none 10.1215/00318108-10294409 Duke University Press Duke University Press 73 148265862 59350 2023053020154412700 10.1215 2023-12-14T12:34:24Z 2023-05-30T20:16:04Z 11 Philosophical Review 0031-8108 1558-1470 04 1 2023 04 1 2023 132 2 Andrew Bacon University of Southern California 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. 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