The second-to-last character in the last line above, just before the final "1",
comes across as "3/4" on my mail reader. What symbol was it supposed to be?
> Now why I don't like the negation constraint.
> [...]
> What is your belief that he has a lung cancer? Let it be alpha.
>
> Then he coughs. So you have ONE symptom.
>
> What is your belief now that he has a lung cancer, still alpha or a little
> larger. [...]
> But then it means that your belief that he does not have lung cancer has
> decreased (as probabilities add to 1).
>
> And thus I don't like.
> Coughing supports lung cancer, but it should not have the effect of
> reducing your belief that the man has no lung cancer (that he is anything
> but a lung cancer case).
Your belief in A increases, but you don't think your belief in (not A) should
decrease? Please explain your reasoning more fully, as such a position seems
inconsistent with deductive logic, and any system for plausible reasoning should
contain deductive logic as a special case (where there is no uncertainty).
For example, if your belief in A increases all the way to certainty that A is
true, then your belief in (not A) MUST decrease all the way to certainty that
(not A) is false, which deductive logic gives us. In a less extreme case, since
exactly one of the propositions { A, (not A) } is true, any evidence in favor of
A is evidence against (not A). To increase your belief in A without decreasing
your belief in (not A) could only be justified if you were willing to admit the
possibility that both A and (not A) could be simultaneously true, in
contradiction to deductive logic.
Thus it seems to me that you can't increase your belief in A while leaving your
belief in (not A) unchanged unless you are willing to toss aside principles of
deductive logic that have been well-established for several thousand years and
form the foundation of all mathematics humanity has developed over that period.
-- Kevin S. Van Horn