Re: Fw: [PEIRCE-L] Lowell Lecture 2.6

[Stephen C. Rose]

I suspect the fundamental reality of Peirce's thought was there at the
start and that his later work was consistent with what he had always
thought. After the PM was in place, everything was clarification. The
revolution lay in the work he anticipated would get done in future times as
a result of his basic insight which conflicted with the past in a
fundamental and world-changing way. It's a sort of forest and trees thing.

amazon.com/author/stephenrose

On Sat, Nov 4, 2017 at 11:01 AM,  wrote:

> John, thanks for clarifying, I guess our perspectives are not so different
> as I thought. But I still think that Peirce’s did not have to wait until
> 1911 to “integrate every aspect of his philosophy” with EGs; I think they
> co-evolved with those other aspects, philosophical problems being reflected
> in EGs and vice versa. In fact that’s the main reason I’m taking a close
> look at EGs in the context of the Lowell lectures.
>
>
>
> The direct quote I should have included as a statement of your position
> was from your Thursday post: “Among the implications: The sharp
> distinction between "formal logic", which is part of mathematics, from
> logic as a normative science and the many studies of reasoning in
> linguistics, psychology, and education.”
>
>
>
> Gary f.
>
>
>
> -Original Message-
> From: John F Sowa [mailto:s...@bestweb.net]
> Sent: 3-Nov-17 15:02
>
>
>
> On 11/3/2017 10:38 AM, g...@gnusystems.ca wrote:
>
> > For you, formal logic is a branch of mathematics; for us, though...
>
>
>
> It's always a bad idea to make claims about anyone else's thoughts,
> contemporary or historical.  It's best to quote their exact words.
>
>
>
> As for me, I completely agree with Peirce:  formal logic is pure
> mathematics, normative logic is part of the normative sciences, applied
> logic is part of any system of reasoning in philosophy or any branch of
> science, and many aspects of logic may be studied by linguists,
> psychologists, and educational psychologists.
>
>
>
> > if EGs are relegated entirely to the realm of pure mathematics, we
>
> > lose the experiential element of their meaning.
>
>
>
> I completely agree.  I would never say that.
>
>
>
> > This is why I don’t find it helpful to consider the Lowell
>
> > presentation of EGs as merely a crude and confused form of more recent
>
> > developments in mathematics.
>
>
>
> I agree.  I never said that.  All I said is that the 1903 and 1906
> versions were early stages in his way of thinking about EGs.  They
> contained too much excess baggage that created obstacles in the "way of
> inquiry".  By discarding the irrelevant details, the 1911 version enabled
> him to integrate every aspect of his philosophy.
>
>
>
> See "Peirce's magic lantern of thought" by Pietarinen:
>
> http://www.helsinki.fi/science/commens/papers/magiclantern.pdf
>
>
>
> On p. 7, Pietarinen quotes from a later part of the letter to Kehler that
> contains Peirce's 1911 version of EGs.  The following quotation begins with
> the part that Ahti quoted and continues with a bit more:
>
> > In great pains, I learned to think in diagrams, which is a much
>
> > superior method [to algebraic symbols].  I am convinced there is a far
>
> > better one, capable of wonders, but the great cost of the apparatus
>
> > forbids my learning it.  It consists in thinking in stereoscopic
>
> > moving pictures.  Of course, one might substitute the real objects
>
> > moving in sold space; and that might not be so unreasonably costly.
>
> > (NEM 3:191)
>
>
>
> I don't believe that it's an accident that Peirce mentioned 3D or even 4D
> (3D + time) in the same letter in which he introduced EGs.
>
> His 1911 semantics can accommodate such things in EGs.
>
>
>
> John
>
>
> -
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> .
>
>
>
>
>
>

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RE: Fw: [PEIRCE-L] Lowell Lecture 2.6

[gnox]

John, thanks for clarifying, I guess our perspectives are not so different
as I thought. But I still think that Peirce's did not have to wait until
1911 to "integrate every aspect of his philosophy" with EGs; I think they
co-evolved with those other aspects, philosophical problems being reflected
in EGs and vice versa. In fact that's the main reason I'm taking a close
look at EGs in the context of the Lowell lectures.

 

The direct quote I should have included as a statement of your position was
from your Thursday post: "Among the implications: The sharp distinction
between "formal logic", which is part of mathematics, from logic as a
normative science and the many studies of reasoning in linguistics,
psychology, and education."

 

Gary f.

 

-Original Message-
From: John F Sowa [mailto:s...@bestweb.net] 
Sent: 3-Nov-17 15:02



 

On 11/3/2017 10:38 AM,   g...@gnusystems.ca
wrote:

> For you, formal logic is a branch of mathematics; for us, though...

 

It's always a bad idea to make claims about anyone else's thoughts,
contemporary or historical.  It's best to quote their exact words.

 

As for me, I completely agree with Peirce:  formal logic is pure
mathematics, normative logic is part of the normative sciences, applied
logic is part of any system of reasoning in philosophy or any branch of
science, and many aspects of logic may be studied by linguists,
psychologists, and educational psychologists.

 

> if EGs are relegated entirely to the realm of pure mathematics, we 

> lose the experiential element of their meaning.

 

I completely agree.  I would never say that.

 

> This is why I don't find it helpful to consider the Lowell 

> presentation of EGs as merely a crude and confused form of more recent 

> developments in mathematics.

 

I agree.  I never said that.  All I said is that the 1903 and 1906 versions
were early stages in his way of thinking about EGs.  They contained too much
excess baggage that created obstacles in the "way of inquiry".  By
discarding the irrelevant details, the 1911 version enabled him to integrate
every aspect of his philosophy.

 

See "Peirce's magic lantern of thought" by Pietarinen:

 
http://www.helsinki.fi/science/commens/papers/magiclantern.pdf

 

On p. 7, Pietarinen quotes from a later part of the letter to Kehler that
contains Peirce's 1911 version of EGs.  The following quotation begins with
the part that Ahti quoted and continues with a bit more:

> In great pains, I learned to think in diagrams, which is a much 

> superior method [to algebraic symbols].  I am convinced there is a far 

> better one, capable of wonders, but the great cost of the apparatus 

> forbids my learning it.  It consists in thinking in stereoscopic 

> moving pictures.  Of course, one might substitute the real objects 

> moving in sold space; and that might not be so unreasonably costly.  

> (NEM 3:191)

 

I don't believe that it's an accident that Peirce mentioned 3D or even 4D
(3D + time) in the same letter in which he introduced EGs.

His 1911 semantics can accommodate such things in EGs.

 

John


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Re: Fw: [PEIRCE-L] Lowell Lecture 2.6

[kirstima]

John, Jon, list

Some comments in response

In Peirce's view logic needs mathematical grounds, but I have not found 
anything to support the view that there should be such sharp distinction 
as you propose. – There were many, many classifications of sciences he 
developed over the years. Of which latest ones should be given 
precedence. According to Peirce, the expession 'should be' has no 
meaning, if no aim is involved. If and when it is agreed that Peirce was 
aiming at something better, then this becomes self-evident, does it not?


I have difficulties in understanding what is meant by

John:

Game theoretical semantics (GTS) is just a mathematical theory.
As pure mathematics, Peirce would not object to it.

My understanding of what Peirce meant by pure math just does not fit 
with this statement. I won't even try to express how and why. Instead, I 
take up the question at hand.


Hintikka's early lectures on game theory were addressed to philosophers 
and social scientists, as part of the curriculum of practical philosophy 
at Helsinki University.


Prisoner's dilemma played a major role. I wonder whether it has been 
taken up by the means of existential graphs? Would like very much to see 
it/them.


My interest lies in that it presents the Dilemma of Achilles and 
tortoise in other cloths. The (seemingly) physical problem is dressed up 
as a  (seemingly) social problem in Prisoner's Dilemma.


Peirce did not object to the former, he just solved it. Thus I see no 
reason why he would have objected the latter, he just would have shown 
it to be a pseudoproblem.


Both dilemmas exist. No doubt about that. – But are they real problems, 
is quite another kind of issue. An issue about the relations between 
thought and language, but not only.


As soon as the latter dilemma is given the name 'Prisoner's dilemma', a 
host of presuppositions are taken in. – Let's just make a seemingly tiny 
change. Let's call it 'Prisoners dilemma', thus omitting a grammatical 
detail, which deeply affects the meaning conveyed. – The logical move 
entails a move from one to many. Not something to be overlooked or 
dismissed, surely.


In GTS it has been. But now I have pointed it out, a needle in the 
haystock of GTS. If you feel no sting, then I must have overestimated 
your logical sensitivity.


