RE: [PEIRCE-L] Jay Zeman's existentialgraphs.com

[gnox]

John S, I've been slow responding to this (busy week behind me) ... my comments 
inserted.

 

Gary f.

 

-Original Message-
From: John F Sowa 
Sent: 30-May-17 18:17



On 5/29/2017 4:38 PM,   g...@gnusystems.ca wrote:

> 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.

 

I agree with both points.  But Peirce wrote his later (1909) version in a 
letter, not a well-edited, peer-reviewed publication.  It's not a "full scale 
revision", but it's one of the best available examples of how his views evolved 
after 1906.

[GF: ] It’s at least an example of how he presented EGs to beginners, which is 
what I’m trying to figure out these days! It seems to end quite abruptly, 
though.

 

> Are you saying that... Peirce “simplified” his system of EGs by 

> abandoning further development of the Gamma graphs and reverting to a 

> version of the Beta?

 

I don't believe that he abandoned the search for ways to represent modality -- 
just that he was still searching.  I interpret his version of 1909 as a merger 
of Alpha and Beta -- more precisely a view of Alpha as a special case of Beta 
with 0-adic relations (medads).

 

> Peirce’s “Improvement on the Gamma Graphs” (CP 4.573-84) is indeed a 

> fascinating read; Frederik Stjernfelt comments on it extensively in 

> Chapter 8 of /Natural Propositions/.

 

That's a good analysis with some important quotations.  On pp. 217, FS cites an 
EG with a "selective" (the letter S) as a replacement for a line of identity, 
but at the bottom of the page, he quotes a comment by Peirce that "three 
essential aims" of lines of identity are "missed by Selectives".

 

I agree with those points.  However, I would emphasize that selectives are a 
valuable adjunct to EGs for mappings to and from (1) variables in algebraic 
notations for logic, (2) indexicals (pronouns and other anaphoric references) 
in natural languages, and (3) formulas in modern computer databases, knowledge 
bases, and theorem provers.

[GF: ] Yes, agreed. To me, though, the iconicity of the graphs is key, because 
I’m looking for a way to use them as visual support for developing a grasp of 
Firstness/Secondness/Thirdness and related semiotic concepts.

 

In the articles and slides that I cited in my previous note, I used EGIF 
notation (Existential Graph Interchange Format), which I had designed to 
convince students *and* professional logicians that Peirce's EGs are just as 
formal and precise as any algebraic notation.

 

I have also found the selectives in EGIF helpful for explaining EG notation to 
students.  In fact, many of Peirce's English explanations would have been much 
clearer if he had used selectives to clarify which lines of an EG he was 
talking about.

 

> 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.

 

What I was trying to emphasize is that 1906 (the full year) was an intermediate 
stage in the development of EGs.  The paragraph CP 4.583 discussed options for 
future development (months or even years).

 

> 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 admit that CP 4.583 is too brief to explain what Peirce had intended, and 
it's likely that he was still working out his ideas.  For my seven points 
(copied below), I started from 1909 and worked my way back to 1906.  That's a 
variant of abduction, not induction or deduction.

 

For point #1, CP 4.583 showed that Peirce was rethinking his ideas.

His 1909 explanations showed that much of the complexity of 1906 was 
irrelevant.  His simplification of 1909 was not a "dumbing down" from 1906, but 
a more elegant version that is clearer and more general.

 

Note the theorem in point #6.  Don Roberts showed that Alpha was equivalent to 
the propositional subset of Gentzen's natural deduction.

But point #6 shows that Peirce's rules of 1909 are a generalization that goes 
beyond what Gentzen had published in 1935.  I'm sure that if Peirce had seen 
Gentzen's system, he would have proved that theorem himself.

 

> I’m also curious as to what people think of my “Rhematics” 

> posthttp://gnusystems.ca/wp/2017/05/rhematics/

> In his ‘Prolegomena to an Apology for Pragmaticism’ (1906), Peirce 

> departed still further from the traditional trichotomy:

>> A familiar logical triplet is Term, Proposition, Argument. In order 

>> to make this a division of all signs, the first two members have to 

>> be much widened.  (CP 4.538)

 

I 

Re: [PEIRCE-L] Jay Zeman's existentialgraphs.com

[John F Sowa]

On 5/29/2017 4:38 PM, g...@gnusystems.ca wrote:

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.


