 The method presented in DNLR [CP 3.141] is interesting for several reasons. First of all, Peirce maintains Boole’s theme that all propositions are represented as equations. Another is that Peirce utilizes the contradictory relation between universal and existential propositions. Even more interestingly and importantly, Peirce brings in his exponentiation notation, exponentiation between relation to property (that is, between binary to unary predicates), to express existential statements.