Jon AS, List
This thread began with my note of August 2nd,
which I include below in the file 2aug20.txt. All the points in that note
are based on the citations included in it. But I changed the subject line
of this note to emphasize Peirce's fundamental insight of 2 June 1911
shortly after 7:40 pm.
That was when Peirce finished writing two of
his three "Illative Permissions" in R669. He then wrote a short
paragraph with a few lines at the top of a new page. And he stopped.
He did not write the third permission (about double negations), he
left most of the sheet blank, and he never resumed R669. Three
questions: Why did he stop when he had enough paper to write the third
permission? Why did he begin a completely new version of EGs in R670
with different notation and terminology? And what did he do in the time
between June 2 and June 7?
My guess: He reviewed his earlier
writings on EGs, especially the ones from 1903 and 1906. The content of
R670 and L231 shows what he rejected. His comments in L378 and L376 show
that he considered the presentation in 1906 "as bad as it could
be". But his comments in R670 show that he considered some
combination of shading with tinctured areas as possible. That would be an
option for Delta graphs, as I mentioned in an earlier note.
JAS>
understanding the entire system of EGs requires familiarity with all
his different writings about them.
Familiarity does not imply
agreement. The writings prior to June 1911 have some useful insights
mixed with some obsolete material. It's necessary to evaluate them in
terms of L231.
JFS> There is no need to derive negation from
anything else.
JAS> Peirce repeatedly says otherwise, as I have
repeatedly demonstrated..
All those quotations are prior to June
1911. They're irrelevant and obsolete.
JAS> In R 669 (May 1911),
he notes--just three weeks before composing RL 231--that necessary
reasoning is possible without the concept of falsity
No, for several
reasons: (1) That is not an exact quotation, since Peirce knew that
affirmation and negation are fundamental to every version of logic from
Aristotle onward. (2) Peirce had forgotten his 1884 point that all
reasoning can be done with just insertions and deletions (W 5:107). And
Peirce's discovery of 2 June 1911 makes the earlier quotations
irrelevant.
JAS> This (R 466:18-19, 1903) 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)
Although Peirce said that the version of 1903 was
better than the version of 1906, it still has obsolete passages, such as
the comments about the scroll.
In R670, he writes "There are
but three peculiar signs that the Syntax of Existential Graphs absolutely
requires." The first is the line of identity. The, the second is
the spot, which may be a medad or it may have one or more pegs. "The
third is one that shall deny a Graph instance, or scribed
assertion." With that explanation and further confirmation in L231,
every previous comment about scrolls is obsolete and irrelevant.
At
this point, I rest my case. I stand by the attached 2aug20.txt and the
additional comments above. Any relevant evidence to the contrary would
have to come from documents later than June 1911.
John
To: ahti-veikko.pietari...@ttu.ee, francesco.belluc...@unibo.it,
jonalanschm...@gmail.com> ``
cc: "De Waal, Cornelis" <cdw...@iupui.edu>, Martin Irvine
<martin.irv...@georgetown.edu>
Dear Ahti, Francesco, and Jon,
I have long maintained that Peirce's best and final version of the
syntax, semantics (endoporeutic), rules of inference, and terminology
for EGs is in L231 and NEM 3.162-169. But Jon quoted some comments by
Ahti that seem to contradict that claim. Instead of debating them on
Peirce-L, I'd like to discuss the issues with this smaller group.
First, I'll summarize my reasons for claiming that the copy in
http://jfsowa.com/peirce/eg1911.pdf should be considered the most
definitive:
1. By 1911, Peirce had abandoned hope of publishing a final version, but
he knew that Lady Welby and her correspondents circulated letters among
a group of well-respected philosophers and logicians. He considered the
letter L231 to be as significant as a formal publication.
2. EG1911 is the clearest, shortest, and most elegant summary of Alpha +
Beta. The shaded areas can be generalized to 3-D regions or to 4-D for
stereoscopic moving images. Aspects of Gamma or Delta graphs could be
added without changing the Alpha + Beta foundation. And eg1911 has a
short, but complete selection of technical terms that could be adapted
to a wide range of notations in any number of dimensions.
3. In L231, Peirce replaced the term 'illative transformation' with the
term 'permission'. Perhaps he realized that the words 'illative' and
'illation' had become archaic. More likely, he realized that his
"permissions" did not require a "a monstrative sign of illation" (CP
4.76). The permissions allow graphs or parts of graphs to be inserted
or erased under specified conditions. A special "sign of illation" is
not required.
4. More important, his three pairs of "permissions" are a generalization
and unification of Gentzen's two systems of the 1930s (natural deduction
and sequent calculus -- AKA clause form). With Peirce's rules, an
unsolved research problem from 1988 has a simple solution. For a
statement of the probem and an outline of the solution, see the attached
ppe65.png.
