So suppose you come to a fork in the road, and there are two people there, one of whom is from the village where people always tell the truth, and one is from the village where people where people always lie, but neither of them is very smart, so neither one is good at evaluating complex questions involving multiple layers of hypotheticals. What do you do then, huh?
The biconditional question example in the article seems error prone. If you ask the (always truth-telling) knight "Are you a knight if and only if Pluto is a dwarf planet?", couldn't they answer, "No, I'm a knight regardless of whether Pluto is a dwarf planet or not."?
For some reason (perhaps my own ineptitude with them?) I have always hated the sorts of logic word problems in the link, and Raymond Smullyan's in particular.
Of course I could be lying, and "hated" could mean "loved."
Pluto is either a planet or not. The "dwarf planet" status is fucked up.
"Planet Emeritus" would work for me. Does somebody know an astronomer? That is, one they are willing to communicate with.
5: the thing is that the knights and knaves never actually speak English, only propositional logic.
I'll keep that in mind next time I proposition a knight or a knave.
3 questions but a search space with 12 possibilities (although figuring out which word maps to which truth value isn't a requirement of the solution), so the questions have to on average reduce the search space by more than half. Fun.
Neil the Ethical Werewolf had the best version of the knights and knaves set up, which uses rappers: "One rapper likes big butts and cannot lie. One rapper likes small butts and always lies. One rapper likes all butts but shares your inability to assess butt size, and will answer yes or no at random if asked whether a butt is big or small. "
I'm the world's worst logic puzzle solver, nevertheless, the world's hardest logic puzzle does seem pretty damn hard.
12: That one was a lot of fun.
Note that unlike the random butt determiner, Random does not randomly answer da or ja with no relation to your question; Random randomly decides whether to answer truthfully or falsely.
"Ranjit," if that is his real name, gives credit to Neil in that very Twitter conversation.
18: If you're responding to me, yes: consider the question "Will your response to this be spoken falsely?" I don't think that's on the solution path per se, but it does get you something.
And to embed the liar's paradox and break Truth: "Is your answer to this question 'da'?"
I guess it only breaks True half the time, but when it doesn't it breaks False.
If I told the other person they had a beautiful body, would they hold it against you?
I can't believe Smullyan is still alive. I read his books religiously as a kid. I loved the problems, but wasn't actually very good at solving them, so I just read the explanations.
Also, my favorite is the philosopher of logic named Boolos. That's a bit too on the nose.
Is anyone still doing this? Didn't check the answer, but this is what I came up with, ROT13ed:
Lbh pna nfx gurz n pnershyyl jbeqrq dhrfgvba fb gung, ertneqyrff bs gur tbq lbh'er gnyxvat gb naq gur inyhrf zrnag ol "qn"/"wn", gurl'yy nyjnlf nafjre jvgu n jbeq bs lbhe pubvpr vss na neovgenel cebcbfvgvba vf gehr. Vs lbh nfx:
Qbrf gung lbh'er nafjrevat gehgushyyl ubyq vs naq bayl vs ("qn" zrnaf gehr vs naq bayl vs cebcbfvgvba K ubyqf)?
Gur tbq jvyy fnl "qn" vs K ubyqf naq "wn" bgurejvfr.
Jbexvat guvf bhg sbe Gehr:
Gehr nyjnlf nafjref gehgushyyl, fb vgf nafjre jvyy nyjnlf or ("qn" = gehr K). Vs "qn" = gehr, Gehr nafjref jvgu gur inyhr bs K, naq fb jvyy fnl "qn" vs gehr be "wn" vs snyfr. Vs "qn" = snyfr, Gehr nafjref jvgu !K naq fb fnlf "qn" zrnavat snyfr vs K vf gehr naq "wn" zrnavat gehr vs K vf snyfr.
Fvapr Snyfr nyjnlf yvrf, gur svefg pynhfr vf snyfr naq gung fgngrzrag qrtrarengrf gb !("qn" = gehr K). Ohg fvapr Snyfr nyjnlf yvrf, lbh artngr gung naq trg onpx gb "qn" = gehr naq gur nafjref ner gur fnzr nf gur nobir.
Enaqbz vf rdhvinyrag gb juvpurire bs Gehr be Snyfr vg orunirf yvxr jura lbh nfx.
Bar lbh unir gung, lbh abj pna hfr nyy guerr dhrfgvbaf gb qrgrezvar gur beqre bs gur tbqf (jurer yrg'f fnl gur beqre vf gur beqre lbh nfx gurz gur dhrfgvbaf). Na rnfl jnl gb qb guvf gung qbrfa'g vaibyir qverpgyl nfxvat n tbq juvpu bs gur guerr vg vf vf:
1. Nfx gur svefg tbq vs gurl'er fbegrq va nfpraqvat be qrfpraqvat nycunorgvpny beqre, vtabevat ebgngvbaf.
2. Nfx gur frpbaq tbq vs gurl'er abg ebgngrq sebz gur nfpraqvat/qrfpraqvat beqre. (Vs gurl nera'g, lbh trg n serr dhrfgvba. Lnl benpyrf.)
3. Vs gurl ner ebgngrq, nfx vs gurl'er ebgngrq bar be gjb cbfvgvbaf.
Just checked the given answer. Mine is similar but I think more elegant since I don't care who Random is and I don't include completely useless clauses like "is Pluto a dwarf planet".
Having been exposed to many opinionated non-classical logicians, I think it's funny how it ends up concluding that the moral of the story is that the law of the excluded middle is awesome, especially given (as I said in 24/25) you can break this problem by taking advantage of that.
Ack, my answer had a bunch of <=> in it to represent "if and only if", but they got stripped out. I won't rewrite it out as that'd be too long, but pretend that I put them in in all the right locations;"da = true X" should be "da = true if and only if X"; most instances of X or !X have an iff before them.
The alligators are fighting over a sandwich.
re 13: the ethical werewolf was at our house night before last and we had an awesome time eating vegetarian food! I had meant to mention it but it's funny to have it be so a propos.