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Topic: Universal Truth Machine (Read 8455 times) |
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Re: Universal Truth Machine
« Reply #25 on: Jan 15th, 2003, 2:55pm » |
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"this sentence is true only if it is false or undecidable but not if it's true"
the other way around.
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AaronSw
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Re: Universal Truth Machine
« Reply #26 on: Nov 17th, 2003, 4:03pm » |
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This problem is impossible. My UTM can always return "true", and it will never violate the requirement of the solution (which requires saying something is <em>false</em>).
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Icarus
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Re: Universal Truth Machine
« Reply #27 on: Nov 17th, 2003, 5:15pm » |
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It's true that this will technically make the current form of the problem unsolvable, (tim makes the same point on August 8, 2002) but I think I could disprove your claim that it is a UTM fairly easily anyway! 
Perhaps the wording should be changed to "Someone has made a seemingly credible claim to have invented ...".
A UTM that always answers 'true' is not even slightly credible.
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"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
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Patashu
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Re: Universal Truth Machine
« Reply #28 on: Sep 1st, 2004, 3:14am » |
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on Sep 8th, 2002, 11:02pm, zarathustra wrote:| I understand that there is a problem that the universal truth machine is impossible if it simply prints out true, false, or undecidable. But how about if it was a little more intelligent? How about it prints out true, false, or if there is some sort of paradox involved then it explained exactly what the problem is and why it would never be able to give a correct result. I wonder if there would still be a way to foul it up... |
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Easy.
Tell the UTM: "You will answer this statement with something besides true."
If it says true, then it's proven the statement false.
If it says false, then it's proven the statement true.
If it says undecided, then it's proven the statement true, thus it is decided.
If it explains the paradox, it's proven the statement true besides realizing how it works. It can't win! (unless I missed something)
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BNC
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Re: Universal Truth Machine
« Reply #29 on: Sep 1st, 2004, 6:13am » |
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on Sep 1st, 2004, 3:14am, Patashu wrote:
Easy.
Tell the UTM: "You will answer this statement with something besides true."
If it says true, then it's proven the statement false.
If it says false, then it's proven the statement true.
If it says undecided, then it's proven the statement true, thus it is decided.
If it explains the paradox, it's proven the statement true besides realizing how it works. It can't win! (unless I missed something) |
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You: "You will answer this statement with something besides true."
UTM: "That's right, Sir. I have just answered with something besides 'true'. "
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How about supercalifragilisticexpialidociouspuzzler [Towr, 2007]
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rmsgrey
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Re: Universal Truth Machine
« Reply #30 on: Sep 1st, 2004, 2:53pm » |
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"Your response to this statement will not indicate it to be true"
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BNC
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Re: Universal Truth Machine
« Reply #31 on: Sep 1st, 2004, 3:46pm » |
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Anyway, the way I see it, it's a clear "undecidable".
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How about supercalifragilisticexpialidociouspuzzler [Towr, 2007]
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rmsgrey
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Re: Universal Truth Machine
« Reply #32 on: Sep 2nd, 2004, 6:29am » |
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The fun comes from the fact that, while the UTM cannot answer the statement correctly, any other person can.
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jonderry
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Re: Universal Truth Machine
« Reply #33 on: Sep 13th, 2004, 5:06pm » |
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I see how it is possible to devise a proposition that the UTM will not be able to correctly solve, however I don't see how to ensure that the proposition is true; suppose there were such a proposition, then the UTM could simply repond "true" unless that made the claim false (in which case the proposition was not necessarily true).
Am I missing something?
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andrewcc32459
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Re: Universal Truth Machine
« Reply #34 on: Jun 11th, 2005, 6:06pm » |
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Ask it "Will the Universal Truth Machine say that the answer to this question is false?"
It cant say true because then the answer would be false
It cant say undecidable because then the answer would be false
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slapee
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Re: Universal Truth Machine
« Reply #35 on: Nov 27th, 2005, 8:16pm » |
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how about asking the UTF a question that can be interpreted more than one way (e.g "0^0 = 0". this can either be true or false depending on how you look at it, since 0 times anything = 0, but anything^0 = 1.) ? would this work, or does the statement have to be boring and have only one interpretation?
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Icarus
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Re: Universal Truth Machine
« Reply #36 on: Nov 28th, 2005, 7:35pm » |
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It would answer that one with "0^0 = 1", since that is the definition. It is far more useful to define 0^0 = 1 than it is to define it to be 0, or to leave it undefined, so the decision was made long ago to choose 1 as its value. This definition is universally accepted.
The fact that 0 times anything = 0 does not enter into this, since 0^0 does not involve multiplying 0 by anything. (The rule that 0 raised to any power is 0 is false. The correct rule is "0 raised to any power other than 0 is 0".)
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"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
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