As we have seen, there was a tradition going back to Locke and Hume according to which having a memory of an event required having a belief that the event occurred.  In their classic essay “Remembering,” C.B. Martin and Max Deustscher read Locke (and others) as claiming that the belief condition is necessary for S's remembering.  In defense of Locke, it can be argued that he was interested in giving an account of what it is that makes a belief a memory belief; if that is correct, then the belief condition surely is unobjectionable.