 Early work on substitutional quantification was developed in Marcus (1961) but it soon became the subject of intense debate in the next two decades as philosophers made use of substitutional quantification in ontology and the philosophy of language and mathematics. Belnap and Dunn (1968), Parsons (1971), Grover (1972), and Kripke (1976) are some of the relevant papers in the debate. For a sense of some of the purported applications of substitutional quantification, the reader may consult the essays collected in Gottlieb 1981. For further discussion, see Hand (2007).