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: [PEIRCE-L] Lowell Lecture 2.6

[kirstima]

OK. Thanks. Kirsti



Jon Awbrey kirjoitti 30.10.2017 20:45:

Kirsti, List,

It would be more accurate to say, and I'm sure it's what John meant,
that 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.

Regards,

Jon

On 10/30/2017 2:33 PM, kirst...@saunalahti.fi wrote:


I attended Hintikka's lectures on game theory in early 1970's. No 
shade of Peirce. I found them boring. No discussion invited nor 
wellcomed. Later on he got more mellow. And very interested on Peirce. 
- I greatly appreciate his latest work, remarkable indeed. Especially 
from a representative of analytical philosophy, to which he remained 
true. - Still, 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. - Must have been a slip.


Is it so that Peirce never gave up his project on developing a 
genuinely triadic formal logic? Even though Part II,  existential 
graphs were the only part he completed in a satisfactory way (to his 
own mind)?


Thanks again,

Kirsti




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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 

Fw: [PEIRCE-L] Lowell Lecture 2.6

[Jeffrey Brian Downard]

Hi Gary F, List,


Gary F:  "The implication is that the form of the “scroll” is in some way 
appropriate to its object, instead of being arbitrarily assigned to that 
object."


The guiding idea for developing each sort of figure in the EG, such as the 
scroll, is to construct a diagram in which the parts of the figure stand in the 
same sorts of formal relations as the things we are trying to represent--such 
as the relation of antecedent and consequent in the conditional de inesse. As 
such, we need to carefully analyze the relations between the parts of 
propositions that express such a conditional, and then we need to see if the 
figure we are using as a diagram has the same sorts of relations--no more and 
no less. In order to make that comparison, we will need to arrive at a clear 
understanding of what kinds of relations are elemental in our experience 
generally--and then we will need to draw on that account of the relations that 
are elemental for the sake of examining how those elemental relations figure 
into (a) the assertion of a conditional proposition and (b) in the construction 
of such a diagrammatic figure.


As far as I can tell, the same procedure is being applied to the construction 
of blot as an iconic representation of logical absurdity. In this case, we need 
to see that the same relations holds through the topological transformation of 
the diagrammatic figure as it is made to disappear. As such, it might look like 
a sleight of hand, but the question is whether or not such a continuous 
transformation is possible. That is, does the continuous transformation of the 
blot so that it disappears preserve or destroy the kinds of relations that we 
were trying to represent in the first place?


--Jeff


Jeffrey Downard
Associate Professor
Department of Philosophy
Northern Arizona University
(o) 928 523-8354

From: g...@gnusystems.ca <g...@gnusystems.ca>
Sent: Saturday, October 28, 2017 1:34:57 PM
To: peirce-l@list.iupui.edu
Subject: RE: [PEIRCE-L] Lowell Lecture 2.6

List,

I hope Jon soon finds time to unpack that post, but in the meantime I’ll make 
my own attempt to answer the questions provoked by Lowell 2.6. I should perhaps 
mention first that I’m posting all these things in HTML format, and anyone 
who’s trying to read them with a mail app that doesn’t handle HTML will not be 
able to see the “blackboard” diagrams that Peirce is referring to throughout. 
To see them, you’ll need to either change the settings in your email reader or 
read the version of Lowell 2 on my website instead.

In 2.6, the point of the “experiment” is “to get an insight into how the scroll 
represents” this kind of conditional. The implication is that the form of the 
“scroll” is in some way appropriate to its object, instead of being arbitrarily 
assigned to that object.

For this experiment we need some “means of expressing an absurdity.” Why do we 
need that? I guess it’s because we are dealing with necessary reasoning here, 
which means we have to assume (without any reason for believing it) that the 
given premisses are true — unless they are logically absurd; so absurdity is 
the only way for a statement to be necessarily false. And it seems we need a 
graph for falsity.

As an example of absurdity, Peirce chooses the assertion “everything is true” — 
and even gives a reason for his choice. But now he wants it so serve as the 
consequent in a scroll, and instead of simply writing the words in the inner 
close, he represents it as a “blot” which fills up the area enclosed by the 
inner cut. It makes a kind of sense, graphically, that if the blank area is the 
place of assertion, the blotted (completely filled) area is the place of 
absurdity or necessary falseness.

At this point the “experiment” resorts to a kind of magic trick: Peirce makes 
the blot disappear (gradually but completely) — yet falsity remains, like the 
grin of the Cheshire Cat. According to Peirce, “This suggests that the relation 
which the cut asserts between the universe of discourse and what is scribed 
within it is simply that what is scribed within is false of the universe of 
discourse.” I guess we are to assume that this is true of any cut, no matter 
how deeply nested within other cuts: the place of that cut is a universe of 
discourse, and whatever is scribed on the area inside the cut is false of the 
universe outside that cut. So we are being asked to believe that (1) the area 
of a cut on the sheet of assertion represents a “universe of supposition” (as 
Peirce said awhile back) AND that any graph written on it is false of the 
universe represented by the sheet of assertion; and (2) the area of the cut 
inside that cut bears that same relation to the area of the cut within which it 
is placed — and so on, all the way down.

