Re: [PEIRCE-L] Modal EGs in Delta vs. Gamma

[John F Sowa]

Jon, List,

Since your article has just been accepted for publication, you probably still 
have time to make a few corrections.  Following are some suggestions.

JAS:   Indeed, given that Peirce already had a notation for metalanguage in his 
1903 Gamma EGs--in fact, five years earlier--how could that be what he had in 
mind for the new Delta part that he added in 1911? What exactly are you 
proposing to add that goes beyond the dotted (or thinly drawn) oval and line 
for asserting propositions about propositions?

What must be added is all of L376.  More would be better, but we can look to 
the future to see what is needed.  More precisely, Peirce had a notation for 
metalanguage in 1898, which is simpler and does not need the useless baggage of 
Gamma graphs.  There is no need for them when you adopt the notation for 
metalanguage.  But metalanguage, by itself, is not sufficient for a proof of 
pragmatism.  There is an open-ended variety of ways for using metalanguage.

I also copied page 340r from the logic notebook (see attached).  Please note 
that EGs that refer to "circumstances" can be translated to ordinary statements 
in Peirce's algebraic notion for first-order logic.  There is nothing special 
about circumstances, by themselves, that makes them modal.  You should make 
that correction in your article.

Did you read the Wikipedia article about Arthur Cayley and the comments about 
Risteen in EP2?  Those topics would explain why Delta graphs (as described in 
L376) have much more structure than just a notation for metalanguage.  Peirce 
used that structure to support a phemic sheet that has multiple "papers".   And 
the remainder of L376 describes how they may be used in an "investigation".  
That is necessary to support a logic of pragmatism.

That additional structure is what makes Delta graphs the fourth kind of logic 
that goes beyond Gamma graphs.  I suggest that you include all of L376 in an 
appendix to your article.  That is what I'm doing.

In summary, Peirce was years ahead of his time, and it's essential to give him 
full credit for his accomplishments.  It would be insulting to claim that he 
didn't realize that his logic of 1892, by itself, was sufficient.

And by the way, when you make these additions to your article, you can include 
an acknowledgment to thank me for all this help in explaining what Peirce was 
doing.

John


From: "Jon Alan Schmidt" 

John, List:

JFS: If Peirce thought that the notations for his Gamma graphs of 1903 were 
adequate to represent everything in Delta graphs, why did he claim that the he 
needed to add a fourth part to his system of EGs?

If the Gamma EGs of 1903 were adequate to represent metalanguage (as I have 
demonstrated), then why would Peirce need to add a new Delta part for that 
purpose in 1911?

JFS: In your diagram below, the row of four EGs on the left represent pure 
first-order predicate calculus. Any sentences outside of the EGs (whether in 
English or EGs or some other notation) do nothing to change those sentences 
from FOL to any version of modal logic. They are pure, unadulterated FOL.

No, I have refuted this claim repeatedly. There is a fundamental semiotic 
difference between describing indefinite individuals (lines of identity) with 
general concepts (names) and describing possible states of things (lines of 
compossibility) with propositions (letters). The additional axioms of modal 
propositional logic do not translate into valid theorems of first-order 
predicate logic as implemented by Beta EGs, and there are no counterparts in 
the latter for iterated modalities and propositions that are actually true 
instead of possibly true (analogous to existentially quantified) or necessarily 
true (analogous to universally quantified).

JFS: In short, that thin line attached to an oval is Peirce's 1898 notation for 
metalanguage--five years before the Gamma graphs.

I agree with you about that. I thanked you for correcting my mistake (and 
Ketner's) in misreading the thin line in the second EG on RLT 151 as part of 
the cursive "i" in the rheme "is false." I brought to your attention Peirce's 
slight revision of that 1898 notation in 1903, only changing from the thinly 
drawn oval and line to the dotted oval and line, presumably to distinguish them 
from the thinly drawn lines that still represented cuts at that time. I suppose 
that it makes little difference once shading replaces cuts, but I prefer the 
dotted oval and line to minimize the potential for confusion.

JFS: The metalanguage of 1898 combined with EGs that contain symbols such as 
"possibly true" in a verb phrase does represent modality.

Exactly! That is why it is very unlikely that Peirce had this in mind when he 
said in 1911 that he needed to add a new Delta part "in order to deal with 
modals."

JAS:  As I have spelled out in a soon-to-be-published paper, "Peirce and Modal 
Logic: Delta Existential Graphs and Pragmaticism" ...

Re: [PEIRCE-L] Peirce's Letter to Risteen (was Higher-Order Logics)

[Jerry LR Chandler]

John:

> On Mar 13, 2024, at 4:24 PM, Gary Richmond  wrote:
> 
> JFS: Once again, Peirce's logic is at the forefront of 21st C developments.

While in one sense, I agree with your ascertain, but probably for different 
reasons.

