Re: [PEIRCE-L] Lowell Lecture 2.13 and 2.14

[Mary Libertin]

GaryF,

Thanks for leading us through Lecture 2. I’ve learned much and look forward
to the next part.

Mary



On Thu, Nov 30, 2017 at 11:36 AM <g...@gnusystems.ca> wrote:

> Jon, list,
>
>
>
> We can certainly call it “modesty” when Peirce introduces himself to Mr.
> Kehler as follows: “I am a person 72 years old. I have accomplished nothing
> in particular.” (Me too!)
>
>
>
> But that comment on EGs can’t be explained as modesty, because it is a
> *relative* judgement about aspects of his own work. There’s nothing
> modest about saying that some parts of your work are “bigger” or “smaller”
> than other parts. Anyway, he makes this remark on p. 23 of a 128-page
> letter, most of which is devoted to other matters; so it could well mean
> that in 1911 he no longer considered EGs all that important, compared to
> some of his other discoveries.
>
>
>
> I’m skeptical of John’s claim that Peirce must have copied much of the
> letter, including, the EG part, from papers he had written earlier. If the
> wording is *exactly the same* as another MS, that is likely to be the
> case; but you can’t read many of Peirce’s manuscripts without seeing that
> he often writes out things that he’s written many times before *in
> slightly different language*; and this is especially true as he gets
> older, probably because he doesn’t remember what he wrote before or at
> least isn’t about to dig through piles of papers to find it. (Being 72
> myself, I can well identify with this.) Besides, added to the end of the
> Kehler letter MS is what appears to be an earlier draft of parts of the
> letter, including the EG parts. When you’re copying something into a
> letter, you don’t make a draft of it.
>
>
>
> Anyway, now that I’ve been through Lowell 2, I think I have a much better
> idea of what existential graphs are good for, and that makes it easier to
> see how they fit into his whole philosophical system, and how they throw
> light on other parts of it. And I’m even more inclined to think that people
> who pick a few plums out of the Peircean pie and ignore the rest are likely
> to be missing its best features.
>
>
>
> Gary f.
>
>
>
> *From:* Jon Alan Schmidt [mailto:jonalanschm...@gmail.com]
> *Sent:* 30-Nov-17 10:05
> *To:* Gary Fuhrman <g...@gnusystems.ca>
> *Cc:* peirce-l@list.iupui.edu
>
>
> *Subject:* Re: [PEIRCE-L] Lowell Lecture 2.13 and 2.14
>
>
>
> Gary F., List:
>
>
>
> I suspect that it was another case of Peirce being modest in this
> particular letter, since elsewhere he referred to the existential graphs as
> "my chef d'oeuvre" (letter to Jourdain, 1908; given by the editors as the
> subtitle for CP 4.347-584).
>
>
>
> Regards,
>
>
> Jon Alan Schmidt - Olathe, Kansas, USA
>
> Professional Engineer, Amateur Philosopher, Lutheran Layman
>
> www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
>
>
>
> On Wed, Nov 29, 2017 at 3:00 PM, <g...@gnusystems.ca> wrote:
>
> One remark I found interesting in the Kehler letter after Peirce had taken
> several pages to explain the syntax of the graphs: on p. 23 he wrote, “By
> the space that I have occupied in explaining this syntax, you will surely
> think it is my chief work. On the contrary, it is one of the smallest, but
> it is the only one of which I could put you in a position to gain some
> understanding without writing a book about it.” That certainly alters my
> impression of the importance Peirce ascribed to his existential graphs. And
> just when I’m beginning to take them more seriously myself!
>
> --
null

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Re: [PEIRCE-L] Lowell Lecture 2.13 and 2.14

[Jon Alan Schmidt]

Gary F., List:

Perhaps by "smallest" he simply meant what he then went on to say
explicitly--that he was capable of explaining the EGs in a letter, but
would need to write an entire book in order to describe any of his other
work adequately; i.e., it was a comment about the length of text required,
rather than the subject matter's importance.

Regards,

Jon S.

