Thread:
SJ:http://permalink.gmane.org/gmane.science.philosophy.peirce/16086
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/16087
JLRC:http://permalink.gmane.org/gmane.science.philosophy.peirce/16089
JBD:http://permalink.gmane.org/gmane.science.philosophy.peirce/16090
JLRC:http://permalink.gmane.org/gmane.science.philosophy.peirce/16091
HR:http://permalink.gmane.org/gmane.science.philosophy.peirce/16092
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/16093
HR:http://permalink.gmane.org/gmane.science.philosophy.peirce/16094
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/16095
HR:http://permalink.gmane.org/gmane.science.philosophy.peirce/16098
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/16099
HR:http://permalink.gmane.org/gmane.science.philosophy.peirce/16100
AM:http://permalink.gmane.org/gmane.science.philosophy.peirce/16107
JLRC:http://permalink.gmane.org/gmane.science.philosophy.peirce/16109
JC:http://permalink.gmane.org/gmane.science.philosophy.peirce/16112
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/16114
Dr. Mani, List,
I have commented from time to time in several places about
a type of triadic relation that can be seen lurking behind
fuzzy logics and fuzzy sets, linking the world of fuzzy with
dominant themes in Peirce's theories of information, inquiry,
and signs.
Here's a typical comment from the FOM list that I reposted on my blog:
1. http://inquiryintoinquiry.com/2012/11/27/fuzzy-sets-and-triadic-relations/
Triadic Relations, Intentions, Fuzzy Subsets : 1 Posted on November 27, 2012
by Jon Awbrey
Re: Lotfi Zadeh
Way back during my first foundational crisis (1967–1972), I had been willing to
consider almost any alternatives to
the usual set theories, so I can remember looking at early accounts of fuzzy
set theory. There was in addition a link
to certain issues that came up in my studies of C.S. Peirce, especially the
idea that many of the dyadic relations we
use in logic, mathematics, and semantics — typically functions that assign
meanings and values to symbols and
expressions — are better understood if taken in the context of triadic
relations that serve to complete and
generalize them.
My line of thought went a bit like this:
Consider a fuzzy set as a triadic relation of the form x ∈r S among an element
x,
a degree of membership r, and a set S.
Ask yourself: Where do these assigned degrees of membership come from? Imagine
that they come from averaging the
results of many judges making binary {0, 1} = {Out, In} = {∉, ∈} decisions.
Now consider the more fundamental triadic relation from which this data is
derived, the relation of the form x ∈j S
that exists among an element x, an interpreter (judge, observer, user) j, and a
set S.
That formulates fuzzy sets in a way that links up with many Peircean themes.
I added a bit more exposition here:
2.
http://inquiryintoinquiry.com/2012/12/07/triadic-relations-intentions-fuzzy-subsets-2/
3.
http://inquiryintoinquiry.com/2012/12/07/triadic-relations-intentions-fuzzy-subsets-3/
We also had some discussion on the Peirce List. Here are my blog re-posts:
a.
http://inquiryintoinquiry.com/2012/12/06/triadic-relations-intentions-fuzzy-subsets-%E2%80%A2-discussion-1/
b.
http://inquiryintoinquiry.com/2012/12/08/triadic-relations-intentions-fuzzy-subsets-%E2%80%A2-discussion-2/
c.
http://inquiryintoinquiry.com/2012/12/09/triadic-relations-intentions-fuzzy-subsets-%E2%80%A2-discussion-3/
Regards,
Jon
On 4/6/2015 4:06 PM, A. Mani wrote:
On Sat, Apr 4, 2015 at 6:06 PM, Jon Awbrey <jawb...@att.net> wrote:
From a mathematical point of view, an "entropy" or "uncertainty" measure is
simply a measure on distributions that
achieves its maximum when the distribution is uniform. It is thus a measure of
dispersion or uniformity.
Measures like these can be applied to distributions that arise in any given
domain of phenomena, in which case they
have various specialized meanings and implications.
When it comes to applications in communication and inquiry, the information of
a sign or message is measured by its
power to reduce uncertainty.
The following essay may be useful to some listers:
http://intersci.ss.uci.edu/wiki/index.php/Semiotic_Information
Adding to the discussion
"entropy" has been extended to neighbourhood systems, granulations with the
intent of capturing roughness and
information uncertainty in rough set theory. There are extensions to fuzzy sets
as well. These measures essentially
contribute to specific perspectives of understanding the ontology of
information semantics relative the systems
The measures implicitly assume a frequentist position - the probabilistic
connections are not good enough. When fuzzy
granulations are used, then the interpretation (by analogy with probabilistic
idealisation) breaks down further.
Regards
A. Mani
Prof(Miss) A. Mani CU, ASL, AMS, ISRS, CLC, CMS HomePage:
http://www.logicamani.in Blog:
http://logicamani.blogspot.in/ http://about.me/logicamani
sip:girlprofes...@ekiga.net
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