6. CHALLENGE. Peirce's Law and Curry's Paradox We start with a simple identity due to philosopher CHARLES PEIRCE (18391914). An odd consequence is Curry's paradox, discovered by logician HASKELL CURRY (19001982). Like Russell's paradox (discussed in lectures), the paradox arises when we allow self-reference. (a) Show that Peirce's law, ((p = q) = p =p is a tautology via truth tables. (b) Suppose that (p = q) Apis true. Use part (a) and modus ponens to deduce q. (c) Argue informally that, for any proposition q, the self-referential sentence p= If p is true, then it implies q satisfies (p = 9) Ap. (d) Combine (b) and (c) to conclude that anything is true. What has gone wrong here? 6. CHALLENGE. Peirce's Law and Curry's Paradox We start with a simple identity due to philosopher CHARLES PEIRCE (18391914). An odd consequence is Curry's paradox, discovered by logician HASKELL CURRY (19001982). Like Russell's paradox (discussed in lectures), the paradox arises when we allow self-reference. (a) Show that Peirce's law, ((p = q) = p =p is a tautology via truth tables. (b) Suppose that (p = q) Apis true. Use part (a) and modus ponens to deduce q. (c) Argue informally that, for any proposition q, the self-referential sentence p= If p is true, then it implies q satisfies (p = 9) Ap. (d) Combine (b) and (c) to conclude that anything is true. What has gone wrong here