I agree with both points.  But Peirce wrote his later (1909) version
in a letter, not a well-edited, peer-reviewed publication.  It's not
a "full scale revision", but it's one of the best available examples
of how his views evolved after 1906.


Are you saying that... Peirce “simplified” his system of EGs by
abandoning further development of the Gamma graphs and reverting
to a version of the Beta?


I don't believe that he abandoned the search for ways to represent
modality -- just that he was still searching.  I interpret his version
of 1909 as a merger of Alpha and Beta -- more precisely a view of
Alpha as a special case of Beta with 0-adic relations (medads).

Peirce’s “Improvement on the Gamma Graphs” (CP 4.573-84) is indeed a 
fascinating read; Frederik Stjernfelt comments on it extensively in 
Chapter 8 of /Natural Propositions/. 


That's a good analysis with some important quotations.  On pp. 217,
FS cites an EG with a "selective" (the letter S) as a replacement
for a line of identity, but at the bottom of the page, he quotes a
comment by Peirce that "three essential aims" of lines of identity
are "missed by Selectives".

I agree with those points.  However, I would emphasize that selectives
are a valuable adjunct to EGs for mappings to and from (1) variables
in algebraic notations for logic, (2) indexicals (pronouns and other
anaphoric references) in natural languages, and (3) formulas in
modern computer databases, knowledge bases, and theorem provers.

In the articles and slides that I cited in my previous note, I used
EGIF notation (Existential Graph Interchange Format), which I had
designed to convince students *and* professional logicians that
Peirce's EGs are just as formal and precise as any algebraic notation.

I have also found the selectives in EGIF helpful for explaining EG
notation to students.  In fact, many of Peirce's English explanations
would have been much clearer if he had used selectives to clarify
which lines of an EG he was talking about.


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.


What I was trying to emphasize is that 1906 (the full year) was an
intermediate stage in the development of EGs.  The paragraph CP 4.583
discussed options for future development (months or even years).


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 admit that CP 4.583 is too brief to explain what Peirce had intended,
and it's likely that he was still working out his ideas.  For my seven
points (copied below), I started from 1909 and worked my way back to
1906.  That's a variant of abduction, not induction or deduction.

For point #1, CP 4.583 showed that Peirce was rethinking his ideas.
His 1909 explanations showed that much of the complexity of 1906 was
irrelevant.  His simplification of 1909 was not a "dumbing down" from
1906, but a more elegant version that is clearer and more general.

Note the theorem in point #6.  Don Roberts showed that Alpha was
equivalent to the propositional subset of Gentzen's natural deduction.
But point #6 shows that Peirce's rules of 1909 are a generalization that
goes beyond what Gentzen had published in 1935.  I'm sure that if Peirce
had seen Gentzen's system, he would have proved that theorem himself.


I’m also curious as to what people think of my “Rhematics” 
posthttp://gnusystems.ca/wp/2017/05/rhematics/
In his ‘Prolegomena to an Apology for Pragmaticism’ (1906), Peirce
departed still further from the traditional trichotomy:

A familiar logical triplet is Term, Proposition, Argument. In order
to make this a division of all signs, the first two members have to
be much widened.  (CP 4.538)


I don't believe that's a departure.  He made the point that a portrait,
by itself, is an icon.  But a portrait with a name below it, such as
"Alexander Hamilton", states a proposition:  "This resembles AH."
Note the following quotation:


By a rheme, or predicate, will here be meant a blank form of
proposition which might have resulted by striking out certain parts
of a proposition, and leaving a blank in the place of each, the
parts stricken out being such that if each blank were filled with
a proper name, a proposition (however nonsensical) would thereby
be recomposed.  (CP 4.560)


This implies that if you erase the name "Alexander Hamilton" but
keep the slot where a name should go, you have a predicate.
This illustrates a nonverbal 

RE: [PEIRCE-L] Jay Zeman's existentialgraphs.com

[gnox]

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.pd

Re: [PEIRCE-L] Jay Zeman's existentialgraphs.com

[John F Sowa]

On 5/26/2017 8:49 AM, g...@gnusystems.ca wrote:

my own site, 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 — 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

For the slides of an introduction to EGs that use Peirce's later
rules and notation, see http://www.jfsowa.com/talks/egintro.pdf

For an article that discusses all seven points above, see
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


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.

