1 2 The announcement must be known by the class 2 3 A selfreferential version of the paradox 3 4 The knower 3 1 An argument for the impossibility ID: 21489
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Somethingiswrongwithyourlineofreasoning,sinceIcanclearlygiveyouasurpriseexam|butwhatisit?2TheannouncementmustbeknownbytheclassWeneedtobeabitcleareraboutthenatureofmyannouncementtotheclass,andaboutwhatexactlyissupposedtobeparadoxicalaboutit.Arsttryistosaythatmyannouncementtotheclassseemsasthoughitshouldbetrue;butthereasoningo eredaboveseemstoshowthatitisisfalse.Butthisisnotquiteright;thereisnoproblemwithanannouncementofthesortdescribedabovebeingtrue;iftheclassdoesnotbelievetheannouncement,thentheywillcertainlybesurprisedbytheexam!Soweneedtosupposethattheannouncementisbothtrueandknowntobetruebytheclass|onthisview,theparadoxisthatthelineofreasoningpursuedaboveshowsthattheannouncementcannotbebothtrueandknownbytheclasstobetrueoneachdayofthesemester.Isthisstillgenuinelyparadoxical?Couldwesimplyrestbysayingthattheteachercangiveasurpriseexam,butonlyifeithertheclassdoesnotknowthathewill,ortheclassfailstoseetheargumentsketchedabove?Wearen't,afterall,sayingthattheteacherhassaidsomethingwhichcannotbetrue.Doesitmakesensetosaythatsomethingcanbetruebutunknowable?Isthatrequiredtoadoptthepresentresponsetotheparadox?Aseparateresponsetothisversionoftheparadoxfocusesonaquestionablestepinthereasoningsketchedabove.WearenowimaginingthattheclassknowsthatTheteacher'sannouncementistrue.Weimaginedthattheclassreasonstotheconclusion,whichtheythenknow,thatIfweknowthattheteacher'sannouncementistrue,thentheexamcannotbeonthelastdayofthesemester.TheyarethensupposedtocombinethesetwopiecesofknowledgetogivethemtheknowledgethatTheexamcannotbeonthelastdayofthesemester.Buthowisthisstepsupposedtowork?Ordinarily,wethinkthatonecanmovefromtheknowledgethatpandtheknowledgethatifp,thenqtotheknowledgethatq.Buttheabovereasoningisnotofthatform;insteadwearemovingfromtheknowledgethatpandtheknowledgethatifIknowthat p,thenqtotheknowledgethatq.Thisseemstomakesenseonlyifweassumenotonlythattheclassknowsthattheteacher'sannouncementis2