Final answer:
c. John Locke
John Locke is the philosopher who believed that memory is a necessary element of personal identity, advocating the psychological continuity theory.
Step-by-step explanation:
The philosopher who considered memory as a necessary element of personal identity was John Locke. In his Essay on Human Understanding, Locke presented the idea of psychological continuity, where our memories and the ability to reflect on them constitute our identity. If a prince and a cobbler had their memories swapped, Locke posited that their identities would be swapped as well, indicating that the body or biological aspect is not what individuates us, but rather the continuity of consciousness.