 One important difference with respect to monadic second-order logic is that instances of plural comprehension are conditionals that state that if something satisfies a certain condition, then some objects are all and only objects satisfying the condition. The antecedent of each conditional is motivated by an interpretation of the plural quantifier \(\exists xx\) to mean “one or more objects”. Indeed, Linnebo (2013) explicitly supplements the theory of plural quantification with an axiom that states that no matter what some objects may be, there is at least one of them: