Remix clone Hacker News

I assume the real point of the puzzle (which is lost in the post) is to demonstrate how not all statements have a definite truth value.

If we assume that the label on the red box must be either true or false then we can prove that the treasure is in the red box. We’d be wrong though, since the treasure is in the green box.

▲

Scarblac 3 days ago | parent | next [-]

No, the point is that even if both labels had said "the treasure is in the red box" then it still could have been in the green box. There is no reason why the labels should be expected to say the truth, they're just labels.

	▲	petesergeant 3 days ago \| parent [-]
		Quite. It’s the difference between: > You wake up in front of a box which has a label that says “treasure inside”. Should you assume there is treasure inside? to which the answer is clearly “maaaaybe?” and > You wake up in a world with accurately labelled boxes, in front of a box which has a label that says “treasure inside”. Should you assume there is treasure inside? Where the answer is yes, and if the person setting the problem says “hahah no!!!” you can say “well look, that wasn’t a fair puzzle”. It is primarily a “do you have sufficient information” problem, like in the GMAT, with a level of misdirection thrown in.

▲

thaumasiotes 3 days ago | parent | prev [-]

Well, that might be the point of the parable of the dagger that he links to. It can't be the point of Mark Dominus's puzzle, because Mark Dominus doesn't understand it:

> So if you said the treasure must be in the red box, you were simply mistaken. If you had a logical argument why the treasure had to be in the red box, your argument was fallacious, and you should pause and try to figure out what was wrong with it.

He doesn't really elaborate on this, because he doesn't know the answer:

> Here are some responses people commonly have when I tell them that argument A is fallacious:

> "If the treasure is in the green box, the red label is inconsistent."

> It could be. Nothing in the puzzle statement ruled this out. But actually it's not inconsistent, it's just irrelevant.

This is an unfortunate point in an otherwise good essay. The problem in the puzzle is precisely that the red label is inconsistent, in the ordinary sense that no matter what you assume about it, a contradiction will result. Its truth implies its falsity, and its falsity implies its truth. Holding the location of the treasure fixed, no Boolean model exists in which the red label has a truth value at all.

The puzzle is an example of the Cretan paradox; there's not much more to it than that. It catches more interest because it's presented as if it were a different kind of puzzle than it is.

▲

Scarblac 3 days ago | parent [-]

No, that is a red herring, as he explains. It's not about the labels at all, there's no reason to assume the writer of the labels even knew anything about the actual location of the treasure. They're not part of the puzzle rules.

▲

thaumasiotes 2 days ago | parent [-]

That won't stop them from being inconsistent.

	▲	Scarblac 2 days ago \| parent [-]
		Or consistent, or whatever. It doesn't matter, they're not relevant to the puzzle. Why do you believe the content of the labels says anything about where the treasure actually is?