 If the distinction between assertoric and ingredient sense is tenable, and if (1)–(4) share the same assertoric content even though they differ in ingredient sense, so that the Rigidity Thesis is false, then this opens the door to holding that proper names share the same content as ordinary, non-indexed descriptions after all, even though names are rigid and ordinary, non-indexed descriptions are not rigid. In that case, something along the lines of the venerable descriptivism associated with Frege and Russell (see the subsection on description theories in the entry on  reference  and the section on descriptive theories of proper names in the entry on  descriptions),  which Kripke is widely thought to have devastated, survives. One way to develop a descriptivism along these lines would be to say that a name like ‘Petrarch’ is something like a disguised description that is shorthand for ‘the famous humanist most closely associated in α with the Italian Renaissance’. Although this description for which ‘Petrarch’ is shorthand is world-indexed, it shares the descriptive content of the non-indexed ‘the famous humanist most closely associated with the Italian Renaissance’. On this suggestion, since ‘Petrarch’ shares the content of the rigid description, it also shares the content of the nonrigid description.