Objectual and Substitutional Interpretations of the Quantifiers
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This chapter discusses objectual and substitutional interpretations of the quantifiers. Although a truth theory for a language with objectual quantification requires an inductive detour through the notion of satisfaction, with truth defined in terms of satisfaction of closed wffs, this detour is unnecessary for substitutional quantification. The reason the detour is needed in customary semantic treatments of languages with objectual quantifiers is that the semantic apparatus determines the semantic value of a nonatomic wff on the basis of the semantic values of its immediate syntactic constituents (the wffs mentioned on the right-hand sides of the inductive clauses). In the case of quantifiers, this means that the specification of a semantic value of a closed wff requires semantic values to be assigned to open wffs. This chapter describes basic concepts related to Quine and ontological commitment, referential and nonreferential base semantics, and the "substitutional strategy." It provides details about Kripke's view on substitutional quantification, the Lycan-Van Inwagen-fine objection(s), and the problem of too many names. Concepts related to natural language substitutionalism are also explained in this chapter. 2007 Elsevier B.V. All rights reserved.
