Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

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

theguardian.com

Post reply on HN
Print view View original

231–240 of 419 posts

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

#231

Post by copypasterepeat »

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…

I guess I don't understand why you think "I don't know" is the only correct answer. It's clearly not, which is the point of the problem in the first place. It's a bit hard to grok, but once you do, it's clear what the right answer is.

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

#232

Post by seanhunter »

whatshisface wrote: post #215
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…

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 are a liar they might not even be talking about hats” are somewhat missing the point:

1) Whether or not they are talking about hats they have made a statement about hats and under the “rules of the game” of formal logic it must be untrue because we are given they are a liar. That’s enough to answer the question.

2) The “rules of the game” are about predicates and properties and inference. The language is plenty precise enough to convey both the question and to deduce the solution.

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

#233

Post by idrios »

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…

If a stranger told me "All of my cars are red" and then I learned that they didn't own a car, I wouldn't call them clever I'd call them a liar.

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

#234

Post by smohare »

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…

[dead]

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

#235

Post by mr_mitm »

out_of_protocol wrote: post #184
aidenn0 wrote: post #157

Earlier quoted context omitted.

Yes we can because if there are no ten-foot tall men, then it is indeed true that "All ten-foot tall men have brown hair"

If that is true then liar said truth.

Indeed, which is why the premise is false. So if a liar who always lies says that thing about ten foot men, ten foot men must exist, and at least one does not have brown hair.

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

#236

Post by nuancebydefault »

SilasX wrote: post #208
gpderetta wrote: post #168

Earlier quoted context omitted.

The question becomes why all_of returns true for an empty list. A better example would use std::accumulate and an 'and' function argument. The original STL documentation [1] described the function argument as having to model the Monoid[2] concept and have an identity value. The identity value for the 'and' Monoid is 'true'. [1] https://www.boost.org/sgi/stl/MonoidOperation.html [2] note: Monoid, not Monad, and yes, c…

>The question becomes why all_of returns true for an empty list. Yes! Before it became a programming problem, I considered the implications of this decision for common speech. In that case, it will generally be expected that when someone says "all my hats are green", they have at least one hat, probably because otherwise it doesn't hit the relevance threshold to make such a statement worth saying.[1] Based on this, w…

I make love to my wife almost every weekday. Almost monday, almost Tuesday, almost Wednesday,...

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

#237

Post by PittleyDunkin »

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…

> It is not formal logic but more about the idiosyncrasies and conventions of the English language

Well yea, that's the fun part! Logic puzzles without interaction with language are dull affairs indeed, basically just computation.

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

#238

Post by [deleted] »

dotancohen wrote: post #220
garciasn wrote: post #139

Earlier quoted context omitted.

> it also makes the puzzle more fun. No; it makes the puzzle illogical and thus about as much fun, for those who prefer logical outcomes, as discussing religion or politics.

That could be - in my country religion and politics is literally a matter of life or death. We discuss them to no end.

[deleted]

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

#239

Post by raincole »

copypasterepeat wrote: post #231
raincole wrote: post #219

Earlier quoted context omitted.

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…

I guess I don't understand why you think "I don't know" is the only correct answer. It's clearly not, which is the point of the problem in the first place. It's a bit hard to grok, but once you do, it's clear what the right answer is.

"I don't know" is the only correct anwser because the original problem isn't properly worded.

You need to (at least) add this statement to the original question:

> The host must open a door in any situation, and you know this rule.

Because "host" in daily language is a human being with agency to choose whether to not open a door. Without this statement, the original problem is actually a game theory problem with two players. The host might be playing a strategy where he only opens the door when he knows you picked the car at the first place, or any other strategy.

The above statement removes the ambiguity and that's what the original author meant (but failed to put in words).

(If you're interesting in this, the wikipedia page linked above actually contains a quite extensive discussion in history over it)

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

#240

Post by LudwigNagasena »

dotancohen wrote: post #217
eblume wrote: post #134

Earlier quoted context omitted.

I'm genuinely perplexed by this, how is the puzzle even a puzzle if you don't judge it by formal logic?

Because in everyday life we do not formally define ideas. Just for example I play a game with my children where we tickle each other when we see a yellow vehicle. Is a yellow tractor a vehicle for purpose of the game? How about a yellow baby cart. How about a billboard with a photograph of a yellow baby's toy car? We honestly have more fun discussing what is a vehicle for purpose of the game than we do tickling. Espe…

Reminds me of "The rule says, “No vehicles in the park”", https://news.ycombinator.com/item?id=36453856
Post reply on HN