What is the self? I can discern six strands of an answer:
experiences reported in a meditative tradition;
the teachings of a meditative tradition - in Buddhism, no soul and rebirth.
My own philosophical reflection and limited understanding of science incline me to accept no soul but not rebirth. In fact, I think that no soul entails no rebirth. It seems contradictory to acknowledge that consciousness is conditioned but to expect it to outlast its conditions.
I believe that:
being determines consciousness;
more specifically, some organism-environment interactions generate and sustain psychophysical states which cease when organic matter reverts to an inorganic state;
thus, individual actions and consequences begin and end within a single lifetime, not in a series of lifetimes;
each individual either does or does not realise enlightenment before death;
there is no intermediate, bardo, state;
if I am wrong about the bardo, then I will find out and hopefully will be as prepared as I can be by regular meditation.
The only fly in my ointment is that some people report apparent memories of previous lives. There are other reported experiences that I do not have and cannot account for as yet but this is to be expected. Omniscience is impossible. We inhabit the intersection between known and unknown.