The Geometry of Representational Asymmetry II: Where the Expression Runs Out

A representational structure that expresses anything must somewhere express nothing. That is the result, and it is derived rather than assumed. A companion paper obtains a non-orientable band from five commitments two published accounts of representation already make. All five are prohibitions, so the object comes out bare: no place on it differs from any other. This paper adds the one positive commitment those accounts also make, that the expression of a division admits of degree, and shows that a null configuration then follows from three premises together. The null proves to be non-orientability met from the expressive side rather than an addition to it, and an opponent who denies that expression comes in degrees is shown to require a Cartesian theatre. Three theorems follow, and the representational asymmetry is located in the last of them: expressed by every content, contained by none.