subject:"\[PEIRCE\-L\] Philosophy of Existential Graphs \(was Peirce's best and final version of EGs\)"

Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

2020-08-31 Thread John F. Sowa




Auke,
I apologize for my previous note.  I accidentally hit SEND
before I wrote anything.

JFS> Formal EGs are the
foundation.  As Peirce himself said, logic as semiotic is much broader. 
It includes the methodeutic for analyzing and developing the immense
variety of the empirical sciences.

AvB> We have discussed
this point before.  It seems to me that you forget about speculative
grammar and only recognize critic and speculative rhetoric...

When I wrote "logic as semiotic", I implied all three
branches.  Then I emphasized methodeutic because I cited some slides and
articles that discussed methods for using EGs in applications to various
subjects.
Among other things, those applications showed how the
eg1911 version enabled a rather simple solution to an unsolved research
problem from 1988.  For over 20 years, some very good logicians were
unable to find a solution by using the algebraic notations for first-order
logic.  
But the symmetric rules of inference (permissions) of
eg1911 indicated a direct path to the solution.  See slides 65 ff of
http://jfsowa.com/talks/ppe.pdf .  After that solution was found, it could
be translated to any other notation for FOL, including any algebraic
version.
Moral of the story:  The iconic structure of EGs and their
rules of inference do not increase the expressive power of FOL.  But they
enable people to "see" or "imagine" reasoning steps
that may be obscured by the algebraic notation.  In this case, the scroll
would be "anti-iconic" because it is asymmetric, and the proof
depends on the symmetry of the rules of inference.
In any case, the
original topic of this thread was very narrow:  Peirce's EGs of 1911 and
their relationship to his earlier EGs.  For other issues, it's better to
start a new thread.

John 
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Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

2020-08-31 Thread John F. Sowa





> John,
> 
> 
>> Op 30 augustus
2020 om 20:55 schreef "John F. Sowa"
:
>>
>>
>>
Auke, I agree with you about the issues and priorities.
>>
>> AvB> Peirce is multi facetted.  Each of us looks from a
particular
>> angle...  I am not interested in what might be
the final version
>> Peirce wrote on the negation vs scroll
issue...  I can agree with
>> you if we are discussing EG as a
formal system.
>>
>> Yes.  Formal EGs are the
foundation.  As Peirce himself said, logic
>> as semiotic is
much broader.  It includes the methodeutic for
>> analyzing and
developing the immense variey empirical sciences.
>>
>

> We have discussed this point before. It seems to me that you
forget about
> speculative grammar and only recognize critic and
speculative rethoric.
> But if we abstract from the apprehension
of the sign as an object when we
> look with the detached eye of
the logician (the realm of critic), we must
> take care when going
to speculative rethoric to again direct our attention
> to the
role the apprehension of the sign as an object plays in our
>
processes of interpretation. We must acknowledge that each interpreter
has
> its own verso sheet. And, that this sheet determines as what
sign a
> representamen gets interpreted.
> 
>
Auke
> 
> 
> 
> 
>>
>> AvB> In a sense when we interpret we look at the input
from all
>> logical perspectives.  Box-X running from  to
, or from
>> doubt to belief.
>>
>>  
  Yes.  All versions of classical first-order logic are sufficiently
>> expressive to define all the patterns of mathematics.  But
the
>> eg1911 version (as stated in L231) has a simplicity and
symmetry
>> that makes the definitions easier to state and the
proofs easier to
>> discover.
>>
>>
For examples, see the slides I presented at an APA conference in
>> 2015 and extended with more examples for another workshop: 
"Peirce,
>> Polya, and Euclid:  Integrating logic,
heuristics, and geometry,"
>>
http://jfsowa.com/talks/ppe.pdf .
>>
>> Note
that the two-dimensional shaded areas of eg1911 can be
>>
generalized to 3-D shaded regions for proofs in solid geometry. 
>> They could even be generalized to 4-D regions for
"stereoscopic
>> moving images", which Peirce
mentioned in L231.  Those
>> generalizations are not possible
with the 1903 scrolls or the 1906
>> recto/verso sides of a 2-D
sheet.
>>
>> Another important example is an
unsolved research problem that was
>> stated in 1988 and
remained unsolved until 2010.  Good logicians
>> failed to find
the proof because they made the same mistake that
>> Peirce
stated in 1893 (CP 4.76):  "For [the reader] cannot reason at
>> all without a monstrative sign of illation."  See the
proof with EG
>> rules in slide 65 ff of ppe.pdf.
>>
>> Examples of signs of illation (or inference)
include Peirce's claw
>> symbol for if-then in Boolean
algebra or his scroll in EGs.  Those
>> symbols are
asymmetric, but the critical step for solving the
>> problem
of
>> 1988 is easier to discover with the symmetric EG
"permissions".
>>
>> As for the time
and date when Peirce discovered the simplicity and
>>
generality of the eg1911 rules, compare R669, which ends abruptly
>> shortly after 7:40 pm on 2 June 1911, to the completely
rewritten
>> R670,
>> which begins on June 7. On
June 22, he began L231, which contains a
>> complete and
polished version of the logic in R670.
>>
>> The
date of the discovery is interesting for Peirce scholars.  But
>> the
>> power and generality of eg1911 is
demonstrated by the applications. 
>> For
>>
more examples, see "Diagrammatic reasoning with EGs and
EGIF",
>> http://jfsowa.com/pubs/diagrams.pdf ;
"Reasoning with diagrams and
>> images",
>>
http://www.collegepublications.co.uk/downloads/ifcolog00025.pdf
>>
>> John
>>
>> _ _ _ _
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>> REPLY ON
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> 

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Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

2020-08-31 Thread Auke van Breemen

John,


> Op 30 augustus 2020 om 20:55 schreef "John F. Sowa" :
> 
> 
> Auke, I agree with you about the issues and priorities.
> 
> AvB> Peirce is multi facetted.  Each of us looks from a particular 
> angle...  I am not interested in what might be the final version Peirce wrote 
> on the negation vs scroll issue...  I can agree with you if we are discussing 
> EG as a formal system.
> 
> Yes.  Formal EGs are the foundation.  As Peirce himself said, logic as 
> semiotic is much broader.  It includes the methodeutic for analyzing and 
> developing the immense variey empirical sciences.
> 

We have discussed this point before. It seems to me that you forget about 
speculative grammar and only recognize critic and speculative rethoric. But if 
we abstract from the apprehension of the sign as an object when we look with 
the detached eye of the logician (the realm of critic), we must take care when 
going to speculative rethoric to again direct our attention to the role the 
apprehension of the sign as an object plays in our processes of interpretation. 
We must acknowledge that each interpreter has its own verso sheet. And, that 
this sheet determines as what sign a representamen gets interpreted.

Auke




> 
> AvB> In a sense when we interpret we look at the input from all logical 
> perspectives.  Box-X running from  to , or from doubt to belief.
> 
> Yes.  All versions of classical first-order logic are sufficiently 
> expressive to define all the patterns of mathematics.  But the eg1911 version 
> (as stated in L231) has a simplicity and symmetry that makes the definitions 
> easier to state and the proofs easier to discover.
> 
> For examples, see the slides I presented at an APA conference in 2015 and 
> extended with more examples for another workshop:  "Peirce, Polya, and 
> Euclid:  Integrating logic, heuristics, and geometry," 
> http://jfsowa.com/talks/ppe.pdf .
> 
> Note that the two-dimensional shaded areas of eg1911 can be generalized 
> to 3-D shaded regions for proofs in solid geometry.  They could even be 
> generalized to 4-D regions for "stereoscopic moving images", which Peirce 
> mentioned in L231.  Those generalizations are not possible with the 1903 
> scrolls or the 1906 recto/verso sides of a 2-D sheet.
> 
> Another important example is an unsolved research problem that was stated 
> in 1988 and remained unsolved until 2010.  Good logicians failed to find the 
> proof because they made the same mistake that Peirce stated in 1893 (CP 
> 4.76):  "For [the reader] cannot reason at all without a monstrative sign of 
> illation."  See the proof with EG rules in slide 65 ff of ppe.pdf.
> 
> Examples of signs of illation (or inference) include Peirce's claw
> symbol for if-then in Boolean algebra or his scroll in EGs.  Those
> symbols are asymmetric, but the critical step for solving the problem of
> 1988 is easier to discover with the symmetric EG "permissions".
> 
> As for the time and date when Peirce discovered the simplicity and
> generality of the eg1911 rules, compare R669, which ends abruptly
> shortly after 7:40 pm on 2 June 1911, to the completely rewritten R670,
> which begins on June 7. On June 22, he began L231, which contains a
> complete and polished version of the logic in R670.
> 
> The date of the discovery is interesting for Peirce scholars.  But the
> power and generality of eg1911 is demonstrated by the applications.  For
> more examples, see "Diagrammatic reasoning with EGs and EGIF",
> http://jfsowa.com/pubs/diagrams.pdf ; "Reasoning with diagrams and
> images", http://www.collegepublications.co.uk/downloads/ifcolog00025.pdf
> 
> John
> 
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Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

2020-08-30 Thread John F. Sowa




Auke, I agree with you about the issues and priorities.

AvB> Peirce is multi facetted.  Each of us looks from a particular
angle...  I am not interested in what might be the final version Peirce
wrote on the negation vs scroll issue...  I can agree with you if we are
discussing EG as a formal system.

Yes.  Formal EGs are the
foundation.  As Peirce himself said, logic as semiotic is much broader. 
It includes the methodeutic for analyzing and developing the immense
variey empirical sciences.

AvB> In a sense when we interpret
we look at the input from all logical perspectives.  Box-X running from
 to , or from doubt to belief.

Yes.  All versions of
classical first-order logic are sufficiently expressive to define all the
patterns of mathematics.  But the eg1911 version (as stated in L231) has a
simplicity and symmetry that makes the definitions easier to state and the
proofs easier to discover.

