alt Hacker NewsOne complication is that in typical English, if you say "All my hats....", you are simultaneously making an existence statement that you have at least one hat... but the usual formal logic "forall" quantifier does NOT presume existence. Here's a formal proof that "forall" has a "surprise" meaning for those not well-versed in formal logic: https://us.metamath.org/mpeuni/alimp-surprise.html
I propose that when translating such statements to a formal logic, if that's what you really mean, use an "allsome" quantifier as I've described here: https://dwheeler.com/essays/allsome.html
It's really easy to forget to include an existence quantifier. Having notation specifically designed to automatically include it can avoid some problems.
Replies
> in typical English you are making an existence statement
No, you're not.
> 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.
> One complication is that in typical English, if you say "All my hats....", you are simultaneously making an existence statement that you have at least one hat... but the usual formal logic "forall" quantifier does NOT presume existence.
Perhaps. But what if someone asks you "are all your hats green?" Then the interpretation is not so clear.