Re: [PEIRCE-L] Existential Graphs in 1911

[John F. Sowa]

On 8 Nov. 1913, Peirce summarized his final position on EGs, and it is
identical to his 1911 EGs.  Nobody has shown any evidence for any other
opinion, no matter what their purpose may be.
Case
closed.
John
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Re: [PEIRCE-L] Existential Graphs in 1911

[Daniel L. Everett]

I agree strongly with John Sowa in his last message. 

In my book, Dark Matter of the Mind: The Culturally Articulated Unconscious, I 
discuss points related to these at length. Our bodies are constantly 
registering experiences in ways that we may not be aware of, “apperceptionally” 
in William James’s terms. Anything that anyone says overtly must be evaluated 
in light of our tacit knowledge. 

This applies to Peirce. When he uses a term, we can only understand it in terms 
of his culture, context, previous writings, and overall philosophy. 

Back in the days when I was religious and was concerned greatly about biblical 
exegesis, context was debated even then. Many of the wacko doctrines of some 
denominations are based on the belief that words can be studied apart from the 
“dark matter” of one’s mind (culture in this sense is dark matter overlap), as 
that forms values, knowledge structures, and social roles. 

Peirce must be understood in this larger sense, not merely by taking what some 
theologians call “proof texts”, verses out of context from a larger body.

I take no stand on what role illative had to Peirce after 1911. But the answer 
can only come from understanding his objectives overall, his context - what was 
he reading, who was he writing, what was he writing, etc.

I am always impressed by the knowledge, however, of technical details of 
Peirce’s work shown on this list. But we should not forget that for Peirce this 
was all a means to an end of understanding. He abandoned anything he came to 
consider a detriment to that understanding. That quest was to me what he meant 
by the “melody of thought” (such a brilliant phase). I am speaking on dark 
matter and music at a music understanding conference in Switzerland this summer 
(I hope) and that phrase will be in the paper. 

Dan



> On Jan 30, 2021, at 10:46 PM, John F. Sowa  wrote:
> 
> 
> Robert,
> 
> Thanks for finding that quotation:
> 
> > Thought is a thread of melody running through the succession of our 
> > sensations” (CP 5.395)
> 
> Now that you mention it, I recall reading that some time ago.  It must have 
> been lurking somewhere in my mind, but well beneath the conscious level.
> 
> In any case, it's very appropriate.  The connection to sensations emphasizes 
> the relation to Bill's term "embodied experience".
> 
> It is also related to my point that the total context is more important than 
> particular words. That doesn't mean that words are irrelevant, but they can 
> be highly misleading when taken out of context.
> 
> John
> 
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Re: [PEIRCE-L] Existential Graphs in 1911

[robert marty]

For the words I have this quotation that I had placed on the front page of
my book (L'algèbre des signes, 1990) and which says almost the same thing
but in the field of language using the "quasi-morphism":
 notes --> words ;  melody --> speech, music score --->algebra
"All speech is but such an algebra, the repeated signs being the words,
which have relations by virtue of the meanings associated with the them "
(CP 3.418)
The best,
Robert
Honorary Professor ; PhD Mathematics ; PhD Philosophy
fr.wikipedia.org/wiki/Robert_Marty
*https://martyrobert.academia.edu/ <https://martyrobert.academia.edu/>*



Le dim. 31 janv. 2021 à 11:58, Frederik Stjernfelt  a
écrit :

> It is interesting Peirce is using the example of melody for his third,
> synthetic kind of consciousness – and also as a metaphor for other
> syntheses like thought, in Robert’s quote.
>
>
>
> Here, there is an interesting parallel to the earliest gestalt theorists
> in Europe around the same time – Stumpf, Ehrenfels – also taking the melody
> as the prime example of gestalts. Only later, gestaltists turned to visual
> examples.
>
>
>
> Best
>
> Frederik
>
>
>
> PS Dear John – I tried to email you at s...@bestweb.net, but it bounces
> back – is there another address where I can reach you?
>
>
>
> *Fra: *John Sowa 
> *Svar til: *John Sowa 
> *Dato: *søndag den 31. januar 2021 kl. 04.46
> *Til: *Robert Marty 
> *Cc: *Auke van Breemen , Cornelis de Waal <
> cdw...@iupui.edu>, Gary Richmond , Jon Alan
> Schmidt , Peirce List ,
> "ahti-veikko.pietari...@taltech.ee" , "
> francesco.belluc...@unibo.it" , "
> martin.irv...@georgetown.edu" 
> *Emne: *Re: [PEIRCE-L] Existential Graphs in 1911
>
>
>
> Robert,
>
> Thanks for finding that quotation:
>
> > Thought is a thread of melody running through the succession of our
> sensations” (CP 5.395)
>
> Now that you mention it, I recall reading that some time ago.  It must
> have been lurking somewhere in my mind, but well beneath the conscious
> level.
>
> In any case, it's very appropriate.  The connection to sensations
> emphasizes the relation to Bill's term "embodied experience".
>
> It is also related to my point that the total context is more important
> than particular words. That doesn't mean that words are irrelevant, but
> they can be highly misleading when taken out of context.
>
> John
>
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Re: [PEIRCE-L] Existential Graphs in 1911

[Frederik Stjernfelt]

It is interesting Peirce is using the example of melody for his third, 
synthetic kind of consciousness – and also as a metaphor for other syntheses 
like thought, in Robert’s quote.

Here, there is an interesting parallel to the earliest gestalt theorists in 
Europe around the same time – Stumpf, Ehrenfels – also taking the melody as the 
prime example of gestalts. Only later, gestaltists turned to visual examples.

Best
Frederik

PS Dear John – I tried to email you at 
s...@bestweb.net<mailto:s...@bestweb.net>, but it bounces back – is there 
another address where I can reach you?

Fra: John Sowa 
Svar til: John Sowa 
Dato: søndag den 31. januar 2021 kl. 04.46
Til: Robert Marty 
Cc: Auke van Breemen , Cornelis de Waal 
, Gary Richmond , Jon Alan Schmidt 
, Peirce List , 
"ahti-veikko.pietari...@taltech.ee" , 
"francesco.belluc...@unibo.it" , 
"martin.irv...@georgetown.edu" 
Emne: Re: [PEIRCE-L] Existential Graphs in 1911


Robert,

Thanks for finding that quotation:

> Thought is a thread of melody running through the succession of our 
> sensations” (CP 5.395)

Now that you mention it, I recall reading that some time ago.  It must have 
been lurking somewhere in my mind, but well beneath the conscious level.

In any case, it's very appropriate.  The connection to sensations emphasizes 
the relation to Bill's term "embodied experience".

It is also related to my point that the total context is more important than 
particular words. That doesn't mean that words are irrelevant, but they can be 
highly misleading when taken out of context.

John
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Re: [PEIRCE-L] Existential Graphs in 1911

[John F. Sowa]

Robert, 
Thanks for finding that quotation:
> Thought is
a thread of melody running through the succession of our sensations” (CP
5.395)
Now that you mention it, I recall reading that some
time ago.  It must have been lurking somewhere in my mind, but well
beneath the conscious level.
In any case, it's very appropriate. 
The connection to sensations emphasizes the relation to Bill's term
"embodied experience".
It is also related to my point that
the total context is more important than particular words. That doesn't
mean that words are irrelevant, but they can be highly misleading when
taken out of context.
John
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Re: [PEIRCE-L] Existential Graphs in 1911)

[John F. Sowa]

Bill, 
Your comment is very close to what I was trying to
say.
> I have been a musician for seventy years, and I was a
serious
mathematician until age twenty. (I graduated with a double degree.) I
can assure you that I don’t think “only in terms of the patterns . . .”
In fact, in my most treasured musical experiences—and
 I’d venture to say the same for mathematics—I barely “think” at all.
It’s an embodied understanding: I “feel” what I apprehend—and only after
 the fact, with a great sense of loss, do I “think” about it. And when I
 do “think” I mostly struggle to find some
 faint simulacrum of my experience. Sometimes that might involve
patterns; sometimes I might draw pictures or notes or words; sometimes I
 simply get up from the desk and pace, wave my arms, sing a little.
(Except for the singing, the same definitely goes for
 mathematics.)  
The phrase "embodied experience" is
excellent.  Peirce, Einstein, Archimedes, Whitehead, and many others
would agree.
In fact, the way you describe your experience and the
difficulty of putting it into words is very close to what Peirce said
about  his "left handed brain" (he was left handed).  And he
admitted that he had considerable difficulty in expressing himself in
words -- that is one reason why he preferred diagrams.  He also hoped to
generalize his diagrams to "stereoscopic moving images" or even
physical models. He would have loved to work with a virtual reality
system.
When I mentioned "structural patterns", I chose
that term because I needed a noun phrase to insert in the sentence.  
Your description is very close to the way that most professional
mathematicians describe their way of thinking.  For examples, and
references see the first ten slides in "Peirce, Polya, and Euclid: 
Integrating logic, heuristics, and geometry"
http://jfsowa.com/talks/ppe.pdf . 
The reason why I used the
analogy of math to music is that I wanted to emphasize the non-verbal way
of thinking in those fields.  Any description in words cannot capture the
essence of what goes on when a mathematician or a musician is deep in the
creative experience.
I'm thinking of the musician who was asked
what his composition meant. As an answer, he played it
again.
Fundamental principle:  For mathematicians and musicians,
words are not just secondary, they're almost irrelevant.  To understand
them, look at what they do, not at what they say.
John
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Re: [PEIRCE-L] Existential Graphs in 1911

[Jon Alan Schmidt]

John, Auke, List, All:

JFS: He [Peirce] insisted that metaphysics should be based on mathematics,
not on Hegel-style verbiage.