For examples, see the slides I
presented at an APA conference in 2015 and extended with more examples for
another workshop:  "Peirce, Polya, and Euclid:  Integrating logic,
heuristics, and geometry," http://jfsowa.com/talks/ppe.pdf .

Note that the two-dimensional shaded areas of eg1911 can be generalized
to 3-D shaded regions for proofs in solid geometry.  They could even be
generalized to 4-D regions for "stereoscopic moving images",
which Peirce mentioned in L231.  Those generalizations are not possible
with the 1903 scrolls or the 1906 recto/verso sides of a 2-D sheet.

Another important example is an unsolved research problem that was
stated in 1988 and remained unsolved until 2010.  Good logicians failed to
find the proof because they made the same mistake that Peirce stated in
1893 (CP 4.76):  "For [the reader] cannot reason at all without a
monstrative sign of illation."  See the proof with EG rules in slide
65 ff of ppe.pdf.

Examples of signs of illation (or inference)
include Peirce's claw
symbol for if-then in Boolean algebra or his
scroll in EGs.  Those
symbols are asymmetric, but the critical step
for solving the problem of
1988 is easier to discover with the
symmetric EG "permissions". 

As for the time and date
when Peirce discovered the simplicity and
generality of the eg1911
rules, compare R669, which ends abruptly
shortly after 7:40 pm on 2
June 1911, to the completely rewritten R670,
which begins on June 7.
On June 22, he began L231, which contains a
complete and polished
version of the logic in R670.

The date of the discovery is
interesting for Peirce scholars.  But the
power and generality of
eg1911 is demonstrated by the applications.  For
more examples, see
"Diagrammatic reasoning with EGs and EGIF",
http://jfsowa.com/pubs/diagrams.pdf ; "Reasoning with diagrams
and
images",
http://www.collegepublications.co.uk/downloads/ifcolog00025.pdf

John
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Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

2020-08-19 Thread Jon Alan Schmidt

John, All:

JAS:  RL 231 (June 1911) includes Peirce's simplest and clearest
explanation of *Beta *EGs (NEM 3:162-169), which are equivalent to
classical first-order logic.  It is also his last thorough explanation of
EGs in the extant manuscripts other than RL 378 (September 1911 in French),
which is fully consistent with it.

JFS:  With this point of agreement, we can end that debate.

The bold was missing from my quoted statement.  As I added later in that
same post (https://list.iupui.edu/sympa/arc/peirce-l/2020-08/msg00063.html),
"understanding the *entire *system of EGs requires familiarity with *all *his
different writings about them."  Presumably we agree about that, as well.

JFS:  There is no need to derive negation from anything else.

Peirce repeatedly says otherwise, as I have repeatedly demonstrated; and
not just in his early writings about EGs, or when later recounting their
original development.

   - In RS 30 (early 1906), he confesses and retracts the "error" of
   omitting the blackened inner close from a cut for negation.
   - In R 490 (April 1906), he first introduces shading ("blue tint") to
   represent "a kind of possibility," not just a denial of actuality.
   - In R 300 (March 1908), he flatly rejects the idea that a consequence
   is correctly and accurately analyzed as a composite of two negations.
   - In R 669 (May 1911), he notes--just three weeks before composing RL
   231--that necessary reasoning is possible *without *the concept of
   falsity, while negation is shorthand for implying the absurdity that "every
   proposition is true."

Here is one more passage to consider.

CSP:  We have seen that there are three relations which subsist between the
parts of graphs. The first is the relation expressed by the scroll [image:
image.png]. This is the most important of all, since this is the relation
of premiss and conclusion; that is, if it be true that if A is true B is
true, then should A occur as a premiss we have a right to conclude B. The
second relation is that expressed by writing two graphs side by side AB,
that is to say, the relation of coexistence, and the third is the relation
of individual identity expressed by the heavy line. Now whatever relation
is analogous to one of these three relations will be expressed by graphs
into which the corresponding element of graphs enters and will therefore
affect reasoning and hence will be of logical importance. (R 466:18-19,
1903)

This comes from one of Peirce's notebooks for the Lowell Lectures, which in
RL 376 (December 1911) he calls "the better exposition" of EGs than
"Prolegomena to an Apology for Pragmaticism" (1906).  The three primitives
are thus consequence (scroll), coexistence (blank), and identity (line); so
again, negation (cut or shading) must be *derived *from consequence, which
is "the most important" of the three primitives.  While it is *simpler* to
treat negation as a primitive in *Beta* EGs (classical FOL), the trade-off
is that it is *less analytical*; i.e., it is contrary to their "real
purpose," which is not "to reach the conclusion from given premisses with
the utmost facility and speed," but rather "to dissect the reasoning into
the greatest possible number of distinct steps and so to force attention to
every requisite of the reasoning" (RL 231, NEM 3:168, June 1911).

Regards,

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

On Tue, Aug 18, 2020 at 5:02 PM John F. Sowa  wrote:

> Jeff BD, Terry R, Jon AS, List
>
> I endorse Jeff's comments about the need to relate any author's work to
> his or her predecessors, contemporaries, and successors.  I copied an
> excerpt from his note after my signature below.
>
> A major reason why Peirce's logic and semiotic were so advanced is that he
> had mastered all the major works from antiquity to the end of the 19th c --
> especially the Scholastic logic, which was far more advanced than the
> typical textbooks of the 19th c.
>
> TR> [human]‘logic’ is essentially sensate and intuitive -- based on
> imminent pre-analytic experiential iconicity but equally vulnerable to
> error, mistake, and dissonance:  e.g., it looks exactly like guacamole...
>
> I agree.  The metaphor I use is "knowledge soup".  William James called it
> the "blooming buzzing confusion".  That's the content of the phaneron.  The
> iconic structure of EGs makes them ideal for selecting lumps" from the soup
> and reasoning about them.
>
> TR> As far as possible-world semantics and models beyond FOL are
> concerned, two of the most helpful seminal works... _Essential Formal
> Semantics_ and _Topics in Conditional Logic_ [by Donald Nute].
>
> I checked the Amazon previews of those two books.  I agree that they
> provide good background for relating Peirce's writings to developments in
> the 20th c.  Since Peirce was thinking "ahead of his time", texts from his
> future can help

Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

2020-08-18 Thread John F. Sowa




Jeff BD, Terry R, Jon AS, List
I endorse Jeff's comments about
the need to relate any author's work to his or her predecessors,
contemporaries, and successors.  I copied an excerpt from his note after
my signature below.
A major reason why Peirce's logic and semiotic
were so advanced is that he had mastered all the major works from
antiquity to the end of the 19th c -- especially the Scholastic logic,
which was far more advanced than the typical textbooks of the 19th
c.
TR> [human]logic is essentially sensate and intuitive --
based on imminent pre-analytic experiential iconicity but equally
vulnerable to error, mistake, and dissonance:  e.g., it looks exactly like
guacamole...
I agree.  The metaphor I use is "knowledge
soup".  William James called it the "blooming buzzing
confusion".  That's the content of the phaneron.  The iconic
structure of EGs makes them ideal for selecting lumps" from the soup
and reasoning about them.
TR> As far as possible-world semantics
and models beyond FOL are concerned, two of the most helpful seminal
works... _Essential Formal Semantics_ and _Topics in Conditional Logic_
[by Donald Nute].
I checked the Amazon previews of those two books. 
I agree that they provide good background for relating Peirce's writings
to developments in the 20th c.  Since Peirce was thinking "ahead of
his time", texts from his future can help us understand some cryptic
comments he had not fully developed.

TR> Not convinced this
is true: "JFS: And the syntax and semantics of any other versions of
logic can be specified by mathematical theories expressed in FOL."

Please note:  I am *NOT* claiming that it's possible to translate
other versions of logic to FOL.  But every known version of mathematics
can be specified by axioms stated in FOL.  For examples, look at tools
such as Mathematica or MathLab.
The semantics of modal logic (every
version, including Peirce's) can be specfied by a purely first-order
theory of possible worlds. You don't have to believe me, you can look at
references I cite (in http://jfsowa.com/pubs/5qelogic.pdf ) or at the
references cited by Donald Nute or anybody else.

JAS> RL 231
(June 1911) includes Peirce's simplest and clearest explanation of Beta
EGs (NEM 3:162-169), which are equivalent to classical first-order logic. 
It is also his last thorough explanation of EGs in the extant manuscripts
other than RL 378 (September 1911 in French), which is fully consistent
with it.

With this point of agreement, we can end that debate. 
I'll add the following observations, which I believe are not
controversial:

1. The explanation of semantics (endoporeutic)
is clearer than Peirce's earlier comments, and it is consistent with Risto
Hilpinen's observation that endoporeutic is a version of Hintikka's
game-theoretical semantics (GTS).

2. The rules of inference
(permissions) are stated as three symmetric pairs instead of five separate
rules.  This symmetry is a major advance over other proof procedures, such
as Frege's or Gentzen's.  Among other important results, it enables a
simple solution to an unsolved research problem
from 1988.

3. The formalization in terms of shaded/unshaded areas permits a direct
generalization to regions in higher-dimenions.  Peirce had previously said
that a limitation to a 2-D sheet required selectives or bridges that would
not be required in 3-D graphs.  And later in L231, he discussed reasoning
in "stereoscopic moving images".  That thought was probably in
the back of his mind while he was writing the earlier pages.

4.
Finally, the smaller number of technical terms reduces the time and effort
for teaching and learning EGs.  The absence of the word 'scroll' also
avoids any questions about a possible difference in meaning.

JAS> Peirce's multiple derivations of negation from the primitive
logical relation of consequence are not "horribly contorted" at
all.

There is no need to derive negation from anything else. 
Affirmation and negation are the foundation for every logic from Aristotle
to the present. For Peirce (L376, December 1911), "A denial is
logically the simpler, because it implies merely that the utterer
recognizes, however vaguely, some discrepancy between the fact and the
speech, while an affirmation implies that he has examined all the
implications of the latter and finds no discrepancy with the
fact."

