22 Feb
2024
22 Feb
'24
9:57 p.m.
Jon, List
I am now busy preparing slides for a Zoom talk on Feb 28, sponsored by Ontolog Forum.
(I'll forward a copy of the announcement to P-List, if anyone is interested.) But
first, I'll respond to some of your doubts.
JFS> The entire letter L376 is about Delta graphs and applications of Delta graphs.
JAS> This conjecture is quite a leap, considering that--as you acknowledged--Peirce
mentions Delta exactly once in that entire 19-page letter, which he left unfinished...
The primary subject of L376 is Delta graphs. That is the only interpretation that unifies
every part. In the following excerpt from L376, the word 'here' refers to the
content of L376. For emphasis, certain passages in this excerpt are printed in bold.
"This syntax, which I have hitherto called the "system of Existential
Graphs" . . . An account of slightly further development of it was given in the
Monist of Oct. 1906. In this I made an attempt to make the syntax cover Modals; but it has
not satisfied me. . . the description fills 55 pages, and defines over a hundred technical
terms applying to it. The necessity for these was chiefly due to the lines called
"cuts" which simply appear in the present description as the boundaries of
shadings, or shaded parts of the sheet. The better exposition of 1903 divided the system
into three parts, distinguished as the Alpha, the Beta, and the Gamma, parts; a division I
shall here adhere to, although I shall now have to add a Delta part in order to deal with
modals. A cross division of the description which here, as in that of 1903, is given
precedence over the other is into the Conventions, the Rules, and the working of the
System."
Note that Peirce had made various attempts to go beyond the 1903 version of modals, but he
was not satisfied with them. Since he never used the 1903 version of modals, except for a
few pages of the Logic Notebook, there is strong evidence that he was looking for a
replacement. When he mentioned the division into Alpha, Beta, and Gamma, he did not say
what each part included. He had that same division with his algebra of 1885, in which
the third part was second-order predicate calculus (quantifiers that range over
relations). Since he planned to keep that division, but with a new version of modals, it
seems unlikely that he would have kept a version of modals that he had never used for any
purpose in the previous eight years.
In the remainder of L376, note the paragraphs that begin with the phrases "The
Conventions." and "the Phemic Sheet." The paragraphs that follow describe
a version of logic that is different from any that Peirce had previously specified. Can
you suggest any reason why he might be specifying a logic other than Delta graphs?
Note that he also mentions probabilities. That suggests another important innovation:
The use of multiple "papers" for specifying both possible and probable parts of
the phemic sheet. That would be a unification that goes beyond most logics of the 21st C.
In fact, it would make a valuable contribution to the latest R & D in artificial
intelligence. That is a topic I mentioned in Section 7 of my recent article on
phaneroscopy, and it would put Peirce into the forefront of ongoing issues in AI. See the
copy of Section 7 I sent to both Peirce and CG lists.
The 2006 version of logic that I have in mind is called IKL, which could be adapted to the
specifications Peirce mentioned in R514, L231, and R376. Since I don't have time to
pare down and discuss the references, I'll cite all of them.
The first version, which suggests, but doesn't specify a modal logic, is from a
conference in Denmark in 2002, and published in a book in 2003: Laws, Facts, and
Contexts: Foundations for Multimodal Reasoning, https://jfsowa.com/pubs/laws.htm . At the
bottom of the text is a photograph of the participants. Hintikka and I are in the center,
both wearing rain coats. We had a long conversation during the conference, and that
influenced the directions I took in the published version and in the following articles.
In that article, I discuss, among other issues, Peirce's logic of 1906 with heraldic
tinctures. But the complexity of the tinctures is irrelevant. I later moved to a much
simpler version of modal logic that is similar to the logic of L376. But note Figure 1
of this article, which cites a graph from RLT (1898). Figure 1 is exactly equivalent to
the "papers" in R514 and L376. That operator, when added to the first-order EGs
of 1911, is sufficient for a modal logic that would be similar to or perhaps identical to
what Peirce is writing about Delta graphs.
Next, see an article published in 2006, but written in 2005: Worlds, Models, and
Descriptions, https://jfsowa.com/pubs/worlds.pdf . I wrote this article while I was
collaborating on the development of the IKL logic, which was also published in 2006. For
a list of references to IKL and the IKRIS project that sponsored the development of IKL,
see https://jfsowa.com/ikl .
Then. look at Five Questions on Epistemic Logic, https://jfsowa.com/pubs/5qelogic.pdf .
That article, which was published in 2010, discusses how a logic such as IKL or
Peirce's delta graphs could represent various issues in modal logic with an emphasis
on epistemic logic -- that is also a consideration for my recent article about
phaneroscopy.
