In order to assign a meaning to the description operator with respect to a referential range, a reference value must be singled out as the nil value. This serves as the reference value of the constant ∗ and as the reference value of the description Ix ρx when the extension of ρ is empty or has more than one member. Then the law for descriptions asserts that either Ix ρx is something that is the sole thing ρ is true of or ρ is not true of exactly one thing and Ix ρx has the nil value.
A definite description is not a sentence, so it is handled in derivations not by exploiting it or planning for it as a goal but by securing it—that is, by insuring that its reference is settled in the way required by the law for descriptions. The rule for doing this is Securing a Description (SD). This rule is enough to enable us to establish meaning postulates, which state that definite descriptions are interpreted as we intend. Allow the argument used for completeness of the system of derivations no longer applies, is it easy to see that the system is complete if we allow the rule LFR to be used to introduce meaning postulates as lemmas. The rule SD introduces a new term, so when searching for finite counterexamples, it should be used in the alternative form Securing a Description Supplemented (SD+).