2 Feb 2017

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



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 [...].



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.



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.




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.



[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.




[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.






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:




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