On Thu, Nov 30, 2017 at 10:36 AM, <g...@gnusystems.ca> wrote:

> Jon, list,
>
>
>
> We can certainly call it “modesty” when Peirce introduces himself to Mr.
> Kehler as follows: “I am a person 72 years old. I have accomplished nothing
> in particular.” (Me too!)
>
>
>
> But that comment on EGs can’t be explained as modesty, because it is a
> *relative* judgement about aspects of his own work. There’s nothing
> modest about saying that some parts of your work are “bigger” or “smaller”
> than other parts. Anyway, he makes this remark on p. 23 of a 128-page
> letter, most of which is devoted to other matters; so it could well mean
> that in 1911 he no longer considered EGs all that important, compared to
> some of his other discoveries.
>
>
>
> I’m skeptical of John’s claim that Peirce must have copied much of the
> letter, including, the EG part, from papers he had written earlier. If the
> wording is *exactly the same* as another MS, that is likely to be the
> case; but you can’t read many of Peirce’s manuscripts without seeing that
> he often writes out things that he’s written many times before *in
> slightly different language*; and this is especially true as he gets
> older, probably because he doesn’t remember what he wrote before or at
> least isn’t about to dig through piles of papers to find it. (Being 72
> myself, I can well identify with this.) Besides, added to the end of the
> Kehler letter MS is what appears to be an earlier draft of parts of the
> letter, including the EG parts. When you’re copying something into a
> letter, you don’t make a draft of it.
>
>
>
> Anyway, now that I’ve been through Lowell 2, I think I have a much better
> idea of what existential graphs are good for, and that makes it easier to
> see how they fit into his whole philosophical system, and how they throw
> light on other parts of it. And I’m even more inclined to think that people
> who pick a few plums out of the Peircean pie and ignore the rest are likely
> to be missing its best features.
>
>
>
> Gary f.
>
>
>
> *From:* Jon Alan Schmidt [mailto:jonalanschm...@gmail.com]
> *Sent:* 30-Nov-17 10:05
> *To:* Gary Fuhrman <g...@gnusystems.ca>
> *Cc:* peirce-l@list.iupui.edu
> *Subject:* Re: [PEIRCE-L] Lowell Lecture 2.13 and 2.14
>
>
>
> Gary F., List:
>
>
>
> I suspect that it was another case of Peirce being modest in this
> particular letter, since elsewhere he referred to the existential graphs as
> "my chef d'oeuvre" (letter to Jourdain, 1908; given by the editors as the
> subtitle for CP 4.347-584).
>
>
>
> Regards,
>
>
> Jon Alan Schmidt - Olathe, Kansas, USA
>
> Professional Engineer, Amateur Philosopher, Lutheran Layman
>
> www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
>
>
>
> On Wed, Nov 29, 2017 at 3:00 PM, <g...@gnusystems.ca> wrote:
>
> One remark I found interesting in the Kehler letter after Peirce had taken
> several pages to explain the syntax of the graphs: on p. 23 he wrote, “By
> the space that I have occupied in explaining this syntax, you will surely
> think it is my chief work. On the contrary, it is one of the smallest, but
> it is the only one of which I could put you in a position to gain some
> understanding without writing a book about it.” That certainly alters my
> impression of the importance Peirce ascribed to his existential graphs. And
> just when I’m beginning to take them more seriously myself!
>
>

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RE: [PEIRCE-L] Lowell Lecture 2.13 and 2.14

[gnox]

Jon, list,

 

We can certainly call it “modesty” when Peirce introduces himself to Mr. Kehler 
as follows: “I am a person 72 years old. I have accomplished nothing in 
particular.” (Me too!)

 

But that comment on EGs can’t be explained as modesty, because it is a relative 
judgement about aspects of his own work. There’s nothing modest about saying 
that some parts of your work are “bigger” or “smaller” than other parts. 
Anyway, he makes this remark on p. 23 of a 128-page letter, most of which is 
devoted to other matters; so it could well mean that in 1911 he no longer 
considered EGs all that important, compared to some of his other discoveries.

 

I’m skeptical of John’s claim that Peirce must have copied much of the letter, 
including, the EG part, from papers he had written earlier. If the wording is 
exactly the same as another MS, that is likely to be the case; but you can’t 
read many of Peirce’s manuscripts without seeing that he often writes out 
things that he’s written many times before in slightly different language; and 
this is especially true as he gets older, probably because he doesn’t remember 
what he wrote before or at least isn’t about to dig through piles of papers to 
find it. (Being 72 myself, I can well identify with this.) Besides, added to 
the end of the Kehler letter MS is what appears to be an earlier draft of parts 
of the letter, including the EG parts. When you’re copying something into a 
letter, you don’t make a draft of it.

 

Anyway, now that I’ve been through Lowell 2, I think I have a much better idea 
of what existential graphs are good for, and that makes it easier to see how 
they fit into his whole philosophical system, and how they throw light on other 
parts of it. And I’m even more inclined to think that people who pick a few 
plums out of the Peircean pie and ignore the rest are likely to be missing its 
best features.

 

Gary f. 

