“All my hats are green” is making two statements and claiming both are true. A clearer way to say it would be “I have at least two hats and each one is green.” To negate an “and” statement, either or both parts must be false, so if we know Pinocchio’s statement is a lie, we know one of a number of things are true:
I have one hat and it is green. Or,
I have one hat and it is not green. Or,
I have no hats and they are green (the “vacuously true” statement). Or,
I have no hats and they are not green.
With the information given, we can’t say anything more than that, so we cannot know that any of the conclusions offered are true.
