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Section I. Rigidity Section Ii. Rigid Designation and Quantified Modal Logic Section Iii. the Descriptive Picture Section Iv. Kripke's Argument and the Rigidity Thesis Section v. the 'actualized' Description Theory

The fact that natural language proper names are rigid designators is an empirical discovery about natural language. However, unlike other empirical discoveries about language made in the past few decades, it is one which has been taken to have great philosophical significance. One reason for this is that it helped simplify the formal semantical representation of ordinary modal discourse. But the central reason is that the discovery threatens a certain picture of the content of names, the descriptive picture, upon which a great deal of philosophy was premised. This paper is mainly intended to be a survey of both the background and contemporary discussion of this discovery. However, the survey takes place in the context of an evaluation of the extent to which the discovery that English proper names are rigid, by itself, threatens the descriptive picture of the content of names. The goal is to show that the exact philosophical significance of the discovery that natural language proper names are rigid designators is still, and should still be, a matter of controversy. Section I discusses different explications of rigidity. Section II is devoted to a sketch of the development of the notion of rigidity. Section III is a discussion of the descriptive picture of the content of names. In Section IV, Kripke's argument for the thesis that natural language proper names are rigid is outlined, as well as an argument based upon this thesis against the descriptive picture. Finally, the remaining three sections cover various possible defenses of the descriptive picture.