The Stoic Ontology of Geometrical Limits

Abstract

Scholars have long recognised the interest of the Stoics' thought on geometrical limits, both as a specifi c topic in their physics and within the context of the school's ontological taxonomy. Unfortunately, insuffi cient textual evidence remains for us to reconstruct their discussion fully. Th e sources we do have on Stoic geometrical themes are highly polemical, tending to reveal a disagreement as to whether limit is to be understood as a mere concept, as a body or as an incorporeal. In my view, this disagreement held among the historical Stoics, rather than simply refl ecting a doxographical divergence in transmission. Th is apparently Stoic disagreement has generated extensive debate, in which there is still no consensus as to a standard Stoic doctrine of limit. Th e evidence is thin, and little of it refers in detail to specifi c texts, especially from the school's founders. But in its overall features the evidence suggests that Posidonius and Cleomedes diff ered from their Stoic precursors on this topic. Th ere are also grounds for believing that some degree of disagreement obtained between the early Stoics over the metaphysical status of shape. Assuming the Stoics did so disagree, the principal question in the scholarship on Stoic ontology is whether there were actually positions that might be called "standard" within Stoicism on the topic of limit. In attempting to answer this question, my discussion initially sets out to illuminate certain features of early Stoic thinking about limit, and then takes stock of the views off ered by late Stoics, notably Posidonius and Cleomedes. Attention to Stoic arguments suggests that the school's founders developed two accounts of shape: on the one hand, as a thought-construct, and, on the other, as a body. In an attempt to resolve the crux bequeathed to them, the school's successors suggested that limits are incorporeal. While the authorship of this last notion cannot be securely identifi ed on account of the absence of direct evidence, it may be traced back to Posidonius, and it went on to have subsequent infl uence on Stoic thinking, namely in Cleomedes' astronomy.

Hierocles and the Stoic Theory of Blending

“…In contrast to Peripatetic accounts, the Hieroclean account does not employ potential being, instead maintaining that the particular bodies that go into the blend persist straightforwardly throughout its existence; and, in contrast to atomist accounts, it views the blending bodies as 62 For this debate, see e.g. Robertson 2004, Ju 2009and Scade 2013 continuous. The concept of pneumatic tensile motion, which turns juxtaposition δι' ὅλων into blending whole through whole, ties the account together and links it to Stoic physics more broadly.…”

Colocation and the Stoic Definition of Blending

“…So, a place wholly occupied by Socrates, for instance, will thus be limited and determined according to the limits of Socrates. 60 60 On Stoic thinking regarding limits, see for instance Ju 2009;Robertson 2004.…”