 When we move from monadic to polyadic logic, substantial changes take place. The following three changes are at the top of the list. First of all, a move from property to relation is a territory expansion. Noting that Aristotelian syllogisms are limited to unary predicates, one expects polyadic logic to represent more than the reasoning involved in Aristotelian syllogism, that is, term logic. Second, monadic logic is decidable while polyadic logic is not decidable, as Church’s theorem proved. In some sense, as the territory is expanded, we are losing its grip. Third, a change in notation is inevitable, which necessitates modern quantification theory. How are these three important aspects are handled by Peirce?