That doesn't seem right. Logically, the claim "I can break X boards" evaluates to true if there exists some configuration of X boards which that person can bre

That doesn't seem right. Logically, the claim "I can break X boards" evaluates to true if there exists some configuration of X boards which that person can break. They aren't claiming "I can break X boards for all possible configurations of those boards". No one can break even one board unqualified, because the board could be 20 inches thick and made of lignum vitae. Thus by your definition the phrase "can break a board" becomes useless.