The so-called "derivation" of negation
from consequence is just a simple theorem of Boolean algebra: "not
p" is equivalent to "if p then 0", where 0 represents
Falsum.  Boole's original algebra had 'not' as a primitive, but it didn't
have 'if' until Peirce introduced his "claw" symbol.

The exaggerated claim that Peirce made for "illation" results
from one of his rare blunders:  "For [the reader] cannot reason at
all without a monstrative sign of illation" (CP 4.76, 1893).

That claim is refuted by Peirce's 1884 discovery (R506, W 5:107):
"Professor O. H. Mitchell's important paper "On a New Algebra of
Logic" has led me to think that the

Aw: Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

2020-08-12 Thread Helmut Raulien

Supp-supplement: But this problem might be solved by just writing the possible into the sheet of assertion, to say, that such a thing generally exists. So: "A(A(A))" would mean: "Possibly A" or "A is possible". Or not again? I am suspecting everything.

Supplement: No, Stop! I wrote no good! " "Unicorns exist" XOR NOT "Unicorns exist" ", and "If unicorns exist, unicorns exist", are both true, but "Possibly unicorns exist" is false. So my XOR-translation to alpha-graphs is false, and broken cuts are justified. Sorry.

John, List,

I mistakenly mentioned the shading. The shading is just making the alpha-graph clearer. To express insecurity, Peirce uses tincture, and broken cuts. I am wondering what is better to express "It possibly rains": To just let the variable stand for, resp. the ingredient be "It possibly rains", or to have a broken cut around "It rains", or to write in Boolean: "It rains" XOR NOT "It rains", which in EG-Boolean (only NOTs and ANDs) would be: NOT ("It rains AND NOT "It rains"). In EG: ("It rains" ("It rains")). This obviously is "If it rains, it rains". But does that mean, that it possibly rains? Maybe, why not? But if it is, why did Peirce introduce the broken cut?

I just am wondering, what are the advantages and disadvantages of expressing possibility either in the ingredient (or what the variable stands for), or with a broken cut, or by translating it via XOR to alpha-graphs. Given, my XOR-translation proposal is correct for possibility. For probability it is much more complicated, I think, because probability, other than possibility, has a value. How might this be handled with graphs?

Best,

Helmut

12. August 2020 um 05:44 Uhr
"John F. Sowa"
wrote:

Jon A, Helmut R, Terry R, Jon AS, List,

JA> I can't imagine why anyone would bother with Peirce's logic if it's just Frege and Russell in another syntax, which has been the opinion I usually get from FOL fans.

That is true. But the EG structure and rules of inference are elegant, and the
algebraic structure is klutzy. For a mathematician, that is a huge difference..
What makes EGs elegant is the simplicity of the structure, minimum of primitives, and symmetry of the rules.

As a result of that structure, note how eg1911 generalizes and relates Gentzen's two systems of natural deduction and sequent calculus. As a result, an unsolved research problem from 1988 is almost trivial in terms of the EG rules. See http://jfsowa.com/talks/ppe.pdf .

JA> Peirce's 1870 Logic of Relatives is already far in advance of anything we'd see again for a century, in principle in most places, in practice in many others, chock full of revolutionary ideas...

I agree. But those ideas are part of the ontology rather than the logic.

HR> I think that "implication, imagination, or belief" mostly do not sit in the symbols of notation such as cuts, but in the variables

I agree that variables are problematical. Three-dimensional graphs show direct connections. But 2-D graphs are forced to use klutzy features like selectives or bridges. The word 'cut' by itself is not bad. But it is a reminder of the recto/verso terminology, which Peirce said was "as bad as it could be".

In eg191, Peirce talks about 'shading'. Although that word takes six letters, the people who the read and write EGs should forget the words and think directly in terms of the diagrams. When doing subtraction, for example, nobody thinks of the words 'minuend' and 'subtrahend'. The words are useful for talking about math, but they should never intrude on the structure of the math.

TR> FOL doesn’t accommodate possible-world semantics, which is necessary (and sufficient) to resolve the paradoxes of material conditionality that persist in FOL. Moreover, possible-world semantics for modalities (necessity, possibility) and intensional (vs. extensional) conditionality are prerequisites for expressing causal laws.

That's true. For the semantics of modal logic, an ontology about possible worlds or something like Peirce's three universes (possibilities, actualities, and the necessitated) must be added. Work on modal semantics during the century after Peirce shows that FOL can be used to define such theories. See http://jfsowa.com/pubs/5qelogic.pdf and http://jfsowa.com/pubs/worlds.pdf .

Peirce was not happy with the earlier versions of his modal EGs. What he intended for Delta graphs is unknown, but any version of FOL (including eg1911) could be used to state a theory of possible worlds that is sufficent to specify a semantics for Delta graphs.whatever that might be.

JAS> As Peirce explains in R 490... "if A then B" is not logically equivalent to "not (A and not-B)".

No. Don Roberts (1973:154) defined a scroll as "Two cuts, one within the other". That makes it exactly equivalent to "not (A and not-B)". That is the way Jay Zeman, Ahti, and many others have defined it, and every EG proof that Peirce wrote is based on that definition. Any

Aw: Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

2020-08-12 Thread Helmut Raulien

John, List,

Best,

Helmut

12. August 2020 um 05:44 Uhr
"John F. Sowa"
wrote:

Jon A, Helmut R, Terry R, Jon AS, List,

JA> I can't imagine why anyone would bother with Peirce's logic if it's just Frege and Russell in another syntax, which has been the opinion I usually get from FOL fans.

JA> Peirce's 1870 Logic of Relatives is already far in advance of anything we'd see again for a century, in principle in most places, in practice in many others, chock full of revolutionary ideas...

I agree. But those ideas are part of the ontology rather than the logic.

HR> I think that "implication, imagination, or belief" mostly do not sit in the symbols of notation such as cuts, but in the variables

JAS> As Peirce explains in R 490... "if A then B" is not logically equivalent to "not (A and not-B)".

It's true that in some MSS, Peirce used a horribly contorted definition of negation in terms of a scroll. But in June 1911 (R670), he remembered that his permissions (rules of inference) depend only on whether an

Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

2020-08-11 Thread John F. Sowa




Jon A, Helmut R, Terry R, Jon AS, List,
JA> I can't imagine
why anyone would bother with Peirce's logic if it's just Frege and Russell
in another syntax, which has been the opinion I usually get from FOL
fans.
That is true.  But the EG structure and rules of inference are
elegant, and the
algebraic structure is klutzy.  For a mathematician,
that is a huge difference..
What makes EGs elegant is the simplicity
of the structure, minimum of primitives, and symmetry of the rules. 

As a result of that structure, note how eg1911 generalizes and
relates Gentzen's two systems of natural deduction and sequent calculus. 
As a result, an unsolved research problem from 1988 is almost trivial in
terms of the EG rules. See http://jfsowa.com/talks/ppe.pdf .

JA> Peirce's 1870 Logic of Relatives is already far in advance of
anything we'd see again for a century, in principle in most places, in
practice in many others, chock full of revolutionary ideas...

I
agree.  But those ideas are part of the ontology rather than the logic.


HR> I think that "implication, imagination, or
belief" mostly do not sit in the symbols of notation such as cuts,
but in the variables

I agree that variables are problematical. 
Three-dimensional graphs show direct connections.  But 2-D graphs are
forced to use klutzy features like selectives or bridges.  The word 'cut'
by itself is not bad.  But it is a reminder of the recto/verso
terminology, which Peirce said was "as bad as it could be".

In eg191, Peirce talks about 'shading'.  Although that word takes
six letters, the people who the read and write EGs should forget the words
and think directly in terms of the diagrams.  When doing subtraction, for
example, nobody thinks of the words 'minuend' and 'subtrahend'.  The words
are useful for talking about math, but they should never intrude on the
structure of the math.

TR> FOL doesnt accommodate
possible-world semantics, which is necessary (and sufficient) to resolve
the paradoxes of material conditionality that persist in FOL.  Moreover,
possible-world semantics for modalities (necessity, possibility) and
intensional (vs. extensional) conditionality are prerequisites for
expressing causal laws.

That's true.  For the semantics of
modal logic, an ontology about possible worlds or something like Peirce's
three universes (possibilities, actualities, and the necessitated) must be
added.  Work on modal semantics during the century after Peirce shows that
FOL can be used to define such theories.  See
http://jfsowa.com/pubs/5qelogic.pdf and http://jfsowa.com/pubs/worlds.pdf
.

Peirce was not happy with the earlier versions of his modal
EGs.  What he intended for Delta graphs is unknown, but any version of
FOL  (including eg1911) could be used to state a theory of possible worlds
that is sufficent to specify a semantics for Delta graphs.whatever that
might be.

JAS> As Peirce explains in R 490...  "if A
then B" is not logically equivalent to "not (A and
not-B)".

No.  Don Roberts (1973:154) defined a scroll as
"Two cuts, one within the other".  That makes it exactly
equivalent to "not (A and not-B)".  That is the way Jay Zeman,
Ahti, and many others have defined it, and every EG proof that Peirce
wrote is based  on that definition.  Any ambiguous comments about scrolls
are irrelevant.

It's true that in some MSS, Peirce used a
horribly contorted definition of negation in terms of a scroll.  But in
June 1911 (R670), he remembered that his permissions (rules of inference)
depend only on whether an area is shaded or unshaded.  Since a scroll is
limited to two levels, it's just a special case.  In R670, he wrote that
Figure 10 with scrolls is identical to Figure 11 with nested areas.  In
L231 and later, he never mentioned the word 'scroll'.  The word 'scroll'
is just a redundant term for a nest of two ovals, and the way of drawing
it cannot be generalized  to 3-D.
JFS> Unless any MSS later than
December 1911 are found which say anything to the contrary, the version in
L231 must be considered definitive.

