 How about essentialism? Whether we want to say that rigidity or transworld identity is committed on that score might well depend on the form of essentialism in question. Not many philosophers would dispute Cartwright’s observation that “‘Shakespeare’ is rigid only if the man Shakespeare could not have existed without being Shakespeare—or as we might equally well say, only if it is essential to Shakespeare that he is Shakespeare” (Cartwright 1998, p. 69). So if Shakespeare could have been Biden instead of Shakespeare, ‘Shakespeare’ would not be rigid.