Abstract
Millianism and Fregeanism agree that a sentence that contains a name expresses a structured proposition but disagree about whether that proposition contains the object that the name refers to (Millianism) or rather a mode of presentation of that object (Fregeanism). Various problems – about simple sentences, propositional‐attitude ascriptions, and sentences that contain empty names – beset each view. To solve these problems, Millianism can appeal to modes of presentation, and Fregeanism can appeal to objects. But this raises a further problem: namely, to explain why the proposition expressed by a sentence that contains a name matters in some cases but not in others.