Post by Eugene 2.0 on Oct 30, 2024 19:59:23 GMT
This is a logical paradox or a joke that reads:
"There's someone in the pub such that, if the one is drinking, then anyone in the pub is drinking".
This can be said in some other way too:
"There's a thing, if this thing is something, then all the things are something the same too".
Quite provocative, isn't it?
What undresses this paradox is a logical form of it. This can be written in predicate logic:
(Ex)(Px→(y)Py)
Where, Ex means "there exists x", Px means "x is P", (y) means "everyone x", and Py, in turn, means "y is P".
And this can be reformulated in more usual propositional logic way:
(p→q)v(p→r)v...v(p→s)
Here, p is the person who drinks, or the thing, q is another person who drinks, or another thing, r is another person, or another thing, and so forth.
So, if we looks closely we can see, that we always can found such a person, or a thing that equals to itself in the later formula, i.e. p=q, or p=r, ..., or p=s. And since, p→p is tautology, then any disjunction possessing the truth (e.g. "a v b v ... v T") is true, so the whole formula is true.
"There's someone in the pub such that, if the one is drinking, then anyone in the pub is drinking".
This can be said in some other way too:
"There's a thing, if this thing is something, then all the things are something the same too".
Quite provocative, isn't it?
What undresses this paradox is a logical form of it. This can be written in predicate logic:
(Ex)(Px→(y)Py)
Where, Ex means "there exists x", Px means "x is P", (y) means "everyone x", and Py, in turn, means "y is P".
And this can be reformulated in more usual propositional logic way:
(p→q)v(p→r)v...v(p→s)
Here, p is the person who drinks, or the thing, q is another person who drinks, or another thing, r is another person, or another thing, and so forth.
So, if we looks closely we can see, that we always can found such a person, or a thing that equals to itself in the later formula, i.e. p=q, or p=r, ..., or p=s. And since, p→p is tautology, then any disjunction possessing the truth (e.g. "a v b v ... v T") is true, so the whole formula is true.