This paper argues that the theory of structured propositions is not undermined by the Russell-Myhill paradox. I develop a theory of structured propositions in which the Russell-Myhill paradox doesn’t arise: the theory does not involve ramification or compromises to the underlying logic, but rather rejects common assumptions, encoded in the notation of the λ-calculus, about what properties and relations can be built. I argue that the structuralist had independent reasons to reject these underlying assumptions. The theory is given both a diagrammatic representation and a logical representation in a novel language. In the latter half of the paper I turn to some technical questions concerning the treatment of quantification and demonstrate various equivalences between the diagrammatic and logical representations and a fragment of the λ-calculus.

中文翻译：

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结构命题理论

本文认为，结构化命题理论并未被 Russell-Myhill 悖论所破坏。我发展了一种结构化命题理论，其中不会出现 Russell-Myhill 悖论：该理论不涉及对基础逻辑的分支或妥协，而是拒绝以λ的符号编码的常见假设-微积分，关于可以建立什么属性和关系。我认为结构主义者有独立的理由拒绝这些潜在的假设。该理论以一种新颖的语言给出了图形表示和逻辑表示。在本文的后半部分，我转向了一些关于量化处理的技术问题，并证明了图解和逻辑表示与 λ 演算的一个片段之间的各种等价性。