 

From: Jon Alan Schmidt [mailto:jonalanschm...@gmail.com] 
Sent: 30-Nov-17 10:05
To: Gary Fuhrman <g...@gnusystems.ca>
Cc: peirce-l@list.iupui.edu
Subject: Re: [PEIRCE-L] Lowell Lecture 2.13 and 2.14

 

Gary F., List:

 

I suspect that it was another case of Peirce being modest in this particular 
letter, since elsewhere he referred to the existential graphs as "my chef 
d'oeuvre" (letter to Jourdain, 1908; given by the editors as the subtitle for 
CP 4.347-584).

 

Regards,




Jon Alan Schmidt - Olathe, Kansas, USA

Professional Engineer, Amateur Philosopher, Lutheran Layman

www.LinkedIn.com/in/JonAlanSchmidt <http://www.LinkedIn.com/in/JonAlanSchmidt>  
- twitter.com/JonAlanSchmidt <http://twitter.com/JonAlanSchmidt> 

 

On Wed, Nov 29, 2017 at 3:00 PM, <g...@gnusystems.ca 
<mailto:g...@gnusystems.ca> > wrote:

One remark I found interesting in the Kehler letter after Peirce had taken 
several pages to explain the syntax of the graphs: on p. 23 he wrote, “By the 
space that I have occupied in explaining this syntax, you will surely think it 
is my chief work. On the contrary, it is one of the smallest, but it is the 
only one of which I could put you in a position to gain some understanding 
without writing a book about it.” That certainly alters my impression of the 
importance Peirce ascribed to his existential graphs. And just when I’m 
beginning to take them more seriously myself!


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Re: [PEIRCE-L] Lowell Lecture 2.13 and 2.14

[Jon Alan Schmidt]

Gary F., List:

I suspect that it was another case of Peirce being modest in this
particular letter, since elsewhere he referred to the existential graphs as
"my chef d'oeuvre" (letter to Jourdain, 1908; given by the editors as the
subtitle for CP 4.347-584).

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt

On Wed, Nov 29, 2017 at 3:00 PM,  wrote:

> One remark I found interesting in the Kehler letter after Peirce had taken
> several pages to explain the syntax of the graphs: on p. 23 he wrote, “By
> the space that I have occupied in explaining this syntax, you will surely
> think it is my chief work. On the contrary, it is one of the smallest, but
> it is the only one of which I could put you in a position to gain some
> understanding without writing a book about it.” That certainly alters my
> impression of the importance Peirce ascribed to his existential graphs. And
> just when I’m beginning to take them more seriously myself!
>

-
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Re: [PEIRCE-L] Lowell Lecture 2.13 and 2.14

[John F Sowa]

On 11/29/2017 4:00 PM, g...@gnusystems.ca wrote:
I gather that your reason for concluding that the 1909/11 rendition 
of EGs was “preferred” by Peirce is that he knew that his letter 
to Kehler would be widely circulated among Lady Welby’s circle and

thought that they could gain more recognition in that way...
that is circumstantial evidence. 


He went to a lot of effort to copy an amount of text that fills
52 printed pages of NEM.  Why did he do that if he didn't expect
to get recognition from Lady Welby and her colleagues?


as far as I can see in the Kehler letter, the boundaries of shaded
regions are precisely and operationally equivalent to cuts. You are
right that the shaded versions are easier to read at a glance,
especially when the enclosures are deeply nested.


Yes.  That's why there is nothing lost when you map the earlier
versions to the later version.


if you have occasion to erase or deiterate a graph in a shaded
area, you have to do it without erasing the shading and thus
negating the negation.


Peirce wrote his MSS in ink.  It wasn't a problem for him then,
and it's not a problem for our computers today.


There is also something of logical importance lost in substituting
shading for cuts.


No.  Every graph and proof in the older notations can be translated
to an isomorphic graph or proof in the 1909/1911 notation.  Therefore,
nothing of logical importance can be lost.


after Peirce had taken several pages to explain the syntax of the
graphs... “By the space that I have occupied in explaining this
syntax, you will surely think it is my chief work. On the contrary,
it is one of the smallest...” That certainly alters my impression
of the importance Peirce ascribed to his existential graphs.


I agree that all the versions of EGs have expressive power that does
not go beyond the algebraic notations.  That is one reason why I would
choose the simplest version.

But I suspect that Peirce had a much broader vision that lies behind
his claim that EGs offer a vision of the "mind in thought".

In a note to Jerry LRC, I said that we can't put words in Peirce's
mouth.  So I won't make any claims about what he may have thought.
However, he did leave some tantalizing hints in his desire for
stereoscopic equipment.

