On 10/11/06, Alberto Monteiro <[EMAIL PROTECTED]> wrote:
.....
He does. Because of the omniintelligence hypothesis, each native
can reason like this:
(a) If there is only one blue dotted native, then, seeing that
everybody else is red dotted, this native will commit ritual
suicide in the first night.
Induction Hypothesis:
(b) Suppose that there are (N+1) blue dotted natives. Then, each
of these natives, noticing that the other (N) blue dotted natives
didn't commit suicide in the N-th night, will commit ritual
suicide in the (N+1)-th night
The naturalist provides information because he starts the process,
by forcing step (a) of the induction.
Alberto Monteiro
This is basically my conclusion as well. I put it differently, though:
with the outsider's pronouncement, each native can know reason about
the beliefs of each of the others. While it is true that the outsider
provides no new information about the physical situation to each blue
dot, each blue dot now knows something new: that each native *must*
believe there to be at least one blue dot, because the stranger told
them all so, where before each blue dot could believe that they
themself were red and the other blue dot ignorant of their status.
With this forcing of belief, the induction argument becomes operative.
~maru
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