Peircers,
Just to get the ball rolling, or ping-pong-ing as the case may be,
let me refer to a couple of points from Sue's and my Inquiry paper
that came first to mind as I skimmed the Rhematics page -- I had
some trouble telling who was saying what at times so I will give
it another go later on.
I see there remains a persistent desire to parse symbols into
simpler signs like icons and indices, or to say that genuine
triadicity has its genesis in some kind of coitus between
degenerate species. I suppose bi-o-logical metaphors are
just bound to lead folks down that path, and I guess we
all fall into the sinns of simile from time to time,
but due care of our semiotic souls should keep us
from turning that error into doctrine, if we wit
what's good for us.
To be continued ...
very scattered time
and mind today ...
Regards,
Jon
On 5/29/2017 5:00 PM, Jon Awbrey wrote:
Gary, List ...
Re: http://gnusystems.ca/wp/2017/05/rhematics/
I hope to comment more fully, eventually, but the uses
to which Susan Awbrey and I turned Aristotle's passage
from De Interp can be found in our paper from 1992/1995:
* Awbrey, J.L., and Awbrey, S.M. (Autumn 1995),
“Interpretation as Action : The Risk of Inquiry”,
''Inquiry : Critical Thinking Across the Disciplines''
15(1), pp. 40–52.
Archive
https://web.archive.org/web/19970626071826/http://chss.montclair.edu/inquiry/fall95/awbrey.html
Journal
https://www.pdcnet.org/inquiryct/content/inquiryct_1995_0015_0001_0040_0052
Online
https://www.academia.edu/1266493/Interpretation_as_Action_The_Risk_of_Inquiry
* Awbrey, J.L., and Awbrey, S.M. (June 1992),
“Interpretation as Action : The Risk of Inquiry”,
''The Eleventh International Human Science Research
Conference'', Oakland University, Rochester, Michigan.
Regards,
Jon
On 5/29/2017 4:38 PM, g...@gnusystems.ca wrote:
John and list,
Peirce’s “Improvement on the Gamma Graphs” (CP 4.573-84) in indeed a
fascinating read; Frederik Stjernfelt comments on
it extensively in Chapter 8 of Natural Propositions. But according to Don
Roberts (1973, p.89), it’s from the spring
of 1906, and preceded the drafts of the “Prolegomena”, which was published
later in that year. You seem to be
reversing that chronology by including it with “further developments” in the
EGs after the Prolegomena. Anyway, what
happened to EGs after 1906 is not at all clear to me, although I’ve worked my
way through the relevant papers on your
site. Given the central role Peirce wanted them to play in his “apology for
pragmaticism,” I’m still trying to
understand this, and your list doesn’t give me many clues.
Roberts (p.92) describes the “Prolegomena” as “Peirce’s last full scale
revision of EG,” and notes that the
“tinctures” did not really solve the problems with representing modal logic
that Peirce thought he had solved in the
spring of 1906. Some of his later comments on the “Prolegomena” (included in
http://www.gnusystems.ca/ProlegomPrag.htm) are quite critical of it — one even
refers to the “tinctures” and
“heraldry” as “nonsensical” — but they don’t really say how these problems can
be solved diagrammatically. Are you
saying that his later manuscripts did solve these problems, or that Peirce
“simplified” his system of EGs by
abandoning further development of the Gamma graphs and reverting to a version
of the Beta?
For me, these questions have large implications for Peirce’s late semiotics,
phaneroscopy, Synechism, pragmaticism and
metaphysics (as he suggested at the end of his “Improvement on the Gamma
Graphs” talk (CP 4.584). I have to confess
that for me, the mapping back and forth between EGs and other diagrammatic or
algebraic systems doesn’t throw any
light on those implications. I’d appreciate any help you (or anyone) can give
toward clarifying them.
I’m also curious as to what people think of my “Rhematics” post
(http://gnusystems.ca/wp/2017/05/rhematics/) and Gary
Richmond’s comment on it, as I have a follow-up in mind …
Gary f.
