From a logic perspective you’d think any epsilon>0 would be enough to rule out the “conditioning on a falsehood” problem. But I second your question, because Scott makes it sound like there’s some sampling process going on that might actually need to do the thing. Which is weird—I thought the sampling part of logical inductors was about sampling polynomial-time proofs, which don’t seem like they should depend much on epsilon.
From a logic perspective you’d think any epsilon>0 would be enough to rule out the “conditioning on a falsehood” problem. But I second your question, because Scott makes it sound like there’s some sampling process going on that might actually need to do the thing. Which is weird—I thought the sampling part of logical inductors was about sampling polynomial-time proofs, which don’t seem like they should depend much on epsilon.