``` ------------------------------------------ PEIRCE-L Digest 1292-- February 10, 1998 ------------------------------------------ ------------------------------------------------------------------- CITATION and QUOTATION from messages on PEIRCE-L is permissable if the individual message is identified by use of the information on DATE, SENDER, and SUBJECT: e.g.: From PEIRCE-L Forum, Jan 5, 1998, [name of author of message], "re: Peirce on Teleology" --------------------------------------------------------------------- --------------------------------------------------------------------- If the type is too large and the message runs off the screen on the right you can shrink the size of the typeface by use of the option on your browser. --------------------------------------------------------------------- Since it is mostly in ASCII format You can download the whole document easily by using the SELECT ALL and COPY commands, then PASTE-ing it into a blank page in your word processor; or you can SELECT, COPY, and PASTE individual messages using your mouse. ---------------------------------------------------------------------- Topics covered in this issue include: 1) Peirce's 1-2-3 nesses, the Semiotic Square and Number by Douglas Moore ---------------------------------------------------------------------- Date: Tue, 10 Feb 1998 22:32:30 +0200 From: Douglas Moore To: peirce-l[…]ttacs6.ttu.edu Subject: Peirce's 1-2-3 nesses, the Semiotic Square and Number Message-ID: <34E0B95E.8F503F5C[…]netvision.net.il> I'm rather puzzled by the way that many list members have been using Peirce's triadic notions. Often the trichotomy is used as some kind of absolute categorization. For example, do numbers have Oneness, Secondness, or Thirdness, or all three? In an endeavor to help clarify the concepts involved, I'll sketch out a quick comparison with the French semiotic equivalent. I'll sprinkle in a few thoughts of my own. For European semiotics, of course, it is not a trichotomy that counts but a fourfold division in the form of a "semiotic square." For the good coverage of the semiotic square, one can refer to the works of the late Professor Greimas of the Ecole des Hautes Etudes, Paris. Perhaps his "Dictionnaire de la Semiologie" might be a good place to start. A fair while back, I quit life as an technical academic (for the first but not the last time) and went to study independently in Paris. I meant to stay only for a few years but ended up spending 12 years there. I had already spent some time reading Peirce and was already imbued with his "first flash" concerning the trichotomy. Of all the courses I followed it was the couple given by Greimas that impressed me, possibly because he had the most tractable approach (always a problem) and was potentially the closest to my technical inclinations. If Peirce saw a trichotomy in anything he thought about, Greimas saw a semiotic square. Thus I was faced with a choice. Was I to remain a trichomaniac like Peirce or become a Cartesian quadramaniac? I ended up being both, as I will explain later. What was interesting about Gremeis's approach was that instead of attempting to apply his brand of wisdom to logical, philosophical and metaphysical questions, as did Peirce, he applied it to more mundane problems. His particular bent was to apply his semiotic square notions to the analysis of discourse - mainly literary discourse but he didn't exclude the scientific. In addition to lectures, his courses involved many workshops, each based on a semiotic analysis in a different area. They included a semiotic analysis of the bible, political speeches, the dicourse on art, literary criticism, literary texts and so on. This type of approach is widely applied in France, particularly in the advertising industry - I still have in my library a report from an advertising company involving a semiotic analysis of the four fundamental ways of advertising under arm deodorant, for example. You can't get more mundane than that. So, in a few brief words, what is the semiotic square and how is it used? For Greimas, the theoretical justification for the semiotic square came from Aristotle's logical square of oppositions. Although harboring few pretensions as a philosopher, he was essentially saying that the basic organizational coherence of any production emanating from a system of signs (a semiology) was articulated out of basic logical units based on the semiotic square. This approach differs somewhat from Peirce's triadic version which he applied to logic to get what he claimed was the fundamental trichotomy of logic - abduction, induction and deduction. For Greimas, and possibly Aristotle in a certain way, the semiotic square itself, was the fundamental logical element in its own right. You don't apply it to the problematic of logic, it _is_ the logical problematic applicable even to itself. A very simple example of discourse analysis would be a novel involving the archetypal villain, the brave hero and the vulnerable but desirable heroin. A Peircien would possibly pick this out as a basic Oneness, Secondness and Thirdness of the piece. The Cartesian semiologist would add a fourth entity into the equation which we could call the People. There are thus