 Substitutional quantifiers \(\Pi \alpha \ A\) and \(\Sigma \alpha \ A\) are interpreted differently. An interpretation associates with them not a domain of quantification, but rather a substitution class, \(C\), of linguistic expressions of an appropriate syntactic category in the initial language. The truth conditions for substitutionally quantified sentences of the form \(\Sigma \alpha \ A\) and \(\Pi \alpha \ A\) may be given in terms of the truth conditions of suitable substitution instances of \(A(\epsilon / \alpha)\) in which each occurrence of the substitutional variable \(\alpha\) has been replaced with a linguistic expression, \(\epsilon\), of the appropriate syntactic category in the substitution class for the quantifier: