Peirce had a more even-handed grasp of comprehensions and extensions
than most of us have been trained to treat them, indeed, he saw them
as paired appendages of the whole body of information that a concept,
symbol, or term embodies. (02)
A "comprehension" is a set of "intensions" (properties or qualities),
while an "extension" is a set of "individuals". In his early papers
Peirce described comprehensions as "logical composites" or "products"
and extensions as "logical sums" or "aggregates", treating these two
aspects of information in a symmetric manner with neither more basic
than the other. (03)
Rich Cooper wrote:
> Quoting from Jon Awbrey's passage 18 of Peirce as posted:
> > Let us now return to the information. The information of a term
> > is the measure of its superfluous comprehension. That is to say
> > that the proper office of the comprehension is to determine the
> > extension of the term. For instance, you and I are men because
> > we possess those attributes -- having two legs, being rational,
> > &c. -- which make up the comprehension of man. Every addition
> > to the comprehension of a term lessens its extension up to a
> > certain point, after that further additions increase the
> > information instead.
> > (Peirce 1866, Lowell Lecture 7, CE 1, 466-467).
> I interpret "comprehension" in this passage as referring
> to the degree of specialization of a "term", or symbol.
> The more specialized a Thing is, with more predicates
> that have to be true of its properties and methods,
> the less general that Thing is. CSP seems to be
> saying that the more specialized a Thing is, the
> more "information" it's designation contains
> to ensure disambiguation from other Things.
> Isn't that increasing the information required to detect
> a Thing which meets the specialization constraints? What
> is that "certain point" which CSP eulogizes? Does it have
> to do with an unambiguous designation among the Things of the
> Universe of discourse? Beyond disambiguating, a designation only
> adds information? Or is there a different interpretant which CSP
> intended to designate? (04)
No, specialization is a process of determination like the one that
Peirce describes as lessening the extension of a term up to a point.
But if we add attributes to the comprehension data without narrowing
the extension beyond that fixed point, then we are adding "superfluous
comprehension", and the measure of that excess is called "information".
In contemporary terms, we speak of "information transmission" as being
related to "redundancy". (05)
inquiry list: http://stderr.org/pipermail/inquiry/
oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey (08)
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (09)