événements). Predicates are not corporeals or properties of corporeals; rather, they are what is said of a corporeal or what is affirmed of a corporeal. By making the predicates incorporeal, the Stoics exclude them from real beings, while at the same time, this places predicates to some extent within the mind. Sextus Empiricus says that when a body acts upon another body, the first one becomes a cause for the second, and what it causes for the second is something incorporeal. [« Tout corps devient ainsi cause pour un autre corps (lorsqu’il agit sur lui) de quelque chose d’incorporel ». See Luhtala Origins section 5.6.2.6, quoting Sextus: “The Stoics say that every cause is a body which becomes the cause to a body of something incorporeal.” (Adv. math. IX,211 = SVF 2.341, tr. Long/Sedley 1987: 333)] We see this mental/linguistic nature of the incorporeal in the concern the Stoics always have for how language expresses the predicate or effect of bodily mixture: the effect is always expressed as a verb. So for example, hypochondria should not be understood as the cause of the fever. Rather, hypochondria should be understood as the cause of the fact that the fever occurs. And in the all the examples [of Clement] that follow this one, the causes are never facts (faits) but are always corporeals expressed as substantives: stones, teacher (maître), and so on. However, the effects are always predicates like “being stable,” “making progress,” and as such, they are always expressed by verbs. [Note, regarding hypochondria, I am not sure how that relates to the spleen and fever example of Clement, Stromata section 8.9, subsection 12.2. I so far have only found a discussion of it in these terms on a google book search, here, at p.224 of Jean-Joël Duhot’s La conception stoïcienne de la causalité. The examples of the stones in the archway having the predicates “remaining together” and the teacher and student “making progress” are found in subsection 12.3 of Stromata section 8.9. For more discussion on this noun/verb relation between causes and effects, see Luhtala Origins for example sections 5.6.2.5- 5.6.2.10]

Ces résultats de l’action des êtres, que les Stoïciens ont été peut-être les premiers à remarquer sous cette forme, c’est ce que nous appellerions aujourd’hui des faits ou des événements : concept bâtard qui n’est ni celui d’un être, ni d’une de ses propriétés, mais ce qui est dit ou affirmé de l’être. C’est ce caractère singulier du fait que les Stoïciens mettaient en lumière en disant qu’il était incorporel, ils l’excluaient ainsi des êtres réels tout en l’admettant en une certaine mesure dans l’esprit. « Tout corps devient ainsi cause pour un autre corps (lorsqu’il agit sur lui) de quelque chose d’incorporel » ². L’importance de cette idée pour eux se fait voir par le souci qu’ils ont d’exprimer toujours dans le langage, l’effet par un verbe. Ainsi il ne faut pas dire que l’hypochondrie est cause de la fièvre, mais cause de ce fait que la fièvre arrive ³, et dans tous les exemples qui suivent les causes ne sont jamais des faits mais toujours des êtres exprimés par un substantif : les pierres, le maître, etc., et les effets : être stable, faire un progrès, sont toujours exprimés par des verbes.

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2. Sexus, ibid. [Sextus Math. IX 211 (S.V.F. II 119, 21) ; cf. les idées d’Archédème (S.V.F. III 262, 31).]

3. Clem. Alex. Loc cit. [Strom. VIII 9 (V.S.F. II 121, 4)]

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1.2.6

[There are two planes of being. {1} There is the plane of real and profound being, in which there are corporeals (physical bodies) that act and are acted upon by other corporeals on account of physical forces driving their interaction. {2} There is the plane of surface (and unreal) being. It lies at the metaphysical limit of the corporeal plane, remaining directly related to the interactions of corporeals, but not existing as something physically real among those interacting bodies. Here facts (predicates) play at the surface of physical being. They are the effects which are caused by the corporeal interactions. As such, the forces driving interaction on the deeper real plane are not exhausted by having produced effects on the incorporeal plane, since these effects are not matters of physical force.]

 

[First I will state the points Bréhier makes, and afterward I will comment.] The incorporeal fact (fait) is in some sense at the limit of the action of bodies. The form of a living being is predetermined in the germ that develops and grows. But this exterior form does not constitute a part of the living thing’s essence. Rather, the living thing’s exterior form is a result of an internal action that extends in space. And this internal action is not determined by the condition of filling out into its limits. In the same way, the action of a body, which is its internal force, is not exhausted in the effects that it produces. The effects of the body’s action do not come at any cost to its internal forces, and it does not affect the corporeal being in any corporeal way. So for example the act of cutting does not add anything to the nature or to the essence of the scalpel. The Stoics put force and thus all of reality not in events, that is, in the multiple, diverse processes that beings accomplish. Rather, they put force and reality into the unity to which belongs all the parts. In a sense, this makes them not too much unlike David Hume and John Stuart Mill, who reduce the universe to facts or events. But in another sense, the Stoics make possible a new sort of conception, which radically separates two planes of being. One the one hand, there is the plane of real and profound [corporeal] being, which includes force; while on the other hand there is the plane of [incorporeal] facts (faits), which are found playing on the surface (surface) of [real corporeal] being and which constitute an infinite multiplicity of incorporeal beings. [My comments on the above points: The incorporeal facts lie at the limit of the action of bodies. This “limit” seems to be a metaphysical limit, meaning that they lie beyond the realm or plane of corporeals, but still at the edge so to remain in an intimate relation with corporeals. It is in this sense that they lie at the surface. A living being will take on a form that is determined by the germ it develops from. But unlike what we saw with the Platonic conception in section 1.1, that form is not like an essence that causes the living thing’s parts to develop the way they do. Rather, it is caused internally by the forces at work among the corporeal elements that are able to act and be acted upon. As we have seen, the cause is corporeal but the effect is incorporeal. So the corporeal cause of development in the corporeal world, which is a matter of the physical forces at work in corporeal action, does not become exhausted in its causal action. Rather, there are just bodies acting and being acted upon by other bodies, which is a matter of new mixtures constantly being created. The effects they have are found on another plane of being, and so it is not like anything was subtracted from the physical forces, as the incorporeal plane does not admit of physical force. What is interesting to keep in mind is that only the corporeal plane is real, and the incorporeal plane is not. So the events/predicates/results of corporeal action are not found as real things among the real bodies of our world. But they are not so distant that our world bears to direct relationship to these incorporeals. Rather, they sort of dance or play at the metaphysical “surface” of physical reality. They are sort of hovering somewhere, but they have no location. They at best can only enter our minds when we conceive them.]

