The latter seems to require that we are, or have, something like souls that, despite their immateriality and apparent complete inaccessibility to any sort of scientific investigation, are the true bearers of our identity and consciousness.
That's not what I mean by "remaining". Consciousness could exist on some small quantum or string level, or other small level we haven't even discovered yet. It's possible that this level is undisturbed when we die, and that we continue to be conscious. And it's possible that as we continue to be conscious, we can't communicate it to living people.
Consciousness could exist on some small quantum [...] level...
Absolutely not. Consciousness is not that basic, and it definitely doesn't belong in the fundamental structure of reality. You're making a huge leap that ignores several levels of organization (in order: atomic, chemical, biological, computational). Consciousness depends on the pattern of neurons communicating inside our heads; examining a single neuron nucleus in the microscope (or taking one of its carbon atoms into a collider) will miss consciousness entirely because you've set the magnifying glass too close to get the pattern.
I've read a fair amount on Less Wrong and can't recall much said about the plausibility of some sort of afterlife. What do you guys think about it? Is there some sort of consensus?
Here's my take:
Edit: People in the comments have just taken it as a given that consciousness resides solely in the brain without explaining why they think this. My point in this post is that I don't see why we have reason to reject the 3 possibilities above. If you reject the idea that consciousness could reside outside of the brain, please explain why.