From: Russell Wallace (russell.wallace@gmail.com)
Date: Thu Sep 15 2005 - 14:11:54 MDT
On 9/15/05, Eliezer S. Yudkowsky <sentience@pobox.com> wrote:
>
> Actually, I also need to specify that at least one nonblack object is
> known to exist in every possible world; along with the requirement that,
> in at least one possible world containing nonblack ravens, the ratio of
> these nonblack ravens to all other nonblack objects does not approach
> zero; and the requirement that the proposition "All ravens are black"
> not initially have prior probability equal to zero; in order for my
> general conclusion to hold that randomly sampling a nonblack object and
> finding it to be a nonraven ALWAYS increases the probability assigned to
> the proposition "All ravens are black." (Assuming I haven't missed any
> other necessary assumptions.)
>
You also need to assume the world has no structure.
Suppose in real life you looked around at random, saw a white speck, and on
closer inspection found it to be a white crow. That's a nonblack nonraven,
but it would actually count as strong evidence _against_ the proposition
that all ravens are black: crows and ravens are closely related, and if the
one species can produce the occasional albino, the other probably can too.
- Russell
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