Objects and existence: Reflections on free logic (Q918948)

The paper proposes a new treatment of constants in free logic. These are eliminated using one-place predicates, but the resulting descriptions are not interpreted in the usual way. Their uniqueness condition is assured axiomatically and their existence condition is dropped. Their third condition, stating that the object described has a certain property, is interpreted in two, non-equivalent ways. Truth of a sentence containing constants is defined with respect to all possible translations using these two alternatives - this reminds of supervaluations. An axiomatic system equivalent in strength to the standard one is given; its metamathematical properties are not stated. Soundness is trivial, but completeness seems rather hard to prove.