One reason why I prefer Peirce's later notation is that it can be
generalized to include *icons* -- and not just 2D diagrams.  They
could be 3D or even 4D (3D + time) "moving images of the action
of the mind in thought".  Following are some slides I presented
in 2015 and am now converting to a more detailed article:
http://jfsowa.com/talks/natlog.pdf .

See slide 69 (copied below), which summarizes the issues.  Peirce's
EGs of 1909/1911 with shading can be generalized to a version that
can address those questions.  But the versions with cuts cannot.

I won't claim that Peirce envisioned this extension in detail,
but his comments inspired me to generalize his EGs in this way.

John


  REASONING WITH AND ABOUT IMAGES

Human language is based on the way people think.  And thinking
is intimately integrated with perception and action.

Icons are more fundamental than indexes and symbols.
● As Damasio said, “Images are the currency of our thought.”
● Icons are derived from perception and serve as goals for action.

How could computer systems reason with icons?
● Start with a graphic notation for logic.
● Incorporate icons as an integral part of the logic.
● Generalize the rules of inference to use icons.
● Generalize the model-theoretic semantics.
● Result: A multimedia logic.

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RE: [PEIRCE-L] Lowell Lecture 2.13 and 2.14

[gnox]

John,

 

Summing up your detailed explanation, I gather that your reason for concluding 
that the 1909/11 rendition of EGs was “preferred” by Peirce is that he knew 
that his letter to Kehler would be widely circulated among Lady Welby’s circle 
and thought that they could gain more recognition in that way. I have my doubts 
whether he could have assumed that, but in any case, that is circumstantial 
evidence. Your reasons for preferring it yourself are clear enough, but I see 
nothing that convinces me that Peirce preferred the 1909/11 version for those 
reasons.

 

You have a preference for “positive (unshaded) and negative (shaded) regions” 
as opposed to “evenly and oddly enclosed areas” (respectively), but as far as I 
can see in the Kehler letter, the boundaries of shaded regions are precisely 
and operationally equivalent to cuts. You are right that the shaded versions 
are easier to read at a glance, especially when the enclosures are deeply 
nested; but there’s also a physical problem with implementing that notation, 
because if you have occasion to erase or deiterate a graph in a shaded area, 
you have to do it without erasing the shading and thus negating the negation.

There is also something of logical importance lost in substituting shading for 
cuts, and that will (I hope) become clear when we look at the next section of 
Lowell 2 (17), so I won’t go into it now. What I will say is, first, Thanks for 
directing my attention to MS L 231; I don’t have access to NEM 3 (except by 
doing a Google search for an unusual phrase in the letter), but now that I’ve 
found a copy of the manuscript online I’ve been reading it with great interest. 
Second, based on that reading, I think you’ve exaggerated the differences 
between the Lowell presentation of EGs and the 1911 presentation in that 
letter. Almost all the differences are due to changes in terminology, such as 
the change from “hooks” to “pegs”; the features named by those terms perform 
exactly the same functions in both versions. In fact, I would say that after 
some complex experimentation with the gamma graphs around 1906, Peirce 
“simplified” his EGs by simply returning to the 1903 version (with very minor 
changes) and leaving out most of the rationale for it. But we can argue that 
point as we move on with Lowell 2.

 

One remark I found interesting in the Kehler letter after Peirce had taken 
several pages to explain the syntax of the graphs: on p. 23 he wrote, “By the 
space that I have occupied in explaining this syntax, you will surely think it 
is my chief work. On the contrary, it is one of the smallest, but it is the 
only one of which I could put you in a position to gain some understanding 
without writing a book about it.” That certainly alters my impression of the 
importance Peirce ascribed to his existential graphs. And just when I’m 
beginning to take them more seriously myself!

 

Gary f.

 

-Original Message-
From: John F Sowa [mailto:s...@bestweb.net] 
Sent: 29-Nov-17 14:28
To: peirce-l@list.iupui.edu
Cc: Dau, Frithjof <frithjof@sap.com>
Subject: Re: [PEIRCE-L] Lowell Lecture 2.13 and 2.14

 

Gary,

 

Please look at the attached diagram egprim.gif.  EGs are truly

diagrammatic:  Every syntactic feature can be shown without any use of 
language.  This is slide 4 of  <http://jfsowa.com/talks/egintro.pdf> 
http://jfsowa.com/talks/egintro.pdf .

 

I apologize for the mistake about 'spot'.  I checked Don Roberts' book, which I 
first read almost 40 years ago.  Don dutifully noted that Peirce had used the 
word 'spot' for the place where the name of a rhema was written.  But it just 
seemed weird to say that the spot, not the name, represented a rhema or 
predicate.

