🚀 go-pugleaf

In article <121@cavell.UUCP>, jiml@alberta.UUCP (Jim Laycock) writes:
>   Consider a much smaller scenario--one in which I have but three beliefs:
> 
> 	1. Bel(p)
> 	2. Bel(q)
> 	3. Bel(~(p^q))
> 
> Surely if such a situation were to come about, you'd have no trouble
> considering me to be inconsistent.

Perhaps this is alright for small cases, but in the real world, people
knowingly hold inconsistent beliefs.  My favorite example is the one
of the proofreader.  He has just finished proofreading a 350-page book
and seen all the typos corrected.  If we ask him "Do you believe there
is a typo on page <n> of this book?" for all 350 possible values of
<n>, he will say "no" each time.

However, if we ask "Do you believe there is a typo somewhere in the
350 pages of this book?" he will answer "yes."  Inconsistent?  Yes.
So why does he hold this set of beliefs?

The best answer I could give him was that his beliefs were not a
matter of simple truth/falsity, but were a matter of degree.  Thus,
the correct questions should have been "Do you believe that there is a
one-in-three-hundred-fifty chance that there is a typo on page <n> of
this book?"  To this, I claimed, he would have answered "yes."  This
makes consistent his reply of "yes" to the final question.

That is, given that he understands probability, and that there is a
1/n chance of a typo per page in an n-page book, it is reasonable to
say that there is a typo in the book.

[Side note: he was not satisfied with this answer.  He remarked that
he did not actively consider such probabilities in his answers and, in
fact, he really had no grasp of what a one-in-three-hundred-fifty
chance meant for proofreading.  His counter-claim was that my answer
was not an explanation, simply a way to rationalize a set of beliefs
that he, the belief-holder, considered inconsistent.]


-- 
Alan Wexelblat
ARPA: WEX@MCC.COM
UUCP: {seismo, harvard, gatech, pyramid, &c.}!sally!im4u!milano!wex

"Oh well, a touch of grey,
 Kinda suits you anyway."