According to the structured theory of propositions, if two sentences express the same proposition, then they have the same syntactic structure, with corresponding syntactic constituents expressing the same entities. A number of philosophers have recently focused attention on a powerful argument against this theory, based on a result by Bertrand Russell, which shows that the theory of structured propositions is inconsistent in higher order-logic. This paper explores a response to this argument, which involves restricting the scope of the claim that propositions are structured, so that it does not hold for all propositions whatsoever, but only for those which are expressible using closed sentences of a given formal language. We call this restricted principle Closed Structure, and show that it is consistent in classical higher-order logic. As a schematic principle, the strength of Closed Structure is dependent on the chosen language. For its consistency to be philosophically significant, it also needs to be consistent in every extension of the language which the theorist of structured propositions is apt to accept. But, we go on to show, Closed Structure is in fact inconsistent in a very natural extension of the standard language of higher-order logic, which adds resources for plural talk of propositions. We conclude that this particular strategy of restricting the scope of the claim that propositions are structured is not a compelling response to the argument based on Russell’s result, though we note that for some applications, for instance to propositional attitudes, a restricted thesis in the vicinity may hold some promise.

根据命题的结构化理论，如果两个句子表达相同的命题，则它们具有相同的句法结构，而相应的句法成分则表达相同的实体。基于贝特朗·罗素（Bertrand Russell）的结果，许多哲学家最近将注意力集中在了反对该理论的有力论据上，该结果表明结构命题的理论在高阶逻辑中是不一致的。本文探讨了对此论点的回应，该论点包括限制命题是结构化的主张的范围，因此它并不适用于所有命题，而仅适用于使用给定形式语言的封闭句可表达的命题。我们称这种限制性原则为封闭结构，并证明它在经典高阶逻辑中是一致的。作为示意性原理，封闭结构的强度取决于所选语言。为了使它的一致性在哲学上有意义，还需要在结构化命题理论家易于接受的语言的每个扩展中都保持一致。但是，我们继续展示，封闭结构实际上，它与高阶逻辑的标准语言的非常自然的扩展不一致，后者为命题的多重讨论增加了资源。我们得出结论，这种限制命题结构主张的范围的特定策略并不是对基于罗素结果的论点的有说服力的回应，尽管我们注意到，对于某些应用（例如，对于命题态度），附近的命题是受限制的。可能抱有希望。