21–30 of 419 posts
And then read https://xkcd.com/169/
Anyway, I'm sure there'll be a YouTube video about this with an AI voiceover soon.
Earlier quoted context omitted.
Yeah, I'm a bit confused there is no option "he has at least one non-green hat", which is what I would answer. Perhaps that means I'm wrong.
Agree it must be true that it has at least one hat, and it must be non-green (he might have other green hats).
My take (possible spoiler): If he had no hats, then his statement would technically be true. Therefore he has at least one hat. He may have some green hats and some non-green hats, but must have at least one non-green hat. He could have any number of green hats, including zero, as long as he has at least one non-green hat. So the only derived statement that we can conclude to be true is A.
So if the liar speaks of "all my hats" while having none, that is deceptive. I would consider it a lie.
Earlier quoted context omitted.
No, in logic that is a vacuous truth. All my hats is true for zero hats. But that would not be a lie. And since the liar always lies, that can not be case.
Do you think regular people, when communicating, use academic logic? Or do you think the liar is an academic?
Earlier quoted context omitted.
No, the liar having no hats would not make the statement true. ‘All my hats implies’ implies the liar stating they have hats. The liar either has zero hats or some amount of hats. The only thing we know for certain is that if they do have hats, there is at least one non Green hat.
I read statement "All my hats are green" as meaning: For every hat H that I have, H is green. If I have no hats, this statement is true, just as * the empty sum is 0, * the empty product is 1, * the empty AND is True, and * the empty OR is False. So with this interpretation, the liar having no hats would make the statement true.
e.g. "all my lamborghinis have magical goat skin seat covers" is true if 1) I have no lamborghinis or 2) All the ones I own have magical goat skin seat covers.
(fr I have no logical or mathematical background)
If we're doing "provoke arguments on the internet using confusingly-stated constructs", they should have some self respect and use the venerable 6÷2(1+2). And then read https://xkcd.com/169/ Anyway, I'm sure there'll be a YouTube video about this with an AI voiceover soon.
And, as usual, the xkcd is fantastic.
My take (possible spoiler): If he had no hats, then his statement would technically be true. Therefore he has at least one hat. He may have some green hats and some non-green hats, but must have at least one non-green hat. He could have any number of green hats, including zero, as long as he has at least one non-green hat. So the only derived statement that we can conclude to be true is A.
If we're doing "provoke arguments on the internet using confusingly-stated constructs", they should have some self respect and use the venerable 6÷2(1+2). And then read https://xkcd.com/169/ Anyway, I'm sure there'll be a YouTube video about this with an AI voiceover soon.
6÷2(1+2) is written in a deliberately confusing fashion. This is a simple math olympiad-style question. All universal quantifications on the empty set are true, for the same reason that the implication A -> B is true when A is false regardless of B. It cannot be any other way. Precedence of infix operators on the other hand is completely arbitrary, we settled on multiplication before addition because otherwise it would be a pain to write polynomials.
My take (possible spoiler): If he had no hats, then his statement would technically be true. Therefore he has at least one hat. He may have some green hats and some non-green hats, but must have at least one non-green hat. He could have any number of green hats, including zero, as long as he has at least one non-green hat. So the only derived statement that we can conclude to be true is A.
No, the liar having no hats would not make the statement true. ‘All my hats implies’ implies the liar stating they have hats. The liar either has zero hats or some amount of hats. The only thing we know for certain is that if they do have hats, there is at least one non Green hat.
> Note: this question was originally set in a maths exam, so the answer assumes some basic assumptions about formal logic. A liar is someone who only says false statements.