this post was submitted on 01 Oct 2025
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And shortly after that some other guy proved that he was wrong. More specifically he proved that you cannot prove that 1+1=2. More more specifically he proved that you cannot prove a system using the system.
Doesn't that only apply for sufficiently complicated systems? Very simple systems could be provably self-consistent.
It applies to systems that are complex enough to formulate the Godel sentence, i.e. "I am unprovable". Gödel did this using basic arithmetic. So, any system containing basic arithmetic is either incomplete or inconsistent. I believe it is still an open question in what other systems you could express the Gödel sentence.