BODY { font-family:Arial, Helvetica, sans-serif;font-size:12px; }I
don't think that Peirce drew the triadic sign as a triangle - [he
used the triangle, as we've noted, in the Lady Welby sign classes but
that's different].
But he writes, in 1.346, The Categories in Detail, in reference to
"genuine triadic relations'..... "You may think that a node
connecting three lines of identity Y is not a triadic idea"...and
then gives an example of this triadic identity...and provides another
example of the syllogism [major premise, minor premise, conclusion].
That 'Y' shape is, in my view, the best image of the semiosic
triad. It explains, as he wrote: "Now a sign is something, A, which
denotes some fact or object, B, to some interpretant thought, C".
That - to me - can be imagized as he said, with a 'Y'. .....a node
connecting three lines of identity'.
Edwina
On Wed 13/12/17 4:38 PM , John F Sowa [email protected] sent:
Gary F,
I changed the title to focus on the more specific issues.
Gary
> I dug out my copy of The Meaning of Meaning, and found no triangle
> diagram in it;
I found the triangle on page 11 of my copy of the 8th edition
(1946).
I scanned that page as the attached MofMp11.jpg.
The labeling on the triangle is different from Peirce's, but one
could relabel it with words from Peirce's writings. It's also
possible to draw a triangular EG with relation labels (rhemes)
taken from Peirce's own words:
1. At each corner of the triangle, place the label of a monadic
predicate taken from Peirce's writings. Example: Mark,
Interpretant, Object.
2. Remove a small line segment from each side of the triangle.
In its place, insert the name of a dyadic predicate that
relates the two corners.
3. In the center pf the triangle, place the label 'Sign', which
would serve as the name of a triadic relation. Then draw a
line
of identity from that label to each of the three corners.
The result of this exercise is an EG. Each corner is a ligature
of three lines of identity that represents one of the three
entities related by a sign. Each side represents a dyad that
is implied by the triad in the middle.
Then it's possible to represent an open-ended variety
of semiotic relationships by linking two or more triangles
at their corners. Each link is a ligature that connects
two corners that are assumed to represent the same entity.
For examples of such triangles, see Figure 1 (p. 4) and Figure 3
(p. 8) of "The role of logic and ontology in language and
reasoning":
http://jfsowa.com/pubs/rolelog.pdf [1]
In those examples, it would be possible to draw the triangles as
EGs.
But the added detail would make them less readable. And by the way,
this is an example of my claim that diagrams of any kind -- or more
generally, icons of any kind -- can be used in "generalized EGs".
See the slides http://jfsowa.com/talks/ppe.pdf [2]
> If someone can point to such a diagram anywhere in Peirce�s
writings
> (either triangular or three-spoked), I will thank them profusely,
> for refuting my claim that neither of those diagramming habits
> started with Peirce.
But the triadic sign relation (as expressed in writing) is as old
as Aristotle, and it was developed in detail by the Scholastics.
For some discussion, see pp. 4 to 8 of rolelog.pdf. Peirce had
studied those authors, and he had written extensively about
diagrams.
> Peirce himself says that 'genuine triadic relations can never be
> built of dyadic relations'... and writes: 'You may think that a
node
> connecting three lines of identity Y is not a triadic idea. But
> analysis will show that it is so".
To illustrate that principle, see the attached giveEG.jpg.
On the left is an EG that asserts the existence of three things,
which are linked by a triadic relation named Gives. It says
that something described as Sue, gives something described as Child
something described as Book.
On the right is an EG with three dyadic relations. But it also
has a ligature, which Peirce described as a teridentity. That
ligature represents something that is linked by three dyadic
relations to the things described as Sue, Child, and Book.
You could, if you wish, call that something an act of giving.
But no matter how you describe it, the teridentity causes it
to serve as a triadic relation.
Dyads, by themselves, can never create a triad. But a combination
of dyads with a teridentity can indeed create a triad. That's why
Peirce considered teridentities important.
It's a pity that Peirce didn't draw more diagrams. He claimed that
all his thought was diagrammatic, and he could have made his prose
more convincing if he had drawn more diagrams.
John
Links:
------
[1]
http://webmail.primus.ca/parse.php?redirect=http%3A%2F%2Fjfsowa.com%2Fpubs%2Frolelog.pdf
[2]
http://webmail.primus.ca/parse.php?redirect=http%3A%2F%2Fjfsowa.com%2Ftalks%2Fppe.pdf
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