Löb’s theorem and Curry’s paradox are two very closely related results in logic. Both are surprising, but one—Löb’s—is considered acceptable while the other—Curry’s—is not. In fact, both should fail.
If a sentence says of itself that it is not true, there is little choice but to take it for its word. But what if a sentence says of itself that it is true, or, in any case, provable? Logically, there is an inconsistency in proving this statement. Martin Löb and Haskell Curry were two mathematical logicians who sought to examine this question.
Relevant First-Order Logic LP# and Curry’s Paradox Resolution
