541Re: [aima-talk] Digest Number 303
- Sep 16, 2005
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...
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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