I think we mostly agree, I was pointing to a strawman of scientific materialism that I used to but no longer hold. Maybe a clearer example is a verbal practice like a mantra, chanting “God is good”—which is incompatible with the constraint to only say things that are intersubjectively verifiable, at least in principle. If someone were to interrupt and ask “wait how do you know that? what’s your probability on that claim?” your answer would have to look something like this essay.
nothing prevents you from visualizing it while remaining aware of the fact that you’re only imagining it.
This does seem to be the case for unbendable arm, but I’m less sure it generalizes to more central religious beliefs like belief in a loving God or the resurrection of the dead! I don’t see an a priori reason why certain beliefs wouldn’t require a lack of conscious awareness that you’re imagining them in order to “work”, so want to make sure my worldview is robust to this least convenient possible world. Curious if you have further evidence or arguments for this claim!
this isn’t evidence against OP? if it’s true that RL lowers pass@k performance for sufficiently large k, we’d certainly expect o1 with 10k submissions to be weaker than base/instruct with 10k submissions.