The question is, what aspects of “21st C developments” are you referring to?

Cheers

Jerry

_ _ _ _ _ _ _ _ _ _
ARISBE: THE PEIRCE GATEWAY is now at 
https://cspeirce.com  and, just as well, at 
https://www.cspeirce.com .  It'll take a while to repair / update all the links!
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON 
PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . 
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu 
with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the 
body.  More at https://list.iupui.edu/sympa/help/user-signoff.html .
► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and 
co-managed by him and Ben Udell.

Re: [PEIRCE-L] Modal EGs in Delta vs. Gamma

[Jon Alan Schmidt]

John, List:

JFS: Since your article has just been accepted for publication, you
probably still have time to make a few corrections.


Actually, my paper was accepted for publication (after review and revision)
six months ago, and I see no need to correct anything at this point
anyway--I stand by everything that I wrote in it.

JFS: More precisely, Peirce had a notation for metalanguage in 1898, which
is simpler and does not need the useless baggage of Gamma graphs.


Simpler than what? Peirce explicitly incorporated the 1898 notation for
metalanguage into Gamma EGs in 1903, only changing the oval/line from
thinly drawn to dotted. Consequently, any EG with that notation is a Gamma
EG.

JFS: But metalanguage, by itself, is not sufficient for a proof of
pragmatism. There is an open-ended variety of ways for using metalanguage.


Peirce never states nor implies in R L376 that he needs to add a Delta part
to EGs in order to use metalanguage or provide a proof of pragmatism.
Instead, he says that he needs to add a Delta part to EGs "in order to deal
with modals," i.e., he needs a new notation for representing and reasoning
about propositions involving possibility or necessity to replace the
unsatisfactory (broken) cuts of 1903 and the nonsensical tinctures of 1906.
Accordingly, ascribing any other purpose whatsoever to Delta EGs is utterly
unwarranted. As you stated not long ago, "Any attempt to say anything
beyond what Peirce wrote is an opinion of the person who does the writing.
... Nobody can claim that their opinion is what Peirce intended" (
https://list.iupui.edu/sympa/arc/peirce-l/2024-01/msg00098.html).

JFS: Please note that EGs that refer to "circumstances" can be translated
to ordinary statements in Peirce's algebraic notion for first-order logic.
There is nothing special about circumstances, by themselves, that makes
them modal.


As I have explained repeatedly, the EGs scribed on R 339:[340r] *cannot *be
properly interpreted as Beta EGs. The heavy lines for "circumstances" or
"times" do not denote indefinite individuals, they represent possible
states of things--*exactly *what is needed for modal logic but missing from
previous versions of EGs. The attached letters "p" and "q" do not denote
general concepts being attributed to individuals, they denote propositions
that would be true in those possible states of things--i.e., *modal
*propositions.
The additional modal axioms added to classical propositional logic do not
correspond to valid theorems in first-order predicate logic as implemented
with Beta EGs. There are no counterparts in the latter for propositions
that are non-modal (no attached heavy lines) or that include iterated
modalities (multiple attached heavy lines).

JFS: Those topics would explain why Delta graphs (as described in L376)
have much more structure than just a notation for metalanguage. Peirce used
that structure to support a phemic sheet that has multiple "papers".


Nothing in the extant 19 pages of R L376 *describes *Delta EGs. Everything
in that letter is applicable to the other three parts, as confirmed by your
ongoing refusal/inability to provide any exact quotations from it to the
contrary, despite my repeated requests. The "many papers" are neither new
nor unique to Delta EGs--they correspond to different *subjects *that
attract "the common attention" of the utterer and interpreter at different
times, such that the collection of *all *of them represents the
*entire *universe
of discourse. Accordingly, nothing precludes them from being employed with
Alpha, Beta, and Gamma EGs; in fact, Peirce was simply reiterating in 1911
what he had already written previously (R 280, c. 1905; CP 4.561n, 1908;
https://list.iupui.edu/sympa/arc/peirce-l/2024-03/msg4.html).

JFS: And the remainder of L376 describes how they may be used in an
"investigation". That is necessary to support a logic of pragmatism.


Why did you put "investigation" in quotation marks? That word never appears
in R L376. Can you provide an exact quotation from that letter where Peirce
describes how the "many papers" may be used in an "investigation"? I am not
seeing it.

JFS: That additional structure is what makes Delta graphs the fourth kind
of logic that goes beyond Gamma graphs.


You say that as if you somehow know *exactly *what Peirce had in mind for
Delta graphs. Perhaps you meant to say, "That additional structure is what
would make my [John Sowa's] candidate for Delta graphs the fourth kind of
logic that goes beyond Gamma graphs." Even so, as I already pointed out,
the "many papers" are equally applicable to Alpha, Beta, and Gamma EGs;
there is nothing about them that specifically deals with modals or would
otherwise be unique to Delta EGs.

