Qualified Definiteness

According to Russell, the definite article ‘the’ in a definite description ‘the F’ is used strictly in case there is a unique F and it is used loosely in case there is more than one F. Russell’s analysis of constructions of the form ‘the F is G’ is concerned only with the strict use. We modify this analysis so as to allow also for the loose use. This is achieved essentially by replacing the usual undefined notion of identity in Russell’s uniqueness clause with the defined 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 predicate constants P) proposed in earlier work. 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. The framework is intended to be acceptable from a foundational intuitionistic point of view. It is applied to natural language constructions with complete, incomplete, and generic definite descriptions. Also constructions with nested and with predicatively used definite descriptions are considered as well as constructions involving possessives. This work incorporates and extends my NCL’24-paper ‘Incomplete descriptions and qualified definiteness’.