The problem of truth-values of indirect meanings is discussed within the semantic theory of indirect meaning proposed by the present authors in a dialogue with Hintikka’s and Sandu’s theory. The authors preserve the key notion of the latter, the meaning line, but putting it into different semantics (non-Fregean situational) and logic (paraconsistent). Like the contradictions, the indirect meanings tend to an explosion (there are always such possible worlds where they are true); to make them meaningful, there is a need of singling out the only relevant transworld connexion among the infinite number of the possible ones. The meaning line serves to this purpose. An analysis of the simplest semantic constructions with indirect meaning (tropes, humour, hints, riddles, etc.) is proposed.