The negation of S is “we don’t observe we have survived”, which is perfectly possible.
Otherwise, your argument proves too much, and undoes all of probability theory. Suppose for the moment that a nuclear war wouldn’t have actually killed us, but just mutated us into mutants. Then let S’ be “us non-mutants observe that there was no nuclear war”. By your argument above, P(S’)=1, because us non-mutants cannot observe a nuclear war - only the mutant us can do so.
But the problem is now entirely non-anthropic. It seems to me that you have to either a) give up on probability altogether, or b) accept that the negation of S’ includes “us mutants observe a nuclear war”. Therefore the negation of a “X observes Y” can include options where X doesn’t exist.
The negation of S is “we don’t observe we have survived”, which is perfectly possible.
What do you mean by this? If you are referring to the fact that we can ask “have we survived the Cold War” and answer “not yet” (because the Cold War isn’t over yet), then I don’t see how this salvages your account. The question you asked to begin with is one which it is only possible to ask once the Cold War is over, so “not yet” is inapplicable, and “no” remains impossible.
If you mean something else, then please clarify.
As for the rest of your comment… it seems to me that if you accept that “us, after we’ve suffered some mutations” is somehow no longer the same observers as “us, now”, then you could also say that “us, a second from now” is also no longer the same observers as “us, now”, at which point you’re making some very strong (and very strange) claim about personal identity, continuity of consciousness, etc. Any such view does far more to undermine the very notion of subjective probability than does my account, which only points out that dead people can’t observe things.
I’m pointing out that the negation of S=”X observes A at time T” does not imply that X exists. S’=”X observes ~A at time T” is subset of ~S, but not the whole thing (X not existing at all at time T is also a negation, for example). Therefore, merely because S’ is impossible, does not mean that S is certain.
The point about introducing differences in observers, is that this is the kind of thing that your theory has to track, checking when an observer is sufficiently divergent that they can be considered different/the same. Since I take a more “god’s eye view” of these problems (extinctions can happen, even without observers to observe them), it doesn’t matter to me whether various observers are “the same” or not.
The negation of S is “we don’t observe we have survived”, which is perfectly possible.
Otherwise, your argument proves too much, and undoes all of probability theory. Suppose for the moment that a nuclear war wouldn’t have actually killed us, but just mutated us into mutants. Then let S’ be “us non-mutants observe that there was no nuclear war”. By your argument above, P(S’)=1, because us non-mutants cannot observe a nuclear war - only the mutant us can do so.
But the problem is now entirely non-anthropic. It seems to me that you have to either a) give up on probability altogether, or b) accept that the negation of S’ includes “us mutants observe a nuclear war”. Therefore the negation of a “X observes Y” can include options where X doesn’t exist.
What do you mean by this? If you are referring to the fact that we can ask “have we survived the Cold War” and answer “not yet” (because the Cold War isn’t over yet), then I don’t see how this salvages your account. The question you asked to begin with is one which it is only possible to ask once the Cold War is over, so “not yet” is inapplicable, and “no” remains impossible.
If you mean something else, then please clarify.
As for the rest of your comment… it seems to me that if you accept that “us, after we’ve suffered some mutations” is somehow no longer the same observers as “us, now”, then you could also say that “us, a second from now” is also no longer the same observers as “us, now”, at which point you’re making some very strong (and very strange) claim about personal identity, continuity of consciousness, etc. Any such view does far more to undermine the very notion of subjective probability than does my account, which only points out that dead people can’t observe things.
I’m pointing out that the negation of S=”X observes A at time T” does not imply that X exists. S’=”X observes ~A at time T” is subset of ~S, but not the whole thing (X not existing at all at time T is also a negation, for example). Therefore, merely because S’ is impossible, does not mean that S is certain.
The point about introducing differences in observers, is that this is the kind of thing that your theory has to track, checking when an observer is sufficiently divergent that they can be considered different/the same. Since I take a more “god’s eye view” of these problems (extinctions can happen, even without observers to observe them), it doesn’t matter to me whether various observers are “the same” or not.