Intuitively, this is not easy to swallow, at least for me; this interpretation 
seems to be arrived at by sleight of hand on Peirce’s part. But appa

Fw: [PEIRCE-L] Lowell Lecture 2.6

[Jeffrey Brian Downard]

Gary F, John S, List,


The EGs are being developed as a mathematical system of logic. Peirce conceives 
of the framework within which the system is being developed as a topological 
system. As such, I'm working on the assumption that it will be helpful to think 
of the EG as a system of mathematical logic that draws on ideas from 
topology--e.g., Euler's work on logic diagrams, Euler's work on graph theory, 
Euler's formula for the topological characteristic of a figure and a surface 
and Listing's later development of this formula--as so many sources that Peirce 
has available at his fingertips.


Setting cosmological matters to the side, I do think that it will be helpful to 
consider these topological ideas as we try to understand Peirce's motivations 
and inspirations as he makes decisions about how to set up the diagrammatic 
relations that are important for using and understanding the EG as a formal 
system. Mathematical inquiry often is driven by some real problem that could 
not be solved by the other sciences. As such, the mathematician is called in to 
help, and the first step is to build a simplified and idealized system that can 
be used to address the most important parts of the problems at hand. If many of 
the problems that are motivating these inquiries are coming from the side of 
the normative sciences--i.e., theory of semiotics including the critical 
logic--then I believe it is natural to suppose that it is a set of perceived 
shortcomings in the algebraic systems of logic that were developed in the 
latter part of the 19th century--including his own algebraic systems--that are 
motivating and inspiring the development of this topological system of logic. 
Making the comparison between the two will be helpful precisely because it will 
clarify where the EGs have analytical advantages over the algebraic systems.


For the purposes of analyzing the elemental steps in both common and in more 
specialized forms of reasoning, the algebraic systems are falling short. 
Instead of spending more time trying to improve those systems, he is moving to 
a more diagrammatic approach that takes recent diagrammatic work in topology as 
a starting point. Having said that, I admit it is an open question as to how 
much we can learn from looking at topological figures and conceptions as we try 
to understand what Peirce is doing in the development of the EG. It is possible 
that we may go too far and import ideas that are out of place. The only way to 
figure out where it will be helpful to draw on these topological ideas and 
where it won't is to push the boundaries, so to speak.


--Jeff


--Jeff


Jeffrey Downard
Associate Professor
Department of Philosophy
Northern Arizona University
(o) 928 523-8354

From: g...@gnusystems.ca <g...@gnusystems.ca>
Sent: Monday, October 30, 2017 11:05:43 AM
To: 'Peirce-L'
Subject: RE: [PEIRCE-L] Lowell Lecture 2.6

Jeff,

I share your interest in Peirce’s topological ideas — mostly because they are 
significant for his cosmology. But EGs are not designed to represent the 
cosmos, and I’m reluctant to apply topological theories to EGs if they’re going 
to complicate the issues instead of simplifying them. Peirce illustrated his 
second Lowell lecture by drawing the diagrams on a blackboard, which itself 
represents the sheet of assertion, and it would be physically impossible to 
draw a line on the blackboard around the blackboard. John hasn’t said what he 
actually had in mind, but I’m guessing that it was a line or double line drawn 
around a part of the sheet of assertion which has a graph on it.

JD: We shouldn't lose sight of the fact that, for the SA, a cut is not simply a 
path. Rather, the cut takes what is inside the boundary and moves the that part 
of the surface to a different surface--one that represents what is negated.

GF: I don’t think so. Inside the cut is another surface, another “area,” but 
the surface in itself does not represent what is negated. The blank sheet of 
assertion is a graph, and does represent everything implicitly understood to be 
true (between graphist and interpreter); but the blank area inside a cut is not 
a graph. It does represent a universe of discourse different from the one 
represented by the sheet of assertion, and any graph scribed in that area is 
read as false of the universe outside the cut. That to me is a very different 
idea from the surface itself representing what is negated.

John’s idea seems still more different from Peirce’s idea in Lowell 2: 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, 
because neither one is being asserted! Hence the need for other areas, other 
universes, to be separated (by cuts) from the places on which the enclosures 
are drawn.

Maybe Peirce was never sat

Re: [PEIRCE-L] Lowell Lecture 2.6

[Jon Awbrey]

Kirsti, List,

It would be more accurate to say, and I'm sure it's what John meant,
that 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.

Regards,

Jon

On 10/30/2017 2:33 PM, kirst...@saunalahti.fi wrote:


I attended Hintikka's lectures on game theory in early 1970's. No shade of Peirce. I found them boring. No discussion 
invited nor wellcomed. Later on he got more mellow. And very interested on Peirce. - I greatly appreciate his latest 
work, remarkable indeed. Especially from a representative of analytical philosophy, to which he remained true. - Still, 
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. - Must have been a slip.


Is it so that Peirce never gave up his project on developing a genuinely triadic formal logic? Even though Part II,  
existential graphs were the only part he completed in a satisfactory way (to his own mind)?