JAS> No one has the
unilateral authority to declare that anything Peirce wrote "must be
considered definitive,"

The only authority is Peirce's
available MSS.  The semantics of first-order EGs in June 1911 is
consistent with earlier versions, and it's simpler, more precise, and more
complete (full classical FOL with a structure that could be extended to
metalanguage, second-order logic, and modal logic by borrowing fatures
from earlier versions).  Peirce continued to use that version until
December 1911, and no later version has bee found.

JAS>
Peirce begins his December 1911 letter to Risteen (RL 376) by stating,
"I mentioned to you, while you were [here] last year, that I have a
diagrammatic syntax which analyzes the syllogism into no less than six
inferential steps.  I now describe its latest state of development for the
first time."

Exactly!  Note that L231 shows the six steps
of the syllogism from the starting Figure 11 to the concluding

RE: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

2020-08-10 Thread John F. Sowa




Gary F,
To answer your questions:
Classical first-order
logic, usually abbreviated FOL, has pride of place among the open-ended
variety of logics that have been specified during the past century. 
Primary reason:  FOL is sufficient to specify 99.99% of all versions of
mathematics from ancient times to the present.  FOL can be used to specify
every digital computer ever built and every program that runs on any
digital computer.  And the syntax and semantics of any other versions of
logic can be specified by mathematical theories expressed in
FOL.
When I say that people in ancient times used FOL to specify
mathematics, I mean that they used the equivalent of the words AND,  OR,
NOT, IF, SOME, EVERY, and EQUALS (=) in a way that could be translated to
any modern notation for FOL, including eg1911. 
(http://jfsowa.com/peirce/eg1911.pdf )
Re Peirce's many versions of
logic:  Peirce made some extensions to Boolean logic in the 1860s, but his
major extension beyond Boolean logic was his logic of 1870, which went
beyond monadic predicates to n-adic predicates for any n>1.  De Morgan
called that work the greatest advance in logic since Aristotle.  And he
was right.
The discovery of complete notations for FOL by Frege
(1879) and Peirce (1885) presented mathematicians with a logic that was
sufficient to specify all of mathematics.   That was a revolutionary
advance.  Peirce (1885) also specified a version of second-order logic. 
That was an important advance beyoind Frege (1879). (See
http://jfsowa.com/peirce/putnam.htm )
Peirce also used logic as a
metalanguage in his 1898 example of an existential graph that stated
"That you are a good girl is much to be wished".  These two
additions (second-order logic and metalanguage) could be added to the
eg1911 notation with the same or similar additions he used with the
earlier versions of EGs.
The semantics of those additions could be
specified along the same lines as modern extensions to the algebraic
notations.  One version I have been using is called Common Logic (CL). 
For references and discussion, see the slides I presented at a conference
in June:  http://jfsowa.com/talks/eswc.pdf 
Re modal logic:  Any of
the notations for modal logic that Peirce introduced before 1911 could be
added to the notation of eg1911.  But Peirce himself was unsatisfied with
them.  He mentioned a replacement, which he called Delta graphs.  But so
far, nobody has found any MSS that specify any detail.  But any extensions
during the past century could be added to the notation of eg1911.  For
some discussion, see http://jfsowa.com/pubs/5qelogic.pdf .
Re
three-valued logic:  Peirce specified truth tables for three-valued logics
in some MSS.  Those could be used with the notation of eg1911.  But the
fact that he presented eg1911 at the beginning of a long letter on
probabilty suggests that he may have been thinking of probabilty as the
way to handle uncertain information.  If so, classical FOL, as expressed
in any notation including eg1911, could be used to reason about
probabilities.
Unless and until any MSS after 1911 are discovered,
nobody knows exactly how Peirce would have extended EGs to handle any of
the above issues.  But eg1911 is a *better* foundation for adding such
extensions than any previous version:
1.  The use of shading instead
of cuts or scrolls supports a simple extension beyond a two dimensional
sheet:  just use shaded regions in N-dimensional space.  In one of his
MSS, Peirce explicitly said that selectives are necessary only for a 2-D
sheet, and that EGs on a plane should be considered *projections* from 3-D
graphs.
2.  The drastic reduction in technical terms in eg1911
clears the way for further extensions.  In L231, he mentioned
"stereoscopic moving images" and regretted that he could not
afford the technology.  Today's virtual reality would be ideal for
allowing anyone to wander through a moving 3-D graph and make dynamic
changes to it.
3.  With today's technology, it's also possible to
include arbitrary images and even 3-d virtual reality inside any region of
an EG.  In a talk I presented at an APA conference in 2015 and later at an
EG workshop in Bogota, I proposed two new rules of inference --
observation and imagination -- which could be added to multi-dimensional
EGs.  Those two rules would be special cases of the rules of iteration and
deiteration.  For the slides, see http://jfsowa.com/talks/ppe.pdf .  Slide
2 of ppe.pdf includes the URL of a 78-page article that was published in
the Journal of Applied Logics,
John
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Aw: RE: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

2020-08-09 Thread Helmut Raulien

 


Gary, Jon, List,

 

I would say, and I think it does not contradict Peirce, that a law is a rule that is valid in a certain region: A juristic law in a county or state, a natural law in the universe, a law of logic or mathematics perhaps in every universe, though we cannot check that. So a law is there just so, by being stated, by whom or what whatever. A principle is there for some reason, as purpose, to achieve something. A principle may include a law by using, taking advantage of it. This harnessing includes representation, but is more than representation.

 

Best,

Helmut

 

09. August 2020 um 14:30 Uhr
 g...@gnusystems.ca
wrote:




Jon AS, you quoted me at the end of your post, but now I’d like to qualify what I said there by quoting Peirce: “we cannot make ourselves understood if we merely say what we mean.” Here’s the context:

 

[[ The acquiring [of] a habit is nothing but an objective generalization taking place in time. It is the fundamental logical law in course of realization. When I call it objective, I do not mean to say that there really is any difference between the objective and the subjective, except that the subjective is less developed and as yet less generalized. It is only a false word which I insert because after all we cannot make ourselves understood if we merely say what we mean. ] ‘Abstract of 8 lectures’ (NEM IV, 140)]

 

Gary f.

 


From: Jon Alan Schmidt 
Sent: 8-Aug-20 16:36
To: peirce-l@list.iupui.edu
Subject: Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)


 



Jeff, List:


 






JD:  Jon S asked for references to texts where Peirce employs the distinction between principles and laws.






 



I specifically asked for references where Peirce supposedly endorses your claim that "a law of logic governs the relations between the facts expressed in the premisses and conclusion of an argument. A principle, on the other hand, is our representation of such a law."



 






JD:  Peirce's definition in the Century Dictionary of the term "principle" is instructive on this point.






 



Quoting those definitions would have been appreciated, rather than expecting everyone on the List to look them up for ourselves, although Ben Udell kindly provided a link to the ones for "principle" (another is below).



 






JD:  See the 4th and 5th senses and the examples of uses by Aristotle, Hamilton, etc.



 







CSP:  4. A truth which is evident and general; a truth comprehending many subordinate truths; a law on which others are founded, or from which others are derived: as, the principles of morality, of equity, of government, etc. In mathematical physics a principle commonly means a very widely useful theorem. ...







5. That which is professed or accepted as a law of action or a rule of conduct; one of the fundamental doctrines or tenets of a system: as, the principles of the Stoics or the Epicureans; hence, a right rule of conduct; in general, equity; uprightness: as, a man of principle. (http://triggs.djvu.org/century-dictionary.com/djvu2jpgframes.php?volno=06=294=principle)






 



There are no accompanying examples of uses by Aristotle, and the only one from Hamilton--which mentions Aristotle--is for the 2nd sense, not the 4th or 5th.



 






CSP:  2. Cause, in the widest sense; that by which anything is in any way ultimately determined or regulated. ...







"Without entering into the various meanings of the term Principle, which Aristotle defines, in general, that from whence anything exists, is produced, or is known, it is sufficient to say that it is always used for that on which something else depends; and thus both for an original law and for an original element. In the former case it is a regulative, in the latter a constitutive, principle." Sir W. Hamilton, Reid, Note A, §5, Supplementary Dissertations






 



Aristotle and Hamilton evidently define "principle" as "that on which something else depends," such as "an original law."  The 4th sense similarly defines it as "a law on which others are founded, or from which others are derived."  The 5th sense seems consistent with my interpretation, rather than yours--excluded middle "is professed or accepted as a law" within classical logic, such that it is "one of the fundamental doctrines or tenets of [that] system."  In any case, Peirce never defines a principle as our representation of a law; on the contrary ...



 






JD:  Compare that the 3rd sense of "law" in his definition of the term.



 







CSP:  3. A proposition which expresses the constant or regular order of certain phenomena, or the constant mode of action of a force; a general formula or rule to which all things, or all things or phenomena within the limits of a certain class or group, conform, precisely and without exception; a rule to which events really tend to conform. (http://triggs.djvu.org/century-dictionary.com/djvu2jpgframes.php?volno=04=705=law)






 



It is

RE: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

2020-08-09 Thread gnox

Jon AS, you quoted me at the end of your post, but now I’d like to qualify what 
I said there by quoting Peirce: “we cannot make ourselves understood if we 
merely say what we mean.” Here’s the context:

 

[[ The acquiring [of] a habit is nothing but an objective generalization taking 
place in time. It is the fundamental logical law in course of realization. When 
I call it objective, I do not mean to say that there really is any difference 
between the objective and the subjective, except that the subjective is less 
developed and as yet less generalized. It is only a false word which I insert 
because after all we cannot make ourselves understood if we merely say what we 
mean. ] ‘Abstract of 8 lectures’ (NEM IV, 140)]

 

Gary f.

 

From: Jon Alan Schmidt  
Sent: 8-Aug-20 16:36
To: peirce-l@list.iupui.edu
Subject: Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and 
final version of EGs)

 

Jeff, List:

 

JD:  Jon S asked for references to texts where Peirce employs the distinction 
between principles and laws.

