You're entire argument seems to confuse possibility with probability. I'm not arguing that death definitely is the end of us, just that the evidence seems to support that conclusion over and above your position of continuance.

So, without continuity, in what way can you say it's "us". You've offered nothing I can see in support of this claim (which seems to be central to your overall claim).

Personally, i'd likely not walk into it, because as far as I can tell, my consciousness depends on my specific neurons - I would cease and a copy (which thought it was a continuation of "me") would continue on the ship.

And yet you still want to claim that it will somehow continue or reappear after the brain, which as far as we can tell is required for that consciousness, is "destoryed".

Is it logically possible that our consciousness will be "re-instantiated", "continue" or otherwise survive death?
Sure it is.

Is it possible in reality?
Maybe, we don't know for sure.

Is it probable/likely in reality?
It doesn't to be given our present knowledge and evidence.

What you need do (and have thus far failed to, it seems) is support this logical possibility as physically probability with arguments and evidence. Failing that, I see no reason to think that your claim is likely/probable, and therefore no reason to accept it (nor a reason why you do).

if there is no continuity, how can you claim some shared identity between the two conscious events?

And the evidence supporting these claims are?
A nice thought experiment, but as far as I can tell, there is no reason to think they obtain in "reality".

Again, the analogy with a computer simulation fails because there is no reason to think it is the case.
And even so, to claim that the contents at a specific address (or however you want to point to an instance) would make the "I", regardless of the contents of that structure seems nonsensical.

Without some kind of identity "mapping" between "I-now" and "I-future", which you've not indicated for your general thesis, there seems no reason to take said thesis seriously.

What evidence would that be? As I see it, the evidence supports both our hypothesis, and mine is simpler, so why give yours preference?

You've said it a number of times, but you still haven't supported the claim.

As far as I can see, atheism only implies a denial of or lack of belief in god or gods. Even if we substitute "materialism" or "naturalism" where you use "atheism", the implied non-existence you claim still doesn't seem to follow.

Only if such a claim followed from atheism (which is doesn't).

You have a very strange view of "the evidence". You give no indication that any sort of continuity exists between this hypothetical future consciousness and ourselves, and there are reasons to think that no such thing exists (ie. reliance upon a specific brain, for example)

Thought experiments are all well and good, but there is no indication that any of the things you mention are possible.
As far as the star trek analogy is concerned, "I" would wake up after being beamed, but I'm not sure it would be the same "I" who was anhilated earlier (though I'm sure it would profess that it was), especially given the possibility of the original still existing (their experiences would diverge instantly, and they'd be "different" people, surely) Your analogies ALL seem to rely upon copying a specific neural pattern, something which you've given no indication of happening with your "general" scenario of some conscious experience at some unknown time in the future through some unknown mechanism/process.
I wonder why I'm skeptical of you claims :-)

There is a difference between not having an explanation currently, and an explanation being impossible. You seem to think the latter, but have given no reason to think that this is the case (especially as there are hypothesis being explored).

You're going well beyond the evidence (again).

If you were talking about Botlzmann brains, or some other hypothetical observer(s) fluctuating into existence, then you may have a point (though the lack of continuity between "us" and the future consciousness would be a serious issue for your claims of them both being "us").

However, you don't seem to be talking about such things (or even some kind of computer simulation, such as Frank Tipler, I think, lays out in one of his fanciful "science" books).
You seem to be saying that at some stage, some other consciousness might (will?) come into being, and that there is some means of assigning identity between it and me/you, while providing absolutely no notion of how that could be the case, against the evidence that it would not be the case.

It seems to me that parsimony/Occam's razor leads us to accept no such continuation of identity likely/possible, provisional on further evidence.
You seem to take the complete opposite stance - accept the less parsimonious hypothesis unless it's shown to be false.
That seems an irrational position to take.

I think, for you to claim it is possible "again", means you need more than simply "it happened before".

Sorry, this statement is incoherent - if the future "us" doesn't resemble the current "us", in what sense can it even be suggested that both share some form of identity? You've failed to provide any meaningful sort of continuity between these two hypothetical "consciousness" events.

If it is the same pieces in the same arrangement, then for most intents and purposes, it would be the same "I" - it at least, would claim some kind of continuance from the "deconstructed I".

Would it's fellow lego soldiers consider it "the same"? No idea.

If we could create a duplicate of a person at the molecular/atomic level, would we consider them the same person? If we destroyed the original at the time of duplication?

Your analogy doesn't point to this - it's much more like the case of a duplicate sketched above than your "life after death".

