Edwina, Mary, Gary f, list, I can't say that I experience the *horror* that Edwina does with the use of the triangle for specific analyses and, in point of fact, Peirce himself uses is for certain purposes (see, for example, the famous diagram of the classification of signs which he sent to Lady Welby). Admittedly such an analysis of sign classes is relatively static, but that is perhaps the point: that for particular purposes of phenomenological, metaphysical, and semiotic tricategorial analysis (although, perhaps, not in representing any *particular* semiosis) that the triangle can be helpful.
But more than that, the triangle is quite useful when considering movement through the categories (which paths of movement I've called categorial vectors) where a bent arrow shows which of the 6 possible vectors is in play. [image: Inline image 3] (I have renamed the vector of analysis that of *involution*, although both terms can be found in Peirce's paper, "The Mathematics of Logic"). For example, taking the vector at the top of the diagram, Peirce says in the N.A. that there are three stages to a discrete inquiry (which involves what I call the vector of process) which begins with a hypothesis (1ns), after which the implications of the hypothesis are deduced for the purpose of devising an experimental testing of the hypothesis (3ns), followed by the inductive testing itself (2ns). This 'movement through the categories' is, in my opinion, best illustrated by a bent arrow either within or outside of a triangle. That the process doesn't end there is well illustrated by John Sowa's 'Knowledge Soup' diagram. As I've noted here before, this *process vector* is the very same one Peirce offers for biological evolution, namely, first, chance 'sporting' (1ns), then, the possibility of new habit-formation (3ns), and finally the possibility of a evolutionary, say, structural change (2ns). Again, if you see the process as triadic, it most certainly doesn't *end* with that evolutionary adaptation. Yet, for me being able to see the direction of the several vectors, comparing (as I just did with inquiry and biological evolution), or contrasting them (for example, contrasting both inquiry and evolution with the semiotic path (the *vector of determination*) whereas the object (2ns) determines the representamen (1ns) which determines the interpretant 3ns) can potentially reveal interesting new relations. So, I agree with Gary F: Yes, it’s a long-running debate whether we should use a triangle or a three-spoke diagram. . . Personally I don’t think it matters much which one you use, as long as you recognize that relation as triadic. And yet (1) it is especially important in, for example, considering the -> representamen -> interpretant path that "you recognize that relation as triadic" and, in the sense of infinite semiosis, neither linear nor arriving at an end point) and (2) for many purposes the three spoked diagram is indeed. preferable. But for some, especially certain analytical purposes, the triangle proves quite helpful. This is one of those areas where I think the decision as to which (the triangle or the spoke) manner of diagramming a triadic relation is most useful for her purposes ought be left up to the individual inquirer, that we ought not insist on what is right or wrong (seek consensus) for others in this matter. Best, Gary R [image: Gary Richmond] *Gary Richmond* *Philosophy and Critical Thinking* *Communication Studies* *LaGuardia College of the City University of New York* *718 482-5690 <(718)%20482-5690>* On Tue, Dec 12, 2017 at 12:47 PM, Edwina Taborsky <[email protected]> wrote: > Mary, list - I fully agree with you. I have always been horrified - and I > mean the word - by the use of the triangle to portray the semiosic triad. > It is, in my view, so completely wrong, for it sets up a closed linear path. > > The' node connecting three lines of identity' [1.347] is, in my view, the > correct image, for as Peirce points out - it clearly shows how such a node > and its relations is networked almost to infinity with other such formats. > As you say - it shows the 'openness inherent in triadic relations'. > > Edwina - > > > > On Tue 12/12/17 3:32 PM , Mary Libertin [email protected] sent: > > Gary, list, > > I prefer the use of Peirce’s Icon/index/symbol of a “genuine triadic > relation”—“a node with three lines of identity” instead of a triangle. > Ogden popularized the Peircean concept of triangle in an appendix in his > book “The Meaning of Meaning”, and that triangle has been repeated over and > over. I believe the node with three lines of identity makes immediate, > diagrammatic sense and I believe shows forth the openness inherent in > triadic relations. I’d like to investigate this—its historical context, > literature on it, etc. Do you think I’m making sense, and /or can you point > me in the right direction? Thanks. > > Mary Libertin > > On Tue, Dec 12, 2017 at 7:01 AM <[email protected]> wrote: > >> Continuing from Lowell