According to Russellian monism, consciousness is constituted at least partly by quiddities: intrinsic properties that categorically ground dispositional properties described by fundamental physics. If the theory is true, then consciousness and such dispositional properties are closely connected. But how closely? The contingency thesis says that the connection is contingent. For example, on this thesis the dispositional property associated with negative charge might have been categorically grounded by a quiddity that is distinct from the one that actually grounds it. Some argue that Russellian monism entails the contingency thesis and that this makes its consciousness‐constituting quiddities epiphenomenal—a disastrous outcome for a theory that is motivated partly by its prospects for integrating consciousness into physical causation. We consider two versions of that argument, a generic version and an intriguing version developed by Robert J. Howell, which he bases on Jaegwon Kim's well‐known “exclusion argument.” We argue that neither succeeds.