Fascinating. I think many people here have applied their own social intuition- - a programmer’s idea of an empty sets- to the puzzle.

True, but "programmer's intuition" is because most programming languages are more or less based on formal logic so they agree with the formal logic interpretation even if many programmers have never studied formal logic.

"More or less" is the key and the rub. The specific semantics must be determined and utilized in place.

For me, the evaluation of the empty set should have separate semantics than that for how a non-empty set's elements are logically combined to produce a value.

This is the result of doing stats programming for grad students, doing lots of database design and programming, and lots of regular programming in imperative and functional languages.

The key is that we are always working within a context, and this problem's context involves both formal logic and regular old language. And, whew!, is there a disconnect and interference pattern.

What a delightfully unserious discussion!

  function areAllTheirHatsGreen(someone) {
      return someone.getHats().every(hat => hat.color === 'green')
  }

I wonder if there's a language or programming paradigm where this function wouldn't be determined simlarly.

I think best you could do is make a validation check that throws an error if there's no hats at all, but would that make sense?

What if you have a function that has to return a boolean and not throw an error.

The best I've found are languages like F# that allow you to return a pair of values, which for your example would be a tuple of (bool, bool), where the first is isError and the second is the evalResult. Of course, you better not mix `em up!

As to paradigms, I've not seen anything yet, but I haven't seen it all, and corporate America has their legacy systems that limit their explorations.