SUO: RE: Logic & Programming Languages
Danny and Bill,
Basic principle: FOL is the standard logic that is used to
solve problems and derive proofs in mathematics. Therefore,
when you are using any version of mathematics, including
probability theory, you are taking advantage of FOL.
DA>Perhaps (coin-) Flipper and his species might have something like the Rev.
>Bayes' material instead of FOL as their main reasoning system?
That is possible. But that is perfectly consistent with their
also using FOL. When I use trigonometry to determine the area
of a structure, I am also taking advantage of geometry and FOL
for analyzing the original problem, deciding how to draw lines
to break it up into suitable triangles, etc.
WT>>... I can see how one can logically select an answer when
>>one result is
>>more probable than another. I just have not yet seen any logical
>>formula that
>>lets me choose between two equally probable results.
That is because there is no information that could logically
be used to increase the probability of either side of the coin
over the other. It's not a failure of logic -- it's simply
a lack of information.
Suppose I gave you a problem: use logic to determine the
date when the first living cell arose on planet earth.
If you fail to answer that question, it is not because you
aren't logical, but because you have no information to use
as the original premises and axioms for a proof.
John Sowa