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Three logicians walk into a bar
(lemmy.ca)
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For this joke to logically work, logicians must be weird people who always know whether they want a beer or not. Because if it happened that the first guy just hadn't made his mind up yet, then the third guy's conclusion could be wrong.
They all had made up their mind. You don't need to know the others decision to answer No to the question, but you do to say yes. If the first didn't want a beer they could definitively answer no. They did, but didn't know the others decisions so couldn't say yes. Same with the 2nd. The third could say yes because he knew the other two didn't say no, so whatever they wanted was the answer
OCs point was that if the first person hadn't made up their mind yet, that would also cause them to say "i don't know", but the two following logicians seem to assume that the first person said "i don't know" because they wanted it but didn't know if the other two did
It's a false dichotomy and faulty logic if you look too closely
But it's a pretty funny joke
Logicians is the keyword here… There are only 2 possible answers: yes (true) or no (false)
In logic there is no other option