Thanks again,

Kirsti



--

inquiry into inquiry: https://inquiryintoinquiry.com/
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isw: http://intersci.ss.uci.edu/wiki/index.php/JLA
facebook page: https://www.facebook.com/JonnyCache

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Re: [PEIRCE-L] Lowell Lecture 2.6

[kirstima]

Thank you very much John for a most enlightening post.

Recto/verso issue (in other forms, of course) was taken up & became 
somewhat popular within feminist philosophy 1980's and 1990's. I felt 
uncomfortable with it. But could not pinpoint the locical (in the narrow 
sense) errors.


A pseudograp is always false, you wrote. If and when probabilies are 
taken seriously. Just as the prefix in naming the concept implies.


In other contexts CSP uses "quasi-", denoting an "as if.." prefix.  
Something, anything in priciple, may be taken as if it were true. - E.g. 
beliefs no one present (in any sense) doubts.


N-valued logic, in abtracto, does not involve time. So I gather? - So, 
even if the possible truth values are unnumerable, innumerable, as soon 
as events and successions of events are involved, (logical) anything 
just vanishes. Then there always (already) is something.


With empereia, there always is something.

To all I know, CSP never used the term 'semantics'. It was introduced & 
became popular after CSP. (If anyone proves me wrong, I'll be glad to 
know better).


I attended Hintikka's lectures on game theory in early 1970's. No shade 
of Peirce. I found them boring. No discussion invited nor wellcomed. 
Later on he got more mellow. And very interested on Peirce. - I greatly 
appreciate his latest work, remarkable indeed. Especially from a 
representative of analytical philosophy, to which he remained true. - 
Still, 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. - Must have been a slip.


Is it so that Peirce never gave up his project on developing a genuinely 
triadic formal logic? Even though Part II,  existential graphs were the 
only part he completed in a satisfactory way (to his own mind)?


Thanks again,

Kirsti











John F Sowa kirjoitti 29.10.2017 19:16:

Jon A and Gary F,

Peirce's way of presenting EGs in his Lowell lectures and his
publications of 1906 is horrendously complex.  The best I could
say for it is "interesting".  But I would never teach it, use it,
or even mention it in an introduction to EGs.  I would only present
it as a side issue for advanced students.

The version I recommend is the 8-page summary that he wrote in a
long letter (52 pages) in 1911.  The primary topic of that letter
is "probability and induction" (NEM v 3, pp 158 to 210).

When he got to 3-valued logic and probabilities, the recto/verso
idea is untenable.  Instead of talking about cuts, seps, and scrolls,
he just talks about *areas* on the sheet of assertion.  To represent
negation, he uses a shaded oval, which he calls an area, not a cut.

The shading makes his notation much more readable.  An implication
(the old scroll) becomes a shaded area that encloses an unshaded area.
His rules of inference are much clearer, simpler, and more symmetric:
just 3 pairs, each of which has an exact inverse.  See the attached
NEM3p166.png.  (URLs below)

Jon

Peirce's introduction of the “blot” at this point is


I would continue that sentence with the word 'confusing'.

Peirce said that a blank sheet of assertion is a graph.  Since
it's a graph, you can draw a double negation around it.  The blank
is Peirce's only axiom, which is always true.  If you draw just
one oval around it, you get a graph that negates the truth.
Therefore, it is always false.  Peirce called it the pseudograph.

In a two-valued logic, the pseudograph implies everything.
But when you get to probabilities or N-valued logic, you can't
make that assumption.  I believe that's why Peirce dropped his
earlier explanations.  For the semantics, he adopted endoporeutic,
which is a version of Hintikka's Game Theoretical Semantics.

Gary

At this point the “experiment” resorts to a kind of magic trick:
Peirce makes the blot disappear (gradually but completely) — yet
falsity remains


Yes.  But it's just another confusing way of explaining something
very simple:  The pseudograph is always false.  If you draw it in
any area, it makes the entire area false.

John
___

I first came across this version of Peirce's EGs from a copy of a
transcription of MS514 by Michel Balat.  (By the way, I thank Jon
for sending me the copy.  I still have his email from 14 Dec 2000.)

For my website, I added a commentary with additional explanation
and posted it at http://jfsowa.com/peirce/ms514.htm

In 2010, I published a more detailed analysis with further
extensions:  http://jfsowa.com/pubs/egtut.pdf

For the published version in NEM (v3 pp 162-169), see
https://books.google.com/books?id=KGhbDAAAQBAJ=PA163=PA163=%22false+that+there+is+a+phoenix%22=bl=LKYw9nZEKh=LEaTyTSTGiEuT-P_-9a6XHEVwWQ=en=X=0ahUKEwi509vA9pPXAhWEOSYKHcDQBZQQ6AEIJjAA#v=onepage=%22false%20that%20there%20is%20a%20phoenix%22=false

Note: I found that volume of NEM by searching for the quoted phrase
"false that there is a phoenix" 

RE: [PEIRCE-L] Lowell Lecture 2.6

[gnox]

Jeff,

 

I share your interest in Peirce’s topological ideas — mostly because they
are significant for his cosmology. But EGs are not designed to represent the
cosmos, and I’m reluctant to apply topological theories to EGs if they’re
going to complicate the issues instead of simplifying them. Peirce
illustrated his second Lowell lecture by drawing the diagrams on a
blackboard, which itself represents the sheet of assertion, and it would be
physically impossible to draw a line on the blackboard around the
blackboard. John hasn’t said what he actually had in mind, but I’m guessing
that it was a line or double line drawn around a part of the sheet of
assertion which has a graph on it.