Le fait incorporel est en quelque façon à la limite de l’action des corps. La forme d’un être vivant est prédéterminée dans le germe qui se développe et qui s’accroît. Mais cette forme extérieure ne constitue pas une partie de son essence ; elle est subordonnée comme un résultat à l’action interne qui s’étend dans l’espace, et celle-ci n’est pas déterminée par la condition de remplir ses limites. De la même façon l’action d’un corps, sa force | interne ne s’épuisent pas dans les effets qu’il produit : ses effets ne sont pas une dépense pour lui et n’affectent en rien son être. L’acte de couper n’ajoute rien à la nature et à l’essence du scalpel. Les Stoïciens mettent la force et par conséquent toute la réalité non pas dans les événements, dans les démarches multiples et diverses qu’accomplit l’être, mais dans l’unité qui en contient les parties. En un sens, ils sont aussi loin que possible d’une conception comme celle de Hume et de Stuart Mill qui réduisent l’univers à des faits ou événements. En un autre sens pourtant, ils rendent possible une telle conception en séparant radicalement, ce que personne n’avait fait avant eux, deux plans d’être : d’une part, l’être profond et réel, la force ; d’autre part, le plan des faits, qui se jouent à la surface de l’être, et qui constituent une multiplicité sans lien et sans fin d’êtres incorporels.

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From the Mark Lester and Charles Stivale translation in The Logic of Sense:

[The Stoics distinguished] radically two planes of being, something that no one had done before them: on the one hand, real and profound being, force; on the other, the plane of facts, which frolic on the surface of being, and constitute an endless multiplicity of incorporeal beings.

(Deleuze 1969: 14; Deleuze 1990: 5; Deleuze 2004: 8)

 

 

 

1.2.7

[We first needed to see how corporeals revolutionized metaphysics so that we can next examine how they revolutionized logic.]

 

We next will examine how incorporeals constitute the material of all Stoic logic. Thus incorporeals will replace the genera and species of Aristotelian logic. We needed first to see how the Stoic’s original conception of incorporeality worked in their physics in order to better grasp how it revolutionized logic.

Nous allons montrer maintenant que ces incorporels constituent la matière de toute la logique stoïcienne, se substituant ainsi dans la logique aux genres et aux espèces de la logique d'Aristote. Il était nécessaire de montrer d'abord dans la physique les raisons de cette révolution de la logique.

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Bréhier, Émile. 1962. La théorie des incorporels dans l'ancien stoïcisme. 3rd Edn. Paris: Vrin.

PDF of a microfilm version available at:

https://archive.org/details/lathoriedesincor00brhi

 

 

Also cited:

Deleuze, Gilles. 1969. Logique du sens. Paris: Les éditions de minuit.

 

Deleuze, Gilles. 1990. The Logic of Sense. Translated by Mark Lester and Charles Stivale. Edited by Constantin Boundas. New York: Columbia University Press.

 

Deleuze, Gilles. 2004. The Logic of Sense. Translated by Mark Lester and Charles Stivale. Edited by Constantin Boundas. London / New York: Continuum [first published in English: Columbia University Press, 1990].

 

Long, Anthony A. and David N. Sedley. 1987. The Hellenistic Philosophers, vol.1: Translations of the Principle Sources, with Philosophical Commentary. Cambridge: Cambridge University Press

 

 

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Sambursky (1.4) Physics of the Stoics, “The Four Categories”, selective summary

 

by Corry Shores

 

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Samuel Sambursky

 

Physics of the Stoics

 

Ch.1

The Dynamic Continuum

 

1.4 The Four Categories

 

Selective summary

 

 

Brief summary [of selected ideas]:

The Stoics held that all things can be metaphysically classified under four hierarchical categories, all of which fall under the concept of the something. In their consecutive order they are: substratum, quality, state, and relative state. The fourth category is divided into two subcategories. {a} A relative state, which is defined by something outside it, like the father-son relation. And {b} a relative, which is something capable of undergoing change between states by matters of degree that are measure by comparing the two states, like being at a level of two degrees of sweetness compared to bitterness. A hexis is an example of a relative, because it is comprised of pneumata that each express a quality such that a continuous variation in the composition of the pneuma will result in a continuous variation in its quality. The four categories fit within the Stoic theory of the dynamic continuum. The substratum is the pneuma which binds the parts of all things and which endows them with qualities. The qualities are determined by the [physical] states of the pneuma, which are always in relative states, given that they are constantly under variation as their pneumata alter their compositions.

