Trikonic diagram observation of Peirce's Classification of
Signs
I asked Ben Udell to modify slightly (through shadings) my
trikonic diagram of Peirce's 10 Sign Classes to add visual clarity to
the analysis I'm attempting below. The trikonic diagram of the
Classification has existed since I presented an outline of trikonic at
an ICCS workshop in 2004 and appears again in my paper "Outline of
trikonic: Diagrammatic Trichotomic" available at Arisbe (all the
graphics in both the slideshow and the paper are by Ben Udell based on
my hand-drawn diagrams). See: http://members.door.net/arisbe/menu/library/aboutcsp/richmond/trikonic.htm
The trikonic diagram tilts Peirce's diagram [CP 2.264] slightly to
the right (as shown below--thanks Ben for also providing the tilted
version of Peirce's diagram). I have given categorial numbers to
Peirce's names based on the nonadic (3 X 3) parameters as they relate
to:
[white tildes used in order to maintain spacing at
Lyris archive]
the sign in--itself:
1 qualisign
|> 3 legisign
2 sinsign
~ ~ ~ the sign for the
interpretant:
~ ~ ~ 1 rheme |> ~ |> 3 argument ~ ~ ~ 2 dicisign the sign in relation to the object:
1 icon |> 3 symbol 2 index Yielding: The small internal arrows give the involution order of the signs, that is, as Peirce names each of the ten types. Here 'involutional' means "starting at thirdness (3ns) which involves secondness (2ns) which in turn involves firstness (1ns)" (this following the discussion of the "Logic of Mathematics" paper I've often commented on on the list). Indeed, and although one cannot insist on the exclusivity of the involutional (also called by Peirce, the analytical) order -- given that there are 5 other orders all of which can be seen to function at places in Peirce' s semeiotic theory -- an involutional order is yet clearly significant at several levels in, for example, theoretical grammar. At another level than the one currently being considered, but in relation to the 10-adic classification schema, Joseph Ransdell recently wrote here that "if you analyze what you have at the end of the process -- the argument (argument symbolic legisign) -- you find that it involves an instance of the sign class of the ninth class (. . . the proposition). which in turn involves an instance of the eighth , and an instance of the seventh. . .[etc.]" This is so, and not only in Theoretical Grammar, but in Critic and Methodeutic as well. So I have recently been arguing that the involutional order in the naming of the signs is not trivial in this diagram. The structure of Peirce's cenopythagorean tetractys (which is what his ordering of the 10 sign classes seems to be) as it relates to (1) the 10 valid arrangements of the 27 possible orderings of
1,2,3 which satisfy Peirce's prescision constraints and which give the
original ordering of 1 through 10 (which is NOT arbitrary),
(2) the same expressed as trees (lattices), and
(3) the collapse of these 10 valid arrangements as trees into the
10 sign classes triangular diagram is exceedingly well diagrammed and
discussed in Luis Merkle's dissertation, section 4.4 (see especially
his Figures 4.5, 4.7, and most especially the "collapse" diagram, 4.9).
What is not considered is the tri-categorial structure of the
diagram at all levels (which I will attempt just below).
It would be helpful if before proceeding that the reader take a
look at the graphic at the top of this message, especially the diagram
on the left. Some preliminary diagram observation of the large triangle
of the Classification shows the following [note: for 1ns, 2ns, 3ns
read, respectively, firstness, secondness, thirdness]
* There are three trikons-of-trikons (ToTs) around a central
single trikon (the rhematic indexical sinsign--which is the only trikon
employing all three of the categorial numbers)
* Categorial 1ns dominates the top left ToT, 2ns the bottom left,
3ns the right hand ToT so that at least two positions of the three
trikons within the ToT in question has that number (viz., 1, 2. OR 3)
Further, the three corner angles of the large triangle are wholly
categorially first, second, or third at this level of analysis (1/1/1,
2/2/2, and 3/3/3) reinforcing the categorial structure.
* For the ToT in the position of 1ns, the sole 2 and 3 of the 9
places are in the position of 1ns at the top of each trikon. For the
ToT in the position of 3ns, the sole 1 and 2 of the 9 places occur in
the position of 3ns at the right of each trikon. For the ToT in the
position of 2ns, the sole 1 and 3 are respectively in the positions of
3ns and 1ns and seems more complex that the other two as needing to
serve as transitioning from 1ns to 3ns
* As mentioned earlier, the singleton trikon, the rhematic
indexical legisign (involutionally 1/2/3) is the only trikon of the
10 which uses all three categorial numbers, suggesting its own
transitional character
* The examples Peirce gives also strongly suggests the trichotomic
structure of the 3 ToTs and of the diagram as a whole. (By the way, I
would concur with Merkle's suggestion that we use all three
involutional expressions when referring to the ten classes.) Some
Peirce examples:
[white tildes used to maintain spacing at Lyris
archive]
1 rhematic iconic qualisign (a color, say, "red")
|> 5 rhematic iconic legisign (the idea of a type of a diagram)
2 rhematic iconic sinsign (an instantiated, actual diagram)
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
~ ~ ~ ~ ~ ~ ~ ~ 8 rheme (a term, an ordinary noun, a "verb" in
EGs)
|> 6 rhematic indexical legisign (a demonstrative pronoun) ~ ~ |> 10 argument
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
~ ~ ~ ~ ~ ~ ~ ~ 9 dicisign (proposition)
3 rhematic indexical sinsign (a spontaneous cry, say, "ouch!")
|> 7 dicentic indexical legisign (a street cry, say,
"newspaper!"
4 dicentic indexical sinsign (a weather vane, a thermometer)
Conclusions:
Luis Merkle, whose dissertation stresses "the importance of going
beyond classificatory schemata," a point with which I am in complete
agreement, notes that Peirce's semeiotic ". . . is triadically
relational, and it is in this horizon that he described sign relations
and [classes] of signs. >From the possible combinations [of] ternary
sign's components, Peirce derived ten [classes] of signs" [238].
He further notes that "The arborescent diagrams [which are
lattices] do not enable a full appreciation of the relational
characteristics among the ten [classes]. Peirce was also interested in
the relations between the [classes], not only in the [classes] as [an]
isolated classification mechanism." [239] The restriction to partially
ordered lattice structure represents an analytical limitation.
In a footnote Merkle writes that "the classification of a certain
sign as an icon, an index, or a symbol, so common in the literature, is
only part of a broader system developed by Peirce to understand
semiotic relations. I understand that within Peirce's scaffold , the
statement that a particular sign is of a certain kind should
necessarily be contingent on historical and subjective factors. In
other words, signs should not be frozen as of a certain kind."
Diagrammatic observation can be a valuable adjunct to
philosophical analysis. It seems to me that even this relatively simple
trikonic analysis of Peirce's diagram of the Classification of Signs
can offer some insight into the deep categorial structure of his
semeiotic. I would hope that all valid diagrams (Merkle's, Marty's,
Udell's and my own, for example) would be considered. Peirce suggested
once that a categorial analysis could never be 'wrong' because it only
tried to offer hints and suggestions which might prove
valuable. And this is all I'm offering in the present analysis--what I
hope may be helpful "hints & suggestions."
Gary Richmond
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