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>Suppose that you can’t remember whether Pluto is a dwarf planet, and you need to find out by asking someone nearby—but you don’t know whether that person is a
by 885895 11y ago
>Suppose that you can’t remember whether Pluto is a dwarf planet, and you need to find out by asking someone nearby—but you don’t know whether that person is a knight or a knave. What’s the one yes-no question you can ask to figure out whether Pluto is a dwarf planet?
>"Are you a knight if and only if Pluto is a dwarf planet?"
>If the person’s a knight and Pluto is a dwarf planet, then you get the answer “yes,” since both statements on each side of if and only if are true, and knights always speak truly.
I don't get how this follows. Surely, the person being a knight or a knave is independent from whether or not Pluto is a dwarf planet so a real knight would say "no" either way since the assumption is bad and a knave would thus say "yes". Thereby, you have not determined whether or not Pluto is a dwarf planet but instead whether the person is a knight or a knave.
Please explain my error.
- tromp 11y agoThere is no assumption. There is just "A if-and-only-if B" where A and B are both true and therefore by definition the whole statement is true.
- fineman 11y ago"If and only if" sounds strange to me too. Like asking if he's a knight when Pluto is a dwarf planet. And on second reading it looks like an awkward way to say And... I think "Is one and only one of [A, B] true?" would be better. Or, (A ^ B).
- anon4 11y agoIt's easier if you see it as logical operations, rather than language. A iff B has the same meaning as A == B, but with the added twist that !B negates the answer in the example (knaves always lie). So let's take A = Pluto is a dwarf planet; B = you're a knight, then "are you a knight if and only if Pluto is a dwarf planet" has the formula (B && (A == B)) || !(!B && (A == B)), which after a bit of simplifying you can see is the same as A == True || !(A == False), or A == True. Very often logic formulas, when translated in English, sound absolutely bonkers, not least because the words if, and, or have pretty loose meanings in ordinary language.