It is often said that the truth predicate serves a logico-expressive function, namely, it allows for the expression of so-called `infinite conjunctions'. This function prompts the formulation of logics or formal theories of truth. We argue that what principles these systems should validate depends on what it means for an infinite conjunction to express or stand in for all its `conjuncts'. We examine two accounts for this phenomenon that are available in the literature and show them to be substantially flawed. We put forward a new approach and discuss whether classical or non-classical logics are to be preferred as basis for theories of truth. We also propose a reconceptualisation of deflationism, according to which the meaning of truth in natural language is largely irrelevant for the deflationist's choice of a truth theory. Furthermore, we discuss a similar approach to the class-theoretic paradoxes and suggest that we should be deflationists about classes as well.