If a paradox resulted whenever one thing had more than one name, then these paradoxes wouldn't be restricted to sets. The names 'Samuel Clemens' and 'Mark Twain' would generate a paradox by referring to the same person. But, of course, there's no paradox here. Everything true of the person named 'Samuel Clemens' is true of the person named 'Mark Twain'. Mark Twain was born in Missouri, and Samuel Clemens wrote The Adventures of Huckleberry Finn. Indeed, all those who know that Mark Twain wrote the novel thereby also know de re (Latin for 'concerning the thing') that Samuel Clemens wrote the novel: they know, concerning the person denoted by 'Samuel Clemens', that he wrote the novel, even if they wouldn't use 'Samuel Clemens' to denote the author.
If a paradox resulted every
If a paradox resulted whenever one thing had more than one name, then these paradoxes wouldn't be restricted to sets. The names 'Samuel Clemens' and 'Mark Twain' would generate a paradox by referring to the same person. But, of course, there's no paradox here. Everything true of the person named 'Samuel Clemens' is true of the person named 'Mark Twain'. Mark Twain was born in Missouri, and Samuel Clemens wrote The Adventures of Huckleberry Finn. Indeed, all those who know that Mark Twain wrote the novel thereby also know de re (Latin for 'concerning the thing') that Samuel Clemens wrote the novel: they know, concerning the person denoted by 'Samuel Clemens', that he wrote the novel, even if they wouldn't use 'Samuel Clemens' to denote the author.