 

JD: We shouldn't lose sight of the fact that, for the SA, a cut is not
simply a path. Rather, the cut takes what is inside the boundary and moves
the that part of the surface to a different surface--one that represents
what is negated. 

 

GF: I don’t think so. Inside the cut is another surface, another “area,” but
the surface in itself does not represent what is negated. The blank sheet of
assertion is a graph, and does represent everything implicitly understood to
be true (between graphist and interpreter); but the blank area inside a cut
is not a graph. It does represent a universe of discourse different from the
one represented by the sheet of assertion, and any graph scribed in that
area is read as false of the universe outside the cut. That to me is a very
different idea from the surface itself representing what is negated.

 

John’s idea seems still more different from Peirce’s idea in Lowell 2: 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, because neither one is being asserted! Hence the need for
other areas, other universes, to be separated (by cuts) from the places on
which the enclosures are drawn.

 

Maybe Peirce was never satisfied with his EGs; maybe he abandoned the gamma
graphs because he concluded that what he was trying to represent with them
could not be visually represented. But if that’s the case, and I’m quite
willing to believe it is, I want to understand why it can’t be done. And I
think the best way of understanding that is to thoroughly investigate
Peirce’s attempts to do it, from the ground up.

 

Gary f.

 

From: Jeffrey Brian Downard [mailto:jeffrey.down...@nau.edu] 
Sent: 30-Oct-17 12:19
Cc: Peirce-L <peirce-l@list.iupui.edu>
Subject: Re: [PEIRCE-L] Lowell Lecture 2.6

 

 

Hello Gary F, John S, List,

 

Gary F has raised the following question about a remark John made concerning
the SA in the EG:  

 

"Having said that, I have to say also that some of the statements in your
post are even more confusing than Peirce’s presentation in Lowell 2. You
wrote, “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?? Can you show us a replica?

 

It would be usual for those of us who learned Euclidean geometry in middle
and high school to think of the SA as a surface that is akin to the
Euclidean plane. Under the postulates that govern this system, parallel
lines never meet, so we picture the plane as stretching out in all
directions endlessly.

 

In topology, we think of an unbounded surface differently. After all, the
figures constructed in a 2-dimensional topological surface can be stretched
and twisted indefinitely without changing any of the continuous connections
between the parts of such figures. Leaving aside the homoloidal character of
lines taken to be straight and the metrical properties of such a surface,
the underlying topology of the Euclidean plane is that of a parabolic
surface. Such a surface is unbounded, but lines return to themselves. The
reason is that the parabola surface has the global structure of a torus. 

 

It is clear that Peirce is reflecting on the topological character of the SA
itself as he explains the starting assumptions for the alpha and beta system
of graphs. Such reflections are prominent in the NEM, the 9th Lecture in
Reasoning and the Logic of Things, etc. The global character of the SA will
be determined by the assumptions that govern the construction of figures in
this 2-dimensional surface. We can study this surface the same that that we
would study any 2-dimensional surface in topology using the Euler
characteristic, and we can study its global properties more carefully by
reflecting on the additional features that Listing and Peirce added to
Euler's version of the equation.

 

For a classification of types of surfaces based on the Euler characteristic,
see:  https://en.wikipedia.org/wiki/Euler_characteristic

For richer explanations of Peirce's understanding and 

Re: [PEIRCE-L] Lowell Lecture 2.6

[Jeffrey Brian Downard]

 of our 
discussion of the 2nd Lowell Lecture is to consider how the part of the surface 
that is inside the inner portion of the scroll is related to the part of the 
surface that is inside the outer part of the scroll. With a clearer idea of 
what that figure represents as a relation between those two parts of the 
surface, we can consider the import of the drawing the pseudograph as a cut 
that is entirely filled in as black. With this diagram, we see Peirce exploring 
a way to represent the relation between what is possible as a positive 
assertion and what is impossible--at least within the context of the 
development of the alpha system that he is explaining here.


--Jeff







Jeffrey Downard
Associate Professor
Department of Philosophy
Northern Arizona University
(o) 928 523-8354

From: John F Sowa <s...@bestweb.net>
Sent: Monday, October 30, 2017 7:20:48 AM
To: peirce-l@list.iupui.edu
Cc: Dau, Frithjof
Subject: Re: [PEIRCE-L] Lowell Lecture 2.6

Gary F,

The issues are far deeper than notation or computer processing.
1903 was a critical year in which Peirce began his correspondence
with Lady Welby.  That led him to address fundamental semiotic issues.

> I’ll have to confess at this point that I have no interest in learning
> EGs for the sake of learning a new notation system, or for the sake
> of knowledge representation in automated systems.

Last week, Ontolog Forum sponsored a telecon, in which I presented
slides on "Context in Language and Logic".  It addressed complex
semiotic issues, and I mentioned Peirce at various points.
Following are the slides.  Slide 2 also has the URL for the audio:
http://jfsowa.com/ikl/contexts/contexts.pdf

> the elementary phenomena of reasoning, that I’d like to understand better.