Actually, he insisted that *all *other sciences are ultimately based on
mathematics, while metaphysics in particular should be based on logic--the
entire normative science that he generalized to semeiotic, not merely
mathematical/formal logic. As I have quoted him many times before,
"Metaphysics consists in the results of the absolute acceptance of logical
principles not merely as regulatively valid, but as truths of being" (CP
1.487, c. 1896).

AvB: So, who suggested that metaphysics should be based on Hegel Style
verbiage? (The destructive destillation paragraph is from Peirce.) Jon most
certainly not.


Indeed, who said anything about metaphysics *at all* before John brought it
up, seemingly out of the blue? What does metaphysics have to do with
anything that we have been discussing in recent List threads about logic
and EGs?

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Structural Engineer, Synechist Philosopher, Lutheran Christian
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt

On Sat, Jan 30, 2021 at 5:33 AM Auke van Breemen 
wrote:

> John,
>
> Let's take the sequence from the architecture of science:  math. logic,
> phenomenology, semiotics, critical logic, ... , methaphysics. You assume
> that my remarks concern the interval logic ... methaphysics. That however
> was not the object of my remarks. My remarks concerned the interval
> phenomenology, semiotics, critical logic. So, who suggested that
> metaphysics should be based on Hegel Style verbiage? (The destructive
> destillation paragraph is from Peirce.) Jon most certainly not. How could
> he, if indeed, as you assume, he focusses to much on words or *literary*
> criticism?
>
> best,
>
> Auke
>
> Op 30 januari 2021 om 0:35 schreef "John F. Sowa" :
>
> Auke,
>
> I agree with your observation, and the conclusion: "It is a line of
> thought I can see leading to what Jon wrote."
>
> Charles' father Benjamin Peirce gave him a thorough training in
> mathematics from early childhood, and Charles devoured Whateley's logic
> book in a week when he was 13.  He insisted that metaphysics should be
> based on mathematics, not on Hegel-style verbiage.
>
> Jon's method  of focusing on the words is a kind of literary criticism
> that would be more appropriate for analyzing Shakespeare than Peirce.
>
> John
>
>
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Re: [PEIRCE-L] Existential Graphs in 1911

[Jon Alan Schmidt]

John, List, All:

JFS: Any logician can "hear" an exciting new melody in R670 and L231 that
was not present in R669 or the Monist article of 1906.  Peirce didn't have
to write a "note to self" about the change.  He just did it.  And any
logician can "hear" it.
But I realize that many people can't feel or hear the difference.


This conveniently establishes a position that is effectively unfalsifiable.
The fact that Peirce never explicitly rejects his earlier writings about
EGs is deemed irrelevant, because "any logician" can simply "hear" the "new
melody" that he supposedly composed in June 1911. Anyone who cannot
likewise "feel or hear" it is apparently *not *a logician and should be
ignored accordingly. Descriptive words are ultimately inadequate since one
must allegedly perceive the patterns directly.

As I have pointed out before, in his late 1911 letters to Robert (RL 378)
and Risteen (RL 376), Peirce does not criticize the *patterns *of the 1906
EGs; he only criticizes his *description *of them at that time in
"Prolegomena," which uses lots and lots of words. He now recognizes that
shading is a much better alternative to thin oval lines for distinguishing
oddly enclosed areas from evenly enclosed areas, and that it is sufficient
in Gamma EGs for shaded/unshaded areas to represent the universes of
possibility/actuality rather than having multiple tinctures corresponding
to different kinds of each, along with the third modality of intentions. He
further simplifies his presentation of EGs for the uninitiated, including
these two men along with the National Academy of Sciences (R 670) and
Kehler (RL 231), by omitting the derivation of negation from consequence
and treating it as a primitive instead, even though this is
"philosophically inaccurate" (Bellucci and Pietarinen).

We really should be able to agree about all this. We should also then be
able agree that for many *practical *purposes, such as teaching classical
logic or using it to prove theorems, negation ovals are the "best" choice
for a third primitive along with the blank sheet and line of identity;
while for many *philosophical *purposes, such as studying logic more deeply
including non-classical alternatives, implication scrolls are the "best"
choice instead. Why be unreasonably adamant that one is superior to the
other for any and every conceivable purpose?

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Structural Engineer, Synechist Philosopher, Lutheran Christian
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt

On Fri, Jan 29, 2021 at 9:38 PM John F. Sowa  wrote:

> Gary R,
>
> My remarks were ad rem, not ad hominem.  Mathematics is like music.  A
> mathematician or a musician thinks only in terms of the patterns, the
> operations on those patterns, and their relationship to whatever notation
> is used to represent them.
>
> The words used to describe those patterns are useful for communication
> among teachers, students, and critics.  But those words are absent from the
> minds of the artists (musical or mathematical) who are imagining and
> creating novel patterns.
>
> Peirce was a great mathematical/logical artist.  In June 1911, he had a
> new insight into the melodies of logic.  Any logician can "hear" an
> exciting new melody in R670 and L231 that was not present in R669 or the
> Monist article of 1906.  Peirce didn't have to write a "note to self" about
> the change.  He just did it.  And any logician can "hear" it.
>
> But I realize that many people can't feel or hear the difference.  I plan
> to post the 1906 version and the 1911 version on my web site, and I'll
> point out exactly where the differences occur and their implications.
>
> I'll post that in the next two days.  And I won't refer to any other
> person's comments or opinions on the subject.
>
> Meanwhile, I recommend the following slides and their quotations of
> mathematicians, logicians, and linguists about their subject:
> http://jfsowa.com/talks/ppe.pdf .  The application of Peirce's EGs to
> Euclidean diagrams is easy with the 1911 EGs, but not with the earlier
> versions.  That application is one of the strongest arguments in support of
> Peirce's claim that EGs represent "the action of the mind in thought."
>
> John
>
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Re: [PEIRCE-L] Existential Graphs in 1911

[Jon Alan Schmidt]

Auke, List, All:

AvB: For him [Peirce], as far as I understood his thought, the formal
structure is not everything. It only is "the formal structure as it
operates in a living intelligence". It did not prevent him from focussing
exclusively on the formal structure, as his formal work shows. But he was
aware of the limitations. You [JFS] seem to be less so.


Indeed, John seems to view all these matters almost exclusively through the
lens of mathematical/formal logic. I brought up the necessary role of "a
living intelligence" myself a few weeks ago because those are Peirce's last
three words in R 669.

CSP: The few examples that shall forthwith be given might tempt a lively
mind to exclaim: Why, this syntax draws conclusions of itself,
automatically. This would be extravagant; but one may say that the Syntax
together with the application of the two illative permissions does so,
provided it be not overlooked that such application can only be made by a
living intelligence. (R 669:23-24[21-22], LF 1:584, 1911)


According to his own testimony below, John has a strong interest in
*artificial *intelligence, which helps to explain his personal opinion that
"the 1911 version" of EGs is "best"--it facilitates more efficient proof
procedures in classical logic, thus lending itself to "automated
reasoning." That is presumably why he dismisses R 669, along with anything
else that Peirce wrote about EGs before June 1911, where over and over he
makes it clear that this was *not *his primary purpose in developing them.

AvB: I think that this quote [CP 1.384, 1887-8] backs up Jon's approach
from a systematic perspective. Systematic here to be taken in the
philosophical sense, not the logical.


I agree; again, my own purposes are primarily philosophical, so *everything
*that Peirce wrote about logic and EGs is potentially relevant.

