 Let us see several different ways Peirce pursued to represent existential statements in a more explicit way. In the above for “\(\binary{l}\unary{w}\)”, the existential quantifier is carried out in the way relation \(\binary{l}\) is applied to a unary predicate “\(\unary{w}\)”, but not explicitly. There are several different explicit ways Peirce represents existential statements. One method: borrowing exponentiation (in which a binary predicate is applied to a unary predicate, e.g., \(\binary{l}^{\unary{w}}\)), Peirce expresses an existential statement as a contradiction of a universal statement: