From I remember from what we did in maths, a liar is usually used to have a NOT so we have something like NOT (All my hats are green) => There is at least one hat that is not green.
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."
#32My 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.
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…
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Re: A liar who always lies says "All my hats are green."
#33My 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.
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…
"You can give me the loan, all my companies have millions in assets."
Re: A liar who always lies says "All my hats are green."
#34My 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.
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.
Whether you are wrong depends on whether you interpret his statement in a mathematical or in a colloquial sense. Colloquially, if I have no cats and tell you "all my cats are brown", you'd say that I'm lying, beause I'm implying that I have cats. Mathematically, if I have no cats, then it is true to say that all of the ones I have, which are zero, are brown.
Re: A liar who always lies says "All my hats are green."
#35Earlier quoted context omitted.
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.
by the same following, this would mean that any statement on the members of an empty set can be made and it would be logically 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)
Yes
Re: A liar who always lies says "All my hats are green."
#36Earlier quoted context omitted.
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.
by the same following, this would mean that any statement on the members of an empty set can be made and it would be logically 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)
I don't have formal logic or any math beyond calculus, either, and it appears that this fact is to our advantage.
Re: A liar who always lies says "All my hats are green."
#37Earlier quoted context omitted.
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.
by the same following, this would mean that any statement on the members of an empty set can be made and it would be logically 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)
Correct.
Common source of confusion/trickery/divergence between ordinary language and formal logic.
Edit: Logically speaking, the following two are equivalent:
They married and had kids.
They had kids and married.
Re: A liar who always lies says "All my hats are green."
#38Earlier quoted context omitted.
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.
by the same following, this would mean that any statement on the members of an empty set can be made and it would be logically 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)
Yes, your statement would be true.
Re: A liar who always lies says "All my hats are green."
#39My 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.
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…
And that's why SO gets mad when I come home with six cartons of milk[1].
[1]: https://blog.bryanbibat.net/2013/01/02/programming-joke/
Re: A liar who always lies says "All my hats are green."
#40Earlier 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.
Perhaps I'm being a bit too logical, but in mathematics and logic the statement For all x in A, x has XYZ property is taken to be true when A is the empty set.
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