I had a problem with my main computer, and I have been using another one
that does not have my usual software on it.
In any case, the note I
was trying to send is attached below as fb2.txt. Below it are two other
attachments MM_AVP.png and R669figs.gif
John
Dear Francesco, Jon, and Dan.
I put Dan Everett on the list because he is a linguist who
recommended a 600-page book on negation and is writing a book about
Peirce. I'd like to hear his comments about a paragraph in R669.
FB> I must say that in the dispute I agree completely with Jon A.
Schmidt. He has supported his points with abundant textual evidence
and with several convincing exegetical arguments.
If we were discussing Peirce's writings prior to 3 June 1911, I would
agree with you. But that does not explain why Peirce began R669 with
the 1906 version of EGs and five days later switched to a new version
for R670.
FB> What we dispute is whether [Peirce's] 1911 presentations of the
logical graphs show that he retracted one of his most stable
logico-philosophical ideas.
Peirce's criterion for significant ideas: "The elements of every
concept enter into logical thought at the gate of perception and make
their exit at the gate of purposive action; and whatever cannot show
its passports at both those two gates is to be arrested as
unauthorized by reason" (CP 5.212).
Note that this criterion says nothing about the words used to define
or explain the concept. Two concepts with different names and verbal
definitions are equivalent if they produce the same interpretations
and responses at the two gates.
FB> What [Peirce] claimed is that implication ("If A then B") mirrors
inference; inference ("A, ergo B") is a transitive, anti-symmetrical
relation, and the only truth-functional operator that is also
anti-symmetrical and transitive is implication.
On that issue, it's irrelevant whether the conditional is primitive
or defined. In MM_AVP.png (attached below), the only effect of the
1911 EGs is to replace the word "define" by "it is true that". The
conditional and any symbol that represents it remain just as iconic,
and all proof procedures remain valid.
But the 1911 EGs support a richer, more general set of logico-
philosophical ideas that go beyond the 1906 ideas. The shaded ovals
for 1911 negations can be generalized to shaded regions in three
dimensions or even 3D plus time. But the 1906 recto/verso semantics
is limited to 2D. On that issue, note what Peirce wrote in L231:
"an algebraist like Boole plainly thought in algebraic symbols; and
so did I, until, at great pains, I learned to think in diagrams,
which is a much superior method. I am convinced there is a far
better one, capable of wonders; but the great cost of the apparatus
forbids my learning it. It consists in thinking in stereoscopic
moving pictures. Of course one might substitute the real objects
moving in solid space; and that might not be so very unreasonably
costly." (NEM 3:191)
For evidence that Peirce's significant ideas are not affected by the
transition from R669 to R670, I recommend Ahti's 2011 article,
"Existential Graphs: What a Diagrammatic Logic of Cognition Might
Look Like", History and Philosophy of Logic, 32:3, 265-281. That
article discusses a wide range of philosophical ideas, including the
quotation from NEM 3:191. But it doesn't mention the idea of
deriving negation from implication. On the contrary, see page 14:
"given two nested cuts, implication is ability to continue a passage
from the area of an outer cut area to the area of the inner cut."
FB quoting Frege> "By means of negation the hypothetical mode can
thus be reduced to conjunction and conjunction to the hypothetical
mode. Looked at from a logical standpoint both appear equally
primitive. But since the hypothetical mode is more closely connected
with drawing inferences, it is best to give it pride of place, and
see it as the primitive form, reducing conjunction to it." (Frege,
Posthumous Writings, 1979, p. 200)
But Frege assumed *both* negation and implication as primitives, and
he defined conjunction in terms of them. That is contrary to Peirce
who assumed that conjunction was so fundamental that he didn't assign
a symbol to it. Conjunction is implicit when two or more EGs are
scribed in the same area.
Although Peirce never mentioned Frege, he did criticize Russell, who
adopted Frege's primitives for his Principles of Mathematics: "true
in the main and throughout, however, he betrays insufficient
reflection on the fundamental conceptions of the subject, with the
primary difficulty... his not having begun with a thorough
examination of the elements". (Houghton Library, Series I, no. 12.
Notes Preparatory to a Criticism of Bertrand Russell's Principles of
Mathematics, 5 February 1912)
That comment shows no sympathy for Frege's primitives. The tone is
milder, but the comments are consistent with the sharp criticisms in
L378 and L376 (copy below).
I also recommend another article by Ahti: "Two papers on existential
graphs by Charles Peirce", Synthese, July 2014. The two "papers"
actually consist of some MSS that Ahti grouped in two chapters.
Chapter 1, "Recent Developments of Existential Graphs and their
Consequences for Logic (MS 498, 499, 470, S-36, 1906)". In R498 and
R499, Peirce discussed a variety of ideas, which do not conflict with
any version of EGs. In R470, he presented the 1906 EGs with
recto/verso semantics for the cut. But he presented the conditional
as a nest of two cuts. He did not define a single cut in terms of a
double cut plus a pseudograph.
