Structure by proxy, with an application to grounding

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.