On 8/11/06, Charles D Hixson <[EMAIL PROTECTED]> wrote:
> While what you say may be true, the typical sentence is of the form
> "Ravens are black". I feel that this should be interpreted as
> "Typically, ravens are black". Further information as to how reliably
> ravens are black isn't contained in the sentence, and must be derived
> exogenously. All that tells you is that you should expect a random
> raven chosen without regard to color to be black. The probability,
> without further information would be somewhere between 50.000000001% and
> 100%, presuming that you are rating your source as 100% reliable. So
> there are, at minimum, two figures of merit: 1) the proportion of
> ravens which are black, and 2) how much do you trust the accuracy of the
> information provided by this source? This is ignoring things like
> sample selection bias of all sorts, including "local data". If I see a
> swan, it will probably be white. There are very few black swans in
> California. If I lived in Australia the answer would be different.
> Then you would have globally there are more white swans, but locally
> there are more black swans. So even with a totally reliable source I
> would need to guess context.
> "Ravens are black". I feel that this should be interpreted as
> "Typically, ravens are black". Further information as to how reliably
> ravens are black isn't contained in the sentence, and must be derived
> exogenously. All that tells you is that you should expect a random
> raven chosen without regard to color to be black. The probability,
> without further information would be somewhere between 50.000000001% and
> 100%, presuming that you are rating your source as 100% reliable. So
> there are, at minimum, two figures of merit: 1) the proportion of
> ravens which are black, and 2) how much do you trust the accuracy of the
> information provided by this source? This is ignoring things like
> sample selection bias of all sorts, including "local data". If I see a
> swan, it will probably be white. There are very few black swans in
> California. If I lived in Australia the answer would be different.
> Then you would have globally there are more white swans, but locally
> there are more black swans. So even with a totally reliable source I
> would need to guess context.
"Ravens are black" is implicitly understood to be universally quantified. In everyday language, it could mean "typically ravens are black", as you suggested. However, p( "typically ravens are black" ) should be 1, because that statement is true. It is only
within that statement that some exceptional ravens are nonblack.
All I'm saying is that, the kind of uncertainty we usually care about, in the sentence "A's are B's", occurs inside the sentence. Attaching probabilities to sentences does not help in such case.
> Sentences of the form "All x are y" are quite rare. Ditto for sentences
> of the form "Some x are y".
> of the form "Some x are y".
(?) "some x are y" is quite common.
YKY
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