The problem of the variable in Quine's perspicuous lingua franca of the sciences

Abstract

Some 55 years after the publication of Russell's seminal ‘On Denoting’, Quine adopted the theory of definite descriptions presented therein to formulate his perspicuous lingua franca for the sciences. This paper illustrates how, in so doing, Quine's lingua franca inherited an old antinomy at the core of Russell's theory of definite descriptions, specifically, the lack of congruency between notation and metaphysical commitments when the variable assumes the role of fundamental singular reference. In this context, the paper contends that the phrase ‘to be is purely and simply to be the value of the variable’ is far from the straightforward solution Quine initially envisioned for his lingua franca. Additionally, it argues that it is unlikely that an attempt to account for a determinate object theory, such as those propounded by Russell and Quine, can prove successful when grounded in a referential theory of quantificational logic where the variable, seen as a simple range of values, holds fundamental singular referent‐position. The paper concludes by suggesting that Meinong's object theory could resolve the problem of the variable, albeit at the cost of potentially undesirable ontological and logical commitments. Alternatively, Kit Fine's recent work on other antinomies in the variable may provide a promising approach to exploring how to salvage the variable as a formal foundation for ontology.