Senecan Geometry and Stoic Surfaces

At many points throughout his philosophical prose corpus, Seneca the Younger encourages his audience to “circumscribe” some part of their life for moral improvement: for example, at Ep. 122.3, Seneca advises Lucilius, circumscribatur nox et aliquid ex illa in diem transferatur, and at De Ira 3.11.2, Seneca makes anger the object of this circumscription (circumscribenda multis modis ira est). However, just a little earlier in that book, Seneca also appeals to this process in a negative sense, by joining circumscriptio...et fraus among other crimes produced by civilization (De Ira 3.2.1), and Seneca applies this negative “deceptive” effect even to a bonus vir who reckons the benefits and injuries done to them such that “they themselves deceive themselves” (Ep. 81.6, se ipse circumscribat). On the one hand, circumscription is a moral imperative; on the other, it is an exercise in self-deception and public fraud.

In this paper, I will trace these two different sense of circumscriptio back to its physical application in the drawing of circles on surfaces. The way that Seneca commands his audience to “circumscribe” shares features with planar geometry, as seen in the use of the semantic equivalent Euclid uses to describe the process of circumscribing a triangle (e.g., Elements 4.5, περιγεγράφθω, translated by Richard Fitzpatrick (2008) as “let it have been circumscribed”), and the related περιγραφή is used by Chrysippus to describe Stoic metaphysical principles (SVF II.154.14) . Despite Gilles Deleuze’s (1990) description of Stoicism as a philosophy of surfaces, generally speaking, the Stoics were not particularly interested in geometry as such unless it was applied to the physical world, as explained by Harold Tarrant (1984) and others. However, as Émile Bréhier (1955) has thoroughly catalogued, one member of the Middle Stoa in particular did embrace theoretical geometry: Posidonius, whomRobert Kaster (2012) notes serves as a major source for the De Ira and whose thought Seneca frequently develops on, as Mireille Armisen-Marchetti (1989) and Jula Wildberger (2006) trace in relation to the nature of the soul and time, respectively.

Posidonius’ influence shows up in a specifically geometric use in the Natural Questions, where Seneca cites his Stoic predecessor’s theory of rainbows and reflection (NQ 1.5.13). In his own treatment of this topic earlier in the book, Seneca explains that rainbow are a product of a single circumscriptio (NQ 1.5.5), and the reflection of the rainbow embodies the more general principle that “every smoothness that is circumscribed and surrounded by its own borders is a mirror (NQ 1.3.6, …omnis circumscripta leuitas et circumdata suis finibus speculum est). While Shadi Bartsch (2014) has authoritatively explored the use of mirrors and optics in Senecan thought, in this paper I focus on the surface produced as a result of circumscriptio. Every circumscribing produces a new surface for reflection, and I contend that Seneca applies surface geometry to figure moral agents negotiating on a surface bounding and being bounded by their virtues and vices.