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The Drinker’s Paradox: A Tale of Three Paradoxes

June 3, 2014

bertrand and friends

Last updated: Oct. 12, 2015

The Drinker’s Theorem:  Consider the set of all drinkers in the world, and the set of all people in a given pub. Then there exists a person who, if he or she is drinking, then everyone in that pub is drinking. 

It doesn’t matter how many people are there. Or how many are drinking. Or how few. No one needs to be taking their cues from some “lead drinker,” but in every pub, in every town and village, it just happens! How is this possible?

There are several possible approaches to this problem. Here, we will turn to British philosopher and mathematician, Bertrand Russell (1872 – 1970). His famous Paradox is the key.

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  1. The ALL(a):[a @ drinkers => a @ pub] and ALL(d):[d @ pub => d @ drinkers] combine to mean you’ve actually shown

    EXIST(c):[c @ drinkers => pub = drinkers]

    which then becomes a little more understandable with the contrapositive:

    EXIST(c):[~pub = drinkers => ~c @ drinkers]

    i.e. There exists a patron where If the pub is not full of drinkers, this patron is not drinking.

  2. Good point, Mark. But how much fun is it looking at a photo of someone not drinking at the pub? Cheers mate!

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  1. Kocsma-paradoxon – Ha valaki iszik, akkor mindenki iszik! | Comsci blog

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