I suspect the analysis needed to prove “(it is probable that) x 100 my goal is achieved” is very similar to the one needed to prove that “(it is probable that) x101 my goal is achieved”. Because of this, it seems likely that there is a degree of reflection beyond which all evidence gathered will strengthen the probability for all subsequent meta-checks. So it is not a given that such an approach would never terminate.
I suspect the analysis needed to prove “(it is probable that) x 100 my goal is achieved” is very similar to the one needed to prove that “(it is probable that) x101 my goal is achieved”. Because of this, it seems likely that there is a degree of reflection beyond which all evidence gathered will strengthen the probability for all subsequent meta-checks. So it is not a given that such an approach would never terminate.