As promised, I have decided to reflect and meditate on whether it is possible to be neither eternal nor impermanent, and also neither exist nor not exist.
One possible hypothesis I have come up with relies on quantum mechanics and quantum probability theory.
In effect, our “self” is like a quantum unit of matter. Existence is not binary but a Hubert space of all possible existence states. The “self” can be likened to a vector in the Hubert space and a lifetime is effective a projection function on the Hubert space.
Just in case anyone thinks this is all theoretical rubbish, remember we can build quantum computers that can compute all possible results for a calculation simultaneously, so quantum mechanics is “real.”
This hypothesis does have a few advantages in that it “explains” what nibbana is (the Hubert space itself), as well as the experiences of the Buddha and the arahants, and curiously my own direct experience.
So according to this hypothesis, when an arahant “attains” nibbana, the arahant has the ability to perceive the Hubert space as a whole, and therefore traverse to any point in that lattice, and therefore have access to all past lives, as well as the ability to move to different points in the latttice (akin to the Buddha “ascending” into the various heavens to teach the devas etc.)
It also explains how arahants apparently lead a “mundane” earthly life until they pass away - they are simply continuing the trajectory of the projection function. When they finally pass away, they will not be reborn as they can “diffuse” the “self” across the entire Hubert space, thus preventing the probability function from coalescing into a new “life”.
In this way, it is possible to confirm the validity of all your four statements - the Buddha can neither be said to be existing, or not existing, or in both states, or in neither states, after death.
In a curious way, it also explains my own direct experience. I’ve had the ability to have lucid dreams for many years, but in recent year or so most of my dreams are not of my “self” but a different self living a different life. Perhaps these are past or alternate lives, but it seems my sub conscious is able to explore the Hubert space in ways my conscious mind is not yet able to do.
Thank you for inspiring me on this line of thinking, which I will need to ponder and reflect on more in the future.