https://www.youtube.com/watch?v=YQykZU8mcZY okay so this video is a great example of the intuitive value of the “intuitionistic" constructive appurroach to mathematical logic, because i think it gives a much better way to understand why the potentially tricky part of the purroblem works
spoilers fur the puzzle in the video
the video gives a kinda wishy-washy explanation fur the notion of vacuously true statements but i think it would be reasonable fur a skeptical student to feel like the notion of vacuous truth is justifiable
in an intuitionistic logic, a statement is true if you can supply a proof of it. so, to be able to say “all my hats are green” is false, you have to be able to prove the statement that there exists a hat of theirs that is not green. that purroof would be an example of a hat of theirs that is not green. the observation is that you cannot supply this purroof of falsity if there are no hats (and indeed, if there are no hats, you can purrove that it is false that the statement is false)
