The Bellhop Problem

[GrandizerII]

Try this one, it seems simple at first blush
 but I have in the past seen flame wars over it.

$30?

He paid $70 because he was given $30 back but overall the store owner has lost $30 because the man stole $100 and the store owner gave $30 back?

Depends on how "lost" is being defined. If by loss, we're also including loss in terms of the item value, then the store owner also loses 70$ because instead of earning 70$, they get 70% of the stolen money back (not new money).

I already knew it relied on assumptions though

The issue is that some of the standard assumptions, according to the author, are not warranted per the wording/description of the original problem that was answered by Marilyn vos Savant. For example, the assumption that Monty would choose a door randomly (given a choice, that is). Not saying I'm not iffy about his reasoning, but I can't help but think he may have a point being "nitpicky" about the assumptions.

These things do! It's why there are no true paradoxes and why I believe the Liar's Paradox was already solved just not many people have accepted the solution because it's so confusing or far fetched to most people (although it makes perfect logical sense to me. P.S. If I was to write a book about logical argumentation it would be called "Contradictions and Equivocations" and it would fundamentally be about how equivocations are just as illogical and commonplace as contradictions and they simply both violate the law of identity in different ways... one does explicitly and the other does implicitly).

What's your proposed solution to the Liar Paradox? How I see it is there is no such thing as an absolute unconditional liar who makes such statements. The best liar can still potentially say truths here and there, even if to this point they have yet to tell a truth. But I admit I have not really thought this through seriously, so perhaps I'm missing something here.

EDIT: Scratch it. I like what Alfred Tarski has to say about this.

Alfred Tarski diagnosed the paradox as arising only in languages that are "semantically closed", by which he meant a language in which it is possible for one sentence to predicate truth (or falsehood) of another sentence in the same language (or even of itself). To avoid self-contradiction, it is necessary when discussing truth values to envision levels of languages, each of which can predicate truth (or falsehood) only of languages at a lower level. So, when one sentence refers to the truth-value of another, it is semantically higher. The sentence referred to is part of the "object language", while the referring sentence is considered to be a part of a "meta-language" with respect to the object language. It is legitimate for sentences in "languages" higher on the semantic hierarchy to refer to sentences lower in the "language" hierarchy, but not the other way around. This prevents a system from becoming self-referential.

Unfortunately, this system is incomplete. One would like to be able to make statements such as "For every statement in level α of the hierarchy, there is a statement at level α+1 which asserts that the first statement is false." This is a true, meaningful statement about the hierarchy that Tarski defines, but it refers to statements at every level of the hierarchy, so it must be above every level of the hierarchy, and is therefore not possible within the hierarchy (although bounded versions of the sentence are possible).

https://en.wikipedia.org/wiki/Liar_paradox