I agree that's important, and I also agree that Peirce was seeking
the most fundamental methods he could discover.  But I also believe
that he abandoned the recto/verso system because (a) the questions
raised by Lady Welby led him to more significant problems, and
(b) those low-level ideas paled in comparison to his goal of
representing "a moving picture of the action of the mind in thought."

> The three pairs of rules you attached (from NEM) are essentially
> the same as the three pairs he gives later on in Lowell 2, except
> for the shading and the absence of lines of identity.

For his EGs of 1903, they are logically equivalent.  In fact, that
is why his recto/verso description and his "magic blot" have no real
meaning:  they have no implications on the use of the graphs in
perception, learning, reasoning, or action.  But the 1911 system
can be generalized to modal logic, 3-valued logic, and probability.

And by the way, that letter of 1911 was addressed to Mr. Kehler,
one of Lady Welby's correspondents, and the main topic was
probability and induction.  That's also significant.

Implications of his 1911 system:

  1. The rules come in 3 symmetric pairs, and each pair consists
 of an insertion rule (i) and an erasure rule (e), each of
 which is the inverse of the other.  This feature supports
 some important theorems, which are difficult or impossible
 to prove with other rules of inference.

  2. The rules are *notation independent*:  with minor adaptations
 to the syntax, they can be used for reasoning in a very wide
 range of notations:  the algebraic notation for predicate
 calculus (Peirce, Peano, or Polish notations); Kamp's discourse
 representation structures; many kinds of diagrams and networks,
 and even natural languages.

  3. They can be adapted to theorem proving with arbitrary icons
 inside an EG.  I demonstrated that with Euclid's diagrams inside
 the ovals of EGs.  But they can also be used with icons of any
 complexity -- far beyond Euclidean-style diagrams.

  4. The psycholinguist Philip Johnson-Laird observed that Peirce's
 notation and rules are sufficiently simple to make them a
 promising candidate for a logic that could be supported by
 the neural mechanisms of the human brain.  That is true of
 his later system, but not the recto/verso system.

For an overview of these issues, see my slides on visualization:
http://jfsowa.com/talks/visual.pdf

To show that Kamp's DRS notation is isomorphic to a subset of EGs,
see slides 20 to 27 of visual.pdf.  To see the application to English,
see slides 28 to 30.  (But this is true only for that subset of English
or other NLs that can be translated to or from Kamp's DRS notation.)

For the option of including icons inside the areas of EGs, see slides
31 to 42 of visual.pdf.  For more detail about Euclid, see slides
19 to 39 of http://www.jfsowa.com/talks/ppe.pdf

Note:  There is considerable overlap between visual.pdf and ppe.pdf,
but slides 19 to 39 of ppe.pdf go into more detail about Euclid.

For theoretical issues, see slides 43 to 53 of visual.pdf.
For the theor

RE: [PEIRCE-L] Lowell Lecture 2.6

[gnox]

John, I'm inserting my (brief) responses. (This is probably the kind of
conversation that would work better in "real time" than email .)

 

Gary f.

 

-Original Message-
From: John F Sowa [mailto:s...@bestweb.net] 
Sent: 30-Oct-17 10:21



Gary F,

 

JFS: The issues are far deeper than notation or computer processing.

GF: Yes, that's why I was disappointed that your post didn't address the
issues I see as deeper!

 

JFS: 1903 was a critical year in which Peirce began his correspondence with
Lady Welby.  That led him to address fundamental semiotic issues.

GF: Yes, and 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. 

 

JFS: Last week, Ontolog Forum sponsored a telecon, in which I presented
slides on "Context in Language and Logic".  It addressed complex semiotic
issues, and I mentioned Peirce at various points.

Following are the slides.  Slide 2 also has the URL for the audio:

 
http://jfsowa.com/ikl/contexts/contexts.pdf

 

GF: I'll have a look when I have a chance.

 

> the elementary phenomena of reasoning, that I'd like to understand better.

JFS: I agree that 's important, and I also agree that Peirce was seeking the
most fundamental methods he could discover.  But I also believe that he
abandoned the recto/verso system because (a) the questions raised by Lady
Welby led him to more significant problems, and (b) those low-level ideas
paled in comparison to his goal of representing "a moving picture of the
action of the mind in thought."

 

GF: This is irrelevant to the discussion of Lowell 2, and the Lowell
Lectures as a whole, because Peirce had not introduced "the recto/verso
system" in 1903. His earliest use of these terms in reference to EGs is in
1906, as far as I know, and he introduced it in order to improve the gamma
graphs.

 

> The three pairs of rules you attached (from NEM) are essentially the 

> same as the three pairs he gives later on in Lowell 2, except for the 

> shading and the absence of lines of identity.

 

JFS: For his EGs of 1903, they are logically equivalent.  In fact, that is
why his recto/verso description and his "magic blot" have no real meaning:
they have no implications on the use of the graphs in perception, learning,
reasoning, or action.  But the 1911 system can be generalized to modal
logic, 3-valued logic, and probability.

