Can conjunctive propositions be identical without their conjuncts being identical? Can universally quantified propositions be identical without their instances being identical? On a common conception of propositions, on which they inherit the logical structure of the sentences which express them, the answer is negative both times. Here, it will be shown that such a negative answer to both questions is inconsistent, assuming a standard type-theoretic formalization of theorizing about propositions. The result is not specific to conjunction and universal quantification, but applies to any binary operator and propositional quantifier. It is also shown that the result essentially arises out of giving a negative answer to both questions, as each negative answer is consistent by itself.

It is a common view among philosophers of language that both propositions and sentences are structured objects. One obvious question to ask about such a view is whether there is any interesting connection between these two sorts of structure. The author identifies two theses about this relationship. Identity (ID) – the structure of a sentence and the proposition it expresses are identical. Determinism (DET) – the structure of a sentence determines the structure of the proposition it expresses. After noting that ID entails DET, the author argues against DET (and therefore also against ID). This argument is based on considerations to do with unarticulated constituents, but it is not ultimately empirical. As well as answering a question suggested by contemporary theories of propositions, the conclusion is significant because some, but not all, of the theories of propositions currently popular entail ID and/or DET. Unless there is a response to the argument here, those theories are refuted.

King develops a syntax-based account of propositions based on the idea that propositional unity is grounded in the syntactic structure of the sentence. This account faces two objections: a Benacerraf objection and a grain-size objection. I argue that the syntax-based account survives both objections, as they have been put forward in the existing literature. I go on to show, however, that King equivocates between two distinct notions of ‘propositional structure’ when explaining his account. Once the confusion is resolved, it is clear that the syntax-based account suffers from both Benacerraf and grain-size problems after all. I conclude by showing that King's account can be revised to avoid these problems, but only if it abandons its motivating idea that it is syntax that unifies the proposition.