 Call the initial language “the object language”. And call the language in which we explain the truth conditions of sentences of the initial language “the metalanguage”. In the metalanguage, we have explained the truth condition for \(\Sigma \alpha \ A\) in terms of what looks like objectual quantification over linguistic expressions. To acknowledge this is of course not to claim that the intended interpretation of substitutional quantification is one on which it is merely objectual quantification over linguistic expressions. But just what the intended interpretation of the substitutional quantifier might be has been the subject of intense controversy. Indeed, van Inwagen (1981) and Fine (1989), for example, have each argued that there is no separate intended interpretation we can understand independently from our grasp of objectual quantification over linguistic expressions of the relevant sort.