I have studied Peirces writings on existential graphs in a preliminary 
way, just to get the general idea & to understand it's proper place 
within Peirce's philosophy. After testing the idea on the contents of 
further (and further…) reading CSP, it holds. After testing it in the 
light of your most valuable teachings, it seems to hold. - Which is why 
I get deeply puzzled if and when your views on CSP are not, well, 
congruent.


Also, I wish to point out the currently common (sense?) misunderstanding 
with the term DIALOGUE. The very word is taken as referring to a 
discussion involving two (and only two) participants. As if Greek 'DIA' 
would mean two, which it does not. It just means 'between'.


Thus I find

Jon:

Peirce's explanation of logical connectives and quantifiers
in terms of a game between two players attempting to support
or defeat a proposition, respectively, is a precursor of many
later versions of game-theoretic semantics.

as neclecting something essential (in a Peircean view). The implied 
third is the audience ( from 'dear reader' on…). 'There is one…' claims 
a possibility. 'All…' claims a necessity. In between the lies the realm 
of probable inference, abduction, hypothesis & the lot.


The idea of continuity is of course needed to understand the the real 
nature both dilemmas and to solve them. Both are pseudoproblems, in the 
positive meaning of the term offered in EG. Really solving them, of 
course, goes beyond the proper realm of existential graphs. Gamma graphs 
would be needed.


But if the meaning of the term 'formal theory' is for starters defined 
as just a part of math, then … Well, what? Does math then mean anything 
else but 'formal'?


Wondering,

Kirsti


John F Sowa kirjoitti 2.11.2017 22:08:

Gary F, Jeff BD, Kirsti, Jon A,

I didn't respond to your previous notes because I was tied up with
other work.  Among other things, I presented some slides for a telecon
sponsored by Ontolog Forum.  Slide 23 (cspsci.gif attached) includes
my diagram of Peirce's classification of the sciences and discusses the
implications.  (For all slides: http://jfsowa.com/talks/contexts.pdf )

Among the implications:  The sharp distinction between "formal logic",
which is part of mathematics, from logic as a normative science and the
many studies of reasoning in linguistics, psychology, and education.

Peirce was very clear about the infinity of mathematical theories.
As pure mathematics, the only point to criticize would be the clarity
and precision of the definitions and reasoning.  But applications may
be criticized as irrelevant, inadequate, or totally wrong.

Gary

as late as 1909 Peirce was still trying 

Re: Fw: [PEIRCE-L] Lowell Lecture 2.6

[John F Sowa]

On 11/3/2017 10:38 AM, g...@gnusystems.ca wrote:

For you, formal logic is a branch of mathematics; for us, though...


It's always a bad idea to make claims about anyone else's thoughts,
contemporary or historical.  It's best to quote their exact words.

As for me, I completely agree with Peirce:  formal logic is pure
mathematics, normative logic is part of the normative sciences,
applied logic is part of any system of reasoning in philosophy or
any branch of science, and many aspects of logic may be studied by
linguists, psychologists, and educational psychologists.


if EGs are relegated entirely to the realm of pure mathematics,
we lose the experiential element of their meaning.


I completely agree.  I would never say that.


This is why I don’t find it helpful to consider the Lowell
presentation of EGs as merely a crude and confused form of more
recent developments in mathematics.


I agree.  I never said that.  All I said is that the 1903 and 1906
versions were early stages in his way of thinking about EGs.  They
contained too much excess baggage that created obstacles in the
"way of inquiry".  By discarding the irrelevant details, the 1911
version enabled him to integrate every aspect of his philosophy.

See "Peirce's magic lantern of thought" by Pietarinen:
http://www.helsinki.fi/science/commens/papers/magiclantern.pdf

On p. 7, Pietarinen quotes from a later part of the letter to Kehler
that contains Peirce's 1911 version of EGs.  The following quotation
begins with the part that Ahti quoted and continues with a bit more:

In great pains, I learned to think in diagrams, which is a much
superior method [to algebraic symbols].  I am convinced there is a
far better one, capable of wonders, but the great cost of the
apparatus forbids my learning it.  It consists in thinking in
stereoscopic moving pictures.  Of course, one might substitute the
real objects moving in sold space; and that might not be so
unreasonably costly.  (NEM 3:191)


I don't believe that it's an accident that Peirce mentioned 3D or
even 4D (3D + time) in the same letter in which he introduced EGs.
His 1911 semantics can accommodate such things in EGs.

