The framework of strict-tolerant consequence championed by Cobreros, Egré, Ripley and van Rooij provides a novel setting that permits one to have a transparent truth predicate without abandoning classical logic. The semantics for this notion of consequence, due to van Rooij, employs the three-valued strong Kleene matrices. A second framework that has received renewed attention is the collection of weak Kleene matrices, which have frequently appeared in the context of so-called logics of nonsense, making the pairing of these topics a natural avenue for investigation. In this talk, I’ll discuss strict-tolerant consequence on the weak Kleene matrices, its corresponding proof theory, and its interpretation. I’ll also discuss how the resulting notion of consequence bears on several matters in philosophical logic, including the content-theoretic interpretation of bounds consequence, the semantic properties of paradoxical sentences in the Principia Mathematica, and debates concerning the logical analysis of category mistakes.