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RE: [PEIRCE-L] Jay Zeman's existentialgraphs.com

[gnox]

John, we owe you thanks for making Jay Zeman’s material on EGs accessible in 
such a complete form.

 

At one time, Zeman’s transcription of Peirce’s “Prolegomena to an Apology for 
Pragmaticism” was the only version online. Since then I’ve put one on my own 
site, http://www.gnusystems.ca/ProlegomPrag.htm, which I think improves on 
Zeman’s version in some respects, even correcting a few errors.

 

Of course your own site has some real treasures. The other day I was reading 
your contribution to the “Five Questions” collection, 
http://www.jfsowa.com/pubs/5qsigns.htm — which i highly recommend to all 
Peirceans! — and one observation you made there about Aristotle’s On 
Interpretation triggered my latest blog post that might also be of interest to 
Peirceans. I called it “Rhematics” because it focusses on Peirce’s use of the 
term “rhema” in his semiotics. It’s at 
http://gnusystems.ca/wp/2017/05/rhematics/ and includes links to your paper and 
to the “Prolegomena.” 

 

Gary f.

 

-Original Message-
From: John F Sowa [mailto:s...@bestweb.net] 
Sent: 25-May-17 11:03



On 5/22/2017 1:40 PM, Jon Awbrey wrote:

> Here is the WayBak link to   
> http://www.existentialgraphs.com/ 

>   
> http://web.archive.org/web/2016021812/http://www.existentialgraphs

> .com/

 

Thanks for finding that copy.  But some links in that copy are broken.

Starting from the first page, click on

"A Proof in" [image for theGraphs]

 

The version at web.archive.org does not contain the images for the diagrams at 
the target location.

 

But the version at the following location does have the images:

  
http://www.jfsowa.com/exgraphs/egcontrollibrary/UQElim.htm

 

If you can find other discrepancies, especially on the version at jfsowa.com, 
please let me know.

 

By the way, the version I downloaded also contained some personal photos (baby 
pictures of "Abigail", "Greg's funeral", and a farm).

But archive.org does not have them.

 

In any case, I sent the personal photos to Norma Zeman and deleted them from my 
web site.  But their absence at archive.org indicates that they did not save 
everything.

 

John


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Re: [PEIRCE-L] Jay Zeman's existentialgraphs.com

[John F Sowa]

On 5/22/2017 1:40 PM, Jon Awbrey wrote:

Here is the WayBak link to http://www.existentialgraphs.com/
http://web.archive.org/web/2016021812/http://www.existentialgraphs.com/


Thanks for finding that copy.  But some links in that copy are broken.
Starting from the first page, click on
"A Proof in" [image for theGraphs]

The version at web.archive.org does not contain the images for
the diagrams at the target location.

But the version at the following location does have the images:
http://www.jfsowa.com/exgraphs/egcontrollibrary/UQElim.htm

If you can find other discrepancies, especially on the version
at jfsowa.com, please let me know.

By the way, the version I downloaded also contained some personal
photos (baby pictures of "Abigail", "Greg's funeral", and a farm).
But archive.org does not have them.

In any case, I sent the personal photos to Norma Zeman and deleted
them from my web site.  But their absence at archive.org indicates
that they did not save everything.

John

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to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . To 
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Re: [PEIRCE-L] Jay Zeman's existentialgraphs.com

[Jon Awbrey]

Here is the WayBak link to http://www.existentialgraphs.com/

http://web.archive.org/web/2016021812/http://www.existentialgraphs.com/

Jon

On 5/22/2017 10:39 AM, John F Sowa wrote:

Jay Zeman's web site at the University of Florida is still available
at http://users.clas.ufl.edu/jzeman/

But the link to existentialgraphs.org is broken.  His wife forgot
to renew the registration.  Fortunately, I downloaded that web site.
I have now posted a copy at http://www.jfsowa.com/exgraphs

For anyone who would like to download the entire site, I packaged it
in a single ZIP file:  http://www.jfsowa.com/exgraphs/jz_eg.zip
It's less than 54 megabytes.

Since I had also downloaded Jay's site at UF, I decided to zip
it as well and post it at http:www.jfsowa.com/exgraphs/jz_uf.zip
It's less than 9 MB.

If anyone finds anything missing in those files, please let me know.

John



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