Question

Locke thought that identity of a self through time could be established on the basis of

Answer 1

i believe the answer is a memory.
He believed that every time we experience the result of our actions, we will engrave all of it within our memory.
Overtime, these memories would be collected and stacked within our subconscious that influence how we perceive ourself (identity)

Answer 2

Locke thought that identifying self through time could be established on the basis of memory. He is an empiricist who thought that the experience originates all the knowledge and did not have any knowledge when we were born. In this case experience includes both sensation and reflection.