 

GF: This too is irrelevant to the study of reasoning that Peirce was
attempting in 1903. Also, in the Kehler letter (dated 1911), Peirce himself
did not apply EGs to modal logic, 3-valued logic, or probability; he
discussed probability and induction in the letter after using EGs to
explicate deduction or "necessary reasoning." I can see (vaguely) how the
1909-11 version of EGs serves your purposes, but that doesn't help me to see
how EGs serve Peirce's purposes - which by the way he stated in almost
exactly the same way in the Kehler letter as he did in the Lowell lectures.
We owe you thanks, by the way, for showing us how to find the Kehler letter
in Google Books.

 

And by the way, that letter of 1911 was addressed to Mr. Kehler, one of Lady
Welby's correspondents, and the main topic was probability and induction.
That's also significant.

 

Implications of his 1911 system:

  1. The rules come in 3 symmetric pairs, and each pair consists

 of an insertion rule (i) and an erasure rule (e), each of

 which is the inverse of the other.  This feature supports

 some important theorems, which are difficult or impossible

 to prove with other rules of inference.

GF: This is equally true of Lowell 2, as we'll see further on.

 

  2. The rules are *notation independent*:  with minor adaptations

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

 range of notations:  the algebraic notation for predicate

 calculus (Peirce, Peano, or Polish notations); Kamp's discourse

 representation structures; many kinds of diagrams and networks,

 and even natural languages.

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 (as Stjernfelt calls it). And to cut things shorter, all of the
points you've listed below are also irrelevant to that iconicity, and to
Peirce's purpose in creating EGs as a replacement - not just another
notation - for other systems of formal logic. That purpose, as far as I can
see, has nothing to do with proving theorems. 

 

  3. They can be adapted to theorem proving with arbitrary icons

 inside an EG.  I demonstrated that with Euclid's diagrams inside

 the ovals of EGs.  But they can also be used with icons of any

 complexity -- far beyond Euclidean-style 

Re: [PEIRCE-L] Lowell Lecture 2.6

[John F Sowa]

Gary F,

The issues are far deeper than notation or computer processing.
1903 was a critical year in which Peirce began his correspondence
with Lady Welby.  That led him to address fundamental semiotic issues.


I’ll have to confess at this point that I have no interest in learning
EGs for the sake of learning a new notation system, or for the sake
of knowledge representation in automated systems.


Last week, Ontolog Forum sponsored a telecon, in which I presented
slides on "Context in Language and Logic".  It addressed complex
semiotic issues, and I mentioned Peirce at various points.
Following are the slides.  Slide 2 also has the URL for the audio:
http://jfsowa.com/ikl/contexts/contexts.pdf


the elementary phenomena of reasoning, that I’d like to understand better.


I agree that's important, and I also agree that Peirce was seeking
the most fundamental methods he could discover.  But I also believe
that he abandoned the recto/verso system because (a) the questions
raised by Lady Welby led him to more significant problems, and
(b) those low-level ideas paled in comparison to his goal of
representing "a moving picture of the action of the mind in thought."


The three pairs of rules you attached (from NEM) are essentially
the same as the three pairs he gives later on in Lowell 2, except
for the shading and the absence of lines of identity.


For his EGs of 1903, they are logically equivalent.  In fact, that
is why his recto/verso description and his "magic blot" have no real
meaning:  they have no implications on the use of the graphs in
perception, learning, reasoning, or action.  But the 1911 system
can be generalized to modal logic, 3-valued logic, and probability.

And by the way, that letter of 1911 was addressed to Mr. Kehler,
one of Lady Welby's correspondents, and the main topic was
probability and induction.  That's also significant.

Implications of his 1911 system:

 1. The rules come in 3 symmetric pairs, and each pair consists
of an insertion rule (i) and an erasure rule (e), each of
which is the inverse of the other.  This feature supports
some important theorems, which are difficult or impossible
to prove with other rules of inference.

 2. The rules are *notation independent*:  with minor adaptations
to the syntax, they can be used for reasoning in a very wide
range of notations:  the algebraic notation for predicate
calculus (Peirce, Peano, or Polish notations); Kamp's discourse
representation structures; many kinds of diagrams and networks,
and even natural languages.

 3. They can be adapted to theorem proving with arbitrary icons
inside an EG.  I demonstrated that with Euclid's diagrams inside
the ovals of EGs.  But they can also be used with icons of any
complexity -- far beyond Euclidean-style diagrams.

 4. The psycholinguist Philip Johnson-Laird observed that Peirce's
notation and rules are sufficiently simple to make them a
promising candidate for a logic that could be supported by
the neural mechanisms of the human brain.  That is true of
his later system, but not the recto/verso system.

For an overview of these issues, see my slides on visualization:
http://jfsowa.com/talks/visual.pdf

To show that Kamp's DRS notation is isomorphic to a subset of EGs,
see slides 20 to 27 of visual.pdf.  To see the application to English,
see slides 28 to 30.  (But this is true only for that subset of English
or other NLs that can be translated to or from Kamp's DRS notation.)

