Stoicism

4. The continuum

Matter is permeated by god, and the passive elements by the active ones which constitute pneuma (see §3). What is this permeation? Mere juxtaposition of particles, such as atomism posits, could never constitute the intimate causal link between god and the matter which makes the Stoic world an inherently and ideally intelligent being. The active body must permeate the passive body ‘through and through’. Stoic theory distinguishes three grades of mixture. ‘Juxtaposition’, for example of mixed grains, conforms to the atomist model. ‘Fusion’ (synchysis) is a kind of interpenetration in which the ingredients irreversibly lose their distinctive properties and a single new stuff is generated. In between these lies ‘blending’ (krasis), which also involves total interpenetration, but with the ingredients retaining their own distinctive properties. A helpful Stoic example, the fire which is seen to permeate a red-hot piece of iron, may clarify how the two ingredients can be seen as literally coextensive, rather than alternating as in ‘juxtapostion’. It is ‘blending’ that describes the relation of pneuma to the material substrate.

‘Division is to infinity, or ‘‘infinite’’ according to Chrysippus (for there is not some infinity which the division reaches, it is just unceasing). And blendings, also, are through and through’ (Diogenes Laertius, VII 150–1). The doctrine of total interpenetration depends on the infinite divisibility of body, because if each of the blended stuffs consisted of indivisibly small particles these could only be juxtaposed, and not further blended. Hence the Stoics are, like Aristotle, committed defenders of the infinite division, on both mathematical and physical grounds.

For example, critics of the continuum had argued that if a finite body is infinitely divisible it will consist of infinitely many equal parts, and hence, impossibly, be infinite in size. Chrysippus replied that a finite object does not consist of any particular number of ultimate parts, finite or infinite. On an old puzzle of Democritus’, whether the two circular planes yielded by horizontally slicing a cone are equal (in which case why isn’t it a cylinder?) or unequal, Chrysippus replied that they are ‘neither equal nor unequal’. Unfortunately our sources are so depleted as to permit little more than speculation about his defence of this claim. The same applies to the traces of a Stoic solution to the celebrated paradox according to which motion through an infinitely divisible continuum is impossible because it would consist of an infinite, and therefore uncompletable, series of sub-motions (see Zeno of Elea §5). They replied that the moving object may complete a distance in a single undivided (though divisible) motion – possibly on the ground that divisions are thought constructs, of which only a finite number can be actually imposed on a distance.