Back in July 2013, Will Sawin (Princeton) and Abram Demski (USC) wrote a technical report describing a result from that month’s MIRI research workshop. We are finally releasing that report today. It is titled “Computable probability distributions which converge on believing true Π_{1} sentences will disbelieve true Π_{2} sentences.”

Abstract:

It might seem reasonable that after seeing unboundedly many examples of a true Π

_{1}statement that a rational agent ought to be able to become increasingly confident, converging toward probability 1, that this statement is true. However, we have proven that this plus some plausible coherence properties, necessarily implies arbitrarily low limiting probabilities assigned to some short true Π_{2}statements.