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Structural Engineer, Synechist Philosopher, Lutheran Christian
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt

On Fri, Jan 29, 2021 at 3:36 AM Auke van Breemen 
wrote:

> John,
>
> During your repeated debates with Jon an experience I had as a freshman
> philosophy kept knocking at my doors of perception. It was the first
> meeting in which each of the students had to read a passage of Hegels
> logic. I was the first to read and started with the first alinea in which
> logic is defined as being concerned with the idea in the formal element.
> Just having had my first course in logic, I relied on what I learned and
> started talking about  that, i.e. as logic trying to lay down the rules of
> formal thought, the formal element. And met with serious opposition from
> the teachers present. I recall that it took them some time to get me to
> realize that the emphazis is on "'idea' in the formal element" and not on
> the formal element severed from any actuality. It is a line of thought I
> can see leading to what Jon wrote.
>
> Jon A. wrote:
>
> In this particular case, my purpose is the same as Peirce's--analyzing
> reasoning into its most fundamental and irreducible elements. Even more
> specifically, I am currently exploring
> intuitionistic/constructive/synechistic logic using EGs, consistent with
> Peirce's own skepticism of excluded middle. John can speak for himself, but
> it is clear by now that he does not share these same objectives.
>
> --
>
> Logical positivism could restrict itself to logic regarded sub species
> eternitate (Tractatus), we know for certain that Peirce was not of like
> opinion. His view on logic is multi-facetted.
>
> He is not just concerned with, I cite:
>
> John wrote:
>
> For mathematicians and logicians, clarity and precision are essential. The
> formal structure is everything, and the words are of minor interest.  The
> fewer, the better.
>
> --
>
> For him, as far as I understood his thought, the formal structure is not
> everything. It only is "the formal structure as it operates in a living
> intelligence". It did not prevent him from focussing exclusively on the
> formal structure, as his formal work shows. But he was aware of the
> limitations. You seem to be less so.
>
> It is in this light that I find the negation - ilation debate of interest.
>
> Kant gives the erroneous view that ideas are presented separated and then
> thought together by the mind. This is his doctrine that a mental synthesis
> precedes every analysis. What really happens is that something is presented
> which in itself has no parts, but which nevertheless is analyzed by the
> mind, that is to say, its having parts consists in this that the mind
> afterward recognizes those parts in it. Those partial ideas are really not
> in the 1rst idea, in itself, though they are separated out from it. It is a
> case of destructive distillation. CP 1.384
>
> I think that this quote backs up Jon's approach from a systematic
> perspective. Systematic here to be taken in the philosophical sense, not
> the logical.
>
> Best,
>
> Auke

Re: Re: [PEIRCE-L] Existential Graphs in 1911

[Edwina Taborsky]

 

Hmm. You seem to be defining 'thinking' as only an act of abstract
intellectual analysis.

But Peircean 'thinking' includes non-analytic feeling [Firstness] as
well as direct physical experience [Secondness] and also, that
abstract analytic process [Thirdness].

Edwina
 On Sat 30/01/21  2:20 PM , "Brooks, William F" w-bro...@illinois.edu
sent:
Hello, everyone,  
  There seems to be a lot of crossfire here. Perhaps I can create a
diversionary skirmish . . . 
  "A mathematician or a musician thinks only in terms of the
patterns, the operations on those patterns, and their relationship to
whatever notation is used to represent them.” 
  Okay, well, first-person accounts are suspect, one can’t
generalise, etc., etc. 
  But.  
  I have been a musician for seventy years, and I was a serious
mathematician until age twenty. (I graduated with a double degree.) I
can assure you that I don’t think “only in terms of the patterns .
. .” In fact, in my most treasured musical experiences—and  I’d
venture to say the same for mathematics—I barely “think” at
all. It’s an embodied understanding: I “feel” what I
apprehend—and only after the fact, with a great sense of loss, do I
“think” about it. And when I do “think” I mostly struggle to
find some  faint simulacrum of my experience. Sometimes that might
involve patterns; sometimes I might draw pictures or notes or words;
sometimes I simply get up from the desk and pace, wave my arms, sing
a little. (Except for the singing, the same definitely goes for 
mathematics.)   
  Now, I don’t know nearly enough about Peirce. But what little I
do know suggests that he was a very physical person, with appetites,
passions, and bodily understandings. How did he apprehend
mathematics, or logic, or—for that matter—music? In  what ways
can we, should we, be informed by our conclusions about the nature of
his apprehension?  
  And what has any of this to do with silence? Or the absence of
logic?  
  Bill 
 William Brooks
 w-bro...@illinois.edu [1]
 Emeritus Professor of Music 
 University of Illinois
 Urbana, IL 61801
 United States
 (+1-217-417-4165)
 William Brooks
 w.f.bro...@york.ac.uk
 Professor of Music
 University of York
 Heslington, York YO10 5DD
 United Kingdom 
 (+44-1904-324449)
 William Brooks
 Senior Research Fellow and Series Editor
 Orpheus Institute, Ghent, Belgium
 william.bro...@orpheusinstituut.be
 Take care of things. And people.   
  On Jan 29, 2021, at 21:38, John F. Sowa  wrote: 
Gary R,  

My remarks were ad rem, not ad hominem.  Mathematics is like music. 
A mathematician or a musician thinks only in terms of the patterns,
the operations on those patterns, and their relationship to whatever
notation is used to represent them.  

The words used to describe those patterns are useful for
communication among teachers, students, and critics.  But those words
are absent from the minds of the artists (musical or mathematical) who
are imagining and creating novel patterns. 

Peirce was a great mathematical/logical artist.  In June 1911, he
had a new insight into the melodies of logic.  Any logician can
"hear" an exciting new melody in R670 and L231 that was not present
in R669 or the Monist article of 1906.  Peirce  didn't have to write
a "note to self" about the change.  He just did it.  And any logician
can "hear" it. 

But I realize that many people can't feel or hear the difference.  I
plan to post the 1906 version and the 1911 version on my web site, and
I'll point out exactly where the differences occur and their
implications. 

I'll post that in the next two days.  And I won't refer to any other
person's comments or opinions on the subject. 

Meanwhile, I recommend the following slides and their quotations of
mathematicians, logicians, and linguists about their subject: 
http://jfsowa.com/talks/ppe.pdf__;!!DZ3fjg!o-XxG2rDqisSRvTETFntihZBRphzzSQPlUzHO-wbSLZObJwfIVahs0glXGwhSAbt84V_$
[3]" target="_blank"> http://jfsowa.com/talks/ppe.pdf [4] .  The
application of Peirce's EGs to Euclidean diagrams is easy with the
1911 EGs, but not with the earlier versions.  That application is one
of the strongest arguments in support of Peirce's claim that EGs
represent "the  action of the mind in thought." 

John  _ _ _ _ _ _ _ _ _ _
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Re: [PEIRCE-L] Existential Graphs in 1911

[Brooks, William F]

Hello, everyone,

There seems to be a lot of crossfire here. Perhaps I can create a diversionary 
skirmish . . .

"A mathematician or a musician thinks only in terms of the patterns, the 
operations on those patterns, and their relationship to whatever notation is 
used to represent them.”

Okay, well, first-person accounts are suspect, one can’t generalise, etc., etc.

But.

I have been a musician for seventy years, and I was a serious mathematician 
until age twenty. (I graduated with a double degree.) I can assure you that I 
don’t think “only in terms of the patterns . . .” In fact, in my most treasured 
musical experiences—and I’d venture to say the same for mathematics—I barely 
“think” at all. It’s an embodied understanding: I “feel” what I apprehend—and 
only after the fact, with a great sense of loss, do I “think” about it. And 
when I do “think” I mostly struggle to find some faint simulacrum of my 
experience. Sometimes that might involve patterns; sometimes I might draw 
pictures or notes or words; sometimes I simply get up from the desk and pace, 
wave my arms, sing a little. (Except for the singing, the same definitely goes 
for mathematics.)

Now, I don’t know nearly enough about Peirce. But what little I do know 
suggests that he was a very physical person, with appetites, passions, and 
bodily understandings. How did he apprehend mathematics, or logic, or—for that 
matter—music? In what ways can we, should we, be informed by our conclusions 
about the nature of his apprehension?

And what has any of this to do with silence? Or the absence of logic?

Bill



William Brooks
w-bro...@illinois.edu
Emeritus Professor of Music
University of Illinois
Urbana, IL 61801
United States
(+1-217-417-4165)

William Brooks
w.f.bro...@york.ac.uk
Professor of Music
University of York
Heslington, York YO10 5DD
United Kingdom
(+44-1904-324449)

William Brooks
Senior Research Fellow and Series Editor
Orpheus Institute, Ghent, Belgium
william.bro...@orpheusinstituut.be

Take care of things. And people.

On Jan 29, 2021, at 21:38, John F. Sowa 
mailto:s...@bestweb.net>> wrote:


Gary R,

My remarks were ad rem, not ad hominem.  Mathematics is like music.  A 
mathematician or a musician thinks only in terms of the patterns, the 
operations on those patterns, and their relationship to whatever notation is 
used to represent them.

The words used to describe those patterns are useful for communication among 
teachers, students, and critics.  But those words are absent from the minds of 
the artists (musical or mathematical) who are imagining and creating novel 
patterns.

Peirce was a great mathematical/logical artist.  In June 1911, he had a new 
insight into the melodies of logic.  Any logician can "hear" an exciting new 
melody in R670 and L231 that was not present in R669 or the Monist article of 
1906.  Peirce didn't have to write a "note to self" about the change.  He just 
did it.  And any logician can "hear" it.