 

I specifically asked for references where Peirce supposedly endorses your claim 
that "a law of logic governs the relations between the facts expressed in the 
premisses and conclusion of an argument. A principle, on the other hand, is our 
representation of such a law."

 

JD:  Peirce's definition in the Century Dictionary of the term "principle" is 
instructive on this point.

 

Quoting those definitions would have been appreciated, rather than expecting 
everyone on the List to look them up for ourselves, although Ben Udell kindly 
provided a link to the ones for "principle" (another is below).

 

JD:  See the 4th and 5th senses and the examples of uses by Aristotle, 
Hamilton, etc.

 

CSP:  4. A truth which is evident and general; a truth comprehending many 
subordinate truths; a law on which others are founded, or from which others are 
derived: as, the principles of morality, of equity, of government, etc. In 
mathematical physics a principle commonly means a very widely useful theorem. 
...

5. That which is professed or accepted as a law of action or a rule of conduct; 
one of the fundamental doctrines or tenets of a system: as, the principles of 
the Stoics or the Epicureans; hence, a right rule of conduct; in general, 
equity; uprightness: as, a man of principle. 
(http://triggs.djvu.org/century-dictionary.com/djvu2jpgframes.php?volno=06 

 =294=principle)

 

There are no accompanying examples of uses by Aristotle, and the only one from 
Hamilton--which mentions Aristotle--is for the 2nd sense, not the 4th or 5th.

 

CSP:  2. Cause, in the widest sense; that by which anything is in any way 
ultimately determined or regulated. ...

"Without entering into the various meanings of the term Principle, which 
Aristotle defines, in general, that from whence anything exists, is produced, 
or is known, it is sufficient to say that it is always used for that on which 
something else depends; and thus both for an original law and for an original 
element. In the former case it is a regulative, in the latter a constitutive, 
principle." Sir W. Hamilton, Reid, Note A, §5, Supplementary Dissertations

 

Aristotle and Hamilton evidently define "principle" as "that on which something 
else depends," such as "an original law."  The 4th sense similarly defines it 
as "a law on which others are founded, or from which others are derived."  The 
5th sense seems consistent with my interpretation, rather than yours--excluded 
middle "is professed or accepted as a law" within classical logic, such that it 
is "one of the fundamental doctrines or tenets of [that] system."  In any case, 
Peirce never defines a principle as our representation of a law; on the 
contrary ...

 

JD:  Compare that the 3rd sense of "law" in his definition of the term.

 

CSP:  3. A proposition which expresses the constant or regular order of certain 
phenomena, or the constant mode of action of a force; a general formula or rule 
to which all things, or all things or phenomena within the limits of a certain 
class or group, conform, precisely and without exception; a rule to which 
events really tend to conform. 
(http://triggs.djvu.org/century-dictionary.com/djvu2jpgframes.php?volno=04 

 =705=law)

 

It is a law, not a principle, that he defines as a proposition--i.e.,. a 
representation.  He goes on to call it "a general formula or rule to which all 
things ... conform, precisely and without exception."  As I said before, 
excluded middle is not a law, because it is not exceptionless.

 

JD:  Here is a famous passage [CP 1.405-406, c. 1896] where Peirce explicitly 
employs the Kantian distinction.

 

Where do you see such a distinction in that passage?  The only mention of the 
word "law" in what you quoted is naming it as

Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

2020-08-08 Thread Jon Alan Schmidt

Jeff, List:

JD:  Jon S asked for references to texts where Peirce employs the
distinction between principles and laws.


I specifically asked for references where Peirce supposedly endorses your
claim that "a law of logic governs the relations between the facts
expressed in the premisses and conclusion of an argument. A principle, on
the other hand, is our representation of such a law."

JD:  Peirce's definition in the Century Dictionary of the term "principle"
is instructive on this point.


Quoting those definitions would have been appreciated, rather than
expecting everyone on the List to look them up for ourselves, although Ben
Udell kindly provided a link to the ones for "principle" (another is below).

JD:  See the 4th and 5th senses and the examples of uses by Aristotle,
Hamilton, etc.

CSP:  4. A truth which is evident and general; a truth comprehending many
subordinate truths; a law on which others are founded, or from which others
are derived: as, the *principles* of morality, of equity, of government,
etc. In mathematical physics a *principle* commonly means a very widely
useful theorem. ...

5. That which is professed or accepted as a law of action or a rule of
conduct; one of the fundamental doctrines or tenets of a system: as, the
*principles* of the Stoics or the Epicureans; hence, a right rule of
conduct; in general, equity; uprightness: as, a man of *principle*. (
http://triggs.djvu.org/century-dictionary.com/djvu2jpgframes.php?volno=06=294=principle
)


There are no accompanying examples of uses by Aristotle, and the only one
from Hamilton--which mentions Aristotle--is for the 2nd sense, not the 4th
or 5th.

CSP:  2. Cause, in the widest sense; that by which anything is in any way
ultimately determined or regulated. ...

"Without entering into the various meanings of the term *Principle*, which
Aristotle defines, in general, that from whence anything exists, is
produced, or is known, it is sufficient to say that it is always used for
that on which something else depends; and thus both for an original law and
for an original element. In the former case it is a regulative, in the
latter a constitutive, *principle*." *Sir W. Hamilton*, Reid, Note A, §5,
Supplementary Dissertations


Aristotle and Hamilton evidently define "principle" as "that on which
something else depends," such as "an original law."  The 4th sense
similarly defines it as "a law on which others are founded, or from which
others are derived."  The 5th sense seems consistent with my
interpretation, rather than yours--excluded middle "is professed or
accepted as a law" within *classical *logic, such that it is "one of the
fundamental doctrines or tenets of [that] system."  In any case, Peirce
never defines a principle as our *representation *of a law; on the contrary
...

JD:  Compare that the 3rd sense of "law" in his definition of the term.

CSP:  3. A proposition which expresses the constant or regular order of
certain phenomena, or the constant mode of action of a force; a general
formula or rule to which all things, or all things or phenomena within the
limits of a certain class or group, conform, precisely and without
exception; a rule to which events really tend to conform. (
http://triggs.djvu.org/century-dictionary.com/djvu2jpgframes.php?volno=04=705=law
)


It is a law, not a principle, that he defines as a proposition--i.e.,. a
representation.  He goes on to call it "a general formula or rule to which
all things ... conform, precisely and without exception."  As I said
before, excluded middle is *not *a law, because it is *not *exceptionless.

JD:  Here is a famous passage [CP 1.405-406, c. 1896] where Peirce
explicitly employs the Kantian distinction.


Where do you see such a distinction in that passage?  The only mention of
the word "law" in what you quoted is naming it as something that calls for
an explanation.  Meanwhile, Peirce straightforwardly equates "a regulative
principle" with "an intellectual hope," which is perfectly consistent with
his description of the *principle *of excluded middle as a *hope *rather
than a *law* in what I quoted previously from NEM 4:xiii.

JD:  At the same time, I'm trying to understand what Peirce is saying by
reading what he is reading. That, I think, is necessary to understand what
he's saying.


I have no doubt that it is helpful and insightful, but I disagree that it
is *necessary*.  Surely it is not a *requirement *for anyone who wants to
understand Peirce's vast corpus of writings to read *everything *that he
was reading at the time, which would obviously be another vast corpus of
writings.  And would we not then also need to read whatever all those *other
*authors were reading when they wrote what they wrote, in order to
understand what *they *were saying?  And so on, *ad infinitum*.

On the contrary, I believe that in most cases a good writer is capable of
being understood on his/her own terms.  As Gary Fuhrman once summarized

Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

2020-08-08 Thread Ben Udell

List, here are two links pertinent to the past few posts:

"principle" in the Century Dictionary:
https://www.google.com/books/edition/_/SzAUAQAAMAAJ?hl=en=1=PA4730=principle+%22cause,+in+the+widest+sense%22

"P" in Peirce Edition Project (UQÀM) - Lists of the Century Dictionary
words for which there are documents in PEP's database.

The words include:
• principal
• principality
• principium
• principle
http://web.archive.org/web/20120324152308/http://www.pep.uqam.ca/listsofwords.pep?l=P

Best, Ben

On 8/7/2020 6:14 PM, Jeffrey Brian Downard wrote:

Jon Schmidt, John Sowa, Gary Fuhrman, Gary Richmond, Robert Marty, List,

Jon S asked for references to texts where Peirce employs the distinction between principles and
laws. Peirce's definition in the Century Dictionary of the term "principle" is
instructive on this point. See the 4th and 5th senses and the examples of uses by Aristotle,
Hamilton, etc. Compare that the 3rd sense of "law" in his definition of the term.

Here is a famous passage where Peirce explicitly employs the Kantian
distinction. It is especially pertinent to the passage you've quoted:

But every fact of a general or orderly nature calls for an explanation; and
logic forbids us to assume in regard to any given fact of that sort that it is
of its own nature absolutely inexplicable. This is what Kant calls a regulative
principle, that is to say, an intellectual hope. The sole immediate purpose of
thinking is to render things intelligible; and to think and yet in that very
act to think a thing unintelligible is a self-stultification. ... Among other
regular facts that have to be explained is law or regularity itself. (1.405-6)\

I am confident that each of us is capable of looking up and analyzing other passages that use the terms
"law", "principle" and "logic" in the CP. As such, I won't offer a laundry list
of such passages.

For my part, I don't think the distinction is new with Kant. In fact it is
quite old. Kant simply tried to clarify well-established use of the
conceptions. Notice how easily we slide from talking about the principles
expressed in a theory, such as the principles of mechanics in Newton's theory
of physics, to talk about the laws. Doing so is often elliptical. We are often
saying on the supposition that this theory is true then the principles express
the real laws in nature. It is not odd to say that the principles in a given
theory turned out to be false. It is odd, however, to say the laws turned out
to be false. Rather, we say our supposition that the laws taken to be real in
given theory turned out to be false.

