Incomplete Descriptions and Qualified Definiteness

TL;DR

This paper proposes a formal account of incomplete and loosely used definite descriptions by introducing the concept of qualified identity, refining Russell's notion of uniqueness and definiteness.

Contribution

It introduces the notion of qualified identity to model incomplete descriptions, providing a formal proof-theoretic framework for qualified definiteness.

Findings

The modified notion of identity captures loose and incomplete descriptions.

Formal proof-theoretic semantics formalizes the concept of qualified definiteness.

The approach distinguishes strict and loose definiteness based on the subset of predicates Q.

Abstract

According to Russell, strict uses of the definite article 'the' in a definite description 'the F' involve uniqueness; in case there is more than one F, 'the F' is used somewhat loosely, and an indefinite description 'an F' should be preferred. We give an account of constructions of the form 'the F is G' in which the definite article is used loosely (and in which 'the F' is, therefore, incomplete), essentially by replacing the usual notion of identity in Russell's uniqueness clause with the notion of qualified identity, i.e., 'a is the same as b in all Q-respects', where Q is a subset of the set of predicates P. This modification gives us qualified notions of uniqueness and definiteness. A qualified definiteness statement 'the Q-unique F is G' is strict in case Q = P and loose in case Q is a proper subset of P. The account is made formally precise in terms of proof theory and proof-theoretic semantics.