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SUMMARY:Do You Really Understand Incompleteness? - Lingyuan Ye (University
  of Cambridge)
DTSTART:20241111T130000Z
DTEND:20241111T140000Z
UID:TALK224269@talks.cam.ac.uk
CONTACT:Ariadne Si Suo
DESCRIPTION:Gödel’s two incompleteness theorems are usually grouped tog
 ether as a single result\, but conceptually they are very different. In pa
 rticular\, I will talk about several “counterexamples” of Gödel’s s
 econd incompleteness theorem\, which says that a computable theory contain
 ing enough arithmetic cannot prove its own consistency. The existence of s
 uch examples highlights the question of what the correct conceptual unders
 tanding of the statement of second incompleteness theorem should be. I wil
 l offer a solution based on categorical logic\, where we can identify *uni
 versal property* of arithmetic. The incompleteness phenomena will then be 
 consequences thereof. 
LOCATION:FS07\, Computer Laboratory
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