>So now you consider the system of [experimenter 2 + [experimenter 1 + system]], and we've got infinite regress — a.k.a. the measurement problem.
At the risk of sending things off an a huge tangent, it's interesting to see physicists recognizing that an infinite regress is, at least sometimes, unsatisfactory (even though there is of course nothing incoherent per se about the concept of an infinite sequence). Physicists usually tend to give short shrift to metaphysical arguments that rule out certain states of affairs on the grounds that they would involve an infinite regress of a problematic kind. But the logic you're using to argue against decoherence as a solution to the measurement problem is very similar to e.g. Aristotle/Aquinas's argument that the causal hierarchy must have a terminus. I'm not saying that in an attempt to start an argument about God. It's just interesting to see similar reasoning used in such different domains. (And of course in neither domain is it entirely clear that the reasoning works.)
The point is that you can prove that a thing is self-consistent without proving it is true. And I think what are calling an "infinite regress" is, in this case, self-consistency.
Proving self-consistency is a decent achievement, and is certainly error. But it is only weak evidence in favour of a position.
At the risk of sending things off an a huge tangent, it's interesting to see physicists recognizing that an infinite regress is, at least sometimes, unsatisfactory (even though there is of course nothing incoherent per se about the concept of an infinite sequence). Physicists usually tend to give short shrift to metaphysical arguments that rule out certain states of affairs on the grounds that they would involve an infinite regress of a problematic kind. But the logic you're using to argue against decoherence as a solution to the measurement problem is very similar to e.g. Aristotle/Aquinas's argument that the causal hierarchy must have a terminus. I'm not saying that in an attempt to start an argument about God. It's just interesting to see similar reasoning used in such different domains. (And of course in neither domain is it entirely clear that the reasoning works.)