5. The reason why the problem by Larry Wos (1988) was unsolved is that
Gentzen assumed that an if-then statement was essential for "illative
transformations" (Peirce's term). But an if-then statement and any
proofs that depend on it are not symmetric. Peirce's EG rules, which
depend only on existence, conjunction, and negation, are simpler and
symmetric. Conclusion: if-then (in any notation) is just a special
case, and the EG permissions are more general and powerful.
For more detail, see the slides from an APA lecture and a workshop in
Bogota: http://jfsowa.com/talks/ppe.pdf . A 78-page article based on
those slides was published in the Journal of Applied Logics. The URL
of that article is in a footnote on slide 2.
The reason why there is some disagreement about these issues is that
Peirce himself had expressed conflicting opinions in various writings.
As CP 4.76 shows, Peirce had once claimed that "a monstrative sign of
illation" was required for deduction. But in 1884, he discovered a more
general principle, which he later adopted as the foundation for his EG
rules of inference:
CSP: The first chapter of [the 1880 Algebra of Logic] develops the
reasons for choosing the copula of inclusion, exhibits its formulae, and
attempts by means of it to consolidate syllogistic with Boolian algebra.
But the study of Professor O. H. Mitchell's important paper "On a New
Algebra of Logic" has led me to think that the passage from premiss to
conclusion ought not to be considered as the essential and elementary
type of logical movement. We have rather two elementary modes of
modifying assertions and two corresponding modes of transforming them.
The two modes of changing assertions are 1st to drop part of what has
been asserted and assert less, and 2nd to add to what has been asserted
and assert more. (Writings 5:107, R506. summer of 1884)
Those two "modes of changing assertions" are the basis for his EG rules
of inference. Each rule inserts or erases an EG or part of an EG in
some area. No rule mentions or requires a scroll (if-then statement).
Peirce discovered that principle a dozen years before he invented EGs.
But in some of his MSS, he continued to talk as if the scroll had a
special status.
Following are two comments by Ahti that Jon quoted:
AVP: R 481 seems to be the very first paper in which the scroll is
indeed recognised as the primitive logical sign to be used, thus
capturing the relation of illation better than any other sign would.
Also realised for the very first time is the fact that negation, on the
other hand, is not a primitive sign of logic, and that in the course of
the logical development of reason, one in fact derives the idea of the
negation from the idea of the scroll. (LoF 1:85)
JFS: R 481 does not state or show that the scroll (or any other
notation for if-then) is more primitive than negation. What Peirce did
show is that not-p can be expressed by an EG that says "p implies
falsum". Unlike most algebraic notations, EGs represent V (verum) by a
blank and F (falsum) by a shaded blank. But it's easier to express
not-p just by shading p or drawing a cut around p.
AVP: These last two manuscripts [R669 and R670] concerning "Assurance
through Reasoning" present what may be Peirces most successful attempt
to explain the logic of existential graphs, and the philosophy
concerning the notation of diagrammatic syntax in particular. The
notions of identity, teridentity, composition of graphs, plurality,
conditional, scroll, and the derivation of the idea of negation as a
consequence of the scroll, all get their fair shares of exposition.
Re R699, dated May 25 to June 2, 1911; R670, June 7 to June 17; L231,
June 22: This is the critical month when Peirce reviewed, rethought,
and restated the foundations for EGs. R699 was a "first draft" when he
still considered the scroll to be essential. R670 was a "second draft"
when he demoted the cut and the scroll to mere punctuation. And L231
was the "final publication" in which he purged every mention of the
words 'cut' and 'scroll'. He also purged the words 'illative' and
'illation'. He reorganized his "permissions" as three symmetric pairs
that depended only on shaded or unshaded areas. He kept the word
'endoporeutic' for the semantics and showed that the permissions
preserved truth, as determined by endoporeutic.
The single worst feature of R669 is the passage where Peirce mentions
his recto/verso terminology of 1906: "we further imagine and speak of
the part of the sheet within the Cut as if it were turned over so that
what were exposed to view were the Verso side." In two later MSS,
Peirce rejects that terminology in the strongest possible way. In L378
(29 September 1911), he wrote (in French), "To dissect deductions more
completely, I use a diagrammatic syntax, which I described very badly
and at an intolerable length in the Monist of October 1906."
In L376 (6 December 1911), he was even more explict: "For although the
system itself is marked by extreme simplicity, the description [in the
Monist of October 1906] fills 55 pages, and defines over a hundred
technical terms applying to it. The necessity for these was chiefly
due to the lines called 'cuts' which simply appear in the present
description as the boundaries of shadings, or shaded parts of the
sheet."
In summary, Peirce originally defined the claw symbol for material
implication in terms of negation and conjunction. In 1884, he
discovered the foundation for his EG rules of inference, but expressed
in terms of his algebraic notation. In June 1911, he finally realized
that the EG "permissions" and shaded areas were more fundamental for
deduction than any symbol for if-then, including the scroll. But a very
significant test for Peirce's eg1911 system is the way it generalizes
and unifies Gentzen's two systems and facilitates the solution of
unsolved research problems. Peirce's EG rules, even when adapted to
a linear notation, passed that test with flying colors.
John
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