For the option of including icons inside the areas of EGs, see slides
31 to 42 of visual.pdf.  For more detail about Euclid, see slides
19 to 39 of http://www.jfsowa.com/talks/ppe.pdf

Note:  There is considerable overlap between visual.pdf and ppe.pdf,
but slides 19 to 39 of ppe.pdf go into more detail about Euclid.

For theoretical issues, see slides 43 to 53 of visual.pdf.
For the theoretical details, see http://jfsowa.com/pubs/egtut.pdf

I'm working on another paper that goes into more detail about Peirce's
"magic lantern of thought".  The 1911 system can support it.  But the
recto/verso system cannot.

John

-
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RE: [PEIRCE-L] Lowell Lecture 2.6

[gnox]

John,

 

I'll have to confess at this point that I have no interest in learning EGs
for the sake of learning a new notation system, or for the sake of knowledge
representation in automated systems. This is probably the reason why I found
your tutorial, and the Peirce text it is based on, uninformative, as an
introduction to EGs. All I managed to learn from them was how to translate
back and forth between EGs and three or four logical algebra systems, none
of which I have any use for ... i.e. from one set of meaningless symbols to
another.

 

I can't speak for others, but what I've been hoping to learn from Lowell 2,
aside from the role of EGs in the larger context of the Lowell lectures
(including the Syllabus), is how they suit the purpose which Peirce
explicitly designed them for, namely "to enable us to separate reasoning
into its smallest steps so that each one may be examined by itself . to
facilitate the study of reasoning" (and not to facilitate reasoning itself).
In other words, I'm trying to get a clearer view not of EGs as a
mathematical system but of the process that their transformations are
supposed to represent. It's not just the signs but their objects, the
elementary phenomena of reasoning, that I'd like to understand better.

 

The three pairs of rules you attached (from NEM) are essentially the same as
the three pairs he gives later on in Lowell 2, except for the shading and
the absence of lines of identity. But if one doesn't see how the spots,
lines and areas of EGs represent propositions, including conditional
propositions, what's the point of knowing these rules? That, I take it, is
why Peirce doesn't start with them, but works up to them from a starting
point which is the universe represented by the sheet of assertion and the
individual "subjects" which make up that universe. From there he proceeds to
the logical form which conveys "the most immediately useful information,"
and eventually works his way from that ground up to the code of permissions
or "rules."

 

Having said that, I have to say also that some of the statements in your
post are even more confusing than Peirce's presentation in Lowell 2. You
wrote, "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?? Can you show us a replica?

 

Then you wrote, "The blank is Peirce's only axiom, which is always true." 

GF: No, in Peirce the blank sheet of assertion does not represent a
proposition, and it takes at least a proposition to be true or false. What
he says is that anything made determinate by being scribed on the sheet of
assertion is assumed to be true. And Peirce does not say that the "blank" is
an "axiom" in any presentation of EGs that I've seen. Can you cite a
reference for that?

 

JFS: "If you draw just one oval around it [any area?], you get a graph that
negates the truth. Therefore, it is always false."

GF: What Peirce says in Lowell 2 is quite different: If you draw a closed
line around a graph on the sheet of assertion, it makes that graph false of
the universe represented by the sheet of assertion.

JFS: "Peirce called it the pseudograph."

GF: No, "pseudograph" in Peirce is another name for the "blot," which is the
inner close of a scroll when it is completely filled, so it is the opposite
of blank. A mere empty cut, or empty area, is not a pseudograph. In Lowell
2, the pseudograph represents an absurd consequent, which by its presence
has the effect of negating the antecedent. It doesn't "negate the truth." 

 

If you don't think Lowell 2 is worth a close look, you're entitled to that
opinion, but if we're going to refer to it at all, or to the Lowell
lectures, then we should do so accurately. I'm trying to do that here, even
when I question the clarity and value of Peirce's arguments, because I'm
hoping others can clarify them better than I've been able to do so far.

 

Gary f.

 

-Original Message-
From: John F Sowa [mailto:s...@bestweb.net] 
Sent: 29-Oct-17 13:17
To: peirce-l@list.iupui.edu
Cc: Dau, Frithjof <frithjof@sap.com>
Subject: Re: [PEIRCE-L] Lowell Lecture 2.6

 

Jon A and Gary F,

 

Peirce's way of presenting EGs in his Lowell lectures and his publications
of 1906 is horrendously complex.  The best I could say for it is
"interesting".  But I would never teach it, use it, or even mention it in an
introduction to EGs.  I would only present it as a side issue for advanced
students.

 

The version I recommend is the 8-page summary that he wrote in a long letter
(52 pages) in 1911.  The primary topic of that letter is "probability and
induction" (NEM v 3, pp 158 to 210).

 

When he got to 3-valued logic and probabilities, the recto/verso idea is
u

RE: [PEIRCE-L] Lowell Lecture 2.6

[gnox]

List,

 

I hope Jon soon finds time to unpack that post, but in the meantime I'll
make my own attempt to answer the questions provoked by Lowell 2.6. I should
perhaps mention first that I'm posting all these things in HTML format, and
anyone who's trying to read them with a mail app that doesn't handle HTML
will not be able to see the "blackboard" diagrams that Peirce is referring
to throughout. To see them, you'll need to either change the settings in
your email reader or read the version of Lowell 2 on my website instead.

