This paper concerns two paradoxes involving propositions. The first is Russell's paradox from Appendix B of The Principles of Mathematics, a version of which was later given by Myhill. The second is a paradox in the framework of possible worlds, given by Kaplan. This paper shows a number of things about these paradoxes. First, we will see that, though the Russell/Myhill paradox and the Kaplan paradox might appear somewhat different, they are really just variants of the same phenomenon. Though they do this in different ways, the core of each paradox is to use the notion of a proposition to construct a function, f, from the power set of some set into the set itself. Next we will see how this paradox fits into the Inclosure Schema. Finally, I will provide a model of the paradox in question, showing its results to be non‐trivial, though inconsistent.

中文翻译：

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悖论性主张

本文涉及涉及命题的两个悖论。第一个是《数学原理》附录B中的罗素悖论，后来Myhill给出了这个版本。第二个是卡普兰给出的可能世界框架中的悖论。本文展示了有关这些悖论的许多信息。首先，我们将看到，尽管拉塞尔/迈希尔悖论和卡普兰悖论看起来可能有所不同，但它们实际上只是同一现象的变体。尽管他们以不同的方式这样做，但每个悖论的核心是使用命题的概念来构造函数f，从某些集合的幂集变为集合本身。接下来，我们将看到这个悖论如何适合“外壳模式”。最后，我将提供一个有关该悖论的模型，说明其结果虽然不一致，但并非无关紧要。