three typed entities in the equation - the villain, the vulnerable heroine and hero types - and one entity of a different kind - the People which is an untyped entity but susceptible to these three types. These four entities could make up a semiotic square. Greimas was particularly skillful, although sometimes rather opaque, in interpreting the relationships between such foursomes in terms of the six oppositions of Semiotic Square. Greimas taught this at the status of an art. One could possibly say that it could also be an embryonic science in the making applicable to anything - or at least anything you could discourse about. In brief, the semiotic square approach doesn't negate the three type trichotomy of Peirce, it merely adds a fourth kind of entity into the equation. In the above example, the fourth element was called the People. One could say that the People entity differs in cardinality from the three typed individual entities. The latter three are all instances of the People so to speak. It also differs from the three by being unqualified, except by being situated relative to them within the implicit logic of the semiotic square. It certainly is of a different kind. But the French semioligist would probably say that this is only the "premier plan." There is always a second plan. In the second plan, the archetypal individual - any individual - always harbors an element of the tyrant, the vulnerable and the heroic. Well written, this novel could become universal literature- the epic story of the villain, the vulnerable and the heroic in You or Me - another twist of the People entity.. And that is what really make the a novel different from a travel documentary. (Good travel documentaries also have good semiotic structure. French documentaries are square shaped) Greimas provides an excellent example of his technique in an analysis of a work by Maupassant. There he discerns a number of semiotic squares as the author's discourse moves from one problematic to another. Greimas explains this in terms of a "debrayage" (changing gears) from one semiotic square to the next. In the case of our novel, there is nothing absolutely fixed about the villains typology, for example. He might start off in a pure villainous "Firstness" position and later move to other positions and even himself show heroic and vulnerable qualities, but not, of course, in the same scene. The villain as temporary hero becomes Firstness as Secondness and so on. It's an art and not a science, just as for Peirce's metaphysical trichotomy approach. Once you start applying the semiotic square -including Peirce's trichotomy, you become hooked. My favorite semiotic square is in electromagnetic wave theory. Maxwell started off with three first order partial differential equations. The first was for Coulombs' Law for electric fields. The second was for Ohms' Law applied to potential fields. The third, the Biot-Savart law for magnetic fields. Maxwell's genius was to first discern this trichotomy a la Peirce. 1-2-3 => electric, potential and magnetic fields. He then, more or less, combined these three single first order equations, canceled a few things out and came up with a second order differential equation - the wave equation for the, as yet, undiscovered phenomena of electromagnetic wave propagation. This a marvelous example of "Fourthness". Without Fourthness, there would be no talk back radio! No blanket TV coverage of the Clinton scandal either! Thank god for Maxwell! Another example of lesser interest is the four dimensional vector used in the space-time of classical relativity theory - three dimensions for space and a "fourthness" dimension for time. If this was a deeply fundamental approach then the three dimensions would have to be typed into firstness, secondness and thirdness. I think that Peirce was very interested in proving the necessity of three dimensionality. Unfortunately all he kept coming up with was the three and not the 1-2-3. To get a reasonable competence of the art of semiotic analysis I strongly recommend applying the construct in many areas, over and over again. It's applicable to anything. If not, its not anything. There is a tautological twist. After mastering the art, then one can start to have a stab at turning this all into some kind of tractable science. Either that or make a living from the proceeds, which is what I'm doing at the moment - applying the art to system software design. Theology and comparative religion is a good stamping ground. Here is a rough example of a "square of semiotic squares" drawn from a rapid comparative religion analysis. In Christian theology the Trinity is God the Father, the Son and the Holy Spirit. The fourth element is simply god unqualified (almost). The Islamic trinity is the Koran, Faith and Divine Justice. The fourth is also an unqualified god, but different to Christianity as it is a different kind of unqualified god - the three triadic types are different. What's interesting is that Islam itself can be considered as Firstness and Christianity as Secondness. In the search for Thirdness one finds Buddhism with its own Trinity (the three jewels) with the Fourthness being the unqualified state of Nirvana. There is no god in this scenario but only a totally unqualified entity. Nirvana is totally unqualified, except that it isn't a god but a state. Here we almost have a semiotic square of semiotic squares. To complete the big square we need "fourthness." In the fourth place we find a religion of a radically different kind. This is the most seemingly eclectic religion on earth: Hinduism, the religion of the unqualifiable brahman. It can be explained that each of these religions is based on an overall prise de position regarding the deep question concerning the explicit relationship between the One and the Multiple. There are 4 possible basic variations. 