ONT Re: What Is Information That A Sign May Bear It? -- Discussion
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WIS Discussion. Note 14
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HT = Hugh Trenchard
JA = Jon Awbrey
Hugh,
Reading over the last couple of exchanges again, I see that
there are a few bits of the Big Picture that I ought to try
and throw some extra light on, at least as I see it, before
declaiming any more of the Peircean Chorus.
The way I was taught Bayes' Rule, it's no big deal, really
just a bit of formula cranking that falls off the logic of
the only sensible definition of conditional probabilities.
In the terms of art that Peirce adopted and adapted from
Kant, Bayes' Rule is a purely "analytic", deductive, or
explicative trick, but it makes no trump when it comes
to supplying any sort of "ampliative," empirical, or
synthetic assist, that is, it does not give you one
bit more of new information than you already have.
This is a thing that a lot of people do not discover until
they take the slick textbook examples into the field, say,
real-life epidemiology or life-and-death medical practice.
But the Big Picture behind this vignette asks the question:
What is the character -- as distinct from the caricature --
of the sort of inquiry that really gives us real knowledge?
And by that I mean the sort of belief systems that most of
us would 'choose' to bet our lives on in actual practice.
Will have to be a bit intermittent over the weekend,
but will make some effort to stay focussed on that.
Jon Awbrey
HT: I just wanted to come back to WIS note 2 for a moment.
I had hoped to follow up on some of your responses to
questions I had, but something else occurred to me today
as I was reading von Baeyer's book, 'Information', over
my lunch hour today. At a number of points in the book
he discusses Bayesian probabilities. I took a few moments
to look into some more details about Bayesian probabilities
on the internet as well.
HT: My question is with respect to the point below where you
discuss compound uncertainty, and my question following in
which I ask whether we should account for the fact that once
a first choice is made, the line tracing compound uncertainty
follows from that point forward only, and that the overall
compound uncertainty is no longer derived from the initial
state of things.
HT: I do not pretend to understand Bayesian probabilities,
especially on a cursory review (and even after thorough
study I'm sure I would still be scratching my head) and
I suspect you have already given much thought to this.
HT: But in general principle, do we need, right from the start,
to factor the probability of a single choice among the four
possibilities in your scenario, the making of which serves
to increase the information quantity at the next step (e.g.
by Bayesian analysis)? If we do, then does this affect the
quantity of compound uncertainty (in your scenario it is 8)?
I have a hunch that it does, but it is only a hunch.
HT: I know you say that you are establishing only a basic analysis
at this point and that for a thorough analysis you could consider
aspects of game theory, but I am wondering if there is something
fundamental that must be considered in terms of probabilities --
something that affects the very principle you are espousing.
HT: Anyway, as I mentioned earlier, I'll take a more thorough
look at your more recent postings over the next few days.
JA: The way I look at things there are real situations
and then there are formal models and theories that
we use, or try to use, to deal with real situations.
JA: Real situations are the real-live scenarios that
we find ourselves cast into somewhat willy-nilly.
There is nothing that says any one real situation
will be one bit like the last one or the next one.
Still, it pays to look for patterns in the action
that can be recognized from one scene to another.
JA: Transacting between "domains of reality" (DOR's)
and "domains of models and theories" (DOMAT's) is
the business of "empirical scientific inference"
(ESI? -- well, no, not very often), which we all
learned some bits about under the venerable head
of "scientific method", but whose principles are
also found in everyday reasoning -- when it works --
so let's unite them under the name of "inquiry".
JA: Whenever we go to lay some DOMAT before some DOR,
there are always assumptions involved in the act,
for starters, that what walks through the DOR is
the sort of thing that was foreseen in the weave
of the DOMAT.
JA: The whole of "probability and statistics" (PAS)
is just another DOMAT that we use to deal with
whatever Nature sends through one of its DOR's,
not just one of the DOR's that is known to us,
but it does not anticipate more than it does,
nor can it dictate what Nature will do next,
nor can it ease our transactions with DOR's
the semblance of which nobody anticipated
in laying out its underlying assumptions.
JA: At any rate, this is how it looks from the long view --
it may be a while before I get back to the close-ups.
JA: One of the themes that I hoped to illustrate with my story of uncertainty
was that concepts, like the concepts of information and now probability,
are more or less complex intellectual instruments that are evolved by
nature and developed by us to their own proper ends, but like many
other forms of complex organization, concepts can have their life,
make their sense, and have their utility only under the requisite
conditions of use, and they fail to have even the token warranty
that they normally have, when those conditions are not in force.
JA: To get a sense of the sort of set-up that has to be put in place,
or that's assumed to be already in place, before the usual array
of concepts from probability theory can even begin to make sense,
you might well look into the first few pages of a standard text,
for instance, the work that I append a few excerpts from below.
PAS. Probability And Statistics
01. http://suo.ieee.org/ontology/msg04885.html
02. http://suo.ieee.org/ontology/msg04886.html
03. http://suo.ieee.org/ontology/msg04887.html
04. http://suo.ieee.org/ontology/msg04888.html
The above material is excerpted from:
| Hoel, P.G., Port, S.C., & Stone, C.J.,
|'Introduction to Probability Theory',
| Houghton Mifflin, Boston, MA, 1971.
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http://www.cs.bsu.edu/homepages/mighty/history.html
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