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

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

#371

Post by btilly »

raincole wrote: post #353
hansvm wrote: post #350

Earlier quoted context omitted.

The two reals are selected via some distribution, and the only way you can do better than chance is if you have some knowledge of that distribution. The question leaves that distribution completely hidden, and your answer smuggles it back in. That feels less like a counter-intuitive math/stats question and more like a badly worded gotcha.

Yes, this two real numbers question suffers from hidden conditions as the original version of Monty Hall problem does, but even more explicitly. We can't have an uniform distribution over all real numbers, so it's quite pointless to discuss if looking into the envelope gives any new information, cause we don't even know the distribution yet.

You don't need a uniform distribution to get guaranteed better than even odds. And many nonuniform distributions work just fine.

There are no hidden conditions. It is just a shocking result that we don't expect.

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

#372

Post by cxr »

cxr wrote: post #125
bradley13 wrote: post #24

Earlier quoted context omitted.

Speaking mathematically , you are right. However, linguistically I disagree. Consider: Someone tells you that "all of their kids are doing great in school". Turns out they have no kids. They obviously were trying to deceive you, and make you think they do have kids - in fact, since plural, more than one kid. Hence, it is effectively a lie. So if the liar speaks of "all my hats" while having none, that is deceptive. I…

That's not right; you're conflating dishonesty with lying. Why do people get weird when it comes to grokking what it means to lie? Mere deception is not lying. (Though it is dishonest.) A mere untrue statement is not a lie. (Though it is conterfactual.) But to lie is to (a) state an untruth (b) that is intended to deceive. Absent both conditions being satisfied, you're not dealing with a lie. There are other forms of…

For what it's worth (to whomever was upset by this): this is not apologetics—there's nothing here in my comment to give anyone cover for being dishonest. It is sufficient for something to be dishonest in order for to it to be deserving of all the judgement that people have for liars. It is the dishonesty that is bad, whether it takes form of a lie or not.

But conflating dishonesty with lying is harmful, because once you do that, you give ammunition to people who employ dishonesty in instances that don't involve lying, because if everyone is taking it as a given that dishonesty and lying are the same, and they can show that they weren't lying, then they can argue they weren't being dishonest. But that's wrong since dishonesty and lying are not synonymous—people can still be dishonest without lying—and, again, it is the dishonesty that is bad.

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

#373

Post by hulium »

LargeWu wrote: post #349
hulium wrote: post #324

Earlier quoted context omitted.

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

The host might be selecting between two goats, or might be selecting between a goat and a car. Either way, it doesn't matter because we don't get any additional information about whether our original choice was correct. (To clarify, this applies to the original problem, not the Crawl variant, where we either sometimes get definitive information, or sometimes get no information) Edit: Furthermore, I don't think that a…

> it doesn't matter because we don't get any additional information about whether our original choice was correct

That's the missing assumption. I would say assuming that people are perfectly random falls into the "standardized test" category.

> you won't get information, and you should still always switch and win 2/3 of the time.

You always get some information, the set of possible results becomes narrower, so saying the probabilities don't change is not sufficient. Not a good idea to discuss the problem in informal language though.

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

#374

Post by Nifty3929 »

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…

Yes - the puzzle should not revolved around semantic ambiguities like this. Let's be clear about the terms of the puzzle, agree on definitions, and then argue from there.

In fact, I would extend this to arguments as well: Let's be clear up front what we mean by important words and go from there. Too often people ending up arguing about definitions, but in roundabout ways.

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

#375

Post by danbruc »

nemomarx wrote: post #258
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.

If you ask whether the sky is blue, the answer yes tells you that you did not speak to False, the answers da or ja on the other hand tell you nothing because either could mean yes.

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

#376

Post by danbruc »

layer8 wrote: post #279
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…

Do the gods know each other?

Yes. As always in such puzzles, they know everything and have perfect reasoning, at least as far as logic permits.

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

#377

Post by hansvm »

btilly wrote: post #371
raincole wrote: post #353

Earlier quoted context omitted.

Yes, this two real numbers question suffers from hidden conditions as the original version of Monty Hall problem does, but even more explicitly. We can't have an uniform distribution over all real numbers, so it's quite pointless to discuss if looking into the envelope gives any new information, cause we don't even know the distribution yet.

You don't need a uniform distribution to get guaranteed better than even odds. And many nonuniform distributions work just fine. There are no hidden conditions. It is just a shocking result that we don't expect.

You need some _known_ distribution though, and it's shocking because the distribution is ommitted from the question, and the presence of the same distribution is snuck into the answer.

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

#378

Post by Volundr »

LudwigNagasena wrote: post #109
ecshafer wrote: post #92

Earlier quoted context omitted.

You implemented the problem wrong, and thus got an error. If hats is a list of colors, then every hat != green is true if the list is empty.

I wouldn’t say it is wrong per se. It certainly defies the conventional translation into FOL, but there is no a priori reason to pick the conventional formalism of FOL for this problem.

