Gary F,
The issues are far deeper than notation or computer processing.
1903 was a critical year in which Peirce began his correspondence
with Lady Welby. That led him to address fundamental semiotic issues.
I’ll have to confess at this point that I have no interest in learning
EGs for the sake of learning a new notation system, or for the sake
of knowledge representation in automated systems.
Last week, Ontolog Forum sponsored a telecon, in which I presented
slides on "Context in Language and Logic". It addressed complex
semiotic issues, and I mentioned Peirce at various points.
Following are the slides. Slide 2 also has the URL for the audio:
http://jfsowa.com/ikl/contexts/contexts.pdf
the elementary phenomena of reasoning, that I’d like to understand better.
I agree that's important, and I also agree that Peirce was seeking
the most fundamental methods he could discover. But I also believe
that he abandoned the recto/verso system because (a) the questions
raised by Lady Welby led him to more significant problems, and
(b) those low-level ideas paled in comparison to his goal of
representing "a moving picture of the action of the mind in thought."
The three pairs of rules you attached (from NEM) are essentially
the same as the three pairs he gives later on in Lowell 2, except
for the shading and the absence of lines of identity.
For his EGs of 1903, they are logically equivalent. In fact, that
is why his recto/verso description and his "magic blot" have no real
meaning: they have no implications on the use of the graphs in
perception, learning, reasoning, or action. But the 1911 system
can be generalized to modal logic, 3-valued logic, and probability.
And by the way, that letter of 1911 was addressed to Mr. Kehler,
one of Lady Welby's correspondents, and the main topic was
probability and induction. That's also significant.
Implications of his 1911 system:
1. The rules come in 3 symmetric pairs, and each pair consists
of an insertion rule (i) and an erasure rule (e), each of
which is the inverse of the other. This feature supports
some important theorems, which are difficult or impossible
to prove with other rules of inference.
2. The rules are *notation independent*: with minor adaptations
to the syntax, they can be used for reasoning in a very wide
range of notations: the algebraic notation for predicate
calculus (Peirce, Peano, or Polish notations); Kamp's discourse
representation structures; many kinds of diagrams and networks,
and even natural languages.
3. They can be adapted to theorem proving with arbitrary icons
inside an EG. I demonstrated that with Euclid's diagrams inside
the ovals of EGs. But they can also be used with icons of any
complexity -- far beyond Euclidean-style diagrams.
4. The psycholinguist Philip Johnson-Laird observed that Peirce's
notation and rules are sufficiently simple to make them a
promising candidate for a logic that could be supported by
the neural mechanisms of the human brain. That is true of
his later system, but not the recto/verso system.
For an overview of these issues, see my slides on visualization:
http://jfsowa.com/talks/visual.pdf
To show that Kamp's DRS notation is isomorphic to a subset of EGs,
see slides 20 to 27 of visual.pdf. To see the application to English,
see slides 28 to 30. (But this is true only for that subset of English
or other NLs that can be translated to or from Kamp's DRS notation.)
For the option of including icons inside the areas of EGs, see slides
31 to 42 of visual.pdf. For more detail about Euclid, see slides
19 to 39 of http://www.jfsowa.com/talks/ppe.pdf
Note: There is considerable overlap between visual.pdf and ppe.pdf,
but slides 19 to 39 of ppe.pdf go into more detail about Euclid.
For theoretical issues, see slides 43 to 53 of visual.pdf.
For the theoretical details, see http://jfsowa.com/pubs/egtut.pdf
I'm working on another paper that goes into more detail about Peirce's
"magic lantern of thought". The 1911 system can support it. But the
recto/verso system cannot.
John
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