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548Re: [aima-talk] Digest Number 303

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  • The Geek
    Sep 23, 2005
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      I don't know if I'm explaining this very well.
      Someone else should feel free to chime in if they've
      got a better way of phrasing it...

      While they haven't spelled it out in detail, I think
      they're using a simple logic system and definition of
      "consistent". In other words, they're not trying to
      allow for an "agent belief" representation where we
      acknowledge that beliefs might be wrong. Instead, if
      you assert a sentance it must be true or you've
      introduced a contradiction.

      If we take 3 sentances:

      A = B.
      B = C.
      A != C.

      If we try to assert all three sentances, we cannot do
      it without creating a contradiction. Since this is
      the definition of "consistency", they would say that
      we cannot "consistently" assert all three sentances,
      since doing so would introduce a contradiction.

      The example is a little more complicated, since
      they're violating a couple of normal rules for logic
      systems - they have a sentance referring to the
      assertability of sentances. But if you reword the
      sentance to say "Agent A cannot assert this sentance
      without being wrong" I think it's a little more clear.

      In this case, as an agent **I** can consistently
      assert the sentance "Agent A cannot assert this
      sentance without being wrong" without introducing a
      contradiction. However if Agent A tries to assert the
      same sentance, he runs into a problem. If he asserts
      it as true and is right, then the sentance is false,
      so he's wrong.

      But the whole point of the illustration is simply to
      show that **sometimes** one agent is unable to
      assert/know/do things that another agent can, but that
      doesn't automatically imply that agent is inferior,
      it's inability to assert/know/do may be related to the
      specific situation.

      Rob G.

      --- Paul Hsueh-Min Chang <avatar@...>
      wrote:

      > 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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