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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."

#301

Post by LargeWu »

hulium wrote: post #285
LargeWu wrote: post #265

Earlier quoted context omitted.

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

That's fine, but given the parameters of the problem change with the Monty Crawl variant, it's not the same problem, and doesn't invalidate the answer of the base variant.

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

#302

Post by naniwaduni »

karmakurtisaani wrote: post #241
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…

But it is in your advantage! Code a simulator and do some numerical experiments. The simulations where you switch end up winning more. Edit: from your other reply I see your beef is more with the wording. Edit edit: although I disagree with your point even then. But it seems to lead to rather fruitless argument, so let's leave it here.

I think reasoning with the 100-door variation is likely to be more enlightening than encoding your assumptions into a simulation.

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

#303

Post by btilly »

LargeWu wrote: post #298
btilly wrote: post #287

Earlier quoted context omitted.

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 y…

I think, canonically, Monty always knows where the prize is, and will always eliminate all doors except for one, and will never eliminate a door with the prize, and will always give you a choice to switch. There's no room for Monty's motivation.

Those assumptions are required for the usual explanation. But they are very rarely stated. And so the usual explanation is not logically solid.

You can't just sneak in the assumptions. You have to state them somewhere.

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

#304

Post by Tarq0n »

layer8 wrote: post #288

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.

That would only be true if the liar speaks in purely boolean statements. Many statements aren't invertible because the possibility space is larger than true or false.

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

#305

Post by Smaug123 »

layer8 wrote: post #288

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.

The article even defines "liar" for you: "A liar is someone who only says false statements." It's not someone who is trying to maximally mislead.

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

#306

Post by LudwigNagasena »

tantalor wrote: post #277
LudwigNagasena wrote: post #264

Earlier quoted context omitted.

So you claim that in normal English “all” doesn’t imply “some”?

Does "when pigs fly" imply that some day pigs will be able to fly? No; people can understand impossibility when it is used rhetorically in every day speech. For example I might say, "all the honest politicians are doing a great job", which conveys my actual meaning, "all politicians are dishonest".

I don't understand what point those examples are supposed to convey.

"All of my unicorns can fly -> some of my unicorns can fly -> at least one of my unicorns can fly" still seems to be a valid inference that may get lost in conventional translation into first order logic. And a proposed "allsome" quantifier still seems like a valid remedy for that.

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

#307

Post by 8note »

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,…

absurd statements are usually jokes

a joke

> "all my hats are green" - bill

> "but green hats catch fire in the sunlight" - joe

> "and thats why i dont have any hats" - bill

from the link:

> Many conversations have goals other than the exchange of information. One is amusement, which speakers often pursue by making jokes (Lepore & Stone 2015: §11.3). Because the goal is not to provide information, the maxims of Quality, Quantity, and Relation do not apply. If for any of these reasons the Cooperative Principle does not apply, reasoning based on it will be unsound.

i think i disagree - the joke is intended to say that bill doesnt have any hats, but would like one, and only a green one, and only if they didnt catch fire in the sunlight

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

#308

Post by golly_ned »

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…

Most english sentences are semantically ambiguous and can often be parsed in hundreds of different ways. And it's true that there is an element of reading comprehension. But a reasonable reader won't assume the thing about the cat.

We know this is occurring on a math exam, so it must be a logic puzzle. The exam-taker would've probably known this refers to a first-order logic question, and have been taught a certain way of translating sentences like this into first-order logic.

This is true of all word puzzles that they need to be mapped to math in a way that assumes knowledge about the world and context.

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

#309

Post by hulium »

LargeWu wrote: post #301
hulium wrote: post #285

Earlier quoted context omitted.

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

That's fine, but given the parameters of the problem change with the Monty Crawl variant, it's not the same problem, and doesn't invalidate the answer of the base variant.

The problem is that the parameter was unspecified in the original problem. Your answer is equivalent to the shaky answer referred to in the paper. Without knowing that the host selects between 2 goats with 50/50 chance, you cannot give a general answer.

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

#310

Post by 8note »

btilly wrote: post #303
LargeWu wrote: post #298

Earlier quoted context omitted.

I think, canonically, Monty always knows where the prize is, and will always eliminate all doors except for one, and will never eliminate a door with the prize, and will always give you a choice to switch. There's no room for Monty's motivation.

Those assumptions are required for the usual explanation. But they are very rarely stated. And so the usual explanation is not logically solid. You can't just sneak in the assumptions. You have to state them somewhere.

the assumption is told to you in that the game is expected to continue after monty opens a door. if he could open the prize door, the game would describe what happens when he does that
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