 

 

 

Selective summary

 

 

Sambursky will now consider a methodological principle of the Stoics, called the Stoic doctrine of categories, which is directly relevant to their physical theory and which “was possibly developed first to fit the conceptual frame of physics and later generalized as a directive for other fields of scientific and philosophical thought” (17). Although they are called “categories”, they share nothing in common with Aristotle’s categories that classify concepts. The categories are not systematized hierarchically in the sense that the categories are not subclassifications of a higher notion. [I am not certain if this is related, but it reminds me of Henry Somers-Hall’s account of how there is no highest genus of being for Aristotle. See section 1.3 of his guide to Difference and Repetition. There he writes, “the ultimate categories through which being is understood must be multiple, as they themselves are species in relation to the undefined genus” (Somers-Hall 27)].

Aristotle’s ten categories⁸² are an attempt – in accordance with a principle not known to us – to compile a list of concepts such that every word of non-compounded meaning can be shown to belong to one of them. This list thus forms a horizontal classification. In other words-the various points of view from which one can look at objects are regarded by Aristotle as a group of co-ordinated notions not bound together by a higher notion embracing all of them.

82. Substance, quantity, quality, relation, place, time, position, state, action, affection.

(17)

 

The Stoic’s four categories, in contrast, “are a vertical classification according to which every object is determined by four successive steps of increasing specification such that every category includes the preceding one” (17). By means of this system, one can provide a “complete ontological definition of an object” (17). Now, although there are four categories, there is a notion that comprises all four, namely, the something. Under it are substratum, quality, state, and relative state (17). [Sambursky here cites in footnote 83: “Simpl., Categ., 66, 32 f.; Plotin, loc. cit., VI, i, 25: ὑποκείμενον, ποιόν, πως ἒχον, πρός τί πως ἒχον.” Refering to footnote 60 on page 11: “60. Plotin, Ennead., II, vii.”]

 

We can relate the categories to the conceptual structure underlying the Stoic’s notion of the physical continuum. [The first category, substratum, is the pneuma. The second category, qualities, arise when the pneuma, which is by itself quality-less, mixes with matter. The third category, state, corresponds to the ratio of Air and Fire making up the pneumata of an object’s hexis and determining its qualities. The sum total of all the pneumata constituting the hexis defines the thing’s physical state. I am not sure if this is the fourth category, relative state. There is a subdivision of this state into two sorts of relations: relative state and the relative. The relative state is defined by something outside it, like the father-son relation. A relative is something capable of undergoing change between states by matters of degree that are measure by comparing the two states, like being at a level of two degrees of sweetness compared to bitterness. I am not sure I follow the next idea. It seems to be the following. Hexis is an example of a relative. The hexis of a thing is the mixture of its pneumata, with each of which expressing one of its qualities and the entire mixture also serving to actively cohere the parts together. Now, if the pneumata alter their composition, they will do so continuously, thereby altering the property they carry continuously. Hexis, it would then seem, is a relative but in a more general sense, because a hexis would seem to contain a variety of relatives, that is, a varied set of many different continuously changeable qualities.]

If we look at the conceptual structure of the physical continuum as we have come to know it in the preceding pages, we perceive a striking analogy with the set-up of the Stoic categories. Shapeless and passive matter is the primary substratum of the cosmos and as such without any qualities.⁸⁷ It is the all-pervading pneuma which, by totally mixing with matter, imbues it with all its qualities,³⁹ and thus represents the second category. The third category, the state, is given by the fact that to each specific quality of the body there is attributed a specific mixture of the pneuma defined by a certain proportion of its two components, air and fire. The sum total of all pneumata permeating the body then defines its physical state. There is a lack of consistency in the extant sources with regard to terminology. Thus we find no direct reference to hexis as a physical state, but Alexander once mentions the “physical property of a body”, which is much the same as hexis, and calls it “pneuma in a certain state”.⁸⁸ Hexis, however, is mentioned expressly in connection with the fourth category, and the passage in Simplicios referring to it⁸⁹ is of great significance for the understanding of the whole subject. Simplicios informs us of a subdivision of the fourth category: the Stoics distinguished between two kinds of relations, the relative state⁹⁰ and the relative⁹¹. The first denoted a state defined by that of another thing outside it, such as the relation father-son or left- and right-hand neighbour. The relative referred to things capable of change (the examples given are sweet and bitter), whereby | the relation is given through comparison of two states of this change (e.g. two degrees of sweetness) . Simplicios quotes hexis as another example of the relative which throws into relief the dynamic notion of Stoic physics, because hexis is the key term of the physical continuum which embraces an infinity of different states. Each of these states can evolve from another by a continuous transition produced through the “change of the former quality”,⁹²  a change which corresponds to that of the spectrum of all pneuma tensions permeating the body involved.

87. Diog. Laert., VII, 137.

[Footnote 39 is on page 7:

39. Plut., De Stoic. repugn., 1053 f.

]

88. Alex. Aphr., Topica. 360, 10.

89. Simpl., Categ., 165, 32-166, 29.

90. πρός τί πως ἔχον.

91. πρός τι.

92. Galen, Method. med., I, 6 (Arnim, II, 494) .

(18-19)

 

 

 

 

From:

Sambursky, Samuel. 1973. Physics of the Stoics. Westport, Connecticut: Greenwood. [First published 1959, London: Routledge and Kagen Paul.]

 

Or if otherwise noted:

Somers-Hall, Henry. 2013. Deleuze’s Difference and Repetition. An Edinburgh Philosophical Guide. Edinburgh: Edinburgh University.

 

 

.

Sambursky (1.3) Physics of the Stoics, “The Problem of Mixture”, selective summary

 

by Corry Shores

 

[Search Blog Here. Index tabs are found at the bottom of the left column.]

 

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[The following is a selective summary, meaning that I select certain ideas to discuss rather than thoroughly summarize the text. All bracketed commentary and boldface is mine. Proofreading is incomplete, so you will encounter distracting typos. I apologize in advance.]

