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prase comments on Starting point for calculating inferential distance? - Less Wrong Discussion
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One of the things I hate in mathematical textbooks are proofs left as exercises for the reader.
I would be really interested to know what conclusion you have made about inferential distance.
Jennifer is suggesting that these ideas could be used to quantify inferential distances. A first attempt might be to say that a Speaker and a Listener are separated by a large inferential distance when the Speaker has a much larger value for P(U|T) than the Listener does.
There seems to me to be something important left out, though. I take inferential distances to be about differences in the plausibility of a conclusion to different people. Even if you understand my claim perfectly (ie, you've mapped my U to the proper T) you might still consider T to be almost certainly wrong, while I consider T to be an inevitable conclusion of self-evident premises, even if it takes a long chain of inferences to get to the conclusion from the premises.
Speaking from my personal experience, when I as a listener had problems accepting a conclusion which was considered natural and perhaps obvious by the speaker, it was rarely because I misinterpreted the meaning (now I am apeaking about conclusions which I have accepted as obvious later, so that I can judge whether I understood what has been said earlier). The reason was rather that I lacked some background knowledge or thinking habits which caused my P(T) being low, not P(U|T).
You may already know this, but:
And remember, if that one doesn't strike your fancy, you can always employ one of these alternative ways for proving your result.