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541Re: [aima-talk] Digest Number 303

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  • Tommy Gun
    Sep 16, 2005
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      Sounds like sort of a contradiction.  The words "cannot consistently" I think give it the flexability to sometimes be true and sometimes not.  If the sentence was definate all of the time, then it would just be a contradiction.   Take "this statement is definately false" is a contradiction, but if it were, "this statement is sometimes false" then there sometimes when it isn't a contradiction.  "cannot  consistently" basically says that's it's sorta random, so sometimes it could make sense. 

      Not sure if that helps, but it's just my $.02...

       - Bruce

      Message: 1
      Date: Sun, 11 Sep 2005 23:08:35 +0800
      From: Paul Hsueh-Min Chang
      Subject: Problem about the J.R. Lucas sentence


      On page 950, the book argues that the sentence "J. R. Lucas cannot
      consistently assert that this sentence is true." is necessarily true,
      but Lucas cannot consistently assert it. There are two arguments on that
      page. I found no problem with the first argument, but could not
      understand the second.

      Here is the second argument.

      "The sentence cannot be false, because if it were then Lucas could not
      consistently assert it, so it would be true."

      But, why couldn't Lucas consistently assert it /if it were false/? One
      can of course assert a false sentence and be consistent at the same
      time, because one is inconsistent if and only if it is /impossible/ that
      all his beliefs are true. If Lucas happens to believe a false sentence,
      he is still consistent.

      Please help/correct me.


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