 

 

 

 

Samuel Sambursky

 

Physics of the Stoics

 

Ch.1

The Dynamic Continuum

 

1.3 The Problem of Mixture

 

Selective summary

 

 

Brief summary [of selected ideas]:

Pneumata combine with substantial parts, binding them together, to compose whole things and to provide them with their qualities. We can characterize the sort of mixture pneumata make with physical parts as being a special kind of mixture that the Stoics invented. Note first that they regarded there being three types of mixtures. {1} Mingling or mechanical mixtures, which are granular in that its smallest parts sit side by side like a mosaic. {2} Fusions, which are like chemical compounds where the properties of the component parts are lost, while the new whole compound gains its own unique properties. {3} Mixtures proper (krasis for liquids and mixis for non-liquids), where the components interpenetrate entirely and thoroughly such that there is no mosaic-like distribution on the smallest scale. Yet somehow despite this constituent homogeneity, each part retains its own properties and can be separated out again. This is the sort of mixture pneumata make with the other physical parts of a thing so to form its hexis.

 

 

 

Selective summary

 

 

[Recall that pneuma is has a two-fold function. On the one hand, it is the binding force that coheres the parts of the world. Here there is a mixture of pneuma with inert matter. On the other hand, it itself is composed of a mixture, being a combination of Fire and Air. See section 1.1 and section 1.2.]

We are thus led to the conclusion that the Stoic theory of hexis was based in a double sense on the process of mixture. On the one hand, mixture of pneuma with inert matter imbues the latter with physical properties, whereas pneuma itself, on the other hand, is a mixture of two components, fire and air. This easily explains the fact that the Stoics were occupied to such a large extent by the problem of mixture [...].

(11)

 

The sources of the Stoic theory of mixtures “are of a fragmentary nature;” nonetheless, “they give us some idea of how the Stoic view on mixture was heavily influenced by their extreme notions of continuity and their basic assumptions concerning the function of the pneuma” (11).

 

In the Stoic theory of mixtures, there are three types. {1} Mingling or mechanical mixture. An example is if we mix wheat and barley. It is characterized as having a “mosaic-like composition”. Its basic parts stand side-by-side rather than interpenetrating one another: “it applies essentially to bodies of a granular structure where a mosaic-like mixture results, each particle of one component being surrounded by particles of the other” (12). It is thus not homogeneous on the smallest scale, although on larger scales it might appear as homogeneous (11-12). {2} Fusion. Here the parts synthetically form a new substance altogether, like chemical compounds. The individual properties of each component are lost, as their compound gains its own new unique properties (12). {3} Mixture proper (krasis for liquids and mixis for non-liquids). This is the most important sort of blending for the Stoics. All the components interpenetrate completely and thoroughly. They retain their own properties, and they can be separated out again (12). [See this summary from John Sellars Stoicism on these mixture types.]

Between these two types lies a third case of “mixture” proper | (krasis for liquids, mixis for non-liquids) which, from the Stoic point of view, represents the most important category of blending. Here a complete interpenetration of all the components takes place, and any volume of the mixture, down to the smallest parts, is jointly occupied by all the components in the same proportion, each component preserving its own properties under any circumstances, irrespective of the ratio of its share in the mixture. The properties are preserved in all cases where – as opposed to the case of fusion – the components can be separated out again from the mixture by physical contrivances.

(12-13)

 

Using current terminology, we might call krasis a solution or a suspension (13). Even a minute portion of one part into a large portion of another can result in the smaller part thoroughly spreading throughout the larger part, keeping its properties, like a drop of wine in the whole sea, where that wine’s properties then are imbued throughout the entirety of the sea.

On the whole, krasis would apply to what in the language of today is called a mixture in any of the three phases, or to a solution or a suspension. Of special interest to the Stoics were, of course, cases of extreme dilution or rarefaction, because they regarded the pneuma which permeates bulky matter without losing its properties as one of these cases. Chrysippos, obviously referring to the passage in Aristotle quoted above,⁶³ stresses this point with deliberate exaggeration: “There is nothing to prevent one drop of wine from mixing with the whole sea.”⁶⁷

63. loc. cit., 328 a 27.

[Referring to footnote 56 on page 11:

56. Arist., De genr. et corr., I, 10.

]

67. Plut., loc. cit., 1078 e.

[Referring to footnote 59 on page 11:

59. Plut., De com. not., ch. 37.

]

(13)

 

This Stoic notion of mixture proper was misunderstood by other philosophers, who thought that the Stoics were claiming that to add to one cup of wine with two parts of water would result in four parts of mixture instead of three. This is because the one cup of wine, now mixing with the water, becomes two cups of wine, which when added to the original two cups of water, makes a total of four cups of mixture. [From Plutarch’s On Common Notions Against the Stoics: “But to the Stoics it is a matter of truth, that when one cup of wine is mixed with two of water, if it is not to be lost but the mixture is to be equalized, it must be extended through the whole and be confounded therewith, so as to make that which was one two by the equalization of the mixture. For the one remains, but is extended as much as two, and thus is equal to the double of itself. Now if it happens in the mixture with two to take the measure of two in the diffusion, this is together the measure both of three and four,—of three because one is mixed with two, and of four because, being mixed with two, it has an equal quantity with those with which it is mixed. ” (Plutarch 411. Also, Perseus Project. See as well the beginning of this summary on the Plutarch text for more discussion.)]