One reason there the meaning of these two terms appears to have changed over time is that
an original use of the term "law" is its juridical use. It appears that the
English term of a legal requirement was later applied to the real regularities in nature.
The order of Peirce's definitions suggests that he understands the history of this term.

Notice the apparent differences in our respective approaches to reading these
texts. In my post, I was drawing on a secondary reference that I hold in high
esteem. Let me state the reference now, which is Richard Smyth's Reading Peirce
Reading. In his interpretation of the early essays, he interprets key arguments
in Peirce's justification of the validity of the laws of logic drawing on
Kantian ideas. This is not surprising given the weight Peirce places on his
reading of Kant's Critiques at this stage in the development of the theory of
critical logic.

When I'm trying to make sense of Peirce's writings, I find it is essential to
draw on the secondary literature and to sort out what seems more and less
helpful. At the same time, I'm trying to understand what Peirce is saying by
reading what he is reading. That, I think, is necessary to understand what he's
saying.

John Sowa suggests that a richer understanding of Peirce's inquiries can be
gained by seeing where they have taken later reachers who have followed in his
wake. As such, there are five sources that seem important to reading Peirce:

1. the texts themselves;
2. the secondary literature on Peirce;
3. the inquiries of philosophers, scientists, mathematicians (etc.) Peirce
was reading--especially those he was drawing on in a sustained manner;
4. the inquiries of those following in Peirce's wake (self-consciously or
not).

In addition to asking how Peirce used this or that term in a given text (as in
1, above), I think that it is essential that we (5) try to reconstruct his
arguments and, at the same time, engage in the inquiries ourselves. After all,
Peirce's writings were not written for armchair philosophers. Rather, they were
written for inquirers willing to engage in philosophy as an experimental
science.

Are there other resources not on this list that should be considered when
interpreting Peirce's arguments and inquiries? If so, then I think it is worth
saying so. That way, we can talk

Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

2020-08-07 Thread Jeffrey Brian Downard

Jon Schmidt, John Sowa, Gary Fuhrman, Gary Richmond, Robert Marty, List,


Jon S asked for references to texts where Peirce employs the distinction 
between principles and laws. Peirce's definition in the Century Dictionary of 
the term "principle" is instructive on this point. See the 4th and 5th senses 
and the examples of uses by Aristotle, Hamilton, etc. Compare that the 3rd 
sense of "law" in his definition of the term.


Here is a famous passage where Peirce explicitly employs the Kantian 
distinction. It is especially pertinent to the passage you've quoted:



But every fact of a general or orderly nature calls for an explanation; and 
logic forbids us to assume in regard to any given fact of that sort that it is 
of its own nature absolutely inexplicable. This is what Kant calls a regulative 
principle, that is to say, an intellectual hope. The sole immediate purpose of 
thinking is to render things intelligible; and to think and yet in that very 
act to think a thing unintelligible is a self-stultification. ... Among other 
regular facts that have to be explained is law or regularity itself. (1.405-6)


I am confident that each of us is capable of looking up and analyzing other 
passages that use the terms "law", "principle" and "logic" in the CP. As such, 
I won't offer a laundry list of such passages.


For my part, I don't think the distinction is new with Kant. In fact it is 
quite old. Kant simply tried to clarify well-established use of the 
conceptions. Notice how easily we slide from talking about the principles 
expressed in a theory, such as the principles of mechanics in Newton's theory 
of physics, to talk about the laws. Doing so is often elliptical. We are often 
saying on the supposition that this theory is true then the principles express 
the real laws in nature. It is not odd to say that the principles in a given 
theory turned out to be false. It is odd, however, to say the laws turned out 
to be false. Rather, we say our supposition that the laws taken to be real in 
given theory turned out to be false.


One reason there the meaning of these two terms appears to have changed over 
time is that an original use of the term "law" is its juridical use. It appears 
that the English term of a legal requirement was later applied to the real 
regularities in nature. The order of Peirce's definitions suggests that he 
understands the history of this term.


Notice the apparent differences in our respective approaches to reading these 
texts. In my post, I was drawing on a secondary reference that I hold in high 
esteem. Let me state the reference now, which is Richard Smyth's Reading Peirce 
Reading. In his interpretation of the early essays, he interprets key arguments 
in Peirce's justification of the validity of the laws of logic drawing on 
Kantian ideas. This is not surprising given the weight Peirce places on his 
reading of Kant's Critiques at this stage in the development of the theory of 
critical logic.


When I'm trying to make sense of Peirce's writings, I find it is essential to 
draw on the secondary literature and to sort out what seems more and less 
helpful. At the same time, I'm trying to understand what Peirce is saying by 
reading what he is reading. That, I think, is necessary to understand what he's 
saying.


John Sowa suggests that a richer understanding of Peirce's inquiries can be 
gained by seeing where they have taken later reachers who have followed in his 
wake. As such, there are five sources that seem important to reading Peirce:


  1.  the texts themselves;
  2.  the secondary literature on Peirce;
  3.  the inquiries of philosophers, scientists, mathematicians (etc.) Peirce 
was reading--especially those he was drawing on in a sustained manner;
  4.  the inquiries of those following in Peirce's wake (self-consciously or 
not).

In addition to asking how Peirce used this or that term in a given text (as in 
1, above), I think that it is essential that we (5) try to reconstruct his 
arguments and, at the same time, engage in the inquiries ourselves. After all, 
Peirce's writings were not written for armchair philosophers. Rather, they were 
written for inquirers willing to engage in philosophy as an experimental 
science.

Are there other resources not on this list that should be considered when 
interpreting Peirce's arguments and inquiries? If so, then I think it is worth 
saying so. That way, we can talk about the relative importance of these 
different resources in our respective approaches. My hope is that we can 
compare notes, acknowledge our differences, and learn from one another.

Doing so will put us all in a better position to engage with philosophers and 
other inquirers who are not following in Peirce's wake--and who insist that 
they have more fruitful assumptions and better methods than the pragmatic 
methods we are looking to Peirce for guidance in putting to better use.

Hope that helps.

--Jeff




Jeffrey Downard
Associate Professor

Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

2020-08-06 Thread Jon Alan Schmidt

Jeff, List:

JAS:  In other words, Peirce denies that excluded middle is an absolutely
exceptionless *law* (NEM 4:xiii, no date), which is presumably why he
typically prefers to call it a *principle *instead.

JD:  On its face, I believe this expresses some confusion about the
differences between principles and laws.

Here is the passage by Peirce that I cited but did not quote.

CSP:  Logic requires us, with reference to each question we have in hand,
to hope some definite answer to it may be true. That *hope *with reference
to each case as it comes up is, by a *saltus*, stated by logicians as a
*law* concerning *all cases*, namely, the law of excluded middle. This law
amounts to saying that the universe has a perfect reality. (NEM 4:xiii, no
date)

Logicians typically treat excluded middle "as a *law* concerning *all cases*,"
but Peirce recognizes that this is "a *saltus*" (leap) grounded in the
regulative *hope *that every question has a definite answer, which is only
true if "the universe has a perfect reality."  Eisele references R 140, but
this excerpt does not actually appear in that manuscript, and Robert Lane
states in *Peirce on Realism and Idealism*, "I have not been able to
identify its actual source" (p. 179 n. 17).

As far as I know, it is the only place in Peirce's vast corpus where he
uses "law of excluded middle," although he discusses the "law of excluded
third" as one of "the three fundamental laws of logic" according to
"Boole's system" in a very early manuscript (NEM 3:316-318, 1865-6).  By
contrast, "law of contradiction" appears five times in CP and is affirmed
as such in each instance.

JD:  According to a neo-Kantian view of rational laws, a law of logic
governs the relations between the facts expressed in the premisses and
conclusion of an argument. A principle, on the other hand, is our
representation of such a law.

To clarify, are you claiming that this was *Peirce's *view of the
relationship between principles and laws, or suggesting that it is how *we*
should distinguish them?  If the former, what specific passages in Peirce's
writings do you interpret as endorsing such a view?

Thanks,

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

On Wed, Aug 5, 2020 at 11:09 PM Jeffrey Brian Downard <
jeffrey.down...@nau.edu> wrote:

> Jon Schmidt, List,
>
> I'd like to take up the distinction between principles and laws.
>
> Jon S:  "In other words, Peirce denies that excluded middle is an
> absolutely exceptionless *law *(NEM 4:xiii, no date), which is presumably
> why he typically prefers to call it a *principle *instead."
>
> On its face, I believe this expresses some confusion about the differences
> between principles and laws. I think Peirce makes the following sort
> of distinction between the two. Consider the following argument, which is
> from the second section of Kant's *Grounding for the Metaphysics of
> Morals*:
>
> Everything in nature works in accordance with laws. Only a rational being
> has the capacity to act in accordance with the representation of laws, that
> is, in accordance with principles, or has a will. Since reason is required
> for the derivation of actions from laws, the will is nothing other than
> practical reason. (Ak 412)
>
> According to a neo-Kantian view of rational laws, a law of logic governs
> the relations between the facts expressed in the premisses and conclusion
> of an argument. A principle, on the other hand, is our representation of
> such a law.
>
> A *logic utens* consists of the habits of inference that embody such
> principles. Those principles are subject to criticism precisely because
> they may not match up with the laws of logic themselves. The purpose of a
> philosophical theory of logic (i.e., a *logica docens*) is to build on
> the criticism of our common sense principles for the sake of arriving at a
> more adequate theoretical representation of the truth concerning the real
> laws that govern the logical relations between such facts.
>
> As such, we can distinguish between the principles embodied in our *logica
> utens* and the principles embodied in a philosophical theory of
> logic--and either or both of these may deviate in some respects from the
> real laws of logic.
>
> This distinction is at the root of the classification of genuine triadic
> relations in "The Logic of Mathematics, an attempt to develop my categories
> from within". In this classificatory scheme, the laws of logic function as
> laws of fact insofar as they govern those facts directly, and they are in a
> genuinely triadic relation to the actual facts and those that are possible
> (i.e., in the future).
>
> The principles of logic, on the other hand, function as symbolic
> representations that govern the self-controlled growth of our
> understanding. The principles of logic, Peirce points out, do not govern
> brute facts with mere

