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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."

#321

Post by karmakurtisaani »

naniwaduni wrote: post #302
karmakurtisaani wrote: post #241

Earlier quoted context omitted.

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.

I'm sure it depends on the person. Some people like to see raw numbers, others a more general problem.

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

#322

Post by Supermancho »

LudwigNagasena wrote: post #311
Supermancho wrote: post #291

Earlier quoted context omitted.

I think the same of your interpretation of some vs all. Some can contain all, just as it contains none. Both some/all imply, but do not assert existence. Claiming it tautologically defies logic is not compelling.

Well, I think showing that it defies logical inference is quite relevant in the context of that thread being about translating typical English into first order logic to do logical inference.

I worry about sets and consideration of edge cases. Legal, programmatic, medical. Adhering to a convention that presupposes meaning and claim that interpretation is the only interpretation, cannot be resolved with repetition. I remain unconvinced.

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

#323

Post by layer8 »

Tarq0n wrote: post #304
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.

I would assume that the possibility space has a truth axis relative to which the whole space can be inverted.

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

#324

Post by hulium »

LargeWu wrote: post #314
hulium wrote: post #309

Earlier quoted context omitted.

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.

I don't follow, which parameter was unspecified in the original problem?

My last sentence. Or which parameter do you think was modified?

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

#325

Post by bingohbangoh »

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…

> This means that I have to try to guess the state of mind of the questioner rather than solve a logic problem

That is an excellent way to put it!

It explains why it appeals to non-math people. They are (usually) better at these more verbal-based games ime.

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

#326

Post by [deleted] »

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…

[deleted]

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

#327

Post by lisper »

Well, let's see...

NOT(FORALL(x): my-hat(x) -> green(x))

EXISTS(x): NOT(my-hat(x) -> green(x)) ; https://en.wikipedia.org/wiki/Universal_quantification#Negat...

EXISTS(x): NOT(NOT(my-hat(x)) OR green(x)) ; https://en.wikipedia.org/wiki/Material_implication_(rule_of_...

EXISTS(x): NOT(NOT(my-hat(x)) AND NOT(green(x)) ; https://en.wikipedia.org/wiki/De_Morgan%27s_laws

EXISTS(x): my-hat(x) AND NOT(green(x)) ; https://en.wikipedia.org/wiki/Double_negation#Elimination_an... (note that this assumes non-intuitionistic logic)

EXISTS(x): my-hat(x) ; https://en.wikipedia.org/wiki/Conjunction_elimination

So yeah, the liar must have at least one (non-green) hat.

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

#328

Post by suggestion »

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…

Perhaps it'll be more intuitive to you if you scale the number of doors up. If there are 100 doors, only one containing a car, you pick one, the host reveals 98/99 remaining doors as goats, it's obvious the correct choice is to switch. The correct answer is a mathematically provable probability. 1% chance you picked the right door, 99% chance the door was in the remaining pool, therefore 99% chance the last remaining door is the correct door.

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

#329

Post by btilly »

8note wrote: post #310
btilly wrote: post #303

Earlier quoted context omitted.

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

No. That condition holds in all three of the scenarios that I stated. And yet you have 3 different answers. Switching 2/3 win, 1/2 win, and 0/1 win respectively.

You specifically need information that we haven't been given about the counterfactuals. What might Monty have done in other scenarios that we have not yet observed? We don't know. And we're not actually told. That makes that an implicit assumption that wasn't specified.

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

#330

Post by bryanrasmussen »

JKCalhoun wrote: post #113
bryanrasmussen wrote: post #43

Actually I would say by the rules of English we cannot conclude any of those multiple choice questions is the absolute case - A) "The liar has at least one hat." cannot conclude because may have no hats, thus the lie is in the "all my hats" B) "The liar has only one green hat." cannot conclude because may have 2+ green hats out of a 3+ set. C) "The liar has no hats." cannot conclude that because he may have hats that…

As others have noted in the comments, if the liar has no hats, then "All my hats are green" is, in some formal understanding, true. The liar cannot make true statement so must in fact have at least one hat. That makes A) a good candidate. But E) can also be true — and in fact both A) and E) can both be correct.

Thank you for clarifying something that I pointed out in my comment while missing the total point of my comment.

on edit: I don't actually think you made my comment "but all of the questions are potentially true." any clearer than I made it, and evidently you seem to think that only A and E are potentially true, which is obviously wrong.

on second edit: ah I see that you believe the idea that some people are saying that All my hats are green indicates that the liar must have hats https://news.ycombinator.com/item?id=42369002 because evidently the assumption is that the 0 hat has a color green for some reason that is not adequately explained.

If that were true then it also follows that if the liar has no hats then all his hats are every color known to humanity. I don't think that is the way it works however.

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