Plutarch, giving an account of the Stoic theory of mixture, also reveals in his criticism a complete lack of understanding of the nature of dilution. According to the Stoics, he says, one measure of wine mixed with two measures of water should give four measures of mixture, as the wine will extend into the whole volume occupied by the water.⁷¹

71. Plut., De comm. not., 1078 a.

(14)

 

[So that is a form of misunderstanding of the theory rather than a valid criticism.] The main reason that the Stoic’s theory was rejected was because of its notion of “total mixture:” the mixture means that it is homogeneous even at the smallest parts. Now, if the parts retain their properties, but the mixture is thoroughly homogeneous, implying that the smallest parts do not lie side by side, then how are they arranged instead? One conclusion was that they superposed, thereby destroying volume. [So one cup of wine plus two water will result in two cups of mixture, but we know that not to be true.] Plotinus however notes that since the parts retain their properties, and since volume is a property, the volume would not be destroyed in the combination.

But the Stoics, taking a radical position with regard to continuity, conceived of mixture as a complete interpenetration of the components which existed simultaneously in the given proportions down to the most minute elements of volume. This conception of total mixture was understood by them in the sense that every element of volume, however small, would be homogeneous with regard to the mixing of the components, and that from no point on would this homogeneity dissolve itself into a mosaic-like structure with bits of the components lying side by side. Alexander Aphrodisiensis and all the later critics – with one exception – saw in this notion of total mixture an infringement upon the principle that one body cannot occupy the place occupied by another. Their view was⁵⁸ that complete interpenetration of bodies must necessarily lead to the volume of the mixture not being the sum of the volumes of the components, but instead it would remain constant as compared with the volume of the largest of the components.⁷³ Plotin⁷⁴  gives a two-dimensional picture in explanation: Total mixture would be comparable not to the juxtaposition of two (material) lines drawn side by side – which would mean an increase in area – but to the superposition of the two lines whereby no increase occurs. In view of the obvious fact that generally a mixture occupies a larger volume than each of its components, the Stoic theory, as interpreted by its critics, was generally rejected. Plotin alone, in his endeavour to give the Stoic ideas a fair trial, attempts to reconcile their views with the facts.⁷⁵ Volume, he says, is one of the many qualities of a body. According to the Stoics, the qualities of the components are preserved in the mixture; in fact, the properties of the latter result from the mixing of those of its components. In the same way, he concludes, the mixture will possess a volume which is exactly or nearly the sum of the volumes of the components – thus resulting in an increase of volume.

[Footnote 58 is on page 11

58. Alex. Aphr., Quaest. et solut., II, 12.

]

73. Cf. Simp., Phys., 530, 29: “A ladle mixed with another one in total mixture shall give again a ladleful.”

74. Plotin, loc. cit. , II, vii, 1, 45.

75. Plotin, loc. cit. , II, vii, 1, 35.

[Footnotes 74-75 refer to footnote 60 on page 11.

60. Plotin, Ennead., II, vii.

]

(15)

 

[Sambursky’s next point seems to be the following. It is one challenge already to conceive of how the physical parts of a mixture can form a total mixture of the kind we described. But the reason we went into that account was not simply to work on that problem. Rather, we are concerned with how to conceptualize hexis. It involves the thorough interpenetration of pneuma throughout the parts of some object. Thus we should think then of the mixture between pneuma and the other physical parts of something as a total mixture. Perhaps this is because the pneuma carries the qualities, and those qualities need to penetrate and inhabit the physical parts.]

We must look at the Stoic theory of total mixture in the light | of the main purpose it was supposed to serve – to give a firm foundation for its conception of hexis. We must remember that pneuma was thought to be an extremely rarefied substance and that its total interpenetration of matter would thus create a case analogous to that of the mixture of a small drop of wine with a large measure of water, i.e. of one component being negligible in bulk as compared with the other. Here again the starting-point for the argument was the organic world. Soul (psyche), the hexis of the living body, was itself corporeal according to the Stoics, who included it in the group of things which are capable of acting and being acted upon. Mutual interpenetration of soul and body, of physis and plants, of hexis and inorganic matter, have all one common feature – the total mixture of a very tenuous and rare component, the pneuma, with a much bulkier one.^{76, 77}  The common denominator in all these cases are the physical qualities or properties which themselves are nothing less than pneumata mixed in definite proportions. And as we have seen, qualities are bodies, like the soul itself, and therefore their mixture with matter – organic and inorganic alike – must be of the nature of a total mixture.⁷⁸

76. Galen, Comm. 5 in Hippocr. epid. 6 (Arim, II, 715).

77. Alex. Aphr., De anima, 26, 10.

78. Simpl., Phys., 530, 9.

(15-16)

 

 

 

From:

Sambursky, Samuel. 1973. Physics of the Stoics. Westport, Connecticut: Greenwood. [First published 1959, London: Routledge and Kagen Paul.]

 

 

Or if otherwise noted:

 

Plutarch. 1878. On Common Notions Against the Stoics. In Plutarch's Morals, vol.4, pp.372-427. Translated from the Greek by several hands. Corrected and revised by William W. Goodwin. Boston: Little, Brown, and Company. Cambridge: Press Of John Wilson and son. Available online at:

https://archive.org/details/plutarchsmorals04plut

 

.

Sambursky (1.2) Physics of the Stoics, “The Physical State of a Body”, selective summary

 

by Corry Shores

 

[Search Blog Here. Index tabs are found at the bottom of the left column.]

 

[Central Entry Directory]

[Stoicism, entry directory]

[Samuel Sambursky, entry directory]

[Sambursky, Physics of the Stoics, entry directory]

 

[The following is a selective summary, meaning that I select certain ideas to discuss rather than thoroughly summarize the text. All bracketed commentary and boldface is mine. Proofreading is incomplete, so you will encounter distracting typos. I apologize in advance.]