 

I also checked Don's glossary, which contains over 50 terms for talking about 
EGs.  Many of them are about semantics.  But to talk about the syntax, you only 
need 6 terms:  line of identity, relation, enclose, shaded area, unshaded area, 
and peg.  All other terminology is about notation-independent logical issues.

 

> [GF] I must apologize to the list for introducing the term “dot”

> into this discussion, as Peirce actually uses that term not in Lowell 

> 2, but in some of his other explanations of existential graphs, 

> notably CP 4.438:

> 

> [CSP] Let a heavy dot or dash be used in place of a noun which has 

> been erased from a proposition. A blank form of proposition produced 

> by such erasures as can be filled, each with a proper name, to make a 

> proposition again, is called a rhema, or, relatively to the 

> proposition of which it is conceived to be a part, the predicate of 

> that proposition.”

 

By the way, this operation is equivalent to Church's lambda abstraction about 
30 years later.  See slide 15 of  <http://jfsowa.com/egintro.pdf> 
http://jfsowa.com/egintro.pdf .

It's important to show the equivalence, but it's irrelevant Whether you use a 
blank, a dot, a

Re: [PEIRCE-L] Lowell Lecture 2.13 and 2.14

[John F Sowa]

Gary,

Please look at the attached diagram egprim.gif.  EGs are truly
diagrammatic:  Every syntactic feature can be shown without any use
of language.  This is slide 4 of http://jfsowa.com/talks/egintro.pdf .

I apologize for the mistake about 'spot'.  I checked Don Roberts' book,
which I first read almost 40 years ago.  Don dutifully noted that Peirce
had used the word 'spot' for the place where the name of a rhema was
written.  But it just seemed weird to say that the spot, not the name,
represented a rhema or predicate.

I also checked Don's glossary, which contains over 50 terms for talking
about EGs.  Many of them are about semantics.  But to talk about the
syntax, you only need 6 terms:  line of identity, relation, enclose,
shaded area, unshaded area, and peg.  All other terminology is about
notation-independent logical issues.


[GF] I must apologize to the list for introducing the term “dot”
into this discussion, as Peirce actually uses that term not in Lowell 2,
but in some of his other explanations of existential graphs, notably
CP 4.438:

[CSP] Let a heavy dot or dash be used in place of a noun which has
been erased from a proposition. A blank form of proposition produced
by such erasures as can be filled, each with a proper name, to make a
proposition again, is called a rhema, or, relatively to the proposition
of which it is conceived to be a part, the predicate of that
proposition.”


By the way, this operation is equivalent to Church's lambda abstraction
about 30 years later.  See slide 15 of http://jfsowa.com/egintro.pdf .
It's important to show the equivalence, but it's irrelevant Whether
you use a blank, a dot, an underscore, or the Greek letter λ.


It could be argued that Peirce’s terminology in referring to a graph
as a “word” is rather sloppy, but after all, this is a personal letter
from a self-described “garrulous old man” to a new acquaintance.


That statement is wrong for several reasons:

1. Peirce had said that every part of an EG asserts something.
The line asserts existence, the predicate named 'man' asserts a type
of entity, and the connection asserts the type of the existing thing.
I admit that modern terminology does not say that a predicate, by
itself, makes an assertion.  But Peirce did so on various occasions.

2. Peirce wrote that letter in reply to "Mr. Kehler", who was a
member of Lady Welby's Significs group.  We don't have the original
letter by Kehler, but it probably began with a flowery introduction
to the esteemed professor Peirce.  In response, Peirce deliberately
described himself very modestly, and he used the word 'garrulous'
as an apology for the length of the letter.

3. This letter is far more important than a casual note to a friend.
Lady Welby had circulated Peirce's letters among the members of her
group, which included many prominent British intellectuals.  Note
that Ogden & Richards included copies of some of Peirce's letters
in the appendix of their book, _The Meaning of 'Meaning'_.


It is not an explanation of EGs intended for publication. I’d like
to know your reasons for claiming that this presentation is Peirce’s
“preferred” version of EGs.


By 1911, Peirce had given up hope of getting further writings published.
The length of the letter (52 printed pages in NEM vol. 3) indicates its
importance.  The practice of sharing letters in Lady  Welby's group was
his best chance of getting a prominent group of scholars to read it.

The length of the letter and the amount of technical detail in it shows
that he copied material from various manuscripts.  I had discovered the
EG content in 2000 from a transcription of MS 514 by Michel Balat. That
MS was dated 1909, when Peirce might have had some hopes of publication.
The fact that he chose that MS to copy for his letter of 1911 indicates
(a) its importance, and (b) its value as a tutorial about the essential
features of EGs.