But I realize that many people can't feel or hear the difference.  I plan to 
post the 1906 version and the 1911 version on my web site, and I'll point out 
exactly where the differences occur and their implications.

I'll post that in the next two days.  And I won't refer to any other person's 
comments or opinions on the subject.

Meanwhile, I recommend the following slides and their quotations of 
mathematicians, logicians, and linguists about their subject:  
http://jfsowa.com/talks/ppe.pdf
 .  The application of Peirce's EGs to Euclidean diagrams is easy with the 1911 
EGs, but not with the earlier versions.  That application is one of the 
strongest arguments in support of Peirce's claim that EGs represent "the action 
of the mind in thought."

John

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Re: [PEIRCE-L] Existential Graphs in 1911

[Auke van Breemen]

John,

Let's take the sequence from the architecture of science:  math. logic, 
phenomenology, semiotics, critical logic, ... , methaphysics. You assume that 
my remarks concern the interval logic ... methaphysics. That however was not 
the object of my remarks. My remarks concerned the interval phenomenology, 
semiotics, critical logic. So, who suggested that metaphysics should be based 
on Hegel Style verbiage? (The destructive destillation paragraph is from 
Peirce.) Jon most certainly not. How could he, if indeed, as you assume, he 
focusses to much on words or literary criticism? 

best,

Auke

 


> Op 30 januari 2021 om 0:35 schreef "John F. Sowa" :
> 
> 
> Auke,
> 
> I agree with your observation, and the conclusion: "It is a line of 
> thought I can see leading to what Jon wrote."
> 
> Charles' father Benjamin Peirce gave him a thorough training in 
> mathematics from early childhood, and Charles devoured Whateley's logic book 
> in a week when he was 13.  He insisted that metaphysics should be based on 
> mathematics, not on Hegel-style verbiage.
> 
> Jon's method  of focusing on the words is a kind of literary criticism 
> that would be more appropriate for analyzing Shakespeare than Peirce.
> 
> John
> 
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Re: [PEIRCE-L] Existential Graphs in 1911

[Robert Marty]

Peirce often uses the musical metaphor ...


Thought is a thread of melody running through the succession of our
sensations” (CP 5.395)



Le sam. 30 janv. 2021 à 04:39, John F. Sowa  a écrit :

> Gary R,
>
> My remarks were ad rem, not ad hominem.  Mathematics is like music.  A
> mathematician or a musician thinks only in terms of the patterns, the
> operations on those patterns, and their relationship to whatever notation
> is used to represent them.
>
> The words used to describe those patterns are useful for communication
> among teachers, students, and critics.  But those words are absent from the
> minds of the artists (musical or mathematical) who are imagining and
> creating novel patterns.
>
> Peirce was a great mathematical/logical artist.  In June 1911, he had a
> new insight into the melodies of logic.  Any logician can "hear" an
> exciting new melody in R670 and L231 that was not present in R669 or the
> Monist article of 1906.  Peirce didn't have to write a "note to self" about
> the change.  He just did it.  And any logician can "hear" it.
>
> But I realize that many people can't feel or hear the difference.  I plan
> to post the 1906 version and the 1911 version on my web site, and I'll
> point out exactly where the differences occur and their implications.
>
> I'll post that in the next two days.  And I won't refer to any other
> person's comments or opinions on the subject.
>
> Meanwhile, I recommend the following slides and their quotations of
> mathematicians, logicians, and linguists about their subject:
> http://jfsowa.com/talks/ppe.pdf .  The application of Peirce's EGs to
> Euclidean diagrams is easy with the 1911 EGs, but not with the earlier
> versions.  That application is one of the strongest arguments in support of
> Peirce's claim that EGs represent "the action of the mind in thought."
>
> John
>
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Re: [PEIRCE-L] Existential Graphs in 1911

[John F. Sowa]

Gary R, 
My remarks were ad rem, not ad hominem.  Mathematics is
like music.  A mathematician or a musician thinks only in terms of the
patterns, the operations on those patterns, and their relationship to
whatever notation is used to represent them. 
 The words used to
describe those patterns are useful for communication among teachers,
students, and critics.  But those words are absent from the minds of the
artists (musical or mathematical) who are imagining and creating novel
patterns.
Peirce was a great mathematical/logical artist.  In June
1911, he had a new insight into the melodies of logic.  Any logician can
"hear" an exciting new melody in R670 and L231 that was not
present in R669 or the Monist article of 1906.  Peirce didn't have to
write a "note to self" about the change.  He just did it.  And
any logician can "hear" it.
But I realize that many people
can't feel or hear the difference.  I plan to post the 1906 version and
the 1911 version on my web site, and I'll point out exactly where the
differences occur and their implications.
I'll post that in the next
two days.  And I won't refer to any other person's comments or opinions on
the subject.
Meanwhile, I recommend the following slides and their
quotations of mathematicians, logicians, and linguists about their
subject:  http://jfsowa.com/talks/ppe.pdf .  The application of Peirce's
EGs to Euclidean diagrams is easy with the 1911 EGs, but not with the
earlier versions.  That application is one of the strongest arguments in
support of Peirce's claim that EGs represent "the action of the mind
in thought."
John 
_ _ _ _ _ _ _ _ _ _
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Re: [PEIRCE-L] Existential Graphs in 1911

[Gary Richmond]

John Sowa wrote:

JFS: Jon's method  of focusing on the words is a kind of literary criticism
that would be more appropriate for analyzing Shakespeare than Peirce.


I found this comment as useless and, frankly, as absurd as this earlier one
of yours in this thread.

JFS: As for Jon's comments about earlier versions, any quotations prior to
June 1911 are irrelevant.


Please do not recommence these preposterous -- in their gross generality --
or ad hominem attacks that were so disruptive last year and, indeed, part
of the year before. Please stick to discussing substantive content. We have
really had more than enough of this on the List for a lifetime.

Best,

Gary Richmond (writing as List moderator)

"Time is not a renewable resource." gnox

*Gary Richmond*
*Philosophy and Critical Thinking*
*Communication Studies*
*LaGuardia College of the City University of New York*







On Fri, Jan 29, 2021 at 6:35 PM John F. Sowa  wrote:

> Auke,
>
> I agree with your observation, and the conclusion: "It is a line of
> thought I can see leading to what Jon wrote."
>
> Charles' father Benjamin Peirce gave him a thorough training in
> mathematics from early childhood, and Charles devoured Whateley's logic
> book in a week when he was 13.  He insisted that metaphysics should be
> based on mathematics, not on Hegel-style verbiage.
>
> Jon's method  of focusing on the words is a kind of literary criticism
> that would be more appropriate for analyzing Shakespeare than Peirce.
>
> John
>
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Re: [PEIRCE-L] Existential Graphs in 1911

[John F. Sowa]

Auke,
I agree with your observation, and the conclusion: "It
is a line of thought I can see leading to what Jon
wrote."
Charles' father Benjamin Peirce gave him a thorough
training in mathematics from early childhood, and Charles devoured
Whateley's logic book in a week when he was 13.  He insisted that
metaphysics should be based on mathematics, not on Hegel-style
verbiage.
Jon's method  of focusing on the words is a kind of
literary criticism that would be more appropriate for analyzing
Shakespeare than Peirce.
John

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Re: [PEIRCE-L] Existential Graphs in 1911

[Auke van Breemen]

John,

During your repeated debates with Jon an experience I had as a freshman 
philosophy kept knocking at my doors of perception. It was the first meeting in 
which each of the students had to read a passage of Hegels logic. I was the 
first to read and started with the first alinea in which logic is defined as 
being concerned with the idea in the formal element. Just having had my first 
course in logic, I relied on what I learned and started talking about  that, 
i.e. as logic trying to lay down the rules of formal thought, the formal 
element. And met with serious opposition from the teachers present. I recall 
that it took them some time to get me to realize that the emphazis is on 
"'idea' in the formal element" and not on the formal element severed from any 
actuality. It is a line of thought I can see leading to what Jon wrote. 

Jon A. wrote:

In this particular case, my purpose is the same as Peirce's--analyzing 
reasoning into its most fundamental and irreducible elements. Even more 
specifically, I am currently exploring intuitionistic/constructive/synechistic 
logic using EGs, consistent with Peirce's own skepticism of excluded middle. 
John can speak for himself, but it is clear by now that he does not share these 
same objectives.

--

Logical positivism could restrict itself to logic regarded sub species 
eternitate (Tractatus), we know for certain that Peirce was not of like 
opinion. His view on logic is multi-facetted. 

He is not just concerned with, I cite:

John wrote:

For mathematicians and logicians, clarity and precision are essential. The 
formal structure is everything, and the words are of minor interest.  The 
fewer, the better.

--

For him, as far as I understood his thought, the formal structure is not 
everything. It only is "the formal structure as it operates in a living 
intelligence". It did not prevent him from focussing exclusively on the formal 
structure, as his formal work shows. But he was aware of the limitations. You 
seem to be less so. 


