351–360 of 419 posts
Earlier quoted context omitted.
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"
If that is true then liar said truth.
2. by the negation rule, there exists a hat h in {liar's hats}, such that it is not true that h is green.
3. there exists a hat in {liar's hats}
This is really basic first order logic guys.
"For all x in {}, P(x)" is always trivially true without regard for P.
Similarly, "there exists an x in {}, P(x)" is always trivially false.
Earlier quoted context omitted.
Just be glad that you didn't go for the 2 envelopes problem which was her next. Vos Savant was wrong about that one, and few people like the real answer. The problem is that you're presented with two envelopes with 2 real numbers inside. You randomly select one, then look, and try to guess if you got the larger number. It doesn't seem like you can do better than even, but you can! Unfortunately everyone hates the ans…
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.
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.
Earlier quoted context omitted.
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 t…
In many forms of linguistic logic you need to have an existent hat to have the property green, therefore if you do not have any hats you have no green hats. Which is my preferred method of dealing with this.
And obviously there are other forms of logic, as https://iep.utm.edu/liar-paradox/#SH3c
Is the column that was linked more likely to be interested in linguistic logic games or formal mathematical logic games? I'm guessing the second, in which case I guess it's true we can conclude A - but I inherently dislike vacuous truths when applied to logic, especially language like this where the normal argument that the second parameter "Green" is never evaluated because we do not have the first "A hat" in the empty set seems suspect to me because we know what Green is separate from a hat, we just need to know if there is a hat we can assign Green to.
Earlier quoted context omitted.
Logic itself is a relatively new invention, and is symbolic itself. That is to say, logic is a map not the territory. That said, if someone can't fathom the most widely used symbolic languages humans use (math, logic, language, etc) they probably do have a cognitive deficit of some sort when compared to those who can.
It is less 'logic is new'... it more about abstract thinking is a skill that is more useful in societies that have complex social arrangements. If you are a primitive farmer abstract thinking isn't really useful to you. Everything you deal with in your life, except religion, can almost entirely be dealt with absolutes with little in the way of abstractions. If it rains at the right time then you can have a good harve…
I agree, but would also say that you should be capable of learning to understand those questions. For example, If you can't speak English, you'll be bad at reading books in English. If you were never taught math, you'll be bad at math. Similarly, If you never learned to reason you'll be bad at solving logic puzzles. It's almost tautological.
However, if a person is incapable of learning to do one of those things, despite the majority of the world being fully capable of doing it, they probably have a cognitive deficit.
> And ultimately that is all IQ testing measures.. your ability to take tests.
I disagree. I think it measures how well you've learned to reason, though I do agree that reasoning is a learned skill for most people.
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.
Earlier quoted context omitted.
> 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.
yes of course, I was trying (and failed?) to draw a connection from all_of to accumulate (i.e. fold).
Earlier quoted context omitted.
No. (assuming you have no unicorns) "all of my unicorns fly" is true; "some of my unicorns fly" is false; "true->false" is false.
So you claim that in normal English “all” doesn’t imply “some”?