The Tetrast2 - Speculation Lounge
Sketcher of various interrelated fourfolds.

Rosen, Saussure, Peirce

March 3, 2010.
(Recentest significant change: December 30, 2010).

In Peirce's semiotic, an irreducible triadic relationship defines object (subject matter), sign, and interpretant. I've argued the need for a fourth element, which I've called a recognizant. Trying to get away from such a psychological-sounding term and to follow the word pattern of "interpretant", I've also called the recognizant the verificant but that's misleading, because I mean not the verificatory evidence but instead that of which the content is the verified or established or corroborated, etc., the lesson learned. As the interpretant is, in a sense, an aspect or moment of an interpreter, so the recognizant is an aspect or moment of the recognizer (who in a sense is a verifier or corroborator, etc. - recognizing or acknowledging a legitimation). In the analogy of semiotic to Shannon's information-theoretic scenario: As interpretant stands to decoding, so recognizant stands to recipient.

Now, among kinds of sign, Peirce's most famous trichotomy is that of icon, index, symbol. The three are defined by how they stand for their objects: icon by its own characters, as resembling its object; the index by factual connection to its object; and the symbol by interpretive norm or habit of reference to its object. The point to notice is that the index represents in virtue its object-connection which it has had; the icon in virtue of its own representative characters as now presented; and the symbol in virtue of how it will be interpreted, i.e., in virtue of its interpretant. You see the pattern:
index : object :: icon : sign :: symbol : interpretant.
So I thought that to complete the pattern for my version of semiotic I would need a fourth kind of sign, one defined by some sort of relationship to the recognizant. The pattern seemed to generate the idea of a sign which represents in virtue of the case that it would be recognized to stand for its object by one observing the object if the object were available. Such would be a sign which stands for its object for observational and experimentational purposes. This I called a proxy. I distinguished proxy from mere surrogate by this consideration: a proxy can make decisions on somebody's or something's behalf, by following some sort of rules for the decisions that that person or thing would make. Of course, in a corporate election, if you have somebody's proxy, you can vote howsoever you want. But I was thinking of things like power-of-attorney, a lawyer representing somebody by acting on that person's behalf according to the rules of that person's best interest, making the decisions that that person would make if they were conscious and present, grasped the law, etc. Eventually it occurred to me that that which Peirce calls diagrams are also proxies. Now, Peirce classes the diagram as a kind of icon. The diagram is subject to the same transformabilities as its object. Peirce holds that the study of mathematics proceeds through experimentation with diagrams, observation of them, etc. Such diagrams may consist in geometric forms or in arrays of algebraic expressions, etc. They need not outwardly resemble their objects at all. So, I speak of semblances, not icons, and class diagrams as proxies, not as semblances. It occurred to me that some physical objects can be proxies for others - electrons can be proxies in experiments for any electrons, they're all the same and follow the same rules. A statistical correlation between two things, on the other hand, may be a mere resemblance independent of underlying sameness of structure, rules, etc. It's the kind of relationship which conduces to inductive generalizations, subject to testing. Anyway, as signs, proxies are no more infallible than semblances and still need to be checked.

I've noticed that the word "proxy" is currently used to refer to surrogate indices, such as tree rings as so-called "proxies" for thermometers. I'm doubtful that that is a good use of the word "proxy." They are alternate indices for the same phenomena. Any, the scientific currency of the word "proxy" in such a sense is certainly inconvenient for me, but there's little that I can do about it.


Somebody who has read my Websites contacted me in late 2008 and, in our subsequent correspondence, mentioned Robert Rosen's modeling relation and gave me this link: I read that and another page at the linked Website The distinction which Rosen made between simulacrum and model is much like mine between semblance and proxy, except that I was unsure that Rosen models could be concrete and not only abstract. Later I learned from a comment by Rosen's daughter Judith that for Rosen a model could be an individual concrete object (, so, as far as I can tell, my proxy is Rosen's model; and my semblance is Rosen's simulacrum. Well, I'm glad that Rosen beat me to it! It suggests that the idea is not just my whimsical notion. He worked it out in terms of considerations of scientific thinking, especially in biology. I arrived at it through consideration of Peircean semiotic, an area in philosophical logic. I've mentioned this fit of my ideas to Rosen's a couple of times on peirce-l, in a May 17, 2009 post and in a July 14, 2009 post. (My earliest peirce-l discussion of proxies that I can find is this December 2, 2004 post.) So which is the better word, proxy or model? Well, a lawyer can be a proxy for, or of, his/her client. But you wouldn't say that the lawyer is or acts as a model for the client, because that suggests that the lawyer's function is to set an example for the client to emulate. On the other hand, as I've noted, the word "proxy" has taken on a specialized and weakened meaning in science. Well, I'll go on speaking of proxies rather than of models, so that it's clear that I'm speaking about the idea of proxy as I've been working on it, not Rosen's idea of model as he worked on it, howsoever they may coincide.

Anyway, for Rosen, a model has that which he calls a synonymy of structure of entailment with the thing or process that is modeled. I'm not sure what is the point of the word "synonymy" in that context. It suggests that the structure itself is some sort of word or symbol. Instead it's enough that the structures of entailment be the same, or isomorphic, or homologous, or whatever, between model and modeled thing, without calling those structures "synonymous." To have the same meaning is to reflect the same norms or parameters, to make the same difference; not necessarily to teach the same lessons through experimentational structural transformations. The reader may think that I'm splitting hairs but I'm dealing with four kinds of sign (index, semblance, symbol, proxy) and they involve meaning in various ways. I need to maintain some sort of careful distinctions, at least sometimes.

A symbol is a kind of sign that has the same value or import as its object even when they have neither a connection nor a resemblance nor a structural sameness (the kind of sameness that allows for parallel transformations). Now, since I can think of concrete objects which are natural indices, natural semblances, and natural proxies, why not symbols? So I have to broaden the idea of the symbol, to that of a sort of functional surrogate or functional equivalent for something, such that it serves as a sign about that thing, irrespectively of connection, resemblance, or homology. Wish I could think of an already existent name for this broadened idea of symbol.


In trying to regularize this tetrachotomy of index, semblance, broadened symbol, and proxy, thinking (as always) of Aristotle's four causes, and so on, I recently started considering the syntagmatic-versus-associative dichotomy of Saussure and, more specifically, Jakobson's refined version, the syntagmatic versus the paradigmatic. The syntagmatic has to do with the way things are compounded or connected in an orderly way; it's a broadening of the idea of syntax. The paradigmatic has to do with sets of options which exclude each other in some sense, anyway involving at least an alternative among words if not among things, as in "She wears a..." scarf or jacket or blouse, etc. They don't have to exclude each other literally, though they can. Paradigmatic relations involve differentiation.
1. Index - thing which represents its object by being in the same syntagm, so to speak, with its object - it is connected to its object. (This involves broadening the idea of syntagm.)

2. Semblance - thing which represents its object by having the same differentiae, the same qualities, differentiating respective parts or stages. (Here a sequence is seen not as a temporal syntagm but as a paradigm going through its alternatives, its various phases, in time). A very simple semblance is when two things simply have the same single quality across respective parts or stages.
3. Broadened symbol - thing which repesents its object by being an alternative to it, but still having the same value, still making (as opposed to having) the same difference.

4. Proxy - thing which represents its object by having the same syntagm, in some sense same structure, following the same rules, and teaching the same lessons.
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