JFS: And by the way, when you make these additions to your article, you can
include an acknowledgment to thank me for all this help in explaining what
Peirce was doing.


I am glad to see that you are maintaining a sense of humor. Again, I have
appreciated the 

Re: [PEIRCE-L] Logical Content of Graphical Signs (was Higher-Order Logics)

[Jerry LR Chandler]

Jon, John:



> On Mar 12, 2024, at 4:59 PM, Jon Alan Schmidt  
> wrote:
> 
> Jerry, List:
> 
> Your questions as posed are extremely general, and their answers depend 
> heavily on the particular context of interest.

Human reasoning is as general or as specific as the situation warrants in the 
mind of an author.

> 
> Peirce assigns specific logical content to certain signs in his Existential 
> Graphs (EGs) and develops the transformation rules for them accordingly.

Assigns?  Ascribes?  Arranges? Asserts?  Abduces? Induces? Relates? Infers? 
Implies? Identifies? Terms?  Terminals? Etc etc etc. 
How many possible semantic terms can be related to the supporting text?


> In all parts, the blank sheet represents the universe of discourse, graphs 
> scribed on it represent propositions that are asserted as true in that 
> universe, juxtaposition represents coexistence in that universe (conjunction),

Conjunction? Or Adjacency? Or Positions?  Or co-positions? Or simply arranges?  
Do these terms all have the same meaning in any two universes of discourse? 
How would you describe the differential meanings in discourse A contrasted 
negatively with B?  …positively with B?

> and a scroll (double cut or ring-shaped shaded area) represents a consequence 
> (material implication) from which a single cut or shaded area is derived as 
> representing negation (implication of falsity/absurdity). In the Beta part, 
> heavy lines of identity denote indefinite individuals and attached names 
> denote general concepts being attributed to those individuals.
Can anyone ascribe any identity to any heavy line based on its terms?
What is the meaning of the profound semantic term “constraint” and how does it 
apply to a heavy line in discourse A relative to the natural constraints in 
discourse B? 

Obviously, I could continue to ask a vast range of interrogatory ‘who, what 
when where why and how questions.

Hopefully, the readers of this message will explore the meanings of such 
questions AS THEY APPLY to semes (thoughts) of various tokens, types, and 
tones.  In particular, one can ask how such questions apply to the logics of 
the sciences (discourse A) and how they might apply to literary narratives 
(Discourse B).

How can anyone find such conjectures compelling?

Cheers

Jerry   



> In the Gamma part, there are various additional signs for various purposes, 
> such as the broken cut for possible falsity (modal logic), the heavy line 
> with dotted lines along both sides for quantifying predicates (second-order 
> logic), and the dotted oval for treating a proposition as a subject that 
> fills the blank in a rheme attached to the oval by a dotted line 
> (metalanguage).


> 
> As I keep emphasizing, we cannot know for sure what Peirce had in mind for 
> the Delta part, other than that it would "deal with modals," unless and until 
> new manuscript evidence turns up, such as the missing pages of R L376. My 
> hypothesis is that he was considering a new notation for representing and 
> reasoning about modal propositions involving possibility or necessity, such 
> as the one that he introduces in his Logic Notebook (R 339:[340r], 1909 Jan 
> 7). In that case, heavy lines represent "circumstances" or "times"--more 
> formally, possible states of things (PSTs)--and attached letters represent 
> propositions that would be true under those circumstances, at those times, or 
> in those PSTs. The transformation rules for these "lines of compossibility" 
> (my term) are different from the ones for the "lines of identity" (Peirce's 
> term) in the Beta part because of the obvious and fundamental semiotic 
> difference between describing things with names (rhemes/semes) and describing 
> states of things with propositions (dicisigns/phemes).
> 
> Regards,
> 
> Jon Alan Schmidt - Olathe, Kansas, USA
> Structural Engineer, Synechist Philosopher, Lutheran Christian
> www.LinkedIn.com/in/JonAlanSchmidt 
>  / twitter.com/JonAlanSchmidt 
> 
> On Tue, Mar 12, 2024 at 8:01 AM Jerry LR Chandler 
> mailto:jerry_lr_chand...@icloud.com>> wrote:
>> Jon, John, List:
>> 
>> The attempts to interpret the on going discussions leads to simple questions 
>> about meaning of symbols and logics. 
>> 
>> Given a graphic object, how does one decipher the logical content of it? 
>> 
>> What types of semantics can be associated with what types of visual 
>> distinctions?
>> 
>> How many distinctions are to be associated with a graphic object? And how 
>> are these distinctions associated with the forms embodied in the objects 
>> with logical premises OF ANY ORDER?
>> 
>> I pose these questions because as the discussion unfolds into the vast 
>> richness of modal logics within the modern forms of symbolic logics, the 
>> roles of individual minds in expressing semes appears to become dominant.   
>> In other words, the boundaries between symbols and icons seems to 
>> disapp

Re: [PEIRCE-L] Modal EGs in Delta vs. Gamma

[John F Sowa]

Jon, List,

Before I read your note below, I had just sent an off-list note to you and Gary 
R. to recommend that you make very important revisions to your article.   It's 
a pity that you had sent the article to the publisher so long ago.  It's 
probably too late to stop the publication and make the necessary revisions.