It is in this light that I find the negation - ilation debate of interest. 

Kant gives the erroneous view that ideas are presented separated
and then thought together by the mind. This is his doctrine that
a mental synthesis precedes every analysis. What really happens is
that something is presented which in itself has no parts, but which
nevertheless is analyzed by the mind, that is to say, its having parts
consists in this that the mind afterward recognizes those parts in it.
Those partial ideas are really not in the 1rst idea, in itself, though
they are separated out from it. It is a case of destructive distillation.
CP 1.384

I think that this quote backs up Jon's approach from a systematic perspective. 
Systematic here to be taken in the philosophical sense, not the logical. 

Best,

Auke


> Op 29 januari 2021 om 5:51 schreef "John F. Sowa" :
> 
> Auke> I was thinking in terms of goals, i.e. what is the object you
> try to understand, not credentials.  I can connect Jon's answer to my
> question with his line of reasoning and I did like that.  There might
> be differences in the goals and then it is always better to asses and
> value the differences, instead of fighting about who is right.
> 
> I have been doing research and teaching in logic, computer science,
> computational linguistics, and artificial intelligence for many
> years.  In 1976, I had published an article on Conceptual Graphs in
> the IBM Journal of Research and Development.
> 
> Then in 1978, I came across Don Roberts' book on EGs, and it was
> exactly what I was looking for.  Peirce's EGs were far more elegant
> and powerful than the AI research in the 1970s.  (including my own).
> I immediatetly adopted it as the foundation for the book I published
> in 1984.  I continued reading Peirce's other writings and various
> publications about Peirce since then.
> 
> Then in 2001, I came across Michel Balat's transcription of a first
> draft of L231 (mistakenly classified as R514).  I realized that it
> was an excellent introduction to EGs, and I posted a copy with
> commentary on my web site:  http://jfsowa.com/peirce/ms514.htm .
> 
> I also realized that this version was far superior to Peirce's
> earlier versions.  In particular, I used it to solve a previously
> unsolved research problem from 1988.  I published the solution in
> Semiotca in 2011:  http://jfsowa.com/pubs/egtut.pdf .
> 
> In April 2015, I presented a lecture on related issues at a Peirce
> Session at the APA conference in Vancouver.  In December of 2015, I
> presented an extended version at a workshop that Zalamea sponsored in
> Bogota.  And in 2018, I publishted a 76-page version that spelled out
> all the details.
> 
> The following slides are minor revisions of the 2015 version:
> http://jfsowa.com/talks/ppe.pdf . Slide 2 has a link to the 2018
> publication in 

Re: [PEIRCE-L] Existential Graphs in 1911

[John F. Sowa]

Auke> I was thinking in terms of goals, i.e. what is the object you
try to understand, not credentials.  I can connect Jon's answer to my
question with his line of reasoning and I did like that.  There might
be differences in the goals and then it is always better to asses and
value the differences, instead of fighting about who is right.

I have been doing research and teaching in logic, computer science,
computational linguistics, and artificial intelligence for many
years.  In 1976, I had published an article on Conceptual Graphs in
the IBM Journal of Research and Development.

Then in 1978, I
came across Don Roberts' book on EGs, and it was
exactly what I was
looking for.  Peirce's EGs were far more elegant
and powerful than
the AI research in the 1970s.  (including my own).
I immediatetly
adopted it as the foundation for the book I published
in 1984.  I
continued reading Peirce's other writings and various
publications
about Peirce since then.

Then in 2001, I came across Michel
Balat's transcription of a first
draft of L231 (mistakenly classified
as R514).  I realized that it
was an excellent introduction to EGs,
and I posted a copy with
commentary on my web site: 
http://jfsowa.com/peirce/ms514.htm .

I also realized that this
version was far superior to Peirce's
earlier versions.  In
particular, I used it to solve a previously
unsolved research problem
from 1988.  I published the solution in
Semiotca in 2011: 
http://jfsowa.com/pubs/egtut.pdf .

In April 2015, I presented a
lecture on related issues at a Peirce
Session at the APA conference
in Vancouver.  In December of 2015, I
presented an extended version
at a workshop that Zalamea sponsored in
Bogota.  And in 2018, I
publishted a 76-page version that spelled out
all the details.

The following slides are minor revisions of the 2015 version:
http://jfsowa.com/talks/ppe.pdf . Slide 2 has a link to the 2018
publication in the Journal of Applied Logics.

The workshop in
Bogota included leading experts in existential
graphs.  Nobody raised
any objection or even any comment about my
use of the 1911 version of
EGs.  For mathematicians and logicians,
clarity and precision are
essential.  The formal structure is
everything, and the words are of
minor interest.  The fewer, the
better.

As for Jon's
comments about earlier versions, any quotations prior
to June 1911
are irrelevant.  But I found Jon's comments useful for
pointing out
issues that I decided to restate more clearly.

John
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Re: [PEIRCE-L] Existential Graphs in 1911

[Auke van Breemen]

John, 

I was thinking in terms of goals, i.e. what is the object you try to 
understand, not credentials. I can connect Jon's answer to my question with his 
line of reasoning and I did like that. Their might be differences in the goals 
and then it is always better to asses and value the differences, instead of 
fighting about who is right.

Best,

Auke

> Op 29 januari 2021 om 0:02 schreef "John F. Sowa" :
> 
> 
> Auke> Since perspective is important, it might be a good idea to 
> explicate the differences in purpose each of you entertain. 
> 
> That's a good question.
> 
> I have been working on research and teaching in logic, computer science, 
> artificial intelligence and related areas for many years.  In the 1970s, I
> 
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Re: [PEIRCE-L] Existential Graphs in 1911

[John F. Sowa]

Auke> Since perspective is important, it might be a good idea to
explicate the differences in purpose each of you entertain.  
That's
a good question.
I have been working on research and teaching in
logic, computer science, artificial intelligence and related areas for
many years.  In the 1970s, I 
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Re: [PEIRCE-L] Existential Graphs in 1911

[Jon Alan Schmidt]

John, Auke, List, All:

JFS: The *opinion* that the EG version of June 1911 is Peirce's best is
Peirce's own, as he stated in December, after six months of further
consideration.


This is false, Peirce states no such thing. Here is the entire relevant
portion of the referenced letter.

CSP: This syntax, which I have hitherto called the “system of Existential
Graphs,” was suggested to me in reading the proof sheets of an article by
me that was published in the *Monist *of Jan. 1897; and I at once wrote a
full account of it for the same journal. But Dr. Carus would not print it.
I gave an oral account of it, soon after, to the National Academy of
Sciences; and in 1903 for my audience of a course of Lectures before the
Lowell Institute, I printed a brief account of it. 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 was, on the whole, as bad as it well could be, in great
contrast to the one Dr. Carus rejected. For although the system itself is
marked by extreme simplicity, 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. (RL 376, R 500:1-3, 1911 Dec 6)


Peirce criticizes his *description *of EGs in the "Prolegomena" article of
1906, directly contrasts it with his very first account of EGs in 1896-7,
and explicitly calls the Lowell Lectures and accompanying Syllabus "the
better exposition of 1903." He never *rejects *these or any other earlier
versions, and certainly never expresses the opinion that either R 670 or RL
231 from June 1911 is his "best" version. What he does say is that shading
is an improvement over cuts for distinguishing different areas--an
assessment with which I agree, as I have repeatedly acknowledged.

JFS: This problem is important for automatically relating two different
proof procedures.


Again, so what? Peirce's own words are unmistakably clear, over and over,
that he was not interested in facilitating "automatic" reasoning or
otherwise improving the efficiency of proof procedures, except as a very
secondary consideration. Instead, his overriding priority as a logician was
to analyze reasoning into its most fundamental and irreducible elements,
maximizing rather than minimizing the number of steps. He states this many
times, including but not limited to passages from 1880 (CP 3.173n), 1891
(8.316), 1902 (3.618, 4.373-375, 4.239), 1903 (4.424), and 1906 (4.581).

JFS: The 1911 EGs can be generalized beyond two dimensions for
"stereoscopic moving images".


This is true, but irrelevant. The scroll could be employed in three
dimensions simply by maintaining the requirement for a single point of
intersection between the outer and inner boundaries.

JFS: Note that observing if-then is impossible


This is false, as I already pointed out by quoting CP 3.363 (1885). We
observe if-then *diagrammatically *when we "see" that the consequent
follows necessarily from the antecedent, just like the deductive conclusion
of an argumentation follows necessarily from the premisses. As such, it is
a *logical* relation, not an *existential* relation. In fact, according to
Peirce, the same goes for coexistence (existence plus conjunction) and
identity.

CSP: We remark among Existential Graphs two that are *continuous*; that is,
they may be regarded as consisting of parts; but all parts of them are
perfectly homogeneous with the whole. Continuity is not an Existential
character; it only belongs to the Object of the nature of Laws.
Consequently, the Continuous Graphs do not express Existential Predicates
but only Logical Predicates. The two continuous Graphs are the Blank, which
expresses Coëxistence and the Line of Identity, which expresses Numerical
(i.e. individual) “Sameness.” (R 499(s):33, 1906)


Moreover, according to Peirce, it is incorrect to think that we become
acquainted with any of these *logical *relations by means of *existential *
observations.

