The drinker paradox (also known as drinker's principle, drinkers'
principle or (the) drinking principle) is a theorem of classical
predicate logic, usually stated in natural language as: There is
someone in the pub such that, if he is drinking, everyone in the pub
is drinking.
The proof begins by recognizing it is true that either everyone in the
pub is drinking, or at least one person in the pub isn't drinking.
Consequently, there are two cases to consider:
1) Suppose everyone is drinking. For any particular person, it
can't be wrong to say that if that particular person is drinking, then
everyone in the pub is drinking because everyone is drinking.
Because everyone is drinking, then that one person must drink because
when ' that person ' drinks ' everybody ' drinks, everybody includes
that person.
2) Suppose that at least one person is not drinking. For any
particular nondrinking person, it still cannot be wrong to say that if
that particular person IS drinking, then everyone in the pub is
drinking because that person is, in fact, not drinking. In this case
the condition is false, so the statement is vacuously true due to the
nature of material implication in formal logic, which states that "If
P, then Q" is always true if P (the condition or antecedent) is false.
Either way, there is someone in the pub such that, if he is drinking,
everyone in the pub is drinking. A slightly more formal way of
expressing the above is to say that if everybody drinks then anyone
can be the witness for the validity of the theorem. And if someone
doesn't drink, then that particular non-drinking individual can be the
witness to the theorem's validity.
The questions I have are:
1. Who the F* is in the pub and not drinking?
2. Why not?
3. What are they NOT drinking?
I'm gonna' go have a drink and think on it.