A liar who always lies says "All my hats are green." • Hacker News Board

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

#281

Post by gabrielhidasy » Mon, Dec 09, 2024, 7:26 PM UTC

lukas099 wrote: post #262

stickfigure wrote: post #251

Earlier quoted context omitted.

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.

Is there not a convention within formal logic defining this type of statement to be true or false?

There is, it's the "Vacuous Truth", generally any affirmation about elements of the empty set is true. It's very useful as it allows you to convert any statement "All elements of x are Y" in "No element in x is Not Y".

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

#282

Post by luxuryballs » Mon, Dec 09, 2024, 7:27 PM UTC

Perhaps they aren’t even his hats at all and the “my” part is the lie.

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

#283

Post by btilly » Mon, Dec 09, 2024, 7:27 PM UTC

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…

What you're saying can only be true to the extent that natural language doesn't look like formal logic.

Unfortunately, there are some obvious discrepancies. My favorite is that "can't" really means something closer to "not can".

This can be demonstrated with a close analysis of the statement, "I can't not do that." To get our usual understanding of the sentence we need to parse it as, "I (not can) (not do that)." And then turn that into, "I must not (not do that)." And now cancel the double negative to get, "I must do that."

Suppose that you try to parse it as, "I can not not do that." You quickly get, "I can do that." Which is not at all what that sentence actually means.

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

#284

Post by raincole » Mon, Dec 09, 2024, 7:28 PM UTC

hansvm wrote: post #266

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…

Perhaps there's another formulation you meant to write, but every time I've seen it, it's been equivalent to the thing you just asked, and the only potentially ambiguous part of the question is "to your advantage". If you stay then you have a 1/3 chance of getting a car, and if you switch you have a 2/3 chance. Yes, it's also correct that you don't "know" the result, and you might prefer goats to cars (even then you…

I regret opening this can of worms called Monty Hall.

But anyway I'll link the relevant section from Wikipedia:

https://en.wikipedia.org/wiki/Monty_Hall_problem#Other_host_...

> The version of the Monty Hall problem published in Parade in 1990 did not specifically state that the host would always open another door, or always offer a choice to switch, or even never open the door revealing the car. However, Savant made it clear in her second follow-up column that the intended host's behavior could only be what led to the 2/3 probability she gave as her original answer. (emphasis mine)

My point was that when people ask this question, they often word it like the very 1990 version did, lefting out this critical statement (which Savant considered needed as well, therefore she clarified in the follow-up column), making the question ambiguous.

(Although Savant also said "Very few (out of people who said is 2/3 is wrong) raised questions about ambiguity"... so perhaps people are actually just bad at probablity...?)

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

#285

Post by hulium » Mon, Dec 09, 2024, 7:29 PM UTC

LargeWu wrote: post #265

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…

The difference here is that the Monty Hall problem has an explanation that while counterintuitive, is statistically sound. You should always switch, because the probability you picked the correct door is locked in at the time you made the choice between 3 doors. It is 1/3 that you picked correctly, and 2/3 that you picked incorrectly. The counterintuitive part is that if you switch, you are effectively selecting all…

Last time I claimed this was the correct answer, I was linked to the Monty Crawl problem. https://www.probability.ca/jeff/writing/montyfall.pdf

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

#286

Post by spencerflem » Mon, Dec 09, 2024, 7:31 PM UTC

aidenn0 wrote: post #157

jp57 wrote: post #131

Earlier quoted context omitted.

Wait a second. If the liar says, "All ten-foot tall men have brown hair," we cannot conclude that there must exist a ten-foot tall man. EDIT: I'll clarify to say I wasn't taking issue with the derivation , but rather with the translation of the English statement into first-order predicate logic. No non-logician would conclude that there must be a ten-foot tall man if "All ten-foot-tall men have brown hair" is false.…

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"

In formal logic, but in regular English that would not be true

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

#287

Post by btilly » Mon, Dec 09, 2024, 7:32 PM UTC

LargeWu wrote: post #265

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…

The difference here is that the Monty Hall problem has an explanation that while counterintuitive, is statistically sound. You should always switch, because the probability you picked the correct door is locked in at the time you made the choice between 3 doors. It is 1/3 that you picked correctly, and 2/3 that you picked incorrectly. The counterintuitive part is that if you switch, you are effectively selecting all…

The problem here is that the usual explanation sneaks in multiple rarely stated assumptions.

If Monty knows the door with the prize and is aiming for the game to continue, then you should switch. (This is the usual argument.)

If Monty doesn't know where the prize is, then you learned nothing. (Monty's result was luck, and he can't impart information that he doesn't have.)

If Monty knows where the prize is and wants you to lose, absolutely don't switch. (Monty will only drag the game out as a way to try to make you lose.)

The reasoning behind these statements is completely solid, and there are no hidden assumptions being snuck in.

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

#288

Post by layer8 » Mon, Dec 09, 2024, 7:32 PM UTC

If everyone knows that the liar always lies, then can he effectively even lie? It’s like he speaks a language where everything means the opposite of what it means in English, and everyone understands this semantically inverted language. So then he might lie by just telling the truth.

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

#289

Post by tlss » Mon, Dec 09, 2024, 7:33 PM UTC

K0balt wrote: post #93

magicalhippo wrote: post #39

Earlier quoted context omitted.

And that's why SO gets mad when I come home with six cartons of milk[1]. [1]: https://blog.bryanbibat.net/2013/01/02/programming-joke/

The joke, loosely, is : A wife asks her programmer husband” on your way home, can you swing by the store and buy one carton of milk, and if they have eggs, get six?” It’s funnier and more relatable to programming if he comes home empty handed, crashes the car into the garage door, and says, with perfect alacrity, “six what?”

English is an interpreted language. We wouldn't have this problem if we can check for undefined references during compilation.

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

#290

Post by chromaton » Mon, Dec 09, 2024, 7:34 PM UTC

ninalanyon wrote: post #190

bingohbangoh wrote: post #154

Earlier quoted context omitted.

I agree. It reminds me of the math "puzzles" on Twitter which go: 1 shoe + 1 shoe = 2 2 shoes + 2 shoes = 4 3 shoes + 2 shoes = ??? And the answer isn't 5 because a) we're not counting shoes and b) the shoe laces were different colors. There's nothing clever, it just teaches you to be hyper cynical and question every little detail which isn't relevant to either Math or the real world.

I have a little monograph written many decades ago on Dimensional Analysis. Since reading it, not quite so many decades ago, I simply dismiss puzzles of this sort because the two sides of the equations are dimensionally incongruent. This means that I have to try to guess the state of mind of the questioner rather than solve a logic problem. It's a handy stance because I'm no good at either solving logic problems or g…

> Another on that really irritates me is the kind that presents a series of integers and asks which integer comes next. Any integer will do, you just have to fit the appropriate polynomial.

This one bugs me to no end because it's part of the standard elementary school curriculum, for example here: https://byjus.com/maths/patterns-questions/

But surely someone with a strong imagination could come up with a pattern to fit any number as the next in the sequence. I doubt most elementary educators even grasp the issue.