From: David Hart (dhart@atlantisblue.com.au)
Date: Sun Sep 11 2005 - 22:25:19 MDT
Jeff Medina wrote:
> Because it is evidence that [all non-black objects are non-ravens]. If
> we know at least one raven exists, and sampling a non-black object
> produces a non-raven on each of N sampling events, then with
> increasing N comes increasing certainty that no non-black object is a
> raven. And [no non-black object is a raven] is, of course, logically
> and conceptually equivalent to [all ravens are black], given the tiny
> extra assumption I left out earlier that at least one raven exists.
> It's pretty clear to me that Hempel's paradox presupposes the
> existence of its referents, but if you disagree and think it's a
> sticking point, I'm happy to concede that a purple goose is only
> evidence that [all ravens are black] if and only if there exists at
> least one raven.
>
Assuming a steady rate of random sampling over time and a finite number
of objects (all objects on Earth), finding non-ravens (of any color)
certainly provides information about the relative abundance of ALL
ravens (i.e. the probability that any given sampled object is a raven),
however stating that finding non-black non-ravens increases the
probability of the hypothesis "all ravens are black" strikes me as
sample double-dipping -- only the discovery of a non-black raven could
decrease P( is_black(x) | is_raven(x) ) -- I don't see how the discovery
of any non-ravens, of any color, should increase P( is_black(x) |
is_raven(x) ), particularly given the is_raven part. Where probability
mathematics is concerned, I'm a near lay-person, so a step-wise
explanation would be good!
David
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