Yan King Yin wrote:
...
To avoid confusion we can fix it that the probability/NTV associated
with a sentence is always interpreted as the (subjective) probability
of that sentence being true.
So p( "all ravens are black" ) will become 0 whenever a single
nonblack raven is found.
If, from experience, 99% of ravens are black (maybe some are painted
white), we can assign p ( "the random raven being black" ) = 0.99.
This resolves the problem of sentence-level and sub-sentential
probabilities.
...
YKY
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.
Sentences of the form "All x are y" are quite rare. Ditto for sentences
of the form "Some x are y".
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