Lecture 3.3, >> >> https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms- >> 464-465-1903-lowell-lecture-iii-3rd-draught/display/13884 >> >> >> >> I will sketch a proof that the idea of Meaning is irreducible to those of >> Quality and Reaction. It depends on two main premisses. The first is that >> every genuine triadic relation involves meaning, as meaning is obviously a >> triadic relation. The second is that a triadic relation is inexpressible by >> means of dyadic relations alone. Considerable reflexion may be required to >> convince yourself of the first of these premisses, that every triadic >> relation involves meaning. There will be two lines of inquiry. First, all >> physical forces appear to subsist between pairs of particles. This was >> assumed by Helmholtz in his original paper on the Conservation of Forces. >> Take any fact in physics of the triadic kind, by which I mean a fact which >> can only be defined by simultaneous reference to three things, and you will >> find there is ample evidence that it never was produced by the action of >> forces on mere dyadic conditions. Thus, your right hand is that hand which >> is toward the east, when you face the north with your head toward the >> zenith. Three things, east, west, and up, are required to define the >> difference between right and left. Consequently chemists find that those >> substances which rotate the plane of polarization to the right or left can >> only be produced from such active substances. They are all of such complex >> constitution that they cannot have existed when the earth was very hot, and >> how the first one was produced is a puzzle. It cannot have been by the >> action of brute forces. For the second branch of the inquiry, you must >> train yourself to the analysis of relations, beginning with such as are >> very markedly triadic, gradually going on to others. In that way, you will >> convince yourself thoroughly that every genuine triadic relation involves >> thought or meaning. Take, for example, the relation of giving. A gives B >> to C. This does not consist in A's throwing B away and its accidentally >> hitting C, like the date-stone, which hit the Jinnee in the eye. If that >> were all, it would not be a genuine triadic relation, but merely one dyadic >> relation followed by another. There need be no motion of the thing given. >> Giving is a transfer of the right of property. Now right is a matter of >> law, and law is a matter of thought and meaning. I there leave the matter >> to your own reflection, merely adding that, though I have inserted the word >> “genuine,” yet I do not really think that necessary. I think even >> degenerate triadic relations involve something like thought. >> >> The other premiss of the argument that genuine triadic relations can >> never be built of dyadic relations and of Qualities is easily shown. In >> Existential Graphs, a spot with one tail —X represents a quality, a spot >> with two tails —R— a dyadic relation. Joining the ends of two tails is also >> a dyadic relation. But you can never by such joining make a graph with >> three tails. You may think that a node connecting three lines of identity >> [image: >> Blocked image] is not a triadic idea. But analysis will show that it is >> so. I see a man on Monday. On Tuesday I see a man, and I exclaim, “Why, >> that is the very man I saw on Monday.” We may say, with sufficient >> accuracy, that I directly experienced the identity. On Wednesday I see a >> man and I say, “That is the same man I saw on Tuesday, and consequently is >> the same I saw on Monday.” There is a recognition of triadic identity; but >> it is only brought about as a conclusion from two premisses, which is >> itself a triadic relation. If I see two men at once, I cannot by any such >> direct experience identify both of them with a man I saw before. I can only >> identify them if I regard them, not as the very same, but as two >> different manifestations of the same man. But the idea of manifestation >> is the idea of a sign. Now a sign is something, A, which denotes some fact >> or object, B, to some interpretant thought, C. >> >> 347. It is interesting to remark that while a graph with three tails >> cannot be made out of graphs each with two or one tail, yet combinations of >> graphs of three tails each will suffice to build graphs with every higher >> number of tails. >> >> [image: Blocked image] >> >> And analysis will show that every relation which is tetradic, pentadic, >> or of any greater number of correlates is nothing but a compound of triadic >> relations. It is therefore not surprising to find that beyond these three >> elements of Firstness, Secondness, and Thirdness, there is nothing else to >> be found in the phenomenon. >> >> >> >> http://gnusystems.ca/Lowell3.htm }{ Peirce’s Lowell Lectures of 1903 >> >> >> > -- > null > > > > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to > [email protected] . 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