Finally, any EG from RTL (1898) or later could be redrawn with the
conventions of 1911, and any proof by any earlier rules could be
translated line-by-line to an equivalent proof by the later rules.
But the later version has important advantages:

 1. The shading makes the graphs more readable *and* more iconic:
it directly shows which rules of inference are applicable.

 2. The syntax is described with fewer words, and the rules
of inference are shorter and more general.  There is no need
to distinguish Alpha and Beta graphs, since they use exactly
the same rules of inference.

 3. The generality of the 1909/1911 rules may be the result of
Peirce's thinking about moving pictures and stereoscopic
imagery.  They are no longer tied to a "sheet" and they
could be applied without change to 3D images or even
3D+time for movies.

 4. As a result of that generality, the rules can be applied
to any notation for logic that allows a distinction between
positive (unshaded) and negative (shaded) regions.  For
examples, see egintro.pdf, slide 23 ff.

RE: [PEIRCE-L] Lowell Lecture 2.13 and 2.14

[gnox]

John,

 

Unfortunately you've added to the rampant confusion by saying that "a spot is 
just a very short line of identity.” This is not true of Peirce’s “final 
preferred version” of EGs because, as you point out yourself, he does not use 
the term “spot” in that version. And it is not true of Lowell 2, because in 
that text, a “line of identity” (however short) is not a “spot”: rather the end 
of that line must be attached to a “spot” (rheme, predicate) at one of its 
“hooks” or “pegs” in order to form a complete graph representing the 
subject-and-predicate (-and-copula, if you like).

 

See the new commentary on 2.14 which I posted just now. 

 

Gary f.

 

-Original Message-
From: John F Sowa [mailto:s...@bestweb.net] 
Sent: 27-Nov-17 02:06
To: peirce-l@list.iupui.edu
Cc: Dau, Frithjof <frithjof@sap.com>
Subject: Re: [PEIRCE-L] Lowell Lecture 2.13 and 2.14

 

Gary F, Mary L, Kirsti, Jerry LRC, and list,

 

In 1911, Peirce presented his clearest and simplest version of EGs.

He explained the essentials in just 8 pages of NEM (3:162 to 169).

I believe that it is his final preferred version, and I'll use it for 
explaining issues about the more complex 1903 version.

 

Gary

> [Mary's] question about the “blot” has me thinking again about “the 

> two peculiar graphs” which are “the blank place which asserts only 

> what is already well-understood between us to be true, and the blot 

> which asserts something well understood to be false”

 

Kirsti,

> instead of warning against confusing SPOT, DOT and BLOT, it would have 

> been most interesting to hear how they are related.

 

In his 1911 terminology, Peirce did not use the words 'spot', 'dot', or 'blot'. 
 Instead, a spot is just a very short line of identity.

The line represents an existential quantifier, and there is no reason to 
distinguish long lines from short lines (spots).

 

He used the word 'peg' instead of 'dot'.   Each relation has zero

or more pegs, to which lines of identity may be attached.

 

He also shaded negative areas (nested in an odd number of negations) and left 
positive areas unshaded (nested in an even number, zero or more, negations).  A 
blot is just a shaded area that contains nothing but a blank.

 

Gary

> [The blank place and the blot] are peculiar in several ways, and each 

> is in some sense the opposite of the other.

 

Each is the negation of the other.  The blank place is unshaded, and the blot 
is a shaded blank.

 

Gary

> For instance, the blank cannot be erased, but any graph can be added 

> to it on the sheet of assertion; while the blot can be erased, but 

> nothing can be added to it, because it “fills up its area.”

 

One reason why the "the blank place" is "peculiar" is that Peirce had talked 
about it in two different ways.  He called the sheet of assertion the universe 
of discourse when it contains all the EGs that Graphist and Grapheus agree is 
true.

 

But the blank, by itself, is true before anything is asserted.

In modern terminology, the blank is Peirce's only axiom.  Any EG that can be 
proved without any other assumptions is a theorem.

 

In 1911, Peirce clarified that issues by using two distinct terms:

'the universe' and 'a sheet of paper'.  The sheet is no longer identified with 
the universe, and there is no reason why one couldn't or shouldn't shade a 
blank area of a sheet.

 

Gary, quoting Peirce

> [A blot] "fills up its area."

 

In 1911, Peirce no longer used this metaphor.  With the rules of 1903 or 1911, 
a blot or a shaded blank implies every graph.

