I'm not sure how fundamental the question is about whether there is only
a finite number of possible "islands". Given that we are dealing with
a parameter space where the parameters are real numbers, even a single
tiny island may admit an infinite number of possible sets of parameters.
Would there be some inherent quantization of parameters such that
changing the mass of an electron by a sufficiently small amount would
make literally zero difference? Maybe if you consider
delta E * delta T > hbar, then if delta E were small enough that delta T
would have to be longer than the age of the universe, this would be true.
It also seems possible (despite what I said earlier) that only a limited
range of possible parameter values will admit life. Maybe the mass
of the electron could be large enough that there are no atoms, and we
could still have life in other forms, but could it be infinitely large?
Could all parameters increase without limit? Seemingly the only way
there could be an infinite number of islands would be if the set of
legal parameters included (virtually) infinite values.
Hal