The Bellhop Problem

[polymath257]

But all apparent paradoxes I am convinced are down to semantic errors (commonly equvocation) and the limits of language... rather than down to any so-called real paradox. The so-called real ones are one that are supposedly unanswered. And many of them are but that doesn't mean they always will be... and even if they will always be... again I think that's down to the limits of our language.

Some of them like the Liar's Paradox I believe have actually already been solved.

If you're curious this is the solution to the Liar's Paradox that I 100% accept:

Arthur Prior asserts that there is nothing paradoxical about the liar paradox. His claim (which he attributes to Charles Sanders Peirce and John Buridan) is that every statement includes an implicit assertion of its own truth. Thus, for example, the statement "It is true that two plus two equals four" contains no more information than the statement "two plus two equals four", because the phrase "it is true that..." is always implicitly there. And in the self-referential spirit of the Liar Paradox, the phrase "it is true that..." is equivalent to "this whole statement is true and ...".

Thus the following two statements are equivalent:

This statement is false.

This statement is true and this statement is false.

The latter is a simple contradiction of the form "A and not A", and hence is false. There is therefore no paradox because the claim that this two-conjunct Liar is false does not lead to a contradiction. Eugene Mills and Neil Lefebvre and Melissa Schelein present similar answers.

That is a very cute argument! It also resolves a more complex version of the Liar's Paradox:
Statement A: Statement B is true
Statement B: Statement A is false.

If these are interpreted as

Statement A: Statement A is true and Statement B is true
Statement B: Statement B is true and Statement A is false,

then the negations are

Neg(A): Statement A is false or statement B is false
Neg(B): Statement B is false or Statement A is true.

In this case, it is fairly easy to see that both Statement A and Statement B have to be false. No remaining paradox!

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