phlip wrote:Can you reword?
Words represent universal concepts. The concept we name "tree" does not change if we call it the German word for tree "Baum" just like the concept we name "1" does not change if we call it "2". So while "a tree can only be a tree" is not an axiom because a tree can be a pine or a tree can be a Baum, if we substitute the words for the concepts they represent, such phrase is an axiom: a [concept of tree] can only be a [concept of tree]
So basically you can substitute "I see someone with blue eyes' is only
a statement in English" for: [concept of I][concept of see][concept someone]....[concept of English], which is an axiom. You have no reason to assume I am talking English right now, but you have conclusive scientific evidence that I am. Some reader of a language written exactly the same as English would not have conclusive evidence that this is his language and not English.
phlip wrote:But if you took the phrase at its German meaning, without preexisting mathematical proof that that was the language he was speaking, then you would still be assuming. Just an assumption that happened to be correct (and an assumption that was probably more likely to be correct given context... though still not 100%).
But how would you express that mathematical proof? in roman numerals?
phlip wrote:So what you're saying is that the conjecture that the puzzle is written in a language commonly used on Earth is a reasonable assumption to make? The conjecture that no-one on the planet has ever created a conlang that intentionally mimics English structure but has different meaning is a reasonable assumption?
I've been thinking about it a bit more and I've come to the conclusion that such a language (let's call it ConEnglish) is actually impossible. You cannot change the definitions of words in such a way that any given text retains it's coherence while at the same time having a coherent grammatical set of rules. If ConEnglish interchanged the concepts of yes and no, you would know you're not reading your ConEnglish as soon as you read: yes is an affirmation
. If you interchanged the concepts of affirmative and negative too you would know you're not reading ConEnglish as soon as you read: "The result is positive; yes, you are pregnant" affirmed the doctor"
. If you also replaced dead with alive you would have a problem reading Did he die?
because you cannot alive. You would have to replace Did with was, but then you would have problems reading "yes, he was correct" because you cannot "do" correct.
phlip wrote:It's not beside the point. The point is that all this waffling about the guru maybe being colour-blind or maybe one of the islanders being deaf (or maybe one of the islanders thinks one of the other islanders is deaf) is so much hot air because there are much more fundamental ambiguities inherent in the mere concept of communication, and it is impossible for them to be eliminated entirely.
The only difference between "I can't tell for 100% certain it's written in English" and "it doesn't explicitly say thing X which is a standard assumption in logic puzzles" is one of scale, a difference in the probability that your assumption is false. You have to draw the "reasonable assumption" line somewhere, and it can't be at zero. To disagree with "reasonable assumptions" outright is to disagree that communication is possible.
If a scientist gathers enough evidence that copper conducts electricity, then he has conclusive evidence that copper is a conductor; he is not saying "it's reasonable to assume copper is a conductor" because science makes no assumptions. It's true that science goes against the problem of induction, but we're using computers for a reason: we have conclusive evidence that they work. Similarly, we have conclusive evidence that the English language works--we're using it right now because of this. However, if we were on a desert island and a guru told us that she can count at least 1 person with blue eyes, we would not have conclusive evidence that the guru is not color blind, is not lying or is not high on whatever leached out of that leaf he cooked his fish in. Also, saying that nobody leaves because an islander has no evidence that the other islanders aren't deaf is a valid solution.
marzis wrote:So, Potatoburg, if we take those above statements to be true (I mean, if you want to say that XKCD could be lying, well, then just stop trying to solve logic puzzles or something, they're not for you) then how is 'the Guru could be color blind' any different from 'one of the islanders could find a mirror'. Sure, we can't know that the Guru isn't colorblind, but is that assumption 'logical' and 'not dumb' and 'not an answer assuming the question is a trick' and 'somehow relevant to the Guru not making eye contact with anyone in particular' and also results in the answer to the riddle being not 'no one leaves'?
I appreciate your objections to the phrasing of the puzzle and the ambiguities of English and all those other things you've mentioned, but XKCD provides us not only with the phrasing of the problem, but also with these guidelines I've copied above, to allow us to say 'okay, a) there is an answer and it is not 'no one leaves', and b) the answer isn't tricky or of the sort that he describes above (which falls into a certain category often found with sub-par logic problems, your objections to which are perfectly valid in those situations) so I don't have to worry about silly things and instead know that focusing on a purely logical solution will, if I am good enough, lead me to the solution'
I don't know if this whole problem arises from a stunted ability to put oneself in the position of others, so let me explain. First, ignore the fact that this is a puzzle. You are a perfect logician and arrive at the island with some people who are also perfect logicians (which implies they do not make assumptions of any kind--maybe that is why they don't talk to anyone, huh?). One of them, the guru, says "I count at least one blue-eyed person on this island who isn't me". Why would you trust her? Even if someone told you "the guru cannot say untruthful statements", why would you trust them? A perfect logician would require evidence that the guru does not lie. Of course, you could say that it is stupid to require evidence because what is the evidence for axioms? we must only know we know nothing (includes eye color). In either case, there is no solution to this puzzle other than "nobody leaves".
I understand you want a logic puzzle, but if the puzzle only gives one possible solution then that's the solution. Real life is like this. Einstein's theory of relativity could be considered an exercise in lateral thinking and a tricky solution, but it's the correct solution. Nobody said "you're wrong because it's reasonable to assume space-time is constant". Another example was how the Copernicus heliocentric-model was not accepted for a long time because it was reasonable to assume that the earth was the center of the universe; so they came up with these relatively complex calculations of the orbits of the planets and called that the solution to the "wanderers".
You can't make assumptions in science. Once you have conclusive evidence then you have facts or theories. Saying "ooh but problem of induction" is not a reasonable refutation, you are using a product of science: a computer. With me you're doing the same, when I say "there islanders have no evidence that the guru is not color blind" you tell me "ooh but you have no evidence that the language that the puzzle is written in is only English" (which begs the question: why are you using it then?). It's childish. To debate in terms of "I only know I know nothing" is itself a performative contradiction given the implicit rules and truths you accept by participating in a debate. For example, you cannot debate that the truth is unknowable because even if you're right, you're wrong, it's unknowable.
Xias wrote: If you want to say that a statement like "the guru is reliable, and this sentence is common knowledge" is a necessary addition to the puzzle to yield the desired solution, then (a) you are demonstrably wrong given the number of people who came to the desired solution without such a statement and (b) we would then have to add an infinite set of further caveats and explanations, and even then we would not have a solvable puzzle by your standard.
You can have a solvable puzzle without adding anything simply by accepting that the solution is "nobody leaves". Why the effort to force the puzzle into an erroneous solution?