INTRODUCTION

Quine's concept of predication is intimately related to his notion of referential opacity. To treat the position of a singular term in a sentence as “purely referential”, and hence the sentence as “referentially transparent”, is to treat the very same sentence as a predication. “Predication”, he says, “joins a general term and a singular term to form a sentence that is true or false according as the general term is true or false of the object, if any, to which the singular term refers.” The conception of predication expressed in the quoted passage is not restricted to its author. Among others who hold it are many free logicians.

Quine has also written that “so long merely as the predicated general term is true of the object named by the singular term … the substitution of a new singular term that names the same object leaves the predication true.” So if a sentence is a predication, it satisfies the substitutivity of identity. Moreover, “in an opaque construction you … cannot in general supplant a general term by a coextensive term (one true of the same objects) … without disturbing the truth-value of the containing sentence. Such a failure is one of the failures of extensionality.”

The theory of predication under consideration is non-extensional precisely in the sense that it does not satisfy the principle that co-extensive general terms substitute for each other salva veritate. The proof of this fact is the first order of business.