Hobbes' (1672/1913) famous puzzle of the Ship of Theseus - in which a wooden ship's parts are replaced plank by plank, and the old planks are subsequently reassembled to create a second ship - has been the source of debate about the criteria that underlie human judgments of individual artifact persistence. This puzzle has led some philosophers to the paradoxical conclusion that an artifact observed at one time is the same persisting individual as two artifacts seen at a later time. We argue that prior discussions of the puzzle have conflated property persistence (judged in conjunction with a description, like "Theseus' ship") with individual persistence (judged in conjunction with a designator, like "X"). In three studies, we manipulated the linguistic expression (description, designator) used to label the original object in the puzzle. When participants solved the puzzle in conjunction with a description, they gave systematically high ratings to any object (either or both) that could be inferred to match the description. Yet when participants solved the same puzzle in conjunction with a designator, they gave significantly higher ratings to one post-change object (the object made of the reassembled old parts) than to the other post-change object (the object made of replacement parts). The results suggest that individual persistence judgments concerning the puzzle (i.e., those made in conjunction with a designating expression) are not paradoxical but rather are based on the continuity of the object's parts/material.