There is much more that could be said, and I plan to write it in the article on Delta
graphs. And by the way, I wonder how you would explain the three questions I asked: Why
did Juliette wash and scrub the floor in Deceber? Why were there papers on the floor?
Why did Peirce slip on them in a very complex way?
John
----------------------------------------
From: "Jon Alan Schmidt" <jonalanschmidt(a)gmail.com>
Sent: 2/21/24 1:25 PM
To: Peirce-L <peirce-l(a)list.iupui.edu>
Subject: Re: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic)
John, List:
JFS: The entire letter L376 is about Delta graphs and applications of Delta graphs.
This conjecture is quite a leap, considering that--as you acknowledged--Peirce mentions
Delta exactly once in that entire 19-page letter, which he left unfinished unless
additional pages somehow disappeared from the manuscript folder at Harvard's Houghton
Library decades ago. Again, here is that lone sentence.
CSP: The better exposition of 1903 divided the system into three parts, distinguished as
the Alpha, the Beta, and the Gamma, parts; a division I shall here adhere to, although I
shall now have to add a Delta part in order to deal with modals.
In the remaining text that we currently have, Peirce never gets around to discussing any
of the individual parts of EGs and their differences, despite stating plainly that he was
going to maintain them as "the better exposition" of the system as a whole. He
also says nothing whatsoever about dealing with modals, which is his only stated purpose
for adding a Delta part to the other three.
JFS: As Peirce wrote, the phemic sheet of a Delta graph contains multiple
"papers", each of which represents one possibility specified by
"postulates" that govern the remaining content of the sheet.
That is not what Peirce wrote in his letter to Risteen. Again, here is the exact
quotation.
CSP: I provide my system with a phemic sheet, which is a surface upon which the utterer
and interpreter will, by force of a voluntary and actually contracted habit, recognize
that whatever is scribed upon it and is interpretable as an assertion is to be recognized
as an assertion, although it may refer to a mere idea as its subject. If “snows” is
scribed upon the Phemic Sheet, it asserts that in the universe to which a special
understanding between utterer and interpreter has made the special part of the phemic
sheet on which it is scribed to relate, it sometime does snow. For they two may conceive
that the “phemic sheet” embraces many papers, so that one part of it is before the common
attention at one time and another part at another, and that actual conventions between
them equivalent to scribed graphs make some of those pieces relate to one subject and part
to another.
Again, there is no mention here of Delta, nor of modals. In fact, there is no mention here
of any of the different parts of EGs, because Peirce is describing the phemic sheet as
employed in every part. He also does not say that the different "papers"
correspond to different possibilities, he says that they correspond to different
subjects--different universes of discourse--to which the utterer and interpreter together
pay attention at different times. So I ask again, how exactly would the use of multiple
"papers" and/or the "red pencil" operation of R 514 facilitate
implementing formal systems of modal logic with EGs? Which specific one, "invented in
2006," do you have in mind?
JFS: Meanwhile, there are some questions to ponder:
Any answers to such questions about the details of Peirce's unfortunate accident are
pure speculation. It seems to me that if it had happened while he was "laying out a
diagram of papers" for a new version of EGs, then he likely would have said so
somewhere.
Regards,
Jon Alan Schmidt - Olathe, Kansas, USA
Structural Engineer, Synechist Philosopher, Lutheran Christian
www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt
On Tue, Feb 20, 2024 at 9:18 PM John F Sowa <sowa(a)bestweb.net> wrote:
Jon,
The entire letter L376 is about Delta graphs and applications of Delta graphs. Since
Peirce began the letter to Risteen shortly after his visit, he was assuming that Risteen
knew a great deal about the material they had discussed. Therefore, he plunged into
examples without much of an intro.
As Peirce wrote, the phemic sheet of a Delta graph contains multiple "papers",
each of which represents one possibility specified by "postulates" that govern
the remaining content of the sheet. There are many ways of partitioning a sheet of paper
to distinguish the postulates from the content they govern. The excerpt from R514 is one
method, and it happens to fill an entire sheet of paper. He may have thought of some
other notation for partitioning the paper, but the logical result would be equivalent.
There is much more to say, and I'll send the full preview later this week.
Meanwhile, there are some questions to ponder: Why did Juliette scrub and polish the
floor in December? Spring cleaning is rarely done in December. Why was there some paper
on the floor? Why did Peirce slip n it? Didn't he see it? Why was his accident so
serious? If he had been walking in a straight line, he might have fallen on his rear.
That might have been painful, but it wouldn't cause a serious injury that took 6
months to heal. Such a serious accident might have occurred if Peirce had been walking
fast while turning or twisting. But why would he be doing that?
Possible answer: Charles had asked Juliette to wash the floor because he wanted to build
a diagram with multiple papers. He was laying out a diagram of papers with a large
example of what he was writing about. As he turned to lay our another layer, he turned
and slipped.
John