 

 

 

 

Samuel Sambursky

 

Physics of the Stoics

 

Ch.1

The Dynamic Continuum

 

1.2 The Physical State of a Body

 

Selective summary

 

 

Brief summary [of selected ideas]:

Pneuma’s function is two-fold: it both coheres the parts of a thing and it also serves as a field carrying the properties of the thing. There are three hierarchical orders of compositional organizations for things. {1a} Discrete non-denumerable entities, where there is a disordered assembly of bodies that are too disorganized for us to count, as in a crowd of people. {1b} Discrete denumerable entities where the elements are arranged in an ordered way allowing for us to count them, as with an army formation. {2} Contiguous structures, whose elements are combined, as with links in a chain. Both discrete and contiguous structures have the property that any part can survive if all the others are destroyed, as they are constituted by an additive principle. The situation is different for {3} unified structures, which are organized by hexis. Hexis is what organizes the parts of inorganic objects, like physis for plants and psyche for animals. Here the units of the thing are not merely the parts but rather the different properties of the thing, which interpenetrate such that a change in one leads to a change in the others, as a result of the “sympathy” holding between the properties. But if it is the same thing, namely, pneuma, that carries the properties of various things, then how do we explain why different things have different properties? In Sambursky’s interpretation, a hexis of a thing is composed of many pneumata, one for each property. What differentiates the pneumata is that they have their own compositional ratio of mixture of Air and Fire. All such pneumata are combined in the thing but without each losing its own identity, hence their particular properties are expressed. But these pneumata are connected as well such that a change in one creates a change in the others.

 

 

Selective summary

 

 

As we saw in the prior section, pneuma’s tension produces the cohesion of matter. But that is just one half of pneuma’s two-fold function. It also generates the physical qualities of matter. [The way this works, as we will see later, is not entirely well known, but it has to do with the proportions of Fire and Air constituting the pneuma that serves as the thing’s hexis.] So, along with being the glue that binds the parts of matter, it is also like a physical field that somehow carries the thing’s specific properties. When we conceive the pneuma as serving these two function, it takes on the more specific meaning of hexis, which is the physical state of the body. This for example can mean that the hexis which binds iron together also gives it its property of hardness. [So perhaps the cohesion can at least explain certain physical properties that are obviously matters of density for instance.] Hexis as the structure of inorganic matter is similar to the way physis structures organic things and psyche living things [see Bréhier, La théorie des incorporels dans l'ancien stoïcisme, §7.]

Cohesion of matter is not the only effect produced by the tension of the pneuma. The latter has a twofold function: besides being a binding force, it is an agent which generates all the physical qualities of matter. [...] By their conception of the pneuma as the generator of physical qualities the Stoics generalized their continuum theory into a field theory; the pneuma is the physical field which is the carrier of all specific properties of material bodies, and cohesion as such thus gets a more specific meaning by becoming hexis, the physical state of the body. The following quotation from a book by Chrysippos On Physical States is very instructive: “The physical states are nothing else but spirits, because the bodies are made cohesive by the. And the binding air is the cause for those bound into such a state being imbued with a certain property which is called hardness in iron, solidity in stone, brightness in silver.”³⁹ And a little later he continues: “Matter, being inert by itself and sluggish, is the substratum of the properties, which are | pneumata and air-like tensions giving definite form to those parts of matter in which they reside.” This gives some idea of the central position in the Stoic theory of matter of hexis, which denotes the structure of inorganic matter in a similar way to which physis expresses organic structure and psyche the structure of the living being.

39. Plut., De Stoic. repugn., 1053 f.

(7-8)

 

The Stoics thought there was a hierarchy of inorganic structures, with hexis being the highest. There are three sorts. [Please see the quotation to follow, as the divisions are not clear to me. It is possible that there are four levels but three qualities they may have. Or perhaps there are three levels, but the first has two distinct subcategories.] The lowest is {1a} discrete non-denumerable entities, where there is a disordered assembly of bodies whose members are too disorganized for us to count, as in a crowd of people. The next highest is {1b} discrete denumerable entities where the elements are arranged in an ordered way allowing for us to count them, as with an army formation. Then there are  {2} contiguous structures, whose elements are combined, as with links in a chain. Both discrete and contiguous structures have the property that any part can survive if all the others are destroyed, as they are constituted by an additive principle. The situation is different for {3} unified structures, which are organized by hexis. Here the units of the thing are not merely the parts but rather the different properties of the thing, which interpenetrate such that a change in one leads to a change in the others. [Consider a metal where when you change one property, like its temperature, you affect its other properties, like its malleability.] This co-existence of the structural elements [the interpenetrating properties] is called sympathy (sympatheia), with the example of a living organism: when one’s finger is cut, the whole body shares that condition.

The structural concept of hexis, also defined as the “binding spirit” of a body,⁴³ represents the highest entity in the hierarchy of inorganic structures as conceived by the Stoics.⁴⁴ These entities are divided into discrete, contiguous and unified.⁴⁵ At the lowest level we have an assembly of bodies in a disordered state, such as a crowd which does not lend itself to numerical determination. The following level is also a discrete state, but here the elements are arranged in an order which allows for numerical determination, such as a choir or an army in formation. This is a “denumerable” entity.⁴⁶ Contiguous structures are composed of conjoined elements, like the links of a chain or the planks of a ship or the stones of a house.⁴⁷ What the discrete and contiguous structures have in common is that each of their elements can continue to exist even if the rest are destroyed,⁴⁸ which is characterized by a simple additive relationship between the elements. [...]

