 The logic of relations formalizes a larger territory than monadic logic, but there is a price to pay for obtaining the additional expressive power: While monadic logic is decidable, polyadic logic is not. Even though we need to wait until Church’s theorem to see the undecidability of first-order predicate logic, Peirce intuited a fundamental difference between the logic of non-relatives versus the logic of relations. Here are Peirce’s suggestive ideas over the comparisons between monadic and relational logic: 