To prove that any graph g can be proved from it:

 

  1. Start with a sheet of paper that contains a shaded blank.

 

  2. By the rule of insertion in a shaded area, insert the graph

 for not-g inside the shaded area.  All the shaded areas of not-g

 then become unshaded, and the unshaded areas become shaded.

 

  3. The resulting graph consists of g in an unshaded area that is

 surrounded by a shaded ring that represents a double negation.

 

  4. Finally, erase the double negation to derive g.

 

Another important point:  In 1911, Peirce allowed any word, not just verbs, to 
be the name of a relation.  From NEM, page 3.162:

> Every word makes an assertion.  Thus ——man means "There is a man" 

> in whatever universe the whole sheet refers to.  The dash before "man" 

> is the "line of identity."

 

This EG is Peirce's first example in 1911.  And note that he begins with a Beta 
graph.  In fact, he does not even mention the distinction between Alpha and 
Beta.  The same rules of inference apply to both.

 

For Peirce's version of 1911 with my commentary, see  
<http://jfsowa.com/peirce/ms514.htm> http://jfsowa.com/peirce/ms514.htm

 

Jerry,

> CSP’s genius [etc.] make it difficult for anyone to project his 

> thoughts into rarefied logical,

Re: [PEIRCE-L] Lowell Lecture 2.13 and 2.14

[kirstima]

John,

Thank you very much! - I was wondering why I did not find PEG in the 
list.


Now it's all making sense.

With gratitude,

Kirsti

John F Sowa kirjoitti 27.11.2017 09:05:

Gary F, Mary L, Kirsti, Jerry LRC, and list,

In 1911, Peirce presented his clearest and simplest version of EGs.
He explained the essentials in just 8 pages of NEM (3:162 to 169).
I believe that it is his final preferred version, and I'll use it
for explaining issues about the more complex 1903 version.

Gary

[Mary's] question about the “blot” has me thinking again about
“the two peculiar graphs” which are “the blank place which asserts
only what is already well-understood between us to be true, and
the blot which asserts something well understood to be false”


Kirsti,

instead of warning against confusing SPOT, DOT and BLOT, it would
have been most interesting to hear how they are related.


In his 1911 terminology, Peirce did not use the words 'spot', 'dot',
or 'blot'.  Instead, a spot is just a very short line of identity.
The line represents an existential quantifier, and there is no
reason to distinguish long lines from short lines (spots).

He used the word 'peg' instead of 'dot'.   Each relation has zero
or more pegs, to which lines of identity may be attached.

He also shaded negative areas (nested in an odd number of negations)
and left positive areas unshaded (nested in an even number, zero or
more, negations).  A blot is just a shaded area that contains
nothing but a blank.

Gary

[The blank place and the blot] are peculiar in several ways,
and each is in some sense the opposite of the other.


Each is the negation of the other.  The blank place is unshaded,
and the blot is a shaded blank.

Gary

For instance, the blank cannot be erased, but any graph can be
added to it on the sheet of assertion; while the blot can be
erased, but nothing can be added to it, because it “fills up
its area.”


One reason why the "the blank place" is "peculiar" is that Peirce
had talked about it in two different ways.  He called the sheet
of assertion the universe of discourse when it contains all the
EGs that Graphist and Grapheus agree is true.

But the blank, by itself, is true before anything is asserted.
In modern terminology, the blank is Peirce's only axiom.  Any EG
that can be proved without any other assumptions is a theorem.

In 1911, Peirce clarified that issues by using two distinct terms:
'the universe' and 'a sheet of paper'.  The sheet is no longer
identified with the universe, and there is no reason why one
couldn't or shouldn't shade a blank area of a sheet.

Gary, quoting Peirce

[A blot] "fills up its area."


In 1911, Peirce no longer used this metaphor.  With the rules
of 1903 or 1911, a blot or a shaded blank implies every graph.
To prove that any graph g can be proved from it:

 1. Start with a sheet of paper that contains a shaded blank.

 2. By the rule of insertion in a shaded area, insert the graph
for not-g inside the shaded area.  All the shaded areas of not-g
then become unshaded, and the unshaded areas become shaded.

 3. The resulting graph consists of g in an unshaded area that is
surrounded by a shaded ring that represents a double negation.

 4. Finally, erase the double negation to derive g.

Another important point:  In 1911, Peirce allowed any word, not
just verbs, to be the name of a relation.  From NEM, page 3.162:
Every word makes an assertion.  Thus ——man means "There is a man" in 
whatever universe the whole sheet refers to.  The dash before

"man" is the "line of identity."