CSP: The *Copulants *are likewise indispensable and have the property of
being *Continuant*. What I mean is that the sign "A is red" can be
decomposed so as to separate "is red" into a Copulative and a Descriptive,
thus: "A possesses the character of redness." But if we attempt to analyze
"possesses the character" in like manner, we get "A possesses the character
of the possession of the character of Redness"; and so on *ad infinitum*.
So it is, with "A implies B," "A implies its implication of B," etc. So
with "It rains and hails," "It rains concurrently 

Re: [PEIRCE-L] Existential Graphs in 1911

[Auke van Breemen]

From the list perspective:

Jas wrote:

I have said it before, I will say it again--we have different purposes, so we 
reach different conclusions.

--

Since perspective is important, it might be a good idea to explicate the 
differences in purpose each of you entertain.

best,

Auke

> Op 24 januari 2021 om 5:32 schreef "John F. Sowa" :
> 
> 
> Jon AS, List,
> 
> The *opinion* that the EG version of June 1911 is Peirce's best is 
> Peirce's own, as he stated in December, after six months of further 
> consideration.  The fact that he stated it in a lengthy letter to a member of 
> Lady Welby's significs group is further evidence of its importance.
> 
> That opinion is further supported by the development of logic in the 
> following century.  Please read beyond slide 12 of 
> http://jfsowa.com/talks/egintro.pdf .  See also 
> http://jfsowa.com/talks/ppe.pdf .  Slide 2 of ppe.pdf has a link to a 76-page 
> article published in the Journal of Applied Logics that goes into all the 
> details.
> 
> One of the most important features of the 1911 version is its ability to 
> serve as a foundation for Gerhard Gentzen's two systems of natural deduction 
> and clause form (published in 1934).  Those two system have had immense 
> influence on modern proof procedures -- including the development of modern 
> methods of computational theorem proving.
> 
> But in 1988, Larry Wos, one of the pioneers in theorem proving methods, 
> published an unsolved problem about relating Gentzen's two systems.  This 
> problem is important for automatically relating two different proof 
> procedures.  In 2011, I published the solution in Semiotica.  For a quick 
> outline, see egintro.pdf or ppe.pdf.  For the details, see the article in the 
> J. of Applied Logics.
> 
> That proof is clean and clear in terms of the 1911 EGs.  It's possible in 
> terms of the earlier versions, but it is more complex and harder to discover.
> 
> Another important point:  The 1911 EGs can be generalized beyond two 
> dimensions for "stereoscopic moving images".  It's not an accident that 
> Peirce mentioned them in L231, but he had not yet decided how to proceed with 
> the details.  ppe.pdf  (and the JAL article) present a generalization.  
> Whether that is what Peirce was thinking is not clear, but it shows that the 
> 1911 EGs are sufficient to support something along the lines that Peirce was 
> contemplating.
> 
> As for the point that negation must be inferred, please reread slides 11 
> and 12 of egintro.pdf.  Note that observing if-then is impossible (for a 
> lengthy discussion, see Hume and the lengthy debates that followed).
> 
> But the inference required for negation is quite simple:  If you expect 
> something and don't observe it, you can use the word 'not'.  Children learn 
> to use the word 'not' sometime after their second birthday -- around the same 
> time that they learn to use the words 'I' and 'you' correctly.  But they 
> don't learn to use 'if-then' and 'or' until much later.
> 
> And the idea that children (or even adults) would learn 'not' from the 
> derivation that Peirce presented in 1906 or the one in R669  is absurd.
> 
> There is much more to say about all these issues, but please read at 
> least to the end of egintro.pdf.  It also has many references for further 
> study.
> 
> John
> 
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Re: [PEIRCE-L] Existential Graphs in 1911

[John F. Sowa]

Jon AS, List, 
The *opinion* that the EG version of June 1911 is
Peirce's best is Peirce's own, as he stated in December, after six months
of further consideration.  The fact that he stated it in a lengthy letter
to a member of Lady Welby's significs group is further evidence of its
importance. 
That opinion is further supported by the development of
logic in the following century.  Please read beyond slide 12 of
http://jfsowa.com/talks/egintro.pdf .  See also
http://jfsowa.com/talks/ppe.pdf .  Slide 2 of ppe.pdf has a link to a
76-page article published in the Journal of Applied Logics that goes into
all the details.
One of the most important features of the 1911
version is its ability to serve as a foundation for Gerhard Gentzen's two
systems of natural deduction and clause form (published in 1934).  Those
two system have had immense influence on modern proof procedures --
including the development of modern methods of computational theorem
proving.
But in 1988, Larry Wos, one of the pioneers in theorem
proving methods, published an unsolved problem about relating Gentzen's
two systems.  This problem is important for automatically relating two
different proof procedures.  In 2011, I published the solution in
Semiotica.  For a quick outline, see egintro.pdf or ppe.pdf.  For the
details, see the article in the J. of Applied Logics.
That proof is
clean and clear in terms of the 1911 EGs.  It's possible in terms of the
earlier versions, but it is more complex and harder to
discover.
Another important point:  The 1911 EGs can be generalized
beyond two dimensions for "stereoscopic moving images".  It's
not an accident that Peirce mentioned them in L231, but he had not yet
decided how to proceed with the details.  ppe.pdf  (and the JAL article)
present a generalization.  Whether that is what Peirce was thinking is not
clear, but it shows that the 1911 EGs are sufficient to support something
along the lines that Peirce was contemplating.
As for the point that
negation must be inferred, please reread slides 11 and 12 of egintro.pdf. 
Note that observing if-then is impossible (for a lengthy discussion, see
Hume and the lengthy debates that followed).
But the inference
required for negation is quite simple:  If you expect something and don't
observe it, you can use the word 'not'.  Children learn to use the word
'not' sometime after their second birthday -- around the same time that
they learn to use the words 'I' and 'you' correctly.  But they don't learn
to use 'if-then' and 'or' until much later.
And the idea that
children (or even adults) would learn 'not' from the derivation that
Peirce presented in 1906 or the one in R669  is absurd.
There is
much more to say about all these issues, but please read at least to the
end of egintro.pdf.  It also has many references for further
study.
John
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Re: [PEIRCE-L] Existential Graphs in 1911

[Jon Alan Schmidt]

John, List, All:

JFS: Again, you have not cited any statements by Peirce after June 1911.
Therefore, nothing in your note contradicts the evidence that the 1911
version of EGs is Peirce's best and last available version.


That it is his *last *version is a fact, as far as we know. That it is
his *best
*version is an opinion. By what criteria? Simplest and most iconic? Sure.
Most analytical? Definitely not.

JFS: Furthermore, Peirce's letters of Sept. and Dec. 1911 explicitly reject
the version of 1906 on which R669 is based.


This is false, and we have been over it before. What Peirce rejects in
those two letters, as well as in another one that he wrote two years later,
is not "the version of 1906" but his lengthy and convoluted *description *of
EGs in "Prolegomena to an Apology for Pragmaticism." That is perfectly
consistent with my hypothesis that in June 1911, Peirce merely decided to
simplify his *presentation *of EGs for the uninitiated--the National
Academy of Sciences (R 670), J. H. Kehler (RL 231), A. Robert (RL 378), A.
D. Risteen (RL 376), and F. A. Woods (RL 477).

Moreover, he tells Risteen that the badness of the "Prolegomena"
description was "in great contrast to the one Dr. Carus rejected" way back
in 1896-7, and that the 1903 Lowell Lectures with accompanying Syllabus was
"the better exposition." He then tells Woods that the 1896-7 attempt was
"the most lucid and interesting paper I have ever written." In other words,
Peirce not only never *rejects *those earlier explanations, he
explicitly *reaffirms
*them.

What he has come to recognize, as he mentions to Risteen, is that shading
is vastly superior to cuts for distinguishing evenly and oddly enclosed
areas--something that I have repeatedly acknowledged myself, and even
implemented in my recently posted Synechistic EGs (
https://list.iupui.edu/sympa/arc/peirce-l/2021-01/msg00011.html). However,
it would be more accurate to say that he *rediscovers *this utility,
because he had already noticed it before. "The *blue *tint, however, of the
area within the cut is a great aid to the understanding" (R 490:13, 1906).
"Some slight shading with a blue pencil of the oddly enclosed areas will
conduce to clearness" (CP 4.617, 1908).

JFS: The most efficient theorem proving methods today do *not* depend on a
sign for if-then.


So what? Peirce was consistently adamant that the proper purpose of the
*philosophical* science of logic is not efficiency in proving theorems, but
thoroughness in analyzing the process of inference into its most basic
constituents. Treating negation as a primitive makes EGs more useful to a
mathematician as a calculus (minimum steps) but detracts from the primary
reason why Peirce the logician created them in the first place (maximum
steps). I have said it before, I will say it again--we have different
purposes, so we reach different conclusions.

