211–220 of 419 posts
As a native English speaker, I'd have said "all my hats are green" is untrue when you don't own any hats, meaning (A) isn't actually implied to be true. The fact the guy is a liar means he's allowed to imply he owns hats when he doesn't, right??
If they always lie, then statement one is false - they lied about having hats.
SPOILER The statement translates to: ∀x ( IsAHatOfMine(x) => Green(x)) That's just equivalent to ∀x (~IsAHatOfMine(x) ∨ Green(x)) by the definition of implication (it's only false if the antecedent is true, and the conclusion false). The negation of that is (by repeated application of De Morgan's): ~∀x (~IsAHatOfMine(x) ∨ Green(x)) ∃x ~(~IsAHatOfMine(x) ∨ Green(x)) ∃x IsAHatOfMine(x) ∧ ~Green(x)) Thus, the liar has a…
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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.…
In the solution they explain why they have to conclude that there should be at least one. Let me try again with a bit more explanation. 1. The liar stating something must mean that the phrase is not true. They cannot state anything that is not false. 2. "All X are Y" is the phrase. Now, if we assume there is no X the phrases "All X are Y" and "Not all X are Y" are both true and false. All X are Y - True. Yes, there i…
We only would know that either X doesn't exists or, if it exists, not all X are Y.
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In the world of logic puzzles, it is understood that a "liar" never makes a true statement, and that "vacuously true" statements are false.
Which seems to be an untenable premise. "I never make a true statement" says the liar.
I’ve never seen one of this puzzles phrasing it like that. With good reason, that would break the puzzle.
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…
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>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. Does that actually happen in academia? It seems to mostly be a social media thing.
So frequently I'd say its the main case. Researchers are extremely poor at controlling for competing explanations, in many cases, strongly incentivsed not to. Suppose you're writing a paper what do you write: option A) Average People Cannot Understand Probaility!?!?!, option B) Inexperienced test takers with unfamiliar notation fail to grasp meaning of a novel question; option C) survey participants on technical ques…
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Only people with formal training in logic, or those who work with formal definitions of logic, have trouble with this aspect of the puzzles. Trying to return to your more naive understanding of logic not only helps understand the intent of the puzzle, it also makes the puzzle more fun.
I'm genuinely perplexed by this, how is the puzzle even a puzzle if you don't judge it by formal logic?
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. Especially when it becomes clear that a yellow baby carriage is a vehicle only if it is daddy to be tickled... Honestly a good lesson to learn early that life is not fair and that rules are subjective.
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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. Because it is, if you'll forgive my Haskell-ese, the only implementation that means that `all_of $ l1 ++ l2 == (all_of l1) && (all_of l2)` for all lists `l1` and `l2`, including empty ones.
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…
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.
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, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice? [1]
The only correct ansewr to this question is "I don't know." People who answer yes are just taking way too many standardized tests.
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Only people with formal training in logic, or those who work with formal definitions of logic, have trouble with this aspect of the puzzles. Trying to return to your more naive understanding of logic not only helps understand the intent of the puzzle, it also makes the puzzle more fun.
> 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.