This paper shows that once we have propositional constants t (the conjunction of all truths) and u (the disjunction of all untruths), paradox ensues, provided you have a conditional in the language strong enough to give you modus ponens. This is an issue for views like those of Jc Beall, Ross Brady, Hartry Field and Graham Priest.
I’m Greg Restall, and this is my personal website. I teach philosophy and logic as Professor of Philosophy at the University of Melbourne. ¶ From August 2021, I will be the Shelby Cullom Davis Professor of Philosophy at the University of St Andrews. ¶ Start at the home page of this site—a compendium of recent additions around here—and go from there to learn more about who I am and what I do. ¶ This is my personal site on the web. Nothing here is in any way endorsed by the University of Melbourne.