 

In 2.6, the point of the "experiment" is "to get an insight into how the
scroll represents" this kind of conditional. The implication is that the
form of the "scroll" is in some way appropriate to its object, instead of
being arbitrarily assigned to that object.

 

For this experiment we need some "means of expressing an absurdity." Why do
we need that? I guess it's because we are dealing with necessary reasoning
here, which means we have to assume (without any reason for believing it)
that the given premisses are true - unless they are logically absurd; so
absurdity is the only way for a statement to be necessarily false. And it
seems we need a graph for falsity.

 

As an example of absurdity, Peirce chooses the assertion "everything is
true" - and even gives a reason for his choice. But now he wants it so serve
as the consequent in a scroll, and instead of simply writing the words in
the inner close, he represents it as a "blot" which fills up the area
enclosed by the inner cut. It makes a kind of sense, graphically, that if
the blank area is the place of assertion, the blotted (completely filled)
area is the place of absurdity or necessary falseness.

 

At this point the "experiment" resorts to a kind of magic trick: Peirce
makes the blot disappear (gradually but completely) - yet falsity remains,
like the grin of the Cheshire Cat. According to Peirce, "This suggests that
the relation which the cut asserts between the universe of discourse and
what is scribed within it is simply that what is scribed within is false of
the universe of discourse." I guess we are to assume that this is true of
any cut, no matter how deeply nested within other cuts: the place of that
cut is a universe of discourse, and whatever is scribed on the area inside
the cut is false of the universe outside that cut. So we are being asked to
believe that (1) the area of a cut on the sheet of assertion represents a
"universe of supposition" (as Peirce said awhile back) AND that any graph
written on it is false of the universe represented by the sheet of
assertion; and (2) the area of the cut inside that cut bears that same
relation to the area of the cut within which it is placed - and so on, all
the way down.

 

Intuitively, this is not easy to swallow, at least for me; this
interpretation seems to be arrived at by sleight of hand on Peirce's part.
But apparently Peirce's argument follows the actual course of development of
EGs in his imagination: The meaning of the cut is derived from the meaning
of the double cut, i.e. the scroll. Roberts has a footnote which reads: In
Ms 650, p. 20, Peirce says "Before I had the concept of a cut, I had that of
two cuts, which I drew at one continuous movement" (as a scroll). That, I
presume, is why we started this exposition with the conditional de inesse.
Anyway, I'm still trying to see this feature of EGs as naturally "iconic."

 

Gary f.

 

From: g...@gnusystems.ca [mailto:g...@gnusystems.ca] 
Sent: 28-Oct-17 04:38
To: peirce-l@list.iupui.edu
Subject: [PEIRCE-L] Lowell Lecture 2.6

 

Continuing from Lowell 2.5:

https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-1903-low
ell-lecture-ii/display/13608

 

In order to get an insight into how the scroll represents the conditional
proposition de inesse, we must make a little experimental research. 

Thus far, we have no means of expressing an absurdity. Let us invent a sign
which shall assert that everything is true. Nothing could be more illogical
than that statement, inasmuch as it would render logic false as well as
needless. Were every graph asserted to be true, there would be nothing that
could be added to that assertion. Accordingly, our expression for it may
very appropriately consist in completely filling up the area on which it is
asserted. Such filling up of an area, may be termed a blot. 

Take the conditional proposition de inesse, "If it rains then everything is
true[":] 



That amounts to denying that it rains. But there is no need of making the
inner cut so large. Let us write 



or even 



This suggests that the relation which the cut asserts between the universe
of discourse and what is scribed within it is simply that what is scribed
within is false of the universe of discourse. 

Then we may interpret 



as meaning "It is false that it rai

[PEIRCE-L] Lowell Lecture 2.6

[gnox]

Continuing from Lowell 2.5:

https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-1903-low
ell-lecture-ii/display/13608

 

In order to get an insight into how the scroll represents the conditional
proposition de inesse, we must make a little experimental research. 

Thus far, we have no means of expressing an absurdity. Let us invent a sign
which shall assert that everything is true. Nothing could be more illogical
than that statement, inasmuch as it would render logic false as well as
needless. Were every graph asserted to be true, there would be nothing that
could be added to that assertion. Accordingly, our expression for it may
very appropriately consist in completely filling up the area on which it is
asserted. Such filling up of an area, may be termed a blot. 

Take the conditional proposition de inesse, "If it rains then everything is
true[":] 



That amounts to denying that it rains. But there is no need of making the
inner cut so large. Let us write 



or even 



This suggests that the relation which the cut asserts between the universe
of discourse and what is scribed within it is simply that what is scribed
within is false of the universe of discourse. 

Then we may interpret 



as meaning "It is false that it rains and that a pear is not ripe." But we
have already seen that this is precisely the whole meaning of the
conditional de inesse; namely that it is false that the antecedent is true
while the consequent is false. Thus, that which the cut asserts is precisely
that that which is on its bottom is not, as a whole, true. 

 

  http://gnusystems.ca/Lowells.htm }{
Peirce's Lowell Lectures of 1903

https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-1903-low
ell-lecture-ii

 


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