-----Original Message-----
From: John F Sowa [mailto:s...@bestweb.net]
Sent: 27-May-17 22:00
To: peirce-l@list.iupui.edu
Subject: Re: [PEIRCE-L] Jay Zeman's existentialgraphs.com
On 5/26/2017 8:49 AM, <mailto:g...@gnusystems.ca> g...@gnusystems.ca wrote:
my own site, <http://www.gnusystems.ca/ProlegomPrag.htm>
http://www.gnusystems.ca/ProlegomPrag.htm, which I think
improves on Zeman’s version in some respects, even correcting a few
errors.
Yes, that looks good.
your contribution to the “Five Questions” collection,
<http://www.jfsowa.com/pubs/5qsigns.htm>
http://www.jfsowa.com/pubs/5qsigns.htm — which i highly recommend
Thanks.
For the further development of EGs, I recommend Peirce's later MSS and his
"Improvement on the Gamma Graphs", which
Jay posted on his site. (See below for an excerpt.)
The later MSS (around 1909) simplified the foundation of EGs, the rules of
inference, and the mapping to and from
algebraic notations and natural languages. Basic innovations:
1. Major simplification in the treatment of lines of identity,
ligatures, and teridentity. (See the excerpt below.)
2. Elimination of talk about cuts, recto, and verso. Instead, he
introduced shaded (negative) and unshaded (positive) areas.
3. Simplification and generalization of the rules of inference to
three pairs of rules: each pair has an insertion rule and an
erasure rule, each of which is an exact inverse of the other.
4. The same rules apply to both Alpha and Beta: therefore, there
is no need to distinguish Alpha and Beta. Any proposition in
Alpha may be treated as a medad (0-adic relation) in Beta.
5. The above innovations make Peirce's proof procedure an extension
and generalization of *both* Gentzen's natural deduction *and*
Alan Robinson's widely used method of resolution theorem proving.
6. Theorem: Every proof by resolution (in any notation for first-
order logic) can be converted to a proof by resolution with
Peirce's rules. Then by negating each step of the proof and
reversing the order, it becomes a proof by Peirce's version of
natural deduction. Finally, that proof can be systematically
converted to a proof by Gentzen's version of natural deduction.
7. Peirce's rules can be stated in a notation-independent way.
With a minor generalization, they can be applied to Peirce-
Peano notation, to Kamp's discourse representation structures,
and to any statement in English that has an exact translation
to and from Kamp's DRS.
For the details of points #1 to #6, see
<http://www.jfsowa.com/pubs/egtut.pdf> http://www.jfsowa.com/pubs/egtut.pdf
For the slides of an introduction to EGs that use Peirce's later rules and
notation, see
<http://www.jfsowa.com/talks/egintro.pdf>
http://www.jfsowa.com/talks/egintro.pdf
For an article that discusses all seven points above, see
<http://www.jfsowa.com/pubs/eg2cg.pdf>
http://www.jfsowa.com/pubs/eg2cg.pdf
For these reasons, I believe that Peirce's publications of 1906 should be
considered an intermediate stage in the
development of existential graphs. The version of 1909 is his preferred
version.
John
____________________________________________________________________
The last four sentences of CP 4.583 anticipate his later MSS on EGs:
<http://www.jfsowa.com/exgraphs/peirceoneg/improvement_on_the_gamma_Graphs.htm>
http://www.jfsowa.com/exgraphs/peirceoneg/improvement_on_the_gamma_Graphs.htm
Since no perfectly determinate proposition is possible, there is one more
reform that needs to be made in the system
of existential graphs.
Namely, the line of identity must be totally abolished, or rather must be
understood quite differently. We must
hereafter understand it to be potentially the graph of teridentity by which
means there always will virtually be at
least one loose end in every graph. In fact, it will not be truly a graph of
teridentity but a graph of indefinitely
multiple identity. (CP 4.583, 1906)
Note by JFS: I interpret the last sentence to imply that a line of (single)
identity and a ligature of several lines
are both treated as "a graph of indefinitely multiple identity."
That would simplify the mapping from an existential graph to other versions of
logic, including Peirce-Peano algebra
or Kamp's DRS notation.
--
inquiry into inquiry: https://inquiryintoinquiry.com/
academia: https://independent.academia.edu/JonAwbrey
oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey
isw: http://intersci.ss.uci.edu/wiki/index.php/JLA
facebook page: https://www.facebook.com/JonnyCache
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