Abstract

The possibility of continuous backwards time travel—time travel for which the traveler follows a continuous path through space between departure and arrival—gives rise to the double-occupancy problem. The trouble is that the time traveler seems bound to have to travel through his or her younger self as the trip begins. Dowe and Le Poidevin agree that this problem is solved by putting the traveler in motion for a gradual trip to the past. Le Poidevin goes on to argue, however, that the gradual trip gives rise to the Cheshire cat problem, a concern about whether the traveler survives the gradual trip. We address the Cheshire cat problem by proposing and considering new continuity constraints on identity over time. Along the way, we come upon an endurantist conception of temporal parts.