1. Islamic monism => The Multiple is One 2. Christian psuedo monism/duality => The One is Multiple 3. The Buddhist Doctrine of Non Self =>There is no One, everything is Multiple Every individual is qualified by a multiplicity of others. Nothing is primordial. The finally we have the 1000 year old problem that frustrated nascent Hinduism, only definitively resolved by Sankara in the tenth century - the problem of characterizing the doctrine of the uncharacterizable. Sankara stated in in terms of:- 4. The Doctrine of Non Duality => There is only the One, all else is illusion. To understand this simple formula, you have to go to the subtle second plan of Fourthness - Sankara's nuance. A lot of this stuff I've discussed a bit in my book "The Metaphysics of the Computer" Edwin Mellon Press 1992. The level of rigor is not much better than used here. Since then, I've made some considerable advances due to insights gained from my software work and plan to write another more rigorous work when I get the free time. The work will be couched in a Stoic framework but may use Peirce as a continual reference point. In short, there's absolutely no problems with Peirce's 1-2-3 doctrine. Peirce argued insistently against a fourth or higher primordial. He was quite right. There are only three primordial types. That's it. Any entity whatsoever can be broken up into three qualified type entities - even protons. However, this any entity whatsoever is not any one of these types or attributes. It's something different as we can see from the theological examples, or from Maxwell's wave equation. In the latter case, there were three force fields. Maxwell's wave equation is not a force field, but a dynamic synthesis of three force fields -something of a different, less qualified, "higher" kind. In brief, there are only three primordial types. However, integrally related to them there is a thing of a different kind. The fourth thing is unqualified in itself. Its three types provide the qualification. They provide the qualifying "boundary conditions" in some way. However, it can be that an entity is seen as being one of these types. Whether something is a type of entity or an entity with a type depends on context. In the grand theological semiotic square example above, The Islamic god is the (almost) unqualified god, qualified in a weak way - as unadulterated Firstness - the most dogmatic and indisputable qualification. This Firstness is relative to the other three World religions. In isolation within its own semiotic square, Firstness is the Koran, an expression of god as Divine knowledge substance. The Christian god is qualified as Secondness relative to the other religions. Within its own semiotic square Secondness becomes the Christ - god living. . Number Thus when Cathy Legg talks about number being Firstness, she should really fill out the rest of the semiotic square, relative to which this statement would be valid. A similar argument could show number as being Secondness or Thirdness as other have claimed, but in a different semiotic square context. Of course, if we take the totally unqualified number, except being qualified as a number, then it should be explainable in terms of it's 1-2-3 qualifying constituents. Number as a Trinity (Fourthness), or number as an element in a Trinity. A number Trinity might be something like: Firstness - Number as a name (symbol) for a value Secondness - Number as a value Thirdness - Number as a place holder for a value (a variable) Fourthness - Any number capable of being so qualified by this trichotomy You mightn't like this trichotomy, but don't worry, there are three other such number trichotomies. This leads to the question of whether my number trichotomy above is itself in a 1, 2, 3 or 4 position in the larger semiotic picture. I think its Secondness in this case. All are valid. After all, it all depends on context. The semiotic square is a fundamental tool for expressing context. However, its not much good for handling context. For that you need yet another element - Fifthness. Greimas's "debrayages" from one context to the next are just too informal to make sense. The quantum mechanics people have already cottoned on to this fifth "context entity," describing it as being "tucked up" and not perceptible. But that is a longer story. Besides, it has all been done before, a long time ago. Doug Moore ============================================== Dr Douglas J H Moore For the month of February in Israel email: djmoore[…]netvision.net.il Usual Australian address email : djhmoore[…]ozemail.com.au ------------------------------ ```