alt Hacker NewsNo. In formal logic, if you have no hats, it is true that all your hats are green. You can claim anything about those hats, it is even true that each one of those hats is the same size as the universe, or that they are all completely green and completely red at the same time. In normal language, this would be different, but that is not the context here.
> Note: this question was originally set in a maths exam, so the answer assumes some basic assumptions about formal logic. A liar is someone who only says false statements.
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> In formal logic, if you have no hats, it is true that all your hats are green.
But told by someone who cannot make a true statement.
That's the thing, the problem isn't written in formal logic. It's written in English, which is vague.
This is a somewhat irritating property of formal logic and mathematics. Natural language receives a “special” grammar that isn’t always declared up front. You just have to sort of be in on it.
In this case, the reader is given the special definition of liar, but not the special definition of “lie”. (As in, it’s not a lie to make definitive claims about nonexistent hats.)
A lot of the “trick” in logic puzzles boils down to this issue of word play. This puzzle could have been drafted so that the liar’s statement leaves proper room for the no-hats case, but then it would be too easy.