What happens to a person in a case of fission? Does it survive? Does it go out of existence? Or is the outcome indeterminate? Since each description of fission based on the persistence conditions associated with our ordinary concept of a person seems to clash with one or more platitudes of common sense about the spatiotemporal profile of macroscopic objects, fission threatens the common-sense conception of persons with inconsistency. Standard responses to this paradox agree that the common-sense conception of persons (...) is unstable, differing over which part of the conception requires revision. I will show that this entrenched view of fission is not compulsory. I will develop a solution to the paradox that maintains the consistency of the common-sense conception of persons on the basis of an ontology of persons and other ordinary objects as double-layered compounds. Each of various descriptions of the outcome of personal fission is compatible with principles about the spatiotemporal profile of persons, because the descriptions and the principles manifest different perspectives on persons and are made true or false by different ontological components of the latter. What holds for the fission of persons, holds for the fission of other kinds of objects. (shrink)