John

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RE: Fw: [PEIRCE-L] Lowell Lecture 2.6

[gnox]

John,

 

Many thanks for those links to the Pietarinen pieces, which I hadn't seen
before. The one at http://www.digitalpeirce.fee.unicamp.br/endo.htm, or at
least the first section of it (headed "Preliminaries") is a very helpful
summary of the basics of EGs as they are presented in the Lowell lectures.
The rest of that article, and the whole of the other one, seems concerned
mainly with claiming Peirce's work as a precursor of more recent
developments in mathematics, mainly model and game theories. I'm sure that
these pieces, like your own presentations of EGs, are of great value to
people who are more or less well versed in formal logic but know little or
nothing about Peirce or about the history of logic.

 

Some of us who are now studying EGs as a component of the Lowell lectures,
though, are a very different audience: we are more or less well versed in
Peircean philosophy but know little or nothing about current trends in
formal logic. For you, formal logic is a branch of mathematics; for us,
though, mathematics is not what Peirce called a "positive science" - and
therefore not a branch of philosophy, as logic is:

"Logic is a branch of philosophy. That is to say it is an experiential, or
positive science, but a science which rests on no special observations, made
by special observational means, but on phenomena which lie open to the
observation of every man, every day and hour" (CP 7.526).

 

>From the perspective that I'm taking in this study of the Lowells, Peirce is
very clear that EGs are a tool for studying deductive reasoning, which is
itself a phenomenon familiar to everybody, although a given person may  not
practice it every day and hour, or even be aware that he practices it at
all. This part of the study does draw mainly on mathematics, because the
objects of attention in pure mathematics are wholly imaginary (see Lowell
2.8!) and deduction - unlike other parts of the inquiry cycle - works
exactly the same with imaginary objects as it does with real, observable,
measureable objects. Logic as a whole, like other positive sciences such as
physics (and phenomenology!), makes use of mathematical reasoning, but if
EGs are relegated entirely to the realm of pure mathematics, we lose the
experiential element of their meaning.

 

This is why I don't find it helpful to consider the Lowell presentation of
EGs as merely a crude and confused form of more recent developments in
mathematics. By the way, in the part of MS 455 which I've omitted from my
online publication of Lowell 2 (as explained yesterday), there is this
interesting 'aside' by Peirce:

"Here we have the three signs [of the alpha part] defined purely in terms of
logical transformations from them and to them without one word being said
about what the signs really mean. They are left to be applied to whatever
there may be that corresponds to them. This is the Pure Mathematical point
of view, a point of view far from easy to a person as imbued with logical
notions as I am."

 

Gary f.

 

-Original Message-
From: John F Sowa [mailto:s...@bestweb.net] 
Sent: 3-Nov-17 00:21
To: peirce-l@list.iupui.edu
Subject: Re: Fw: [PEIRCE-L] Lowell Lecture 2.6

 

Gary F,

 

There are two separate issues here: (1) the isomorphism between Peirce's

1911 system and his earlier presentations; and (2) the relationship between
Peirce's endoporeutic and GTS.

 

About #1, the issues are clear for first-order logic (Alpha + Beta):

every graph drawn according to the 1903 or 1906 rules can be converted to
one according to the 1911 rules by shading the negative areas.

The rules of inference are also equivalent:  a proof by one set of rules is
also a valid proof by the other rules.

 

There is one point about the scroll, which Peirce does not mention in 1911
as distinct from a nest of two ovals.  But that point has no effect on any
of the graphs or any proof.

 

Therefore, I regard the 1911 rules as a cleaner, simpler, and more elegant
version of his earlier treatment.  But I believe that this simplicity is a
major *improvement* because it makes the rules more general and more
flexible.  (As I summarized in my previous note.)

 

Re graphist and interpreter:  Peirce wrote many versions over the years, in
some of them the two parties cooperated and in others they were more
competitive.  See the comment by Pietarinen below:

 

> But this is *very* different from Peirce's own account of the dialog 

> between graphist and interpreter in the Lowell lectures, in CP 4.431

 

Peirce wrote many fragmentary remarks about the dialog, most of which were
unpublished.  Pietarinen has a summary of the various passages:

 <http://www.digitalpeirce.fee.unicamp.br/endo.htm>
http://www.digitalpeirce.fee.unicamp.br/endo.htm

 

For a more systematic treatment, see the following by Pietarinen:

 
<https://www.google.com/url?sa=t=j==s=web=16=rja
ct=8=0ahUKEwjH9b2dqKHXAhUp8IMKHfP-Bo44ChAWCDQwBQ=https%3A%2F%

Re: Fw: [PEIRCE-L] Lowell Lecture 2.6

[John F Sowa]

Gary F,

There are two separate issues here: (1) the isomorphism between Peirce's
1911 system and his earlier presentations; and (2) the relationship
between Peirce's endoporeutic and GTS.

