 Whatever the philosophical import of substitutional quantification, Kripke (1976) makes plain that there is no technical obstacle to introducing substitutional quantifiers into a given language. In what is perhaps the canonical treatment of substitutional quantification, he explained how to extend an interpreted language \(\mathcal{L}\) into a substitutional language \(\mathcal{L}^{\Sigma}\) equipped with substitutional quantification over a class of expressions in \(\mathcal{L}\). One first expands the vocabulary of \(\mathcal{L}\) with an infinite stock of variables \(\alpha_1\), \(\alpha_2\), … and a substitutional quantifier \(\Sigma\). (Kripke defines \(\Pi\) as the dual of \(\Sigma\), where \(\Pi \alpha \ A\) abbreviates: \(\lnot \Sigma \alpha \lnot \ A\).)