JFS: By demoting the scroll to *nothing but* a nest of two negations,
Peirce's methods are a major simplification and clarification of Gentzen's
system.


One more time--Peirce never "demotes" the scroll; on the contrary, he
*explicitly
denies* that a consequence can be reduced to two negations.

CSP: Indeed, so far is the concept of *Sequence* from being a composite of
two Negations, that, on the contrary, the concept of the Negation of any
state of things, X, is, precisely, a composite of which one element is the
concept of Sequence. Namely, it is the concept of a sequence from X of the
essence of falsity. (R 300:50[51], 1908)


Again, as your own slide 11 rightly affirms, "Even negation ~ must be
inferred."

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Structural Engineer, Synechist Philosopher, Lutheran Christian
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt

On Sat, Jan 23, 2021 at 4:42 PM John F. Sowa  wrote:

> Jon, List,
>
> Again, you have not cited any statements by Peirce after June 1911.
> Therefore, nothing in your note contradicts the evidence that the 1911
> version of EGs is Peirce's best and last available version.
>
> Furthermore, Peirce's letters of Sept. and Dec. 1911 explicitly reject the
> version of 1906 on which R669 is based.  That does not mean that every
> statement he wrote about EGs prior to 1911 is obsolete, but it means that
> everything he wrote prior to June 1911 must be evaluated in terms of his
> 1911 version.
>
> Finally, an enormous amount of research on, with, and about logic has been
> done during the century following Peirce.  The claim that a "sign of
> illation" is important or even useful for inference is false.  The most
> efficient theorem proving methods today do *not* depend on a sign for
> if-then.
>
> I suggested slides 11 and 12 of http://jfsowa.com/talks/egintro.pdf in my
> previous note.  For further evidence why a sign for if-then can be an
> *impediment* to inference, please read the slides about Gentzen's method of
> natural deduction and Peirce's *improvement* on it.  For more detail, see
> the various 

Re: [PEIRCE-L] Existential Graphs in 1911

[John F. Sowa]

Jon, List,
Again, you have not cited any statements by Peirce
after June 1911.  Therefore, nothing in your note contradicts the evidence
that the 1911 version of EGs is Peirce's best and last available
version.
Furthermore, Peirce's letters of Sept. and Dec. 1911
explicitly reject the version of 1906 on which R669 is based.  That does
not mean that every statement he wrote about EGs prior to 1911 is
obsolete, but it means that everything he wrote prior to June 1911 must be
evaluated in terms of his 1911 version.
Finally, an enormous amount
of research on, with, and about logic has been done during the century
following Peirce.  The claim that a "sign of illation" is
important or even useful for inference is false.  The most efficient
theorem proving methods today do *not* depend on a sign for
if-then.
I suggested slides 11 and 12 of
http://jfsowa.com/talks/egintro.pdf in my previous note.  For further
evidence why a sign for if-then can be an *impediment* to inference,
please read the slides about Gentzen's method of natural deduction and
Peirce's *improvement* on it.  For more detail, see the various
references, especially http://jfsowa.com/talks/ppe.pdf .
By demoting
the scroll to *nothing but* a nest of two negations, Peirce's methods are
a major simplification and clarification of Gentzen's system.  Also note
that Frege's proof procedure, which is the basis for the Principia by
Whitehead and Russell, puts the sign for if-then at the center.  But that
results in a horribly complex proof procedure:  43 steps to prove a
theorem that takes 7 steps by Peirce's rules (which depend only on
negations).
There is much more to say about all these issues.  But
the main point is very clear:  In June 1911, Peirce realized that all
inferences depend on inserting or erasing graphs or parts of a graph in
positive or negative areas.  That's is the foundation for defining an
open-ended variety of derived rules of inference -- modus ponens is just
one of many.  Aristotle's syllogisms are others.  So are Gentzen's methods
and many versions used in computer systems.
John
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Re: [PEIRCE-L] Existential Graphs in 1911

[John F. Sowa]

Jon AS, 
All your citations are prior to R670, which demotes the
scroll to nothing but a way of drawing two ovals (negations) without
raising the pen.
In R670, Peirce states the three primitives: 
existence, conjunction, and negation.  And in L231, he drops the adjective
'illative' in front of the three permissions (rules of inference).  All
three of them are stated in terms of negations, and none of them mention
or depend on the scroll in any way.
Furthermore, the meaning of any
general is determined by its implications for the future.   Please read
the slides that introduce EGs to beginners (and advanced students who
learned the algebraic notations for logic): 
http://jfsowa.com/talks/egintro.pdf .
The first ten slides are a
basic intro.  But slides 11 and 12 state why the scroll (or any other
symbol for if-then) is not a primitive or necessary for deduction.  The
remaining slides show how Peirce's 1911 EGs are a major *improvement* on
the mainstream logics of the 20th century and why they are an important
foundation for the future.
As Peirce said explicitly in Sept. and
Dec. 1911, the 1906 version was as bad as it could be.   Unless you can
find any quotation after June 1911 where he uses the words 'illation' or
'illative' or deviates from his 1911 EGs, I consider the case to be
closed.
John
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Re: [PEIRCE-L] Existential Graphs in 1911

[Jon Alan Schmidt]

List, All:

For the benefit of those on the cc: line who are not List members, here is
a link to my entire post to which John Sowa was replying.

https://list.iupui.edu/sympa/arc/peirce-l/2021-01/msg2.html


In addition, here are links to an earlier exchange between us, in which I
provided several relevant excerpts from a 2016 paper by Bellucci and
Pietarinen (
https://www.cambridge.org/core/journals/review-of-symbolic-logic/article/existential-graphs-as-an-instrument-of-logical-analysis-part-i-alpha/9C4689940BDC5B17F739C34A87C2B77F
).

https://list.iupui.edu/sympa/arc/peirce-l/2020-12/msg00086.html
https://list.iupui.edu/sympa/arc/peirce-l/2020-12/msg00095.html


As they rightly observe, "Taking the idea of negation as primary is
philosophically inaccurate ... . Negation is not a primitive idea; rather,
it is a conception derived from that of implication. Therefore, the sign of
negation ought to be considered as a complication or determination of a
more primitive sign, the scroll" (pp. 220-221). I sincerely hope that Parts
II and III on Beta and Gamma are still forthcoming from them, and I would
welcome any feedback from them and/or others on what follows.

JFS: I realized that Peirce's insight on 2 June 1911 was that the adjective
'illative' is irrelevant and misleading for all three permissions (rules of
inference).


This is obviously false. Peirce does state in R 669 that although the
double cut rule "ought to be reckoned as a permission," it nevertheless "is
not an illative permission, i.e. a permission authorizing a species of
inference." However, he then goes on to present deletion/insertion as the
"First Illative Permission" and iteration/deiteration as the "Second
Illative Permission." In other words, only these two permissions are rules
of *inference*, such that together they "will suffice to enable any valid
deduction to be performed."

JFS: I believe that R669 is the *last* MS in which he wrote the words
'illative' or 'illation'.  I have not read all his extant MSS, but I very
strongly doubt that he would continue using a word he had rejected.


Omission is not rejection. I am not aware of any textual evidence that
Peirce ever explicitly *rejects *the words "illation" and "illative," let
alone the associated concept.

JFS: Any comment about modal issues in 1913 should be evaluated in terms of
the Delta graphs, for which we don't have any MSS.


I agree, with one major exception--there is an important modal aspect to
shading since it corresponds to a universe of possibility rather than
actuality. In fact, Peirce ultimately considers Beta EGs plus shading to be
the Gamma part (CP 4.576-581, 1906) as a welcome simplification of the
"nonsensical tinctures" that he later regrets introducing in "Prolegomena"
(RL 477, 1913). That is why a new Delta part would be necessary to include
and extend the additional modal considerations that he had explored
previously in the Gamma part of 1903.

JFS: In R670, negation is a primitive.  The scroll is nothing but a way of
drawing a nest of two negations without raising the pen.


I agree, and I continue to acknowledge that the same is true in RL 231, RL
378, and RL 376. However, I disagree strongly about Peirce's *reason *for
taking this approach. In my view, he deliberately *simplifies *his
presentation of EGs for the uninitiated, accepting the tradeoff of making
it *less analytical* by not explaining how shading for negation is derived
from the scroll for consequence. The latter is the true third primitive in
addition to the blank sheet for coexistence and the heavy line for identity.

CSP: We have seen that there are three relations which subsist between the
parts of graphs. The first is the relation expressed by the scroll. This is
the most important of all, since this is the relation of premiss and
conclusion; that is, if it be true that if A is true B is true, then should
A occur as a premiss we have a right to conclude B. The second relation is
that expressed by writing two graphs side by side AB, that is to say, the
relation of coexistence, and the third is the relation of individual
identity expressed by the heavy line. (R 466:18-19, 1903)


I am not aware of any textual evidence that Peirce ever explicitly *rejects
*this analysis.

