An issue much discussed by Indian philosophers and Western philosophers alike is one that concerns the need to assume a continuing self (or subject of experience) in giving an account of the world and our experience of it. This paper concentrates on two arguments put forward by the eighth-century AD Indian philosopher Śankara, in a short passage of his commentary on Bādarāyana's Brahmasūtra. The innovative peculiarity of these arguments is that they rest on an appeal to the content of memory judgements. Śankara takes the line that an analysis of the content of memory judgements shows that a Buddhist attempt to reconstrue memory as mere similarity between successive experiences is fundamentally flawed. Our concern, therefore, is whether Śankara's account of the content of memory judgements is correct, and whether it establishes the required continuity.