|

The situation is completely different in the case of unified structures, such as stone or wood or metal which are “ruled by a single state”.⁴⁴ It is not an additive principle which defines the relation between the physical state of a body, hexis, and its elements. We must realize that the elements of hexis are not mere localized units but physical properties which interpenetrate and create a totality where each of them shares in the existence of the rest. In our modern terminology: all the qualities which define the physical state of a certain body – its mechanical, thermic, electric, optical properties – have their origin in common roots and are therefore interdependent and not additive. Every one of them is affected if all or some of the others change. The physical state is an organization of dynamic character, each of its elements subsisting only in co-existence with the rest, and not able to exist if the organization as a whole disintegrates. The Stoic term for this form of co-existence of the elements of the highest structure was “sympathy” (sympatheia), and it is again significant that analogies from the living organism were given to exemplify this condition: when a finger is cut, the whole body shares in its condition.⁴⁸

43. Achill., Isagoge, 14 (Arnim, II, 368).

44. Sext. Emp., Adv. math., IX, 78; Plut., Praec. conug., 34: De def. orac., 29; Achill., Isagoge, 14.

45. διεστῶτα, συναπτόμενα, ἡνωμένα.

46. ἀριθμῷ ληπτός.

47. Seneca, Natur. quaest., II, 2.

48. Sext. Emp., loc. cit., 80.

(8-9. Note, the footnote enumerations in the text can be out of order, but it seems that means to refer to a footnote on a previous page.)

 

We now wonder, given “the unmistakable connection between hexis and pneuma” what is “the mechanism by which different physical states were thought to arise out of the pneuma pervading the bodies”? (10). The problem with determining this is that “The very scanty remnants of Stoic physics do not permit us more than vague conjectures about the details of their theory on this topic” (10). One clue comes from Galen, who says that the Stoics distinguish the pneuma of physis and psyche by saying that the pneuma of physis is more humid  and colder, while the pneuma of psyche is drier and hotter. What we gather from this is that at least with regard to these two sorts of pneuma, there can be a differentiation in the composing mixtures of Air and Fire:

Some light is thrown on this problem in the passage in Galen already mentioned above⁹: “According to them (the Stoics), psyche is a sort of pneuma, as is also physis, but the pneuma of physis is more humid and colder, while that of psyche is drier and hotter. This pneuma is a kind of matter akin to psyche, and the specific quality of this matter is given by the proportions admixed of the airy and fiery substance.” Here a principle of differentiation is stated for the world of animals and plants, derived from the basic assumption of the composite nature of the pneuma which allows for different ratios of mixture of its two components – a definite proportion of this mixture defining a definite quality.

9. Galen, De anim. mor. (Arim, II, 787); cf. also Arnim, II, 446.

(10 / footnote: 2)

 

In similar vein, Diogenes of Apollonia, who seemed to have some influence on the Stoics,

identifies soul and intelligence with air, and the variations in the former are explained by the difference in proportion of hot and cold, dry and wet in air. The differences in the degree of warmth of the soul in animals and in human beings is particularly stressed by Diogenes. The multitude of possible variations of the mixture is the reason for the observed diversity in form, way of life, and intelligence.

(10)

 

So far, Sambursky’s point is that in the organic realm, differences between types of pneumata, like between that of plants, animals, and humans, was accounted for on the basis of differences in the mixture of Fire and Air in the pneuma. His made that point so that now, by analogy, we might infer the same principle would hold for the hexis of inorganic objects. In other words, what accounts for the different properties in objects is that they have a different hexis, whose variations are based on differences of composition, that is, different ratios of Fire and Air. Sambursky it seems further suggests that for each property there is a different pneuma. So a single hexis would be made of various pneumata, each retaining their individual and thus each property being distinct, while at the same time the various pneumata are physically interrelated such that a change in one property/pneuma corresponds with a change in the others.

We have seen already that hexis was regarded by the Stoics as | a notion equivalent in the inorganic realm to that of physis and psyche in the organic, and we may therefore assume by analogy that here, too, the same principle of differentiation was used in Stoic physics. In other words, each of the physical properties of a body, according to this principle, would be defined by a specific sort of pneuma, characterized by a definite mixture of fire and air. All these different sorts of pneuma permeate the body and mix with each other without losing their identity, since the properties to which they are co-ordinated are well defined and stable in spite of the fact that by coalescing they form the specific nexus by which an inert lump of matter is endowed with hexis.³⁹

39. Plut., De Stoic. repugn., 1055 f.

(10-11 footnote: 7)

 

 

 

 

 

 

Sambursky, Samuel. 1973. Physics of the Stoics. Westport, Connecticut: Greenwood. [First published 1959, London: Routledge and Kagen Paul.]

 

 

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Sambursky (1.1) Physics of the Stoics, “Pneuma and Coherence”, selective summary

 

by Corry Shores

 

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[The following is a selective summary, meaning that I select certain ideas to discuss rather than thoroughly summarize the text. All bracketed commentary and boldface is mine. Proofreading is incomplete, so you will encounter distracting typos. I apologize in advance.]

 

 

 

 

Samuel Sambursky

 

Physics of the Stoics

 

Ch.1

The Dynamic Continuum

 

1.1 Pneuma and Coherence

 

Selective summary

 

 

Brief summary [of selected ideas]:

The Stoics held that the cosmos is a continuous whole surrounded by a void. The continuity of the whole is a dynamic continuity resulting from a cohering activity of a very rarified substrate called pneuma. Pneuma is composed of a mixture of the active elements, Air and Fire, while Water and Earth are the other two passive elements that pneuma serves to bind. Pneuma has two physical features that give it this cohering role: {1} tonos, the tension which holds things together, and {2} gravitational neutrality, which means it gathers neither too high nor too low but instead equally pervades all domains of the cosmos.

