A list of groceries, Professor Anscombe once suggested, might be used as a shopping list, telling what to buy, or it might be used as an inventory list, telling what has been bought (Anscombe 1957). If used as a shopping list, the world is supposed to conform to the representation: if the list does not match what is in the grocery bag, it is what is in the bag that is at fault. But if used as an inventory list, the (...) representation is supposed to conform to the world: if the list does not match what is in the bag, it is the list that is at fault. The first kind of representation, where the world is supposed to conform to the list, can be called "directive"; it represents or directs what is to be done. The second, where the list is supposed to conform to the world, can be called "descriptive"; it represents or describes what is the case. I wish to propose that there exist representations that face both these ways at once. With apologies to Dr. Doolittle, I call them pushmi-pullyu representations or PPRs. (shrink)