The Surprise Examination Paradox and the Second Incompleteness Theorem by S. Kritchman and R. Raz
Paper of Week 2
The Surprise Examination Paradox and the Second Incompleteness Theorem by S. Kritchman and R. Raz can be found here.
<<The Paper of the Week serves as an extension of the topics covered by the current Book of the week. Ruminating over the choice for this category I struggled not to make an exception and to suggest other nice books such as Gödel’s Proof by E. Nagel, J.R. Newman and D.R. Hofstandter, Meta Math!: The Quest for Omega BY G. Chaitin or The Best Writing on Mathematics 2011 by Mircea Pitici and F. Dyson.
The choice is a teaser for the readers willing to expand towards the Second Incompleteness Theorem, Chaitin’s Incompleteness Theorem and Kolmogorov-Chaitin Complexity via the intriguing route of paradoxes, a broad source for numerous philosophical and logical inquiries.
Moreover given the proximity of the exam period the paper paradox choice has a nice academic flavor e.g.: “The surprise examination paradox: the teacher announces in class: “next week you are going to have an exam, but you will not be able to know on which day of the week the exam is held until that day.” The exam cannot be held on Friday, because otherwise, the night before the students will know that the exam is going to be held the next day. Hence, in the same way, the exam cannot be held on Thursday. In the same way, the exam cannot be held on any of the days of the week.” >> Lucian Isar