December 2010
2 posts
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Goedel's incompleteness theorem
To paraphrase Boolos paraphrasing Goedel paraphrasing himself: It is true that 2 plus 2 is 4. I hope you can at least believe that much. Of course, it can be proved that 2 plus 2 is 4. It can also be proved that it can be proved that 2 plus 2 is 4. Moreover, it can be proved that it can be proved that it can be proved that 2 plus 2 is 4. We could continue in this seemingly trivial manner, but...