Convention T and Substitutional Quantification
John Wallace · Noûs · 1971
It is sometimes suggested or hinted or assumed that there are two workable approaches-which I will tag 'referential' and 'substitutional'2-to the semantics of sentences built on the pattern of first order quantification theory; i.e., that there are two adequate accounts of how the truth value of a sentence of this kind depends on semantic features of its parts. The heart of the referential approach is a recursive definition of satisfaction, a relation which connects sentences open and closed with non-linguistic things, whose characterization makes essential appeal to a range of quantification, and in terms of which truth can be explicitly defined. The substitutional approach, on the other hand, attempts a direct recursive characterization of truth. Truth conditions for closed atomic sentences are given somehow outright. And the key recursion clauses are the following ones for quantifiers: