Jabba, I agree with jsfisher that science doesn't say anything about immaterial selves because no hypothesis about immaterial selves makes testable predictions.
I am on board with this as well. In order for a hypothesis to be testable, it must make predictions that correlate one set of observable conditions to another set of observable conditions. Then the correlation must be tested in various ways to eliminate confounding or accidental methods of causation. Jabba has identified no observation of human existence that fits these criteria.
Specifically, there are no observations about human existence that are not both correlatively and causatively attributed to the brain. When there are no outstanding observations available to predict because known causes already predict them, then there is no need to hypothesize beyond the existing model. Therefore science doesn't. This is the rule of parsimony, one of the things that makes science powerful.
If Jabba wants to explore scientifically the hypothesis that immaterial, immortal souls exist, he must first identify a relevant observation that isn't predicted in the existing model. That's how science revises, refines, and extends its models.
Jabba knows he cannot do this.
This is likely why he sidesteps the ordinary requirements of science by claiming souls have no characteristics. He thinks that if he can obviate the mechanism of testability, he can force his critics into accepting a different method of proof.
This is likely why he formulates the problem as a statistical exercise, misapplying predictability for probability in a way science already knows is a rat hole. And not even an exercise to prove his claim, but rather to suggest that the null hypothesis is improbable -- and for no reason other than its failure to predict him as a special snowflake.
If you think, as I do, that everything about the human self is material, then it follows that the death of the material body means the death of the self.
And, carrying this further, it does not necessarily follow that if a portion of the self is immaterial, it is also immortal. An immaterial aspect to the self may be just as limited in longevity as the material aspects. There is nothing about immateriality that necessarily leads to immortality. In other words, immateriality is not a proxy for immortality, no matter now much you think it would be easier to argue that way.