▁statement ▁( A ), ▁the ▁argument ▁is ▁blocked . ▁ ▁This ▁suggests ▁that ▁a ▁better ▁form ulation ▁would ▁in ▁fact ▁be : ▁ ▁The ▁prisoner ▁will ▁be ▁h anged ▁next ▁week ▁and ▁its ▁date ▁will ▁not ▁be ▁dedu cible ▁the ▁night ▁before ▁using ▁this ▁statement ▁as ▁an ▁ax iom ▁( B ). ▁ ▁F itch ▁has ▁shown ▁that ▁this ▁statement ▁can ▁still ▁be ▁expressed ▁in ▁formal ▁logic . ▁Using ▁an ▁equivalent ▁form ▁of ▁the ▁par ado x ▁which ▁reduces ▁the ▁length ▁of ▁the ▁week ▁to ▁just ▁two ▁days , ▁he ▁proved ▁that ▁although ▁self - reference ▁is ▁not ▁il leg it imate ▁in ▁all ▁circumstances , ▁it ▁is ▁in ▁this ▁case ▁because ▁the ▁statement ▁is ▁self - contr ad ict ory . ▁ ▁Ep ist em ological ▁school ▁Vari ous ▁ep ist em ological ▁form ulations ▁have ▁been ▁proposed ▁that ▁show ▁that ▁the ▁prisoner ' s ▁t ac it ▁assumptions ▁about ▁what ▁he ▁will ▁know ▁in ▁the ▁future , ▁together ▁with ▁several ▁pla us ible ▁assumptions ▁about ▁knowledge , ▁are ▁incons istent . ▁ ▁Ch ow ▁( 1 9 9 8 ) ▁provides ▁a ▁detailed ▁analysis ▁of ▁a ▁version ▁of ▁the ▁par ado x ▁in ▁which ▁a ▁surprise ▁h anging ▁is ▁to ▁take ▁place ▁on ▁one ▁of ▁two ▁days . ▁ ▁App lying ▁Ch ow ' s ▁analysis ▁to ▁the ▁case ▁of ▁the ▁unexpected ▁h anging ▁( ag ain ▁with ▁the ▁week ▁short ened ▁to ▁two ▁days ▁for ▁simplicity ), ▁we ▁start ▁with ▁the ▁observation ▁that ▁the ▁judge ' s ▁announ cement ▁seems