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A liar who always lies says "All my hats are green."

theguardian.com

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Re: A liar who always lies says "All my hats are green."

#251

Post by stickfigure »

seanhunter wrote: post #232
whatshisface wrote: post #215

Earlier quoted context omitted.

The article said that the problem was based in formal logic and appeared on a "maths test." That means it isn't ambiguous question about the English language.

Yes. It isn’t ambiguous and is entirely solvable using old school formal logic of the “All Cretans are liars” sort. If the liar owns no hats the statement “All my hats are green” would be true. Under the parameters of the question it must be a lie and therefore cannot be true. So the liar owns at least one hat which is not green. They may own additional hats which can be of any colour. People who are saying “if they…

I think there's a sort of divide-by-zero problem here. Does an empty set of hats have a color? You could arbitrarily define "all my hats are green" for the empty set as either true or false as part of a consistent logical system. There isn't enough information in the question to know whether we should pick one or the other, though there's probably a colloquial preference for true.

Re: A liar who always lies says "All my hats are green."

#252

Post by tantalor »

scoofy wrote: post #207
tantalor wrote: post #175

Earlier quoted context omitted.

> in typical English you are making an existence statement No, you're not.

Oh boy... so I actually wrote a thesis in graduate school on conversational implicature, Paul Grice, and various other theories of implying things. I would actually agree user dwheeler here. Whether or not you agree with Gricean implicature theory (I do not), the point is that making a claim about a group that doesn't exist is absurd. Absurd statements do not convey meaning, and language is a tool for communication,…

Granted all that, but we're not really talking about normal everyday English, but a hypothetical conversation with some mythical entity who can only lie, which is not really a capability of humans; even the most pathological liar among us can and will tell the truth.

So I'd put all that theory in a drawer somewhere and acknowledge that, when we're talking about logic puzzles, the rules of logic are paramount, not grammar.

Re: A liar who always lies says "All my hats are green."

#253

Post by SirMaster »

mr_mitm wrote: post #224
SirMaster wrote: post #206

Earlier quoted context omitted.

Then the puzzle shouldn't use the word lie, because to lie can mean to be deceptive, and saying all your hats are green when you have no hats is clearly deceptive and thus can be considered a lie.

It's not deceptive, it's simply true in formal logic. I've been thought in linear algebra 101: all statements about the elements of the empty set are true. That's the core of this puzzle, and contrary what OP claimed, it's a matter of logic, not language.

But the question is being presented to humans via language and without any formal logic training.

If it's a formal logic problem it should be presented in formal logic terms (presumably that only those with formal logic training would even understand) so then there is no possibility of language ambiguity.

I'm not trying to be argumentative, but this is just how this come across to me, and I am pretty confident most humans would consider it a lie which I think would count for something given the place and the way in which the question was presented.

Re: A liar who always lies says "All my hats are green."

#254

Post by dllthomas »

rawgabbit wrote: post #103

I never liked this type of puzzle. It is not formal logic but more about the idiosyncrasies and conventions of the English language. I put this puzzle on par with Agatha Christie’s murder mysteries. It requires a suspension of disbelief and logic to be believable. Someone who always lies means in the purest sense means you cannot trust anything they say. Even the word “hat” could mean they are talking about their pet…

I think the puzzle is better if the person "only speaks falsehoods" than if they "always lie" - depending on context, a true statement can be a lie.

Re: A liar who always lies says "All my hats are green."

#255

Post by MrMcCall »

gpderetta wrote: post #223
MrMcCall wrote: post #169

Earlier quoted context omitted.

But you have specifically initialized your AND and OR results to be True and then False, respectively, thus specifying the resulting value for their processing of the empty set. What I'm saying is that you always need to specify that default value to handle the empty set properly. In no way would I consider ANDing or ORing an empty set's boolean values to be automatically True or False, (no pun intended). You have ch…

> But you have specifically initialized your AND and OR results to be True and then False No other value would be meaningful. > What I'm saying is that you always need to specify that default value to handle the empty set properly no you need a default value to handle the base case of the recursion. The result of the empty set falls off from it.

IIUC, using your function with an empty set in SPSS or SAS will result in a NULL value, which is neither True nor False (NPI).

Do you know the truth tables that include NULL? I don't off-hand, but I seem to remember that combining NULL with a True or False results in NULL, which is why I catch my NULLs before they become operands in my operations.

ANDing or ORing the lack of values in the empty-set is always specified by someone's semantics. You're just determining those semantics as a by-product of the way ANDs and ORs are calculated.

This is why the reality of "All my hats are green" has a great deal of real-world ambiguity when there are no hats, because "Color( NULL[-hat] )" is NULL. Now, how you interpret NULL in that case is up to you, because NULL is neither True nor False, in my experience and understanding.

I am open to learning, tho.

ETA: Wouldn't your method also mean that the liar saying "All my hats are not green" would also be true? And, I'm no mathematician, but if "All my hats are green" and "All my hats are not green" both eval to True, I think something has gone very wrong. That looks like why the NULL value is so useful in SQL and stats.

Re: A liar who always lies says "All my hats are green."

#256

Post by [deleted] »

raincole wrote: post #219
mjburgess wrote: post #116

Earlier quoted context omitted.

This is generally the case for the vast majority of puzzles, and it equally drives me mad in those areas where academics set "puzzles" and conclude that people's inabilty to "solve" them is some cognitive deficiency. I've rarely encountered a case where it is isnt an extreme lack of self-awareness in the questioner -- eg., being extremely overfit to language/notation/etc. localised to their own area of expertise.

My favorite example is Monty Hall problem. "Smart" people often use it as the evidence of how bad general people are at probability. It really isn't. The problem is usually given in this form: > Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, s…

[deleted]

Re: A liar who always lies says "All my hats are green."

#258

Post by nemomarx »

danbruc wrote: post #230

Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes–no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own…

I wonder what the language adds? I suppose it's one more layer of convolution and cuts off the "what would the other gods answer" kinda things.

Re: A liar who always lies says "All my hats are green."

#260

Post by tantalor »

LudwigNagasena wrote: post #177
Supermancho wrote: post #167

Earlier quoted context omitted.

> All my hats....", you are simultaneously making an existence statement that you have at least one hat It does not. All my unicorns fly. There is no assumption that I have a unicorn. There is an assumption, based on the claim but it is not a fact. The puzzle also assumes that "my" implies there is some ownership (we'll take for granted "my" means "has" for simplicity), which is another quibble that unravels the whol…

Would you agree with the following proposition: “if all of my unicorns fly, then some of my unicorns fly”?

No.

(assuming you have no unicorns) "all of my unicorns fly" is true; "some of my unicorns fly" is false; "true->false" is false.

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