Integrated assessment models (IAMs) are economists' primary tool for analyzing the optimal carbon tax. Damage functions, which link temperature to economic impacts, have come under fire because of their assumptions that may produce significant, and ex-ante unknowable misspecifications. Here I develop novel recursive IAM frameworks to model damage uncertainty. I decompose the optimal carbon tax into channels capturing parametric damage uncertainty, learning, and misspecification
concerns. Damage learning and using robust control to guard against potential
misspecifications can both improve ex-post welfare if the IAM's damage function is misspecified. However, these ex-post welfare gains may take decades or centuries to arrive.