JFS: Oostra's choice of the scroll as a marker for intuitionistic rules has
no similarity to Peirce's use for any version of EGs.


On the contrary, Peirce on multiple occasions uses the scroll to derive the
cut for negation from a consequence with falsity as its consequent (CP
4.402, 1903; CP 4.454-456, 1903; CP 4.564n, c. 1906; R 669:18-20[16-18],
1911). This is precisely how negation is defined in intuitionistic logic.
Moreover, he calls it an "error" and an "inaccuracy" to analyze "if A then
B," which is represented by a scroll, as strictly equivalent to "not-(A and
not-B)," which is represented by nested cuts (R 300:48-49[47-48], 1908).
The latter can be inferred from the former in intuitionistic logic, but not

Re: [PEIRCE-L] Existential Graphs in 1911

[John F. Sowa]

Jon AS, List,

For anyone who is not familiar with Peirce's 1911
EGs, see my
introduction to EGs, which is based on the 1911 version. 
The first
10 slides are sufficient for an overview. The remaining
slides show
features of the 1911 EGs that make a major advance over
the logics
of the 20th century: 
http://jfsowa.com/talks/egintro.pdf
  
The following comment
shows why Peirce rejected R669 and replaced
it with R670 and L231:

JAS> Peirce had a very good reason for not writing a third rule
at
the end of R 669, and it was not because "he suddenly
realized"
something at that moment in time and
"abruptly" abandoned his
previous train of thought.  It was
simply because he had already
stated the third rule a few paragraphs
earlier, and had explicitly
pointed out that it is not an illative
permission; i.e., it is not
a rule of inference.

After
reading that comment, I realized that Peirce's insight on
2 June 1911
was that the adjective 'illative' is irrelevant and
misleading for
all three permissions (rules of inference).  The
rules depend only on
negation.  They do not depend on a "sign of
illation", such
as a scroll or other symbol for if-then.

In L231, Peirce called
all three rules permissions (without the
adjective 'illative').  I
believe that R669 is the *last* MS in
which he wrote the words
'illative' or 'illation'.  I have not
read all his extant MSS, but I
very strongly doubt that he would
continue using a word he had
rejected.

See slides 11 and 12 of egintro.pdf for an
explanation in terms
of the 20th c logics.  For the details about
Peirce's five MSS that
document his development of the 1911 EGs and
his rejection R669, see
the attached file eg1911x,pdf.JAS> The
final sentences [of R669] note the inadequacy of automated
reasoning
to apply "the two illative permissions," since they
require
"a living intelligence" (R 669:23-24[21-22], LoF 1:584).

No.  Modern theorem provers can use Peirce's rules (and other
rules
derived from them) quite efficiently.  For an overview of the
issues,
see the slides in http://jfsowa.com/talks/ppe.pdf . For more
detail,
slide2 of ppe.pdf has a link to a 76-page article in the
Journal of
Applied Logics,

JAS> Unlike
"Prolegomena" (CP 4.569), none of these manuscripts
includes a "4th Permission" expressing "the strange
rule" that Peirce
deemed to be inconsistent with "the
reality of some possibilities" as
affirmed by his pragmatism (CP
4.580-581, 1906), such that he was
ultimately "sceptical as to
the universal validity of" it (RL 477:33[13], 1913).

That
gets into his modal logic, which he intended to replace with Delta
graphs.  Any comment about modal issues in 1913 should be evaluated
in terms of the Delta graphs, for which we don't have any MSS.

JAS> deriving negation from... a scroll with a blackened inner
close...
is more analytical because it preserves the fundamental
asymmetry of
reasoning and can thus be easily adapted for
intuitionistic/triadic
logic without excluded middle, which "is
universally true" (R
339:515[344r]).

No. In R670,
negation is a primitive.  The scroll is nothing but a
way of drawing
a nest of two negations without raising the pen.
Since negation is a
primitive in R670, it would be absurd to derive
negation from a nest
of two negations plus a pseudograph.

In structure, motivation,
and applications, intuitionistic and
3-valued logic are totally
different from each other and from any
version of Peirce's EGs. 
Oostra's choice of the scroll as a marker
for intuitionistic rules
has no similarity to Peirce's use for any
version of EGs.  There is
much more to say about these issues, and
I'll write another note
about them.

John


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[PEIRCE-L] Existential Graphs in 1911

[Jon Alan Schmidt]

List:

In light of the following statements by John Sowa last month, I decided to
take a fresh look at R 669-670, including both the online digital images (
https://rs.cms.hu-berlin.de/peircearchive/pages/home.php) and the
transcriptions published by Ahti-Veikko Pietarinen in 2014 (
https://www.researchgate.net/publication/271419583_Two_Papers_on_Existential_Graphs_by_Charles_Peirce)
as well as in the first volume of *Logic of the Future: Writings on
Existential Graphs* (LoF).

JFS: R669 is based on the 1906 notation, but it ends abruptly just after
Peirce wrote the first two rules of inference. He did not write the third
rule, even though there was enough room on the page. Five days later, he
began R670 with the same title, but with a summary of the new version. (
https://list.iupui.edu/sympa/arc/peirce-l/2020-12/msg00075/eg1911x.png)

JFS: While Peirce was writing the three EG rules of inference around 8 pm
on 2 June 1911, he suddenly realized that the rules depend *only* on
whether an area is positive or negative. (
https://list.iupui.edu/sympa/arc/peirce-l/2020-12/msg00087.html)


It turns out that Peirce had a very good reason for not writing a third
rule at the end of R 669, and it was *not *because "he suddenly realized"
something at that moment in time and "abruptly" abandoned his previous
train of thought. It was simply because he had *already *stated the third
rule a few paragraphs earlier, and had explicitly pointed out that it is
not an *illative *permission; i.e., it is not a rule of *inference*.

CSP: It now only remains to formulate those general permissions to modify
what has already been scribed which express the logicality of those several
forms of elementary deductive inference, out of which all other deductions
can be built up. There are but two of these general illative permissions;
but before stating them there is one other thing that has to be said.
Namely, it is to be imagined that every graph-instance anywhere on the
sheet can be freely moved about upon the sheet; and since a scroll both of
whose closes are empty asserts nothing, it is to be imagined that there is
an abundant store of empty scrolls on a part of the sheet that is out of
sight, whence one of them can be brought into view whenever desired. What
is here said ought to be reckoned as a permission, but it is not an
illative permission, i.e. a permission authorizing a species of inference.
(R 669:21-22[19-20], LoF 1:583)


Pietarinen comments in a footnote, "This corresponds to the double-cut
rule," which is the "Third Permission" in "Prolegomena to an Apology for
Pragmaticism" (CP 4.567, 1906). After proceeding to present
deletion/insertion as the "First Illative Permission" and
iteration/deiteration as the "Second Illative Permission," Peirce
concludes, "These two permissions will suffice to enable any valid
deduction to be performed" (R 669:23[21], LoF 1:584). This echoes his
remark in "Prolegomena" that "These two Rules (of Deletion and Insertion,
and of Iteration and Deiteration) are substantially all the undeduced
Permissions needed; the others being either Consequences or Explanations of
these" (CP 4.567). Hence the exposition of existential graphs in R 669 is
in fact complete, such that only "The few examples that shall forthwith be
given" are missing. The final sentences note the inadequacy of automated
reasoning to apply "the two illative permissions," since they require "a
living intelligence" (R 669:23-24[21-22], LoF 1:584).

Peirce does not discuss *any *of the transformation rules in R 670, whose
first page is dated five days after the last page of R 669. However, in RL
231 a couple of weeks later he presents deletion/insertion as the "1st
Permission," iteration/deiteration as the "2nd Permission," and double-cut
as the "3rd Permission" (NEM 3:166). His descriptions of the first two are
very similar to those in R 669, except that he replaces "evenly enclosed"
with "unshaded" and "oddly enclosed" with "shaded" as an alternative way of
distinguishing the different areas. For the third, he similarly refers to
"a vacant ring-shaped area" rather than "empty scrolls." Unlike
"Prolegomena" (CP 4.569), none of these manuscripts includes a "4th
Permission" expressing "the strange rule" that Peirce deemed to be
inconsistent with "the reality of some possibilities" as affirmed by his
pragmatism (CP 4.580-581, 1906), such that he was ultimately "sceptical as
to the universal validity of" it (RL 477:33[13], 1913).

Again, I readily acknowledge that shading is *more iconic* than thin oval
lines for signifying that oddly enclosed areas are a different surface from
evenly enclosed areas, representing a universe of possibilities rather than
the universe of actuality. I also concede that for classical/dyadic logic
with excluded middle, which "is not absolutely false" (R 339:515[344r],
1909), treating shading as a primitive for negation is *simpler *than
properly recognizing that the scroll is a primitive for consequence and