41–50 of 419 posts
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?
A) "The liar has at least one hat." cannot conclude because may have no hats, thus the lie is in the "all my hats"
B) "The liar has only one green hat." cannot conclude because may have 2+ green hats out of a 3+ set.
C) "The liar has no hats." cannot conclude that because he may have hats that are not green.
D) "The liar has at least one green hat." cannot conclude that because he may have no hats, or no green hats.
E) "The liar has no green hats." cannot conclude that because of the "all my" modifier means that he can have some green hats.
This is however different than what is true or not. Concluding from a set of multiple choice questions is not choosing ones that are potentially true, concluding is choosing something that is definitely true. There is not a single statement in that list of questions that is definitely true given the requirements, but all of the questions are potentially true.
on edit: all questions are potentially true, but not all potentially true at the same time of course - some of them lock out the others.
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.
They are not even remotely the same. 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 bef…
It might be a math Olympiad question, but a math Olympiad participant is supposed to know how, say, a vacuous truth works, and, moreover the mapping of formal English to logical operators (see also: the inclusive or) and that is not how everyone in the world will parse the statement of the problem.
Is the point here to educate people on a quirk of formal logic, or is a smugbait to promote a book? Oh look, there's a book. Quelle surprise.
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…
"You can give me the loan, all my companies have millions in assets."
I tried to figure it out but got stuck on the linguistic dilemma if he's lying about the concept of himself existing ("All of MY hats"). Then I decided I have better things to do.
He may also be claiming that the hats are ecologically friendly.
Are we also to assume that if all the hats were each mainly green on the outside but had brown linings, they are, or are not, each said to be "all green"?!
I need a pint.
Earlier quoted context omitted.
Agree it must be true that it has at least one hat, and it must be non-green (he might have other green hats).
Why would you conclude that the liar is telling the truth that they have any hats at all?
(other systems of logic exist which will attempt to resolve this. Forcing such statements to be false makes things much trickier formally, as does e.g. three-valued logic to try to avoid assigning truth or falsity to such statements)
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.
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.
It amounts to an assumption of an implied conditional ("If I have hats...") which is not always warranted. The "gotcha" here says more about the vacuous truth assumption than it does someone who falls for it.
Earlier quoted context omitted.
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.