“Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say.” — Bertrand Russell, The Scientific Outlook (1931)
• Russell in Your Head-Roe — Bertrand Russell on mathematics
• A Ladd Inane — Bertrand Russell on solipsism
• Math Matters — Bertrand Russell on math and physics
• Whip Poor Wilhelm — Bertrand Russell on Friedrich Nietzsche
From Raymond Smullyan’s Logical Labyrinths (2009):
We now visit another knight/knave island on which, like on the ﬁrst one, all knights tell the truth and all knaves lie. But now there is another complication! For some reason, the natives refuse to speak to strangers, but they are willing to answer yes/no questions using a secret sign language that works like this:
Each native carries two cards on his person; one is red and the other is black. One of them means yes and the other means no, but you are not told which color means what. If you ask a yes/no question, the native will ﬂash one of the two cards, but unfortunately, you will not know whether the card means yes or no!
Problem 3.1. Abercrombie, who knew the rules of this island, decided to pay it a visit. He met a native and asked him: “Does a red card signify yes?” The native then showed him a red card.
From this, is it possible to deduce what a red card signiﬁes? Is it possible to deduce whether the native was a knight or a knave?
Problem 3.2. Suppose one wishes to ﬁnd out whether it is a red card or a black card that signiﬁes yes. What simple yes/no question should one ask?