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Mistake is often made that ZFC is the be-all and end-all ultimate foundation of mathematics. Unfortunately, 1st-order ZFC (often referred to as just "ZFC") is a very weak theory.

For example, if O is the type of the ordinals, then

          O
   Boolean  // type of all functions from ordinals into type Boolean
cannot be represented in ZFC because it does not exist in the cumulative hierarchy of sets.



No, I mean, why me, specifically? Did I accidentally say something to give the impression I find your odd rantings interesting? Because if I did, please let me know so I can correct the misunderstanding.


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