The standard Hintikka semantics of clausal embedding treats the complementizer "that" as vacuous, and takes the meaning of the CP to simply inherit the meaning of the TP. We present data from CP conjunction and disjunction in Russian and Hebrew to show that this is wrong. In Russian and Hebrew CP con/disjunction doesn't have the same interpretation as the corresponding TP con/disjunction under a single C. Adopting the decompositional approach to attitude reports initiated by Kratzer (2006), we develop an analysis that makes crucial use of the **equality** hypothesis (Moulton 2015, Elliott 2017): the content of the event expressed by an attitude predicate equals the proposition expressed by the embedded sentence. Complementizers, on our analysis, contribute the "equality" part. We show how the Russian and Hebrew data fall out from this analysis. English and Italian behave differently from Hebrew and Russian with respect to CP conjunction. We hypothesize why that might be based on the observation that in English and Italian, unlike Russian and Hebrew, CPs have a more flexible syntactic distribution: they can appear bare in subject position. We therefore propose that CPs in English and Italian are more type-flexible, \ being able to denote type-e elements and be conjoined by a non-Boolean *and*. *Tanya Bondarenko and Itai Bassi*