Abstract
Criteria for the transtemporal identity of composite artifacts are best understood in terms of functions, histories, and the intentions their makers. As long as certain background-conditions are fulfilled, composite artifacts can undergo changes in all of their parts with no breakdown in their identities, even to the point of being unrecognizable as sharing their identities with themselves as they were originally constituted. They can be repaired, modified, or improved without a resulting breakdown of transitivity. I defend this view against views according to which there must be some limit to how much change artifacts can undergo while still retaining their identities, against views according to which any changes result in breakdowns of transitivity, and against views according to which there are no criteria of identity over time.