Re: Fw: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

2020-08-06 Thread John F. Sowa




Jeff,
To be iconic, a notation must have some resemblance to the
structure or image of which it is an icon.  Any claim that some notation
is iconic must be justified by showing the original which it
resembles.
JBD> As far as I can
see, the scroll is a
special kind of iconic sign because it expresses the continuity in the
relationship between antecedent and consequent of the conditional, and
this mirrors the continuity in the relationship between premisses and
conclusions
 in an argument.
During the month of June 1911, Peirce was
reviewing and reorganizing his logical, philosophical, and semiotic
foundations for EGs.  He had several goals, one of which was a clear and
precise summary for his most receptive audience, Lady Welby and her
significs group.
On May 25 (R669), Peirce began with a summary of
his writings since 1896.   For that purpose, the scroll was significant,
since it was his inspiration for switching from entitative to existential
graphs..
But in June  7 to 17 (R670), he remembered that the rules
of inference depended only on whether an area was positive or negative. 
"It is only the color of the area itself which has the force of
affirming, if it be white or evenly enclosed... or of denying if it be
shaded or oddly enclosed."
He said that a cut was just the
boundary of an area, and it had no more meaning than punctuation.  He
also showed a scroll in Fig 10 as an alternate way of representing the
shading in Fig 11.  In fact, he did not use the word 'scroll' to describe
Fig 10.  He just wrote "the lines that represent the cuts". 
Apparently, he considered the word 'scroll'  to be so meaningless that it
was not worth mentioning. 
In L231 (June22), he adopted pencil
shading, which was easy to draw.  Therefore, he had no need to draw or
mention  cuts or scrolls.  The words would be useless verbiage that could
only cause confusion.
But L231 also mentioned steroscopic moving
images.  Shaded areas could easily be generalized to shaded regions in
3D.  Cuts might be represented as closed regions, but there is no
convenient way to represent  a 3-D analog of a scroll.
Shaded and
unshaded regions are iconic notations, but there is no way to represent a
3-D scroll.  Therefore, he did not mention cuts or scrolls in
L231.
John

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[PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

2020-08-05 Thread Jeffrey Brian Downard

Jon Schmidt, List,


I'd like to take up the distinction between principles and laws.


Jon S:  "In other words, Peirce denies that excluded middle is an absolutely 
exceptionless law (NEM 4:xiii, no date), which is presumably why he typically 
prefers to call it a principle instead."


On its face, I believe this expresses some confusion about the differences 
between principles and laws. I think Peirce makes the following sort of 
distinction between the two. Consider the following argument, which is from the 
second section of Kant's Grounding for the Metaphysics of Morals:


Everything in nature works in accordance with laws. Only a rational being has 
the capacity to act in accordance with the representation of laws, that is, in 
accordance with principles, or has a will. Since reason is required for the 
derivation of actions from laws, the will is nothing other than practical 
reason. (Ak 412)


According to a neo-Kantian view of rational laws, a law of logic governs the 
relations between the facts expressed in the premisses and conclusion of an 
argument. A principle, on the other hand, is our representation of such a law.


A logic utens consists of the habits of inference that embody such principles. 
Those principles are subject to criticism precisely because they may not match 
up with the laws of logic themselves. The purpose of a philosophical theory of 
logic (i.e., a logica docens) is to build on the criticism of our common sense 
principles for the sake of arriving at a more adequate theoretical 
representation of the truth concerning the real laws that govern the logical 
relations between such facts.


As such, we can distinguish between the principles embodied in our logica utens 
and the principles embodied in a philosophical theory of logic--and either or 
both of these may deviate in some respects from the real laws of logic.


This distinction is at the root of the classification of genuine triadic 
relations in "The Logic of Mathematics, an attempt to develop my categories 
from within". In this classificatory scheme, the laws of logic function as laws 
of fact insofar as they govern those facts directly, and they are in a 
genuinely triadic relation to the actual facts and those that are possible 
(i.e., in the future).


The principles of logic, on the other hand, function as symbolic 
representations that govern the self-controlled growth of our understanding. 
The principles of logic, Peirce points out, do not govern brute facts with mere 
necessity. Rather, they function as imperatives that dictate how we ought to 
think. As such, the principles of logic differ from the laws of logic insofar 
as they are in thoroughly genuine triadic relations to the premisses and 
conclusions that are part of our inquiries. The principles that govern our 
deductive inferences are capable of growth even if the laws of deductive logic 
are, in some sense, necessary laws.


Yours,


Jeff




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



From: Jon Alan Schmidt 
Sent: Tuesday, August 4, 2020 6:59 PM
To: s...@bestweb.net
Cc: peirce-l@list.iupui.edu; ahti-veikko.pietari...@ttu.ee; 
francesco.belluc...@unibo.it; cdw...@iupui.edu; martin.irv...@georgetown.edu; 
Gary Richmond
Subject: [PEIRCE-L] Re: Philosophy of Existential Graphs (was Peirce's best and 
final version of EGs)

John, All:

JFS:  I sent a complete analysis of these issues to you and others on the CC 
list.

Any analysis of these issues that treats cuts/shading as primitive in EGs, 
rather than derived from the scroll, is incomplete.  Peirce himself never 
claims in R 670 or in RL 231 to be giving a complete analysis or explanation of 
EGs.

JFS:  In response to the other comments in your recent note, I'll reply with a 
copy of Peirce's comments about scrolls in L231:  "  ", AKA silence.

An argument from silence is always logically weak, in this case especially so 
since Peirce elsewhere explicitly denies that a consequence is a composite of 
two negations and explicitly derives the cut from the scroll with a blackened 
inner close.  Again, I am not at all questioning the value of shading as a 
simpler and more iconic improvement over thin lines for representing these 
relations.  In fact, according to what seems to be Peirce's very first 
introduction of shading in EGs ("blue tint"), written five years earlier than R 
670 and RL 231, it is precisely what revealed to him that "if A then B" is not 
strictly equivalent to "not (A and not-B)."

CSP:  But I had better tell you that practically, I content myself with 
performing these cuts in my imagination, merely drawing a light line to 
represent the cut. The blue tint, however, of the area within the cut is a 
great aid to the understanding. How great I have only recently discovered. ...
The new discovery, which sheds such a light is simply that, as the main part of 
the sheet

Re: Fw: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

2020-08-05 Thread Gary Richmond

Jon, Jeff, All,

JAS:  After all, *"when we have carried analysis so far as to leave only a
continuous predicate, we have carried it to its ultimate elements"* (SS 72,
1908 Dec 14).  Accordingly, my analysis of an EG is that *the names and
lines are subjects, respectively denoting abstract general concepts and
concrete indefinite individuals*, while *the syntax of their attachments
signifies the pure/continuous predicate*.[emphasis added: GR]

GR: I obviously agree.

Best.

Gary R

"Time is not a renewable resource." gnox

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








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On Wed, Aug 5, 2020 at 8:56 PM Jon Alan Schmidt 
wrote:

> Jeff, All:
>
> JD:  As far as I can see, the scroll is a special kind of iconic sign
> because it expresses the continuity in the relationship between antecedent
> and consequent of the conditional, and this mirrors the continuity in the
> relationship between premisses and conclusions in an argument.
>
>
> I agree; in fact, it expresses and mirrors not just the *continuity* of
> that relationship, but also its *asymmetry*.  All semeiosis is
> inferential process, a continuous hyperbolic sequence that always and only
> has one direction--from premiss to conclusion, from antecedent to
> consequent, from object to interpretant.
>
> I am in general agreement with your other comments, as well.  In
> particular, my interests here are primarily philosophical--as the subject
> line reflects--which is why I keep insisting on the derivative nature of
> negation while recognizing that treating it as a primitive does not
> necessarily affect the *appearance *of the resulting EGs.  As I just
> noted in my other post, it does make an important difference in the 
> *interpretation
> *of those EGs, which is why I believe that we should follow Peirce's
> advice to add a small darkened circle to a shaded area when it is intended
> to represent negation rather than the antecedent of a consequence.
>
> Another potential difference in interpretation is where we choose to draw
> the line between the subjects and predicate of a proposition.  I take
> Peirce seriously when he states that "the proper way in logic is to take as
> the subject whatever there is of which sufficient knowledge cannot be
> conveyed in the proposition itself, but collateral experience on the part
> of its interpreter is requisite ... leaving the *pure *predicate a mere
> form of connection" (NEM 3:885, 1908 Dec 5).  After all, "when we have
> carried analysis so far as to leave only a continuous predicate, we have
> carried it to its ultimate elements" (SS 72, 1908 Dec 14).  Accordingly, my
> analysis of an EG is that the names and lines are subjects, respectively
> denoting abstract general concepts and concrete indefinite individuals,
> while the syntax of their attachments signifies the pure/continuous
> predicate.
>
> Regards,
>
> Jon Alan Schmidt - Olathe, Kansas, USA
> Structural Engineer, Synechist Philosopher, Lutheran Christian
> www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
>
> On Tue, Aug 4, 2020 at 10:17 PM Jeffrey Brian Downard <
> jeffrey.down...@nau.edu> wrote:
>
>> Jon Schmidt, John Sowa, List,
>>
>> It might be helpful to make a clearer distinction between what is
>> advantageous for the purposes of developing the EGs as a formal system of
>> mathematical logic and what is advantageous for the purposes of developing
>> theories of philosophical logic.
>>
>> For the sake of illustrating the importance of the distinction, let me
>> take up the following assertion
>>
>> Jon Schmidt:  "Hence I continue to maintain that the cut for negation
>> must be *derived *from the scroll for consequence with a blackened inner
>> close, rather than treated as a primitive, even when shading is employed
>> instead."
>>
>> For the purposes of developing systems of mathematical logic, the
>> logician can adopt various starting points in setting up the logical
>> grammar for a given system. In symbolic systems, the rules determine what
>> does and does not count as a well-formed-formula. The same holds in the
>> case of the EGs. The grammatical rules determine what counts as a
>> well-formed-graph.
>>
>> Given all the work he has done on the symbolic systems of logic, Peirce
>> sees that there are a number of different ways of setting up the
>> grammatical rules that will, when taken together with the rules of
>> inference and transformation, yield consistent results. For the sake of the
>> EGs considered as a formal system, the scroll and two nested circles are
>> logically equivalent. What is more, it makes no difference for the beta
>> graphs whether the scroll

Re: Fw: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

2020-08-05 Thread Jon Alan Schmidt

Jeff, All:

JD:  As far as I can see, the scroll is a special kind of iconic sign
because it expresses the continuity in the relationship between antecedent
and consequent of the conditional, and this mirrors the continuity in the
relationship between premisses and conclusions in an argument.

