The linguistics imo are pretty ill defined.

"All" bring a common colloquial term doesn't have a strict set theory definition here. It is reasonable many people think zero hats is means the lie is in this very first word.

A lot of people will consider "all" to implicitly mean 1 or more, while I think strict logicians will map colloquial all to 0 or more.

All mat imply colloquially 2 or more as well, as why bother say "all" if you had one hat in the truthful sense

"My hats" contrasts with the "has a hat" because having a hat in your possession that you could have borrowed does not confer ownership that the word "my" can imply.

So great, a three letter word and a two letter word and we are knee deep in ambiguity.

They could be wearing the hat to try to publicly locate the true owner who might say "hey I lost that hat at x".

"Are green"... Green as in vegetable? Green as in the specific wavelength defined as green and not lime or some other named shade? Completely green dyed being undermined by a black spot or a pattern on the hat?

Imo zero hats of ownership is a viable lie to the statement, as is having one red-green hat.

My favorite example is Monty Hall problem. "Smart" people often use it as the evidence of how bad general people are at probability.

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.

[1]: https://en.wikipedia.org/wiki/Monty_Hall_problem

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.

In my opinion a lot of these puzzles are about empathy toward the examiner as they generally ask variations of "what would I answer to this question?".

In the case of a logician and the properties of the elements of the empty set the frame of mind of the examiner is probaly going to be about using algebraic logical connectives.

For another nice example I can quote [0] via [1]

> Luria: All bears are white where there is always snow. In Novaya Zemlya there is always snow. What color are the bears there?

> Peasant: I have seen only black bears and I do not talk of what I have not seen.

> Luria: What what do my words imply?

> Peasant: If a person has not been there he can not say anything on the basis of words. If a man was 60 or 80 and had seen a white bear there and told me about it, he could be believed.

This is a more extreme case, but in my opinion it is the same phenomenon of being asked to take external things as true and work on them.

[0] https://languagelog.ldc.upenn.edu/nll/?p=481

[1] https://www.astralcodexten.com/p/somewhat-contra-marcus-on-a...

It works better for everybody when these puzzles are told as inside jokes instead.

>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.

It’s not so much that an inability to solve them means you’re deficient, as it is that an ability to solve them means you’re capable in ways most people aren’t. My wife is great at puzzles, and it’s always humbling to watch her sail through them.

I agree that puzzles alone shouldn’t e.g. determine whether you’re a good fit for a job, though. That’s one of the more annoying parts of software interviewing.