Abstract
This paper is about persistence of material objects through time and across possible worlds. It starts with the well-known argument from undetached parts, that is put as an objection to endurantism raised by four-dimensionalists who claim to have a nice treatment of it themselves. While it will be acknowledged that, indeed, four-dimensionalism has a good explanatory power here, and has an advantage over endurantism, we will then see a modified (modalized) version of the argument that will not be so easily dismissed by the four-dimensionalist. To provide a solution to this second puzzle, a proposal will be made to use the four-dimensionalist's strategy in the case of modality and use this notion of perdurance across possible worlds to answer the modalized version of the objection. Finally, I examine some objections to this theory of modal perdurants, and try to answer them.