Your "consciousness after brain death" claim seems to require a duplicate of our brains (and bodies, as they're a very important part of the "I") be created sometime in the future by some unknown mechanism/party. You've not supported this (unstated?) assumption with argument or evidence as yet.

And you know this how?

How consciousness (possibly) arises from the NCCS is still a problem. I wouldn't say it's still as mysterious as it was to the ancients - currently we don't postulate an entirely different realm (with the vast array of attendant difficulties that engenders) to account for it ;-)

You assume that focussing on neural correlates of consciousness is ignoring consciousness. I (and I assume neuroscientists) would disagree with you.

We know that it's "like something" to have experiences. That doesn't mean out "folk" conceptions of consciousness are correct :-)

Granted. Your case seems to hinge on us being unable to understand it, and yet understanding it in some fashion (your claims seem to require consciousness, or the "I", to survive the death of the brain, for example). How did you come by that knowledge if, as you claim, we're rather ignorant of "consciousness"?

With you so far - it's exceedingly implausible "sounding".

Fairly uncontroversial there...

This is where you're claim fails. It seems there is absolutely no reason to think that it happens again, and you're still not supplying any. The rational position would be, not to claim it's impossible (as you seem to think atheists claim), but that there is no reason to think that it is possible or likely - remain agnostic and accept the null hypothesis - that it does not happen. sadly for your case, there is evidence AGAINST it happening, such as the mentioned reliance of the mind on the brain - once the brain is "gone" you've given no sensible way that the "I" could some into existence again. You've not only failed to supply supporting evidence for your claim, but have failed to account for the disconfirming evidence presented.

I understand what you're claiming, it's just that it seems nonsensical, incoherent and lacking correspondence with reality.

I'd think that the serious issues with "supernaturalism" make the problems with "materialism"/"naturalism" (which is what I think you mean when you say "atheism") pale into insignificance. Nothing you've mentioned in this (admittedly short) exchange has done anything to demonstrate "a very serious problem for atheists" as you're claiming :-)

Well, since "I" relies rather heavily upon the physical brain, there seems to be no evidence that this "I" will come back again, and you've offered none to support that contention.

Bad philosophy almost always does. Good philosophy can generally be explained if it sounds like nonsense. From what I've read of your claims so far, I unfortunately put you in the former category, not the latter.

Because the underlying physical hardware is (barely) disrupted and changed. This is not support for your position (and the experience of "not I()" when under a general would still seem to count against you).

So, can you offer any reason why, in the absence of the same or similar physical substrate on which "I" depends (your brain, for example), there would ever be something which could coherently be thought of as being a "reemergence" of that same "I"?

The "robots" in your example would presumably know exactly what it was that we were experiencing when we experienced consciousness. What they wouldn't know is what it was like to experience it - we have privileged access to our own experiences, but that doesn't mean someone couldn't "read our minds" and know what we were experiencing.

I think you mean't haven't explained it, not can't Also, Dennett's "Multiple Drafts" hypothesis isn't the only game in town. There's the Global Workspace theory for a start.

The neurons which make contribute to "me" are attached to my eyes, and vice versa? Doesn't seem particularly arbitrary to me, unless you happen to be claiming that the "you" and "I" are something more than, and independent (to a large degree) of the brain

You keep claiming that atheism has a hard time dealing with this issue (you probably mean materialism/naturalism, rather than atheism), yet I don't see how or why that would be the case.
As for why there is anything at all, we could get into it, but I'm happy with "I don't know, neither do you, but lets keep looking into it", how about you? :-)

Well, from what I understand it, neuroscience is in the process of showing that our folk concept of consciousness is an illusion "stiched" together by various parts of our brains. Is that what these people were claiming?

What evidence, though? You don't seem to be making much of a point. Sure the atoms that make me up could reform into a newborn, but since it seems that "I" am reliant upon the relationships between neurons etc in my brain, then how can you say it would happen to "I"? Different neuronal relationship, different person, different "I"

It wouldn't (couldn't?) be you. Your sentence sounds like nonsense to me.

Not really. Been under a general? That seems a reasonable data point for "nothingness" of the "I". If you didn't wake up, you'd never know. Again, your claims of an afterlife being some kind of default position doesn't follow.

Not really. If there was any way for those in the after life to have an effect on reality, there could (and surely would) be evidence. Think ghosts, angels etc.

Regarding evidence against, I was thinking more about the minds reliance on the brain, and therefore the likely inability for the "mind", and almost certainly what we would refer to as "I" to survive the death of the brain.

If there is life after death, it's not going to be "you" who enjoys it :-)