Higher-order free logic and the Prior-Kaplan paradox
Andrew Bacon, John T. Hawthorne, Gabriel Uzquiano · 2018
See also McGee [27] for a discussion of the second-order variant. 7It's arguable that the rejection of UI is also the key part to a Russell-style treatment of many other paradoxes, but we shall not defend the broader claim here. 8Suppose that p ≡ p. Then by EG, we can infer ∃q p ≡ q.We then have ∃q p ≡ q by necessitation, ∀p ∃q p ≡ q by universal generalisation, and finally ∀p ∃q p ≡ q by necessitation again.