## Abstract

An argument going back to Russell shows that the view that propositions are structured is inconsistent in standard type theories. Here, it is shown that such type theories may nevertheless provide entities which can serve as proxies for structured propositions. As an illustration, such proxies are applied to the case of grounding, as standard views of grounding require a degree of propositional structure which suffices for a version of Russell’s argument. While this application solves some of the problems grounding faces, it introduces problematic limitations: it becomes impossible to quantify unrestrictedly over the relata of ground. The proposed proxies may thus not save grounding, but they shed light on what exactly Russell’s argument does and does not show.

## Keywords

Structured propositions Russell–Myhill Grounding Higher-order logic Type theory## Notes

### Acknowledgements

For very helpful discussion and comments on drafts of this paper and its (in some cases distant) precursors, I would like to thank Andrew Bacon, Luke Burke, Cian Dorr, Jeremy Goodman, Bryan Pickel, Jim Pryor, Gabriel Uzquiano, Natalia Waights Hickman, Clas Weber, Juhani Yli-Vakkuri, two anonymous referees for *Synthese*, several anonymous referees for other journals, and audiences at the Universities of Agder, Oslo, Edinburgh, Bielefeld, and Glasgow. Special thanks to Harvey Lederman who, in comments on an earlier version, recommended pursuing the application of *t*-complexes to grounding; this led not only to the development of the second half of this paper, but also to several other papers, including Fritz (unpublished) and Fritz (forthcoming).

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