This EG is Peirce's first example in 1911.  And note that he begins
with a Beta graph.  In fact, he does not even mention the distinction
between Alpha and Beta.  The same rules of inference apply to both.

For Peirce's version of 1911 with my commentary, see
http://jfsowa.com/peirce/ms514.htm

Jerry,

CSP’s genius [etc.] make it difficult for anyone to project his
thoughts into rarefied logical, mathematical, scientific or
philosophical atmospheres.


Yes.  He wrote volumes of insights that we still need to explore.
But you can't put words in his mouth.  If you can't find where he
stated something explicitly, you can't claim him as the source.

Note my discussion above.  Every one of my claims is based on
something that Peirce explicitly wrote.

John



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Re: [PEIRCE-L] Lowell Lecture 2.13 and 2.14

[John F Sowa]

Gary F, Mary L, Kirsti, Jerry LRC, and list,

In 1911, Peirce presented his clearest and simplest version of EGs.
He explained the essentials in just 8 pages of NEM (3:162 to 169).
I believe that it is his final preferred version, and I'll use it
for explaining issues about the more complex 1903 version.

Gary

[Mary's] question about the “blot” has me thinking again about
“the two peculiar graphs” which are “the blank place which asserts
only what is already well-understood between us to be true, and
the blot which asserts something well understood to be false”


Kirsti,

instead of warning against confusing SPOT, DOT and BLOT, it would
have been most interesting to hear how they are related. 


In his 1911 terminology, Peirce did not use the words 'spot', 'dot',
or 'blot'.  Instead, a spot is just a very short line of identity.
The line represents an existential quantifier, and there is no
reason to distinguish long lines from short lines (spots).

He used the word 'peg' instead of 'dot'.   Each relation has zero
or more pegs, to which lines of identity may be attached.

He also shaded negative areas (nested in an odd number of negations)
and left positive areas unshaded (nested in an even number, zero or
more, negations).  A blot is just a shaded area that contains
nothing but a blank.

Gary

[The blank place and the blot] are peculiar in several ways,
and each is in some sense the opposite of the other.


Each is the negation of the other.  The blank place is unshaded,
and the blot is a shaded blank.

Gary

For instance, the blank cannot be erased, but any graph can be
added to it on the sheet of assertion; while the blot can be
erased, but nothing can be added to it, because it “fills up
its area.”


One reason why the "the blank place" is "peculiar" is that Peirce
had talked about it in two different ways.  He called the sheet
of assertion the universe of discourse when it contains all the
EGs that Graphist and Grapheus agree is true.

But the blank, by itself, is true before anything is asserted.
In modern terminology, the blank is Peirce's only axiom.  Any EG
that can be proved without any other assumptions is a theorem.

In 1911, Peirce clarified that issues by using two distinct terms:
'the universe' and 'a sheet of paper'.  The sheet is no longer
identified with the universe, and there is no reason why one
couldn't or shouldn't shade a blank area of a sheet.

Gary, quoting Peirce

[A blot] "fills up its area."


In 1911, Peirce no longer used this metaphor.  With the rules
of 1903 or 1911, a blot or a shaded blank implies every graph.
To prove that any graph g can be proved from it:

 1. Start with a sheet of paper that contains a shaded blank.

 2. By the rule of insertion in a shaded area, insert the graph
for not-g inside the shaded area.  All the shaded areas of not-g
then become unshaded, and the unshaded areas become shaded.

 3. The resulting graph consists of g in an unshaded area that is
surrounded by a shaded ring that represents a double negation.

 4. Finally, erase the double negation to derive g.

Another important point:  In 1911, Peirce allowed any word, not
just verbs, to be the name of a relation.  From NEM, page 3.162:
Every word makes an assertion.  Thus ——man means "There is a man" 
in whatever universe the whole sheet refers to.  The dash before

"man" is the "line of identity."


This EG is Peirce's first example in 1911.  And note that he begins
with a Beta graph.  In fact, he does not even mention the distinction
between Alpha and Beta.  The same rules of inference apply to both.

For Peirce's version of 1911 with my commentary, see
http://jfsowa.com/peirce/ms514.htm

Jerry,

CSP’s genius [etc.] make it difficult for anyone to project his
thoughts into rarefied logical, mathematical, scientific or
philosophical atmospheres.


Yes.  He wrote volumes of insights that we still need to explore.
But you can't put words in his mouth.  If you can't find where he
stated something explicitly, you can't claim him as the source.

Note my discussion above.  Every one of my claims is based on
something that Peirce explicitly wrote.

John

-
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 the 
line "UNSubscribe PEIRCE-L" in the BODY of the message. More at 
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