About #1, the issues are clear for first-order logic (Alpha + Beta):
every graph drawn according to the 1903 or 1906 rules can be converted
to one according to the 1911 rules by shading the negative areas.
The rules of inference are also equivalent:  a proof by one set of
rules is also a valid proof by the other rules.

There is one point about the scroll, which Peirce does not mention
in 1911 as distinct from a nest of two ovals.  But that point has
no effect on any of the graphs or any proof.

Therefore, I regard the 1911 rules as a cleaner, simpler, and more
elegant version of his earlier treatment.  But I believe that this
simplicity is a major *improvement* because it makes the rules more
general and more flexible.  (As I summarized in my previous note.)

Re graphist and interpreter:  Peirce wrote many versions over the
years, in some of them the two parties cooperated and in others
they were more competitive.  See the comment by Pietarinen below:

But this is *very* different from Peirce’s own account of the dialog 
between graphist and interpreter in the Lowell lectures, in CP 4.431


Peirce wrote many fragmentary remarks about the dialog, most of which
were unpublished.  Pietarinen has a summary of the various passages:
http://www.digitalpeirce.fee.unicamp.br/endo.htm

For a more systematic treatment, see the following by Pietarinen:
https://www.google.com/url?sa=t=j==s=web=16=rja=8=0ahUKEwjH9b2dqKHXAhUp8IMKHfP-Bo44ChAWCDQwBQ=https%3A%2F%2Fdialnet.unirioja.es%2Fdescarga%2Farticulo%2F4729798.pdf=AOvVaw1DgzAp3gS_pYb_5wiN9gu5

From page 2:

Peirce coined a plethora of names... assertor and critic, concurrent
and antagonist, speaker and hearer, addressor and addressee, scribe and
user, affirmer and denier, compeller and resister, Me and Against-Me...


Pietarinen also said "these names can easily be confused with one
another."  That's why I chose the terms proposer and skeptic, which
seem to be clearer and more memorable.  The skeptic is willing to be
persuaded, but only after checking all the details.

Summary:  Peirce's ideas and terminology were in flux.  He didn't
have the advantage of modern computers and the 20th c. techniques
of recursive functions and game-playing programs.  But his notion
of a dialog with two parties collaborating and/or competing keeps
recurring in all those discussions.

My specification of the game (URL below) is based on familiarity
with software for playing games like chess.  Peirce did not have
that experience, but I believe that he would agree with the method.

John
__

From page 18 of http://jfsowa.com/pubs/egtut.pdf

In modern terminology, endoporeutic can be defined as a two-person 
zero-sum perfect-information game, of the same genre as board games like 
chess, checkers, and tic-tac-toe. Unlike those games, which frequently 
end in a draw, every finite EG determines a game that must end in a win 
for one of the players in a finite number of moves. In fact, Henkin 
(1961), the first modern logician to rediscover the game-theoretical 
method, showed that it could evaluate the denotation of some infinitely 
long formulas in a finite number of steps. Peirce also considered the 
possibility of infinite EGs:  “A graph with an endless nest of seps 
[ovals] is essentially of doubtful meaning, except in special cases” (CP 
4.494). Although Peirce left no record of those special cases, they are 
undoubtedly the ones for which endoporeutic terminates in a finite 
number of steps. The version of endoporeutic presented here is based on 
Peirce’s writings, supplemented with ideas adapted from Hintikka (1973), 
Hilpinen (1982), and Pietarinen (2006)...


What distinguishes the game-theoretical method from Tarski’s approach
is its procedural nature. One reason why Peirce had such difficulty
in explaining it is that he and his readers lacked the vocabulary
of the game-playing algorithms of artificial intelligence...

[Follow the URL for the details.]

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Re: Fw: [PEIRCE-L] Lowell Lecture 2.6

[Jerry Rhee]

Gary f, John, list:

Gary, so I take by your post that you're the skeptic and John is the
proposer?

