If one is in doubt whether the distance is far enough to allow him to shorten the prayer,
is it permissible for him to shorten it?
If one does not know and there is nothing to indicate whether or not the distance is far enough, then a traveler is not allowed to shorten the prayers. The completion of prayers is the default requirement and cannot be abrogated or over-ridden by doubt or uncertainty (as per the Shafi'yah opinion).