ONT Re: What Is Information That A Sign May Bear It? -- Discussion
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WIS. Discussion Note 17
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HT = Hugh Trenchard
JA = Jon Awbrey
Re: WIS Dis 16. http://suo.ieee.org/ontology/msg05346.html
Hx: WIS. http://suo.ieee.org/ontology/thrd20.html#04317
Hx: ICE. http://suo.ieee.org/ontology/thrd1.html#05274
Hugh,
I continue from where I left off, adding a clarifying line to my last paragraph.
HT: You note that Bayes theorem is akin to a "two-step fox-trot", while Peirce
is a "three-step Waltz", but all I am wondering is if there is some scope
for combining the two approaches for perhaps a yet more accurate -- or
perhaps synthesized -- measure of the information quantity in certain
situations.
JA: Okay, that was too cryptic. I was not trying to create any opposition
between Bayes and Peirce. Properly understood there's no real problem
about the statistics. Here I was talking about different models of the
inquiry process, which is a bigger issue as to how one uses statistics.
The 2-step model thinks in terms of induction and deduction, while the
3-step model adds a step up front, "abductive" hypothesis formation,
followed by deductive prediction and lastly by inductive probation.
Cf: | Awbrey & Awbrey, "Interpretation as Action: The Risk of Inquiry"
| http://www.chss.montclair.edu/inquiry/fall95/awbrey.html
HT: It seems to me you are saying the two approaches are rather incompatible.
But isn't it one of the aims of mathematicians to find grand unifying
theories, to bridge disconnected formalistic islands, ultimately so
we may see more clearly the grand platonic mathemosphere? If this
is not an aim of mathematicians, then surely it is a necessity in
order for certain things to be proven -- Andrew Wiles in proving
Fermat's theorem comes to mind (obviously among myriad other
examples.) Incidentally, it is from this broad philosophical
perspective that one such as myself can love and appreciate
mathematics without necessarily toiling through its rigours.
HT: Maybe a Peirce-Bayes synthesis is not possible -- again, I am in no
position to question your wisdom on the question, and I do not wish
to bog you down with questions that ultimately do not advance your
cause -- in which case I won't pursue the question further.
Integration can be worthwhile, but not at the risk of logical inconsistency.
Either way, it is first necessary to understand what the difference between
opinions is really about. You must understand that I initially learned my
statistics in philosophically bowdlerized kindergartens where all of the
sex and violence about subjectivist/objectivist controversy would have
been nicely expunged from the kiddie liturgy, and if there were any
mention of it at all, it would have been some passing-slighting
reference to "how confused the philosophers get themselves
about a simple matter of mathematics", or something to
that effect. So I haven't studied the history well
enough to know whether all of the opinions that
are currently eponymed on Bayes really stick.
http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Bayes.html
At any rate, Bayes lived and died a whole century before
the 19th century fights broke out that invoked his name.
I do remember reading a bit more about the 19th century battles, and I believe
that those involved Peirce on one side versus Neymann and Pearson on the other,
but I wouldn't want to swear to it without refreshing my memory and reading up
more on the history of the case. My general impression though was that it was
the SOSO ("same ole same ole") SPITN ("ships passing in the night") that often
happens when people with radically divers models of methodology get to talking
too fast past one another.
I went to the SEOP ("Stanford Encyclopedia Of Philosophy")
to see how Bayes' Rule is presented in a standard account:
http://plato.stanford.edu/entries/bayes-theorem/
SEOP requests citation of the archive entry:
| Joyce, James, "Bayes' Theorem", The Stanford Encyclopedia of Philosophy
| (Winter 2003 Edition), Edward N. Zalta (ed.), URL =
| <http://plato.stanford.edu/archives/win2003/entries/bayes-theorem/>.
This pretty much confirms my prior distribution of impressions.
I will pick up from this point after I get some more coffee.
Jon Awbrey
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http://www.cs.bsu.edu/homepages/mighty/history.html
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