[peirce-l] Trikonic diagram observation of Peirce's 10 Sign Classes

[Gary Richmond]

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 --- Message from peirce-l forum to subscriber archive@mail-archive.com