alt Hacker News> All my hats....", you are simultaneously making an existence statement that you have at least one hat
It does not. All my unicorns fly. There is no assumption that I have a unicorn. There is an assumption, based on the claim but it is not a fact.
The puzzle also assumes that "my" implies there is some ownership (we'll take for granted "my" means "has" for simplicity), which is another quibble that unravels the whole thing.
E is correct. I don't see how A comes to be the accepted answer.
Replies
E cannot be correct.
"All my hats are green" is still false even when I own a red hat and a green hat.
I mean, it's important to remember that the axioms of first-order logic are arbitrary. We could easily argue that the truth value of an empty group is undecidable, and that would better correlate to natural language logic.
The fact that we compact these edge cases into arbitrary truth values is just for ease of computing.
This is also relevant to the arbitrary choice of the 'inclusive or' as a default over an 'exclusive or', which most people use in natural language.
Would you agree with the following proposition: “if all of my unicorns fly, then some of my unicorns fly”?