Best,
J

On Thu, Nov 2, 2017 at 7:15 PM, <g...@gnusystems.ca> wrote:

> John, Jon A, list,
>
>
>
> John, you wrote, “Peirce's motivation [for his dialogic approach to EGs]
> was the similarity to his theory of inquiry: a dialog between two parties,
> one who proposes a theory and one who is skeptical. The proposer is trying
> to find evidence for it, and the skeptic is trying to find evidence against
> it.” But this is *very* different from Peirce’s own account of the dialog
> between graphist and interpreter in the Lowell lectures, in CP 4.431, in
> the Lowell Lectures, in the Syllabus and in every later text on EGs that
> I’ve seen. In CP 4.395, for instance, we find: “*Convention No. I*. These
> Conventions are supposed to be mutual understandings between two persons: a
> *Graphist*, who expresses propositions according to the system of
> expression called that of *Existential Graphs*, and an *Interpreter*, who
> interprets those propositions and accepts them without dispute.”
>
>
>
> If the player you designate as the “skeptic” is essential to game theory,
> then I am skeptical of your claim that EGs can be understood in
> game-theoretical terms, unless you can show some textual evidence. As with
> the other discrepancies I’ve already pointed out between your account of
> EGs and Peirce’s account in the Lowells, I think this can only sow
> confusion for those of us trying to understand exactly what Peirce was
> doing in the Lowell Lectures. I don’t think it’s helpful to gloss over the
> differences by claiming that your version is “isomorphic” to Peirce’s 1903
> version, and then blame the resulting confusion on Peirce.
>
>
>
> Gary f.
>
>
>
> -Original Message-
> From: John F Sowa [mailto:s...@bestweb.net]
> Sent: 2-Nov-17 16:08
> To: peirce-l@list.iupui.edu
> Cc: Dau, Frithjof <frithjof@sap.com>
> Subject: Re: Fw: [PEIRCE-L] Lowell Lecture 2.6
>
>
>
> Gary F, Jeff BD, Kirsti, Jon A,
>
>
>
> I didn't respond to your previous notes because I was tied up with other
> work.  Among other things, I presented some slides for a telecon sponsored
> by Ontolog Forum.  Slide 23 (cspsci.gif attached) includes my diagram of
> Peirce's classification of the sciences and discusses the implications.
> (For all slides: http://jfsowa.com/talks/contexts.pdf )
>
>
>
> Among the implications:  The sharp distinction between "formal logic",
> which is part of mathematics, from logic as a normative science and the
> many studies of reasoning in linguistics, psychology, and education.
>
>
>
> Peirce was very clear about the infinity of mathematical theories.
>
> As pure mathematics, the only point to criticize would be the clarity and
> precision of the definitions and reasoning.  But applications may be
> criticized as irrelevant, inadequate, or totally wrong.
>
>
>
> Gary
>
> > as late as 1909 Peirce was still trying (apparently without success)
>
> > to get Lady Welby to study Existential Graphs. And the graphs he sent
>
> > her to study look pretty much the same as the graphs he introduced in
>
> > the Lowell Lecture 2: nested cuts, areas defined by the cuts, and no
>
> > shading.
>
>
>
> That failure may have been one of the inspirations for the 1911 version,
> which he addressed to one of her correspondents.
>
>
>
> >> [JFS] The rules are *notation independent*:  with minor adaptations
>
> >> to the syntax, they can be used for reasoning in a very wide range of
>
> >> notations...
>
> >
>
> > [GF] This does not explain why Peirce was dissatisfied with algebraic
>
> > notations (including his own) and invented EGs for the sake of their
>
> > optimal iconicity
>
>
>
> On the contrary, simplicity and symmetry enhance iconicity and
> generality.  See the examples in http://jfsowa.com/talks/visual.pdf :
>
>
>
>   1. Shading of negative phrases in English (slides 28 to 30) and the
>
>  application of Peirce's rules to the English sentences.
>
>
>
>   2. Embedded icons in EG areas (Euclid's diagrams, exactly as he drew
>
>  them) and the option of inserting or erasing parts of the diagrams
>
>  according to those rules (slides 33 to 42).
>
>
>
>   3. And the rules can be generalized to 3-D virtual reality.  I couldn't
>
>  draw the examples, but just imagine shaded and unshaded 3-D blobs
>
>  that contain 3-D icons (shapes) with parts connected by lines.  I'm
>
>  sure that Peirce imagined such applications when he was writing
>
>

RE: Fw: [PEIRCE-L] Lowell Lecture 2.6

[gnox]

John, Jon A, list,

 

John, you wrote, "Peirce's motivation [for his dialogic approach to EGs] was
the similarity to his theory of inquiry: a dialog between two parties, one
who proposes a theory and one who is skeptical. The proposer is trying to
find evidence for it, and the skeptic is trying to find evidence against
it." But this is very different from Peirce's own account of the dialog
between graphist and interpreter in the Lowell lectures, in CP 4.431, in the
Lowell Lectures, in the Syllabus and in every later text on EGs that I've
seen. In CP 4.395, for instance, we find: "Convention No. I. These
Conventions are supposed to be mutual understandings between two persons: a
Graphist, who expresses propositions according to the system of expression
called that of Existential Graphs, and an Interpreter, who interprets those
propositions and accepts them without dispute."

