 Modern quantificational logic has chosen to focus instead on formal counterparts of the unary quantifiers “everything” and “something”, which may be written \(\forall x\) and \(\exists x\), respectively. They are unary quantifiers because they require a single argument in order to form a sentence of the form \(\forall xA\) or \(\exists xA\). Frege (and Russell) devised an ingenious procedure for regimenting binary quantifiers like “every” and “some” in terms of unary quantifiers like “everything” and “something”: they formalized sentences of the form \(\ulcorner\)Some \(A\) is \(B\)\(\urcorner\) and \(\ulcorner\)Every \(A\) is \(B\)\(\urcorner\) as \(\exists x(Ax \wedge Bx)\) and \(\forall x(Ax \rightarrow Bx)\), respectively. They analyzed a sentence like “some apples are delicious” in terms of the sentence “something is an apple and delicious”, whereas they parsed the sentence “every material object is extended” as “everything is extended, if it is a material object”. Unfortunately, this procedure cannot be generalized to cover quantifier phrases like “many”, “most”, or “few”. It would be a mistake to regiment the sentence “most planets are visible to the naked eye” by means of “most things are planets and visible to the naked eye” or “most things are such that they are visible to the naked eye, if they are planets”. Instead, they are better analyzed as irreducibly binary quantifiers, and their study has given rise to the theory of generalized quantifiers, which has become a fruitful subject of study partly because of its applications in the semantics of natural language.