Sally Latham examines the construction of identity through memory.
Concerning the identity of the person themselves – the thinking being – perhaps surprisingly for his time and culture, Locke claims that personal identity is not tied up with the soul. This is because he thinks that the same soul could in fact play host to different consciousnesses. It is your consciousness which makes you the same person over time; specifically it is the continuity of your memories.
The soul. On the other hand, what is the point of connecting the dots between "I" and a "soul" if there does not appear to be a way [philosophically or otherwise] in which to pin down what a soul/the soul/my soul is?
It's just another configuration of God, for all practical purposes. As for the conscious self going back to the cradle and forward to the grave, my own arguments still seem entirely reasonable to me. Some things we become conscious of are there for all rational people to become conscious of in turn. While other conscious assessments never seem able to get much further than personal opinions. And Locke's personal identity here would seem no less problematic than yours or mine.
The continuation of personal identity through memory is crucial for justice. For instance, in order to properly see the consequences of our actions and maintain our full responsibility for them, we must be able to contemplate our future selves as connected to the person about to carry out an action now, and we also must remember an action for it to qualify as really being ‘me’ who did it.
Yes, technically. But if different "souls" can't agree on what either does or does not constitute, say, social and political justice, how do they manage to configure their individual memories into one frame of mind in which those disagreement dissipate and then fortuitously are subsumed in the best of all possible worlds?
Again the part that most "serious philosophers" authoring articles like this, almost never seem interested in exploring.