Gary,
Please look at the attached diagram egprim.gif. EGs are truly
diagrammatic: Every syntactic feature can be shown without any use
of language. This is slide 4 of http://jfsowa.com/talks/egintro.pdf .
I apologize for the mistake about 'spot'. I checked Don Roberts' book,
which I first read almost 40 years ago. Don dutifully noted that Peirce
had used the word 'spot' for the place where the name of a rhema was
written. But it just seemed weird to say that the spot, not the name,
represented a rhema or predicate.
I also checked Don's glossary, which contains over 50 terms for talking
about EGs. Many of them are about semantics. But to talk about the
syntax, you only need 6 terms: line of identity, relation, enclose,
shaded area, unshaded area, and peg. All other terminology is about
notation-independent logical issues.
[GF] I must apologize to the list for introducing the term “dot”
into this discussion, as Peirce actually uses that term not in Lowell 2,
but in some of his other explanations of existential graphs, notably
CP 4.438:
[CSP] Let a heavy dot or dash be used in place of a noun which has
been erased from a proposition. A blank form of proposition produced
by such erasures as can be filled, each with a proper name, to make a
proposition again, is called a rhema, or, relatively to the proposition
of which it is conceived to be a part, the predicate of that
proposition.”
By the way, this operation is equivalent to Church's lambda abstraction
about 30 years later. See slide 15 of http://jfsowa.com/egintro.pdf .
It's important to show the equivalence, but it's irrelevant Whether
you use a blank, a dot, an underscore, or the Greek letter λ.
It could be argued that Peirce’s terminology in referring to a graph
as a “word” is rather sloppy, but after all, this is a personal letter
from a self-described “garrulous old man” to a new acquaintance.
That statement is wrong for several reasons:
1. Peirce had said that every part of an EG asserts something.
The line asserts existence, the predicate named 'man' asserts a type
of entity, and the connection asserts the type of the existing thing.
I admit that modern terminology does not say that a predicate, by
itself, makes an assertion. But Peirce did so on various occasions.
2. Peirce wrote that letter in reply to "Mr. Kehler", who was a
member of Lady Welby's Significs group. We don't have the original
letter by Kehler, but it probably began with a flowery introduction
to the esteemed professor Peirce. In response, Peirce deliberately
described himself very modestly, and he used the word 'garrulous'
as an apology for the length of the letter.
3. This letter is far more important than a casual note to a friend.
Lady Welby had circulated Peirce's letters among the members of her
group, which included many prominent British intellectuals. Note
that Ogden & Richards included copies of some of Peirce's letters
in the appendix of their book, _The Meaning of 'Meaning'_.
It is not an explanation of EGs intended for publication. I’d like
to know your reasons for claiming that this presentation is Peirce’s
“preferred” version of EGs.
By 1911, Peirce had given up hope of getting further writings published.
The length of the letter (52 printed pages in NEM vol. 3) indicates its
importance. The practice of sharing letters in Lady Welby's group was
his best chance of getting a prominent group of scholars to read it.
The length of the letter and the amount of technical detail in it shows
that he copied material from various manuscripts. I had discovered the
EG content in 2000 from a transcription of MS 514 by Michel Balat. That
MS was dated 1909, when Peirce might have had some hopes of publication.
The fact that he chose that MS to copy for his letter of 1911 indicates
(a) its importance, and (b) its value as a tutorial about the essential
features of EGs.
Finally, any EG from RTL (1898) or later could be redrawn with the
conventions of 1911, and any proof by any earlier rules could be
translated line-by-line to an equivalent proof by the later rules.
But the later version has important advantages:
1. The shading makes the graphs more readable *and* more iconic:
it directly shows which rules of inference are applicable.
2. The syntax is described with fewer words, and the rules
of inference are shorter and more general. There is no need
to distinguish Alpha and Beta graphs, since they use exactly
the same rules of inference.
3. The generality of the 1909/1911 rules may be the result of
Peirce's thinking about moving pictures and stereoscopic
imagery. They are no longer tied to a "sheet" and they
could be applied without change to 3D images or even
3D+time for movies.
4. As a result of that generality, the rules can be applied
to any notation for logic that allows a distinction between
positive (unshaded) and negative (shaded) regions. For
examples, see egintro.pdf, slide 23 ff.
In summary, the system of 1909/1911 is superior in every way.
There is no philosophical or practical reason for Peirce to
prefer any of the older versions. For Peirce's own tutorial,
see http://jfsowa.com/peirce/ms514.pdf .
If anybody can find anything better in any of the older versions,
I would love to see it.
John
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