I don't think that's true. What if the liar buys a red hat?

    liar.hats.push("red")
This only works if hats is an empty array. If hats is just not a property people have (undefined in the example), then you can't represent adding them.

Now you might argue hats can be null when a user doesn't have them, or a non-empty array, but that's clearly not a great way to represent that. Now you have owning no hats represented two different ways as an empty array or null, and must build special casing around the null case (unless you are using a language where nil and the empty array are one and the same)

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

#379

Post by raincole »

btilly wrote: post #371
raincole wrote: post #353

Earlier quoted context omitted.

Yes, this two real numbers question suffers from hidden conditions as the original version of Monty Hall problem does, but even more explicitly. We can't have an uniform distribution over all real numbers, so it's quite pointless to discuss if looking into the envelope gives any new information, cause we don't even know the distribution yet.

You don't need a uniform distribution to get guaranteed better than even odds. And many nonuniform distributions work just fine. There are no hidden conditions. It is just a shocking result that we don't expect.

https://www.alexirpan.com/2015/09/09/the-other-two-envelope-...

If your solution is the same as this article's, it's plain wrong. Even the natural number case is plain strong.

It's very easy to demostrate as well: consider a trivia case where the distribution is just {P(1)=1/3, P(2)=1/3, P(3)=1/3} and you see 2 in the first envelope. There is no strategy to get a better chance than 50%. Therefore, any strategy that gives a better chance than 50% must implicitly make an assumption over the initial distribution (and therefore excludes a distribution like {P(1)=1/3, P(2)=1/3, P(3)=1/3})

Actually the article is even "wronger" than this, because "started A" and "switched" aren't independent and one can't simply use the product of their probability. The above example is a quick way to demonstrate it's not a general strategy without assumption to get >50% winning chance. Similarily, one can just use {P(1)=1/3, P(2)=1/3, P(3)=1/3} (this is a valid distribution over real numbers!) to demonstrate the real number strategy isn't general.

Again, for both natural number and real number case, the discussion over strategies is only meaningful is we know something about the distribution.

Interestingly, this article is wrong more or less in the same way as believing switching does give you more expected value in the original "twice money in another envelope" variation.

Edit: For people who are interested in the switching strategy, check Randomized Switching in the Two-Envelope Problem (2009). Spoiler: full of discussion over the initial distribution.

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

#380

Post by scoofy »

foxglacier wrote: post #345
scoofy wrote: post #207

Earlier quoted context omitted.

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,…

Is "absurd" a term of art here, or you just mean it conflicts with common intuition? This sort of thing comes up a lot in programming languages. For example, is Null=Null true or false? What about Null!=Null? Maybe they can both be true or both false. It's strange because there's no simple obvious right answer but we need some answer and programming languages manage to define that sort of thing so it ends up logicall…

I'll add the exchange back here to continue this thread

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>>scoofy: I mean, it's important to remember that the axioms of first-order logic are arbitrary. We could easily argue that the truth value of an empty group is undecidable, and that would better correlate to natural language logic.

The fact that we compact these edge cases into arbitrary truth values is just for ease of computing.

This is also relevant to the arbitrary choice of the 'inclusive or' as a default over an 'exclusive or', which most people use in natural language.

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>foxglacier: This addresses my previous reply to you, thanks. I wonder though if there's a problem in that common natural language is inherently limited to common concepts. Scientists famously use confusing language in their papers but they're writing for people who use the same language so it's OK. For example, they use "consistent with zero" to mean "might be zero" even though a common-language reader can interpret it as "not zero". I suppose logicians use "or" to mean inclusive or in their papers too.

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"Absurd" here I wouldn't say is a term of art. I just mean things that not only don't mean anything, but can't mean anything. Here, existence is always extremely relevant. This goes back to Kant's idea that existence can't/shouldn't be a predicate. The idea of talking about the actual color of a nonexistent hat is absurd in that a nonexistent hat can not have a color, period, because having a color presumes existence.

So, when I talk about the logic of natural language, we have to get really philosophical. I presume that there as at least significant equivalence from formal logic to natural language, if not ultimately being fully equivalent. Formal logic is effectively a model trying to capture logical reasoning, and there are some notable differences for simplicity's sake (the Frege-Russell ambiguity thesis is a common example: https://link.springer.com/chapter/10.1007/978-94-009-4780-1_... ), however, most-if-not-all of these formal logic ambiguity concerns are trivial for natural language to deal with as any ambiguity can be clarified by an interlocutor.

Where things get really weird, however, is as you go up to the axioms of logic, and try to justify them. The idea that foundations of logic itself is determined either inductively or instinctually is just bizarre. And mapping an inductive/instinctual logic to a formal system runs into a lot of philosophical problems that aren't really practical to worry about. It just gets weird and solipsistic, as it does when you get too caught up in philosophy.

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