“More precisely, we are driven, by the foregoing reasoning, to conclude that there is no robot-knowable set of computational mechanisms, free of genuinely random ingredients, that the robot could accept as being even a possibility for underlying its mathematical belief system-provided that the robot is prepared to accept that the specific procedure that I have been suggesting for constructing the formal system Q(M) from the mechanisms M actually does encapsulate the totality of Pi1-sentences that it believes in unassailably-and, correspondingly, that the formal system Qm(M) encapsulates the totality of Pi-1-sentences that it unassailably believes would follow from the hypothesis M. Moreover, there is the further point that genuinely random ingredients might have to be included into the mechanisms M if the robot is to achieve a potentially consistent mathematical belief system.”