 Still, in saying that rigidity is widely favored, we should be prepared to qualify in view of those I’ve called “serious counterpart theorists,” who must adopt a revisionist understanding of what it is for a designator to designate “rigidly” (or alternatively, they can just frame their position as a rejection of rigidity: e.g., Varzi 2003, already quoted). Usually, counterpart theorists are motivated by objections to some of the necessity that rigidity secures, according to the usual understanding. It appears to some (e.g., Gibbard 1975) that not all identity statements containing just names are necessarily true. Consider this scenario: you mold one chunk of clay into the top half of a statue, and another chunk of clay into the bottom half. You stick the halves together, thus bringing into existence both a statue, call it ‘David’, and a large lump of clay, call it ‘Lumpl’. Suppose, next, that you explode the statue: both David and Lumpl go out of existence. It is tempting to say that ‘David = Lumpl’ is true, but not necessarily true. It could have been that: David exists and Lumpl exists but ‘David ≠ Lumpl’ is true. This would have been the case had Lumpl survived David: e.g., had you squeezed the clay statue into a ball, thereby changing the shape of the relevant lump of clay, instead of exploding it, thereby bringing an end to the lump of clay.