I agree; in fact, it expresses and mirrors not just the *continuity* of
that relationship, but also its *asymmetry*.  All semeiosis is inferential
process, a continuous hyperbolic sequence that always and only has one
direction--from premiss to conclusion, from antecedent to consequent, from
object to interpretant.

I am in general agreement with your other comments, as well.  In
particular, my interests here are primarily philosophical--as the subject
line reflects--which is why I keep insisting on the derivative nature of
negation while recognizing that treating it as a primitive does not
necessarily affect the *appearance *of the resulting EGs.  As I just noted
in my other post, it does make an important difference in the *interpretation
*of those EGs, which is why I believe that we should follow Peirce's advice
to add a small darkened circle to a shaded area when it is intended to
represent negation rather than the antecedent of a consequence.

Another potential difference in interpretation is where we choose to draw
the line between the subjects and predicate of a proposition.  I take
Peirce seriously when he states that "the proper way in logic is to take as
the subject whatever there is of which sufficient knowledge cannot be
conveyed in the proposition itself, but collateral experience on the part
of its interpreter is requisite ... leaving the *pure *predicate a mere
form of connection" (NEM 3:885, 1908 Dec 5).  After all, "when we have
carried analysis so far as to leave only a continuous predicate, we have
carried it to its ultimate elements" (SS 72, 1908 Dec 14).  Accordingly, my
analysis of an EG is that the names and lines are subjects, respectively
denoting abstract general concepts and concrete indefinite individuals,
while the syntax of their attachments signifies the pure/continuous
predicate.

Regards,

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

On Tue, Aug 4, 2020 at 10:17 PM Jeffrey Brian Downard <
jeffrey.down...@nau.edu> wrote:

> Jon Schmidt, John Sowa, List,
>
> It might be helpful to make a clearer distinction between what is
> advantageous for the purposes of developing the EGs as a formal system of
> mathematical logic and what is advantageous for the purposes of developing
> theories of philosophical logic.
>
> For the sake of illustrating the importance of the distinction, let me
> take up the following assertion
>
> Jon Schmidt:  "Hence I continue to maintain that the cut for negation
> must be *derived *from the scroll for consequence with a blackened inner
> close, rather than treated as a primitive, even when shading is employed
> instead."
>
> For the purposes of developing systems of mathematical logic, the logician
> can adopt various starting points in setting up the logical grammar for a
> given system. In symbolic systems, the rules determine what does and does
> not count as a well-formed-formula. The same holds in the case of the EGs.
> The grammatical rules determine what counts as a well-formed-graph.
>
> Given all the work he has done on the symbolic systems of logic, Peirce
> sees that there are a number of different ways of setting up the
> grammatical rules that will, when taken together with the rules of
> inference and transformation, yield consistent results. For the sake of the
> EGs considered as a formal system, the scroll and two nested circles are
> logically equivalent. What is more, it makes no difference for the beta
> graphs whether the scroll (used to represent the conditional) or a shaded area
> within a boundary (used to represent negation) is taken as "primitive" in
> one sense or another.
>
> Having said that, I do think there is a special philosophical significance
> that Peirce attaches to the scroll as a representation of the conditional.
> I do not think that it is mere artifact of his early explorations of the
> graphs. As Peirce points out, the graphs can be used to express any sort of
> proposition. As such, they can be put to use in philosophical inquiry for
> the sake of analyzing the logical relationships between any set of
> premisses and conclusions.
>
> For the sake of giving a deeper philosophical analysis of the different
> classes of arguments we need to apply the EGs to the problem of analyzing
> synthetic forms of inference. In doing so, it will be helpful to have a
> variety of different icons that can be used to study the grounds of the
> validity of inductive and abductive inference. (MS 296, 499)
>
> As far as I can see, the scroll is a special kind of iconic sign because
> it expresses the continuity in the

Re: Fw: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

2020-08-04 Thread John F. Sowa




Jeff, 
In the note I just sent, I was talking about the version
of EGs in L231.  For that version of logic, there can be no difference in
semantics between a scroll and a nest of two ovals.
JBD> In the
case of inductive and abductive inferences, the conditionals may
take a variety of forms:  epistemic, alethetic, deontic, etc. In each of
 these cases, the topological character of the relations may vary.
I
agree.  People who adopt EGs for classical FOL may need to extend the
notation for other kinds of logic.  Since Peirce dropped the scroll in
1911, anyone might choose to adopt it for some new purpose.
But
it's important to emphasize that the new purpose would not be identical
to anything Peirce had previously written -- unless (and this is a big
UNLESS) they could prove that it was indeed identical to what Peirce had
previously intended.
John
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Fw: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

2020-08-04 Thread Jeffrey Brian Downard

Jon Schmidt, John Sowa, List,


It might be helpful to make a clearer distinction between what is advantageous 
for the purposes of developing the EGs as a formal system of mathematical logic 
and what is advantageous for the purposes of developing theories of 
philosophical logic.


For the sake of illustrating the importance of the distinction, let me take up 
the following assertion


Jon Schmidt:  "Hence I continue to maintain that the cut for negation must be 
derived from the scroll for consequence with a blackened inner close, rather 
than treated as a primitive, even when shading is employed instead."


For the purposes of developing systems of mathematical logic, the logician can 
adopt various starting points in setting up the logical grammar for a given 
system. In symbolic systems, the rules determine what does and does not count 
as a well-formed-formula. The same holds in the case of the EGs. The 
grammatical rules determine what counts as a well-formed-graph.


Given all the work he has done on the symbolic systems of logic, Peirce sees 
that there are a number of different ways of setting up the grammatical rules 
that will, when taken together with the rules of inference and transformation, 
yield consistent results. For the sake of the EGs considered as a formal 
system, the scroll and two nested circles are logically equivalent. What is 
more, it makes no difference for the beta graphs whether the scroll (used to 
represent the conditional) or a shaded area within a boundary (used to 
represent negation) is taken as "primitive" in one sense or another.


Having said that, I do think there is a special philosophical significance that 
Peirce attaches to the scroll as a representation of the conditional. I do not 
think that it is mere artifact of his early explorations of the graphs. As 
Peirce points out, the graphs can be used to express any sort of proposition. 
As such, they can be put to use in philosophical inquiry for the sake of 
analyzing the logical relationships between any set of premisses and 
conclusions.


For the sake of giving a deeper philosophical analysis of the different classes 
of arguments we need to apply the EGs to the problem of analyzing synthetic 
forms of inference. In doing so, it will be helpful to have a variety of 
different icons that can be used to study the grounds of the validity of 
inductive and abductive inference. (MS 296, 499)


As far as I can see, the scroll is a special kind of iconic sign because it 
expresses the continuity in the relationship between antecedent and consequent 
of the conditional, and this mirrors the continuity in the relationship between 
premisses and conclusions in an argument. In the case of inductive and 
abductive inferences, the conditionals may take a variety of forms:  epistemic, 
alethetic, deontic, etc. In each of these cases, the topological character of 
the relations may vary.


Based on my own inquiries using the graphs to analyze these forms of inference, 
thinking about the relationship between the scroll and the shaded area 
representing negation has been a fruitful endeavor. It is possible that it has 
been fruitful given the fact that I am still at an early point in my 
application of the graphs to these problems of critical logic.


Yours,


Jeff


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

From: Jon Alan Schmidt 
Sent: Monday, August 3, 2020 7:06:34 PM
To: s...@bestweb.net; peirce-l@list.iupui.edu
Cc: ahti-veikko.pietari...@ttu.ee; francesco.belluc...@unibo.it; 
cdw...@iupui.edu; martin.irv...@georgetown.edu; Gary Richmond
Subject: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and 
final version of EGs)

John, All, List:

With your permission given below, I am posting this reply on Peirce-L.  Anyone 
is obviously still free to respond off-List if that is preferred.

JFS:  The theory of EGs that Peirce presented in L231 (which I have been 
calling eg1911) is the one he wished Lady Welby and her group to consider his 
last and best version of EGs.

This claim is a plausible interpretative hypothesis based on the circumstances 
and timing of the letter, but it should be acknowledged that the text itself 
does not state or imply any such specific intention on Peirce's part.

JFS:  Some readers might be misled by Peirce's earlier writings to think that 
there is some "deeper" meaning that is not expressed by a nest of two ovals.

Such an impression is not misleading at all, since Peirce explicitly denies 
that a consequence (scroll) is strictly equivalent to a composite of two 
negations (nested cuts).  I already quoted the following passage in one of my 
Peirce-L posts, but it is worth repeating.

CSP:  The second failure of Selectives to be as analytical as possible lies in 
their encouraging the idea that negation, or denial, is a relatively simple 
concept, and that the concept of

Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

Aw: Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

Aw: Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

RE: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

Aw: RE: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

RE: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

Re: Fw: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

[PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

Re: Fw: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

Re: Fw: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

Re: Fw: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

Fw: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)

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