 

 

Selective summary

 

For the Stoics, the cosmos is a continuous whole surrounded by a void. The coherence of its continuity stems from its substratum of pneuma, whose role is to create cohesion between the parts of matter in the cosmos.

According  to the Stoic conception, the cosmic scene of  material events, including conglomerate matter as well as space between bodies, is made up of a continuous whole. Like Aristotle, the Stoics exclude emphatically any possible existence of a void within the cosmos.¹ However, their cosmos is, in contradiction to that of Aristotle, an island embedded in an infinite void.² The cosmos is filled with an all-pervading substratum called pneuma, a term often used synonymously with air.³ A basic function of the pneuma is the generation of the cohesion of matter and generally of the contact between all parts of the cosmos. The term coherence was originally used by Aristotle to express continuity in an essentially geometrical and topological sense,⁴ but the Stoics gave it the physical and dynamic significance of cohesion within the physical world.

1. Diog. Laert., VII, 140; Cleom., De motu circulari, I, 1 (ed. Ziegler), p. 8.

2. Plut., De Stoic. repugn., 1054 b, says that this theory was repeatedly mentioned in Chrysippos’ writings.

3. e.g. Plut., loc. cit., 1053 f.

4. Arist., Metaph., 1069 a 6; cf. also Metaph., 1061 a 33. See p. 5 in connection with Metaph., 1015 b 36. For pre-Socratic origins of συνέχεια, cf. Parmenides (Diels, 28 B 8, 25): τῷ ξυνεχὲς πᾶν ἐστιν, ἐὸν γὰρ ἐόντι πελάζει.

(1)

 

Pneuma can be understood in biological terms as being like breath, which mixes the cold air with the heat of the body:

As air represents the principle of Cold, the warmth of the human body makes it likely that the stuff souls are made of is a mixture of cold and hot, of air and fire. [...] the Stoics expanded the idea of mixture by adding the other two qualities of Dry and Moist, thus making possible the differentiation between the pneuma of the soul (psyche) and that of the world of plants (physis). The former is dry and warm whereas the pneuma of physis is moist and cold.

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Of the four elements, the Stoics classify “Air and Fire as active, and Earth and Water as passive elements” (3). Since pneuma is made of Air and Fire, that makes it as active as a mixture can be. Part of its active nature is to provide the cohesive force keeping together the passive elements. With Aristotle, we are to think of the continuum of the cosmos geometrically, where parts cohere simply by being spatially contiguous, that is, their extremities are in direct contact. [See Aristotle’s Physics, Book 6, section 1.] There is no force or activity involved there. But since the Stoics regard cohesion as involving the work of pneuma, that makes it a dynamic continuum rather than a geometrical one. However, Aristotle did go beyond the notion of continuity stemming from geometrical coherence when he conceived of unity as involving a binding agent, like a string binding together a bundle of sticks or glue binding together pieces of wood. [See Aristotle, Metaphysics, Book 5.] Aristotle also comes close to a dynamic conception of continuum when he speaks of things being continuous when their motion is one. [See Aristotle, Metaphysics, Books 5 and 8.] Nonetheless, the Stoics make the clear step of identifying continuity with an active sort of cohering.

The mixture of air and fire which was identified in Stoic physics with the pneuma thus became the active agent par excellence in their cosmos. Pneuma or one of its components was also defined by the collective “pneuma-like matter”, and the Stoics attributed to them the property of coherence in the twofold sense of being cohesive and making cohesive,²⁵ whereas the passive elements (“hyle-like matter”) were denied any such faculty. Without the active interference of air or fire or the two mixed together, the passive elements would disintegrate as they themselves do not possess the “cohesive force”.²⁶ Coherence thus appears here distinctly as a force, and the geometrical continuum of Aristotle is in this way transformed into a dynamic one. It should be mentioned, however, that Aristotle has occasionally used the term “cohesive” in a structural | sense; e.g. in his analysis of the concept of unity²⁷: continuity is achieved by a binding agent and not by geometrical contact alone, as for instance a faggot which is made one by its string, and pieces of wood by glue. This is a static analogy, but immediately afterwards Aristotle comes very close to a dynamic conception when he calls a thing continuous “whose motion is essentially one and cannot be otherwise”. But the Stoics undoubtedly identified continuous with cohesive and thus completed the transformation of the geometrical concept into a physical one.

25. Galen, De multitud., 3 (Arnim, II, 439 and 440).

26. συνεκτικὴ δύναμις.

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27. Arist., Metaph., 1015 b 36 f.

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The physical property of pneuma is tension (tonos).

[...] the specifically physical property ascribed by the Stoics to the pneuma, or the “pneumalike matter” in general: tension (tonos). [...] since pneuma pervades the whole universe, the pneuma-like tonos makes the cosmos into a single cohesive unit³⁴ and thus the pneuma becomes the first version of the aether with all the characteristic functions ascribed to it from the seventeenth century on.

34. Clemens Alex., Stromat., V, 8 (Arnim, II, 447).

(5)

 

Another physical feature of air and fire, which compose pneuma, is that they are gravitationally neutral, which means that neither rise nor fall to the extremes and thus can pervade all regions to serve as the universal binding agent.

The whole emphasis in this | text [on Zeno of Citium’s cosmology] is on the gravitationally neutral character of air and fire who both participate in the cosmic tendency towards the centre, and at the same time stretch from there to the extreme regions, and thus contribute to the communication between all the parts of the universe.

(6-7, bracketed insertion mine)

 

 

 

 

Sambursky, Samuel. 1973. Physics of the Stoics. Westport, Connecticut: Greenwood. [First published 1959, London: Routledge and Kagen Paul.]

 

 

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