AAP 2026 CONFERENCE

It has long been observed that many bad logical results—especially Curry's paradox—rely on a rule called contraction. Logics without contraction thus point in a more promising direction. But it has also been observed, for almost as long, that paradoxes are very resilient; each step down the non-contractive path neutralises one variant of the paradox only for a new, more terrible one to appear. After sketching the basics, I will review a few of these successive problems, including some very recent. Does this story show we been running around putting out fires, instead of getting to grips with what is really going on? Or are we closing in on the true source of the problem, approaching an Ultimate Curry? The goal is to get a higher-level view.