 Much like in the case of pure quantificational logic, no model—standard or otherwise—for the language of second-order logic interprets the quantifiers to range over a universal domain of discourse. But if there are interpretations of the language of second-order logic to which no model corresponds, the question arises again of whether truth in all models is tantamount to truth under all interpretations of the language. Unfortunately, in the absence of a Completeness theorem, Kreisel’s argument is not available for second-order logic with standard models.