🚀 go-pugleaf

In article <2400@hoptoad.uucp> laura@hoptoad.uucp (Laura Creighton) writes:
>In article <4865@milano.UUCP> wex@milano.UUCP writes:
>>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.
>>
>>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.

Suppose each page of the book was simply a list of 100 numbers
which (should) add up to 1000.  Suppose also that the book source
was on-line and with the appropriate tools all the numbers added
by the computer and the result was 349999.  The probability of there
being an error is extremely high (say 0.999).  What do you believe is
the probability of an error on any given page?  If you say 1/350 then
the probability of an error in the book should be, according to
simple probability theory, 1-(349/350)^350 = 0.63.  If you say 10/350
(or whatever is needed to get the 0.999 figure) then the expected
number of errors greatly increases (which I think is unreasonable).

How can this paradox be resolved without admitting inconsistent
beliefs?

	Lee Naish

	lee@mulga.oz.au
	lee@munnari.oz.au
	munnari!lee@seismo.css.gov
	{seismo,mcvax,ukc,ubc-vision}!munnari!lee