 

If the player you designate as the "skeptic" is essential to game theory,
then I am skeptical of your claim that EGs can be understood in
game-theoretical terms, unless you can show some textual evidence. As with
the other discrepancies I've already pointed out between your account of EGs
and Peirce's account in the Lowells, I think this can only sow confusion for
those of us trying to understand exactly what Peirce was doing in the Lowell
Lectures. I don't think it's helpful to gloss over the differences by
claiming that your version is "isomorphic" to Peirce's 1903 version, and
then blame the resulting confusion on Peirce.

 

Gary f.

 

-Original Message-
From: John F Sowa [mailto:s...@bestweb.net] 
Sent: 2-Nov-17 16:08
To: peirce-l@list.iupui.edu
Cc: Dau, Frithjof <frithjof@sap.com>
Subject: Re: Fw: [PEIRCE-L] Lowell Lecture 2.6

 

Gary F, Jeff BD, Kirsti, Jon A,

 

I didn't respond to your previous notes because I was tied up with other
work.  Among other things, I presented some slides for a telecon sponsored
by Ontolog Forum.  Slide 23 (cspsci.gif attached) includes my diagram of
Peirce's classification of the sciences and discusses the implications.
(For all slides:  <http://jfsowa.com/talks/contexts.pdf>
http://jfsowa.com/talks/contexts.pdf )

 

Among the implications:  The sharp distinction between "formal logic", which
is part of mathematics, from logic as a normative science and the many
studies of reasoning in linguistics, psychology, and education.

 

Peirce was very clear about the infinity of mathematical theories.

As pure mathematics, the only point to criticize would be the clarity and
precision of the definitions and reasoning.  But applications may be
criticized as irrelevant, inadequate, or totally wrong.

 

Gary

> as late as 1909 Peirce was still trying (apparently without success) 

> to get Lady Welby to study Existential Graphs. And the graphs he sent 

> her to study look pretty much the same as the graphs he introduced in 

> the Lowell Lecture 2: nested cuts, areas defined by the cuts, and no 

> shading.

 

That failure may have been one of the inspirations for the 1911 version,
which he addressed to one of her correspondents.

 

>> [JFS] The rules are *notation independent*:  with minor adaptations 

>> to the syntax, they can be used for reasoning in a very wide range of 

>> notations...

> 

> [GF] This does not explain why Peirce was dissatisfied with algebraic 

> notations (including his own) and invented EGs for the sake of their 

> optimal iconicity

 

On the contrary, simplicity and symmetry enhance iconicity and generality.
See the examples in  <http://jfsowa.com/talks/visual.pdf>
http://jfsowa.com/talks/visual.pdf :

 

  1. Shading of negative phrases in English (slides 28 to 30) and the

 application of Peirce's rules to the English sentences.

 

  2. Embedded icons in EG areas (Euclid's diagrams, exactly as he drew

 them) and the option of inserting or erasing parts of the diagrams

 according to those rules (slides 33 to 42).

 

  3. And the rules can be generalized to 3-D virtual reality.  I couldn't

 draw the examples, but just imagine shaded and unshaded 3-D blobs

 that contain 3-D icons (shapes) with parts connected by lines.  I'm

 sure that Peirce imagined such applications when he was writing

 about stereoscopic equipment (which he could not afford to buy).

 

Gary

> "Peirce said that a blank sheet of assertion is a graph.  Since it's a 

> graph, you can draw a double negation around it."  - Eh? How can you 

> draw anything around the sheet of assertion, which (by Peirce's

> definition) is unbounded??

