Truth and Conventional Implicature

Are all instances of the T-schema assertable? I argue that they are not. The reason is the presence of conventional implicature in a language. Conventional implicature is meant to be a component of the rule-based content that a sentence can have, but it makes no contribution to the sentenceʹs truthconditions. One might think that a conventional implicature is like a force operator. But it is not, since it can enter into the scope of logical operators. It follows that the semantic content of a sentence is not given simply by its truth-conditional content. So not all instances of the T-schema are assertable in the relevant sense. Consequently, there is a strong case to be made against truth-conditional semantics of the disquotational variety and deflationism about truth.