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



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[PEIRCE-L] A test

[kirstima]

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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 
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 development of this

Re: [PEIRCE-L] Lowell Lecture 2.6

[Jeffrey Brian Downard]

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 development of this 
formula, see:  Havenel, Jérôme. "Peirce’s topological concepts." New essays on 
Peirce’s mathematical philosophy (2010): 283-322.


Let's consider an example taken from the table that classifies the different 
kinds of surfaces. The projective plane is an non-orientable unbounded surface, 
and it has an Euler characteristic of 1. The global properties of this surface 
are quite interesting. Within the system of postulates that govern the 
generation of the surface, all parallel lines converge. This is something we 
can picture in a more familiar way by considering a perspective drawing in 
which all parallel lines converge on the infinitely distant horizon. In effect, 
the projective space is a generalization on this idea from perspective 
geometry. What we should note is that the absolute in a projective surface is 
effectively a generalization of the infinitely distant horizon within the 
perspective geometry.


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--i.e., as the line that serves as the absolute. Is 
there any restriction on doing the same kind of thing in other sorts of 
topological surfaces? That is can we draw a path all of the way around a 
spherical (i.e., elliptical) or toroidal surface?


If such a path can be drawn "all the way around" these sorts of unbounded 
surfaces, is there a restriction on making a cut "all the way around" the SA? 
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. As 
such, already in the Alpha graphs, the SA is not a simple 2 dimensional 
surface. Rather, the SA can be used to represent is all that can be positively 
asserted, and this surface appears to be related--in some fashion--to another 
surface that represents all that can be denied.


Spending some effort on the question of how those surfaces are related within 
the Alpha and Beta systems might be worth our time. My hunch is that there is a 
significant difference between the way they are related in these two systems, 
and and even more significant difference when we consider, as John S suggests, 
what they represent when we are using these systems--especially gamma--to 
analyze synthetic forms of inference such as induction.


The first step in approaching this sort of question here in the context of our 
discussion of the 2nd Lowell Lecture is to 

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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