ONT Re: What Is Information That A Sign May Bear It? -- Discussion
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WIS. Discussion Note 18
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HT = Hugh Trenchard
Re: WIS Dis 17. http://suo.ieee.org/ontology/msg05347.html
Hx: WIS. http://suo.ieee.org/ontology/thrd20.html#04317
Hx: ICE. http://suo.ieee.org/ontology/thrd1.html#05274
HT: Hi Jon. Thanks for these comments. I see even by email,
our various invisible moods can be made apparent. I hope
you will have taken this exchange re: Bayes in the spirit
of my inquiry, which was that of a student to his teacher.
One mood ring to rule them all ...
I'm afraid we're all students on this bus ...
But you have piqued my interest in the true history of it all,
as I can see that the snatches of historical gossip I picked up
in my stats and quantitative methods courses amounted to little
more than random smattergrams of representative points selected
from various traditions without all that much care paid to the
actual time series of influences. Still, I think that I got
enough data to recognize some familiar trends well enough.
HT: As you know my inquiry was ultimately about measures of information,
and whether Bayes' theorem is at least complementary, if not logically
consistent, with the description/quantification of information as stated
by Peirce.
Just from what I know in my current state of information, I can't see
how Peirce would do anything but accept Bayes' theorem as a theorem.
The question is not with the validity of this piece of deduction.
The question is how deductive truths fit into the larger process
of empirical inquiry, otherwise known as the "logic of science".
You cannot acquire and develop experience-based knowledge by
deductive means alone. As a theorem, Bayes' Rule falls out
immediately from the standard definition of a conditional
probability. As far as its status as a theorem goes,
it's just an abstract truth. Like any other theorem,
it has no particular bearing on experience until
someone brings it to bear on experience in
a particular way. Now, what way is that?
Specifically, by what form of reasoning
is the deductive truth brought to bear
on a question of empirical concern?
To express the question more concretely, where do we get
the notion that knowing Prob(D_i | S_j), the probability
of Demon_i given Sindrome_j, tells us one whit about the
patient or penitent presenting with the condition S_j?
We get that notion from a very complex piece of approximate, fallible,
inexact, non-deductive, or non-demonstrative reasoning. It involves
the idea that our Patient x is a member of a Population X, and that
we have information of a generally applicable, if approximate and
fallible sort about any member of Population X by virtue of the
fact that we have fairly sampled Population X and computed an
estimate of Prob(D_i | S_j) for this population. That's how
we apply the abstract theorem to an empirical case, and any
application of this kind is eminently risky, never exact.
HT: In addition to the acquisition of knowledge, sometimes all
a student seeks is the simplest of phrases: "Well, gee,
that's actually a good idea, but ..."
Gee, I thought I said that already ...
HT: In any event, just to "put you on notice" as they say, I may have some
questions regarding the compatibility of Peirce and quantum information!
I consider it noticed.
Jon Awbrey
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http://www.cs.bsu.edu/homepages/mighty/history.html
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