 

But note Jeff's comments about projective geometry and topology (which
Peirce knew very well):

 

Jeff

> My reason for picking this example of a topological surface is that it 

> provides us with an example of a 2 dimensional space in which a path 

> can be drawn all of

Re: Fw: [PEIRCE-L] Lowell Lecture 2.6

[John F Sowa]

Gary F, Jeff BD, Kirsti, Jon A,

I didn't respond to your previous notes because I was tied up with
other work.  Among other things, I presented some slides for a telecon
sponsored by Ontolog Forum.  Slide 23 (cspsci.gif attached) includes
my diagram of Peirce's classification of the sciences and discusses the
implications.  (For all slides: http://jfsowa.com/talks/contexts.pdf )

Among the implications:  The sharp distinction between "formal logic",
which is part of mathematics, from logic as a normative science and the
many studies of reasoning in linguistics, psychology, and education.

Peirce was very clear about the infinity of mathematical theories.
As pure mathematics, the only point to criticize would be the clarity
and precision of the definitions and reasoning.  But applications may
be criticized as irrelevant, inadequate, or totally wrong.

Gary

as late as 1909 Peirce was still trying (apparently without success)
to get Lady Welby to study Existential Graphs. And the graphs he sent
her to study look pretty much the same as the graphs he introduced
in the Lowell Lecture 2: nested cuts, areas defined by the cuts,
and no shading.


That failure may have been one of the inspirations for the 1911 version,
which he addressed to one of her correspondents.


[JFS] The rules are *notation independent*:  with minor adaptations
to the syntax, they can be used for reasoning in a very wide range
of notations...


[GF] This does not explain why Peirce was dissatisfied with algebraic
notations (including his own) and invented EGs for the sake of their
optimal iconicity


On the contrary, simplicity and symmetry enhance iconicity and
generality.  See the examples in http://jfsowa.com/talks/visual.pdf :

 1. Shading of negative phrases in English (slides 28 to 30) and the
application of Peirce's rules to the English sentences.

 2. Embedded icons in EG areas (Euclid's diagrams, exactly as he drew
them) and the option of inserting or erasing parts of the diagrams
according to those rules (slides 33 to 42).

 3. And the rules can be generalized to 3-D virtual reality.  I couldn't
draw the examples, but just imagine shaded and unshaded 3-D blobs
that contain 3-D icons (shapes) with parts connected by lines.  I'm
sure that Peirce imagined such applications when he was writing
about stereoscopic equipment (which he could not afford to buy).

Gary

“Peirce said that a blank sheet of assertion is a graph.  Since it's
a graph, you can draw a double negation around it.”  — Eh? How can
you draw anything around the sheet of assertion, which (by Peirce’s
definition) is unbounded??


But note Jeff's comments about projective geometry and topology
(which Peirce knew very well):

Jeff

My reason for picking this example of a topological surface is that
it provides us with an example of a 2 dimensional space in which
a path can be drawn all of the way "around" the surface...


Yes.  And that infinite space bounded by its infinite circle can be
mapped -- point by point -- to a finite replica on another sheet.
In any case, the formal logic does not depend on the details of any
representation.  We can just use the word 'blank' to name an empty
sheet of assertion or any finite replica of it.

Gary

I’m reluctant to apply topological theories to EGs if they’re going
to complicate the issues instead of simplifying them.


For a mathematician, Jeff's method is an enormous simplification.
Finite boundaries in mathematics and computer science are always
a nuisance.  But when you're teaching EGs to students, you can just
use the word 'blank' for an empty area.  A pseudograph is just an
enclosure that contains a blank.

Gary

John appears to regard all graphs, all partial graphs and all areas
as being on the sheet of assertion. But Peirce says explicitly that
neither the antecedent nor the consequent of a conditional can be
scribed on the sheet of assertion...


My diagrams (with or without shading) are isomorphic to Peirce's.
Talking about sheets doesn't generalize to other logics or to 3-D
icons.  It makes the presentation more complex and confusing.

Kirsti

I attended Hintikka's lectures on game theory in early 1970's.
No shade of Peirce. I found them boring.


Game theoretical semantics (GTS) is just a mathematical theory.
As pure mathematics, Peirce would not object to it.

Kirsti

it hurts my heart and soul to read a suggestion that Peirce's
endoporeutic may have or could have been a version of Hintikka's
game theoretical semantics.


Jon

Peirce's explanation of logical connectives and quantifiers
in terms of a game between two players attempting to support
or defeat a proposition, respectively, is a precursor of many
later versions of game-theoretic semantics.


Risto Hilpinen (1982) showed that the formal theory of Peirce's
endoporeutic is equivalent to GTS.  As a formal theory, Peirce
would have no objection to GTS or to any proof of formal
equivalence.

Peirce's motivation was the similarity to