Chapter 2, "Assurance Through Reasoning (MS 669 & MS 670, 1911)."
For this "paper", Ahti placed R670 first, and treated it as an
introduction to the more detailed R669. He did not comment on any
discrepancies between them.
But on page 27 of R670, Peirce states "There are but three peculiar
signs that the Syntax of Existential Graphs absolutely requires. The
first of these is a sign of identity." On p. 28, "This way of
asserting identity... [furnishes] the second general sign required
by the syntax of existential graphs. This is the "Spot of
Teridentity". On p. 29, "the third indispensable peculiar sign of
the Syntax of Existential Graphs... is one that shall deny a
Graph-instance, or scribed assertion... But that Conditional
Proposition just written may be expressed by the aid of a sign of
Negation in the form, 'That the Antecedent is true and the Consequent
not true, is not true'. On p. 31, "It is a help to shade the
oddly-enclosed areas and omit the lines that represent the cuts, as
in Fig. 11 [just shading], which is equivalent to Fig. 10 [drawn as a
scroll with no shading]."
Peirce added two non-peculiar signs to the three peculiar signs:
"according to this syntax any single word is an assertion" (p. 27)
which may have zero or more pegs for attaching lines. Conjunction is
another non-peculiar sign, which is represented by drawing two or
more EGs in the same area.
Altogether, the R670 syntax has five signs: peculiar (existence,
teridentity, and negation) and non-peculiar (words and conjunction).
The words represent predicates or rhemes. The conditional is defined
by two negations and a conjunction.
These definitions, which preserve all the logical ideas, also
preserve philosophical ideas that are violated by the 1906 semantics.
For observation (phaneroscopy), the only logical operators that can
be observed are existence, conjunction and negation: any sensation
is a sign that something exists; any observation of a difference is a
sign of a conjunction (A and B) and a sign of negation (A is not B).
>From those three operaters all others can be derived.
Since Francesco and Jon claim that the following paragraph is
significant, I'd like to ask for Dan's opinion: Based on your study
of linguistics and related issues, what is your opinion about the
following paragraph? Would you consider it a convincing argument for
adopting the conditional as primitive and negation as derivative?
>From R669, p. 43: "The Cut came to be thought of because of the
immense frequency of occasions on which it was necessary to express
the assertion "If X be true, then every assertion is true". It was
forced upon the logicians attention that a certain development of
reasoning was possible before, or as if before, the concept of
falsity had ever been framed, or any recognition of such a thing as a
false assertion had ever taken place. Probably every human being
passes through such a grade of intellectual life, which may be called
the state of paradisiacal logic, when reasoning takes place but when
the idea of falsity, whether in assertion or in inference, has never
been recognized. But it will soon be recognized that not every
assertion is true; and that once recognized, as soon as one notices
that if a certain thing were true, every assertion would be true, one
at once rejects the antecedent that lead to that absurd consequence.
Now that conditional proposition "If A is true, every proposition is
true", is represented, in the model of Fig. 24, "If A is true, C is
true" by blackening the entire inner close, as if there were no room,
in reason, for any additional consequence. This gives Fig. 25: "If
A be true whatever can be asserted is true", which is as much as to
say that "A is not true and the inner close being cut very small", we
get, first Fig. 26 and finally Fig. 27, in which the idea of flat
falsity is first matured." (R669, p. 43)
My opinion: this paragraph ie embarrassingly bad. For years, Peirce
derided the typical reasoning of metaphysicians who start with a
conclusion they claim is infallible and generate evidence that makes
it seem plausible. In this paragraph, Peirce is doing the same
thing. He fabricated a dubious explanation for the derivation in
Figures 24 to 27 (copy attached in R699figs.png).
But Peirce knew he was fallible. If he had reviewed this paragraph
(on or about 3 June 1911), he would not have been satisfied. Five
days later, he wrote R670. On June 22, he began writing the more
polished L231.
In summary, the 1911 version discards a huge amount of irrelevant
verbiage (see the quotations below), But it's sufficiently general to
go beyond two dimensions (see http://jfsowa.com/talks/ppe.pdf ). That
generalization supports a wide rage of new logico-philosophical ideas
without discarding any significant ideas from the earlier versions.
John
____________________________________________________________________
L378 (Sept. 1911) and L376 (Dec. 1911) confirm the fact that R670 and
L231 are a total rejection of R669 and the 1906 version of EGs on
which it is based. In L378, Peirce wrote: "I use a diagrammatic
syntax, which I described very badly and at an intolerable length in
the Monist of October 1906." In L376, he was more explicit about the
1906 version: "For although the system itself is marked by extreme
simplicity, the description 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." _ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON
PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] .
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to [email protected]
with no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of
the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and
co-managed by him and Ben Udell.
