What do memories represent? At best they represent some fragments derived from our experience of a past event. That ‘experience’ may have intersected with ‘reality’ to some degree. So the fragments preserved in memory derive from our experience of reality, also to some degree. The brain non-consciously and automatically ‘fills in’, by making unconscious inferences, much of the detail of a ‘memory’. Memories are constructed in the remembering-imaging system (RIS), where future events are also imagined, as well alternative pasts. In this paper I consider how errors and false memories can arise in the RIS for past and future events.