In Naming and Necessity Kripke introduces the concept of a rigid designator and argues that proper names are rigid designators. He argues that in this way they are different from typical definite descriptions (though he allows that some definite descriptions, e.g., 'the actual winner of the lottery', 'the square of 3', are rigid designators). His opponents have either argued that names can be regarded as abbreviations of rigid descriptions (e.g., 'actualized' ones) or have tried to deny that names are rigid designators. I shall argue that no unambiguous descriptions are non-rigid. All unambiguous descriptions are rigid. The appearance of non-rigidity in descriptions is simply an illusion, a manifestation of ambiguity. I shall then go on to show that an explanation of the difficulty which has been found in extending the rigid/non-rigid distinction from singular terms to predicates follows.
Noonan, H. (2023). All Designators are Rigid. Metaphysica, 24(1), 101-107. https://doi.org/10.1515/mp-2021-0040