Basic point:  Peirce added the notation for metalanguage to EGs in 1898 (RLT).  
That is 5 years before the Gamma graphs of 1903.  That addition is sufficient 
to support modality.  It makes the modal features of Gamma graphs irrelevant.

But modality alone is not sufficient for a proof of pragmatism (a major goal of 
Peirce's last decade). Metalanguage is a prerequisite, but much more is 
necessary.  I have been urging you (and other subscribers to P-list) to read 
the developments of the IKRIS project of 2004 to 2006, which uses a 
metalanguage feature added to the ISO standard for Common Logic.  See 
https://jfsowa.com/ikl .

I was just one of a committee of 9 who defined the IKL logic.  But that logic, 
by itself, was not sufficient to support the major developments needed for a 
proof of pragmatism.  The critical additions are closely related to what Peirce 
specified in L376.  I call that material a specification of Delta graphs.  I 
don't care what you call it.  The specifications are important.  The names are 
irrelevant.

Allan Risteen was also highly influential in discussing the issues with Peirce 
before he started to write L376. Please read the references to Risteen in EP2 
-- they're all listed in the index.  And one of Risteen's areas of expertise 
was his study of the mathematics by Arthur Cayley (see his Wikipedia page).

I realize that you insist in ignoring everything but the first two paragraphs 
of L376.  I believe that is a serious mistake.  You are deliberately putting 
blinders on your eyes.  I think that we can all agree that it's unwise to 
reject anything Peirce wrote just because of some preconceived notion that it's 
irrelevant.

I have a strong background in mathematics and logic and their applications to 
computer systems.  By working with a logic similar to the one Peirce developed 
(IKL), I learned how such a logic is important for scientific and engineering 
applications.  The IKRIS project is an important example.  That is one reason 
why I have been so enthusiastic about L376.  Modern technology is more 
advanced, but the principles of pragmatism are just as important.

In summary, the specifications in L376, supplemented with R514, L231, and the 
kinds of topics Peirce would have discussed with Risteen, are essential for a 
proof of pragmatism.  The iKRIS project of 2004-2006 shows the value of a very 
similar logic, but much more is needed beyond the metalanguage   Peirce knew 
that, and the full IKRIS project (much more than just the logic) demonstrated 
that.  What you or Peirce or I may call it is irrelevant.

John


From: "Jon Alan Schmidt" 

Subject: Re: [PEIRCE-L] Modal EGs in Delta vs. Gamma

John, List:

JFS: Since your article has just been accepted for publication, you probably 
still have time to make a few corrections.

Actually, my paper was accepted for publication (after review and revision) six 
months ago, and I see no need to correct anything at this point anyway--I stand 
by everything that I wrote in it.

JFS: More precisely, Peirce had a notation for metalanguage in 1898, which is 
simpler and does not need the useless baggage of Gamma graphs.

Simpler than what? Peirce explicitly incorporated the 1898 notation for 
metalanguage into Gamma EGs in 1903, only changing the oval/line from thinly 
drawn to dotted. Consequently, any EG with that notation is a Gamma EG.

JFS: But metalanguage, by itself, is not sufficient for a proof of pragmatism. 
There is an open-ended variety of ways for using metalanguage.

Peirce never states nor implies in R L376 that he needs to add a Delta part to 
EGs in order to use metalanguage or provide a proof of pragmatism. Instead, he 
says that he needs to add a Delta part to EGs "in order to deal with modals," 
i.e., he needs a new notation for representing and reasoning about propositions 
involving possibility or necessity to replace the unsatisfactory (broken) cuts 
of 1903 and the nonsensical tinctures of 1906. Accordingly, ascribing any other 
purpose whatsoever to Delta EGs is utterly unwarranted. As you stated not long 
ago, "Any attempt to say anything beyond what Peirce wrote is an opinion of the 
person who does the writing. ... Nobody can claim that their opinion is what 
Peirce intended" 
(https://list.iupui.edu/sympa/arc/peirce-l/2024-01/msg00098.html).

JFS: Please note that EGs that refer to "circumstances" can be translated to 
ordinary statements in Peirce's algebraic notion for first-order logic. There 
is nothing special about circumstances, by themselves, that makes them modal.

As I have explained repeatedly, the EGs scribed on R 339:[340r] c