shooting while opponent blocks should yield u(0,0), right?
Well, I could make a table for the state where no one has any bullets, but it would just have one cell: both players reload and they go back to having one bullet each. In fact, the game actually starts with no one having any bullets, but I omitted this step.
Also, in both suggestions, you are telling me that the action that leads to state x should yield the expected utility of state x, which is correct, but my function u(x,y) yields the expected utility of the resulting state assuming that you’re coming from the original, neutral one. Otherwise, it would need an additional argument to say what state you’re currently in. Instead of writing the utility of each action as u(current state, next state), I wrote it as u(next state)- u(current state). Each state is an ordered pair of positive integers, the two player’s bullets. So, to write it the way you suggested, the function would need four arguments instead of two.
Maybe I won’t exist as Epirito, the guy who is writing this right now, who was born in Lisbon and so on. Or rather I should say, maybe I won’t exist as the guy who remembers having been born in Lisbon, since Lisbon and any concept that refers to the external world is illegitimate in BLEAK.
But if the external world is illegitimate, why do you say that “I probably won’t exist in the next instant anyway”? When I say that each instant is independent (BLEAK), do you imagine that each instant all the matter in the world is randomly arranged, such that my brain may or may not be generated?
But the whole point of talking about external objects is that they do things and these things sometimes cause you to perceive something (this is the problem with Descartes’ purely extended matter, whose definition doesn’t talk about sensibility, in opposition to the scholastics’ sensible matter. This makes cartesian matter indistinguishable from the merely ideal shapes that e.g. a geometrical treatise might talk about). If the external world consists only in an inanimate snapshot of itself, then there’s no sense in talking about an external world at all. There’s no sense in talking about brains, or atoms, or Lisbon, or any other object. If you can’t shoot with a gun even in principle, if you can’t even hold it, is it really a gun?
For this reason, I believe the instants in BLEAK should be understood as pure qualia. And the total population of possible instants, as possible experiences. Now, looking at the neatness of the organization of the first sample, the only one we’ve got, we might be compelled to expect that this wasn’t a coincidence, and the total population of possible experiences is biased towards coherent ones. But this would be like concluding that you must be somehow special for having a very rare disease, when in reality, in a world with so many people, someone or another was bound to get it. In the same way, even if this was a huge coincidence and most instants are pretty uninteresting and nonsensical, why shouldn’t another similarly coherent instant appear to me after millennia of me experiencing phenomenological white noise? And, since in these flashes of lucidity I can’t remember the white noise, but only (some of) the other coherent moments I experienced (since otherwise that would make the instant that contains the memories of the white noise also partly white noise), what difference does the white noise make?
And that would mean that these perceptions are not so illusory after all. And I should expect to live normally, just as humans naturally expect. If I try to catch a ball, then, after an eternity of phenomenological white noise I won’t remember anyway, I will actually catch it and continue my life normally, whereas the Boltzmann brain should expect to have abnormal experiences. He should expect to deteriorate and die in the middle of outer space, instead of continuing his normal functioning.