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546Re: [aima-talk] Digest Number 303

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  • Paul Hsueh-Min Chang
    Sep 21, 2005
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      But my question is that being false does *not* equal being contradictory
      (i.e. necessarily false). If the sentence were merely false but not
      contradictory, he surely could consistently assert it.

      So lets review the argument:

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

      Consider two conditions:
      1. If the sentence were meant to be merely false, then Lucas could
      consistently assert it, so the argument is invalid.
      2. If the sentence were meant to be contradictory, then nobody could
      consistently assert it, but then the argument would have a very strange
      form: "if p were contradictory then A could not assert it, so p would be
      true." Consider the following argument of the same form: "If 'Saddam
      Hussein is the US President' were contradictory, then I could not assert
      it, so he would be the US President". Clearly absurd.

      Again, please correct me if I am wrong.

      Paul

      The Geek wrote:

      > I believe if you look at the "setup" on the previous
      > page you'll see the authors intended the term
      > "consistent" to be the logical definition. (see pages
      > 137 and 353) That is, for something to be consistent,
      > it cannot be contradictory. Therefore, if the
      > sentance were false, he couldn't assert the sentance
      > and still be consistent, which therefore makes the
      > sentance true.
      >
      > But the point of the paragraph is that because of the
      > construction of the sentance, the agent "J.R. Lucas"
      > cannot assert something that other agents can.
      > However the authors are pointing out that this doesn't
      > make him inferior.
      >
      > Rob G.
      >
      > --- Paul Hsueh-Min Chang <avatar@...>
      > wrote:
      >
      > > Hi Bruce,
      > >
      > > I think "this statement is definitely false" is more
      > > a paradox than a
      > > contradiction, for when you decide it is false then
      > > it is true, and vice
      > > versa. A contradiction is always false. And
      > > "consistently" has two
      > > readings, one is the randomness you meant, and
      > > another reading common in
      > > philosophical literature is that it is possible for
      > > a set of
      > > propositions to all true. I'm just not sure which
      > > meaning the authors
      > > seem to imply.
      > >
      > > Paul
      > >
      > > Tommy Gun wrote:
      > >
      > > > 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
      > > >
      > > > Hi,
      > > >
      > > > 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.
      > > >
      > > > Paul
      > > >
      >
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