The Tetrast2 - Speculation Lounge
Sketcher of various interrelated fourfolds.

Symbols

March 14, 2010.
I discussed kinds of sign (index, semblance, symbol, proxy) in terms of some broadened notion of Jakobson's syntagmatic-paradigmatic distinction in my recent post "Rosen, Saussure, Peirce". Of course I went too far in that broadening - I was reaching for an analogy that might be a bridge or shortcut to a better understanding of what a symbol would be in my four-fold division of signs. I was whizzing along there, using words like "homology" rather too loosely. Anyway, I wish to gain an idea of symbol that seems consistent with my ideas of index, semblance, and proxy, and also seems as simple as them. As to consistency, for instance, since I allow of concrete individual natural indices, semblances, and proxies, I need to conceive of a concrete individual natural symbol. I thought I might need to broaden the idea of symbol somehow. Obviously I'm going against Peirce in various ways here, but that's for another discussion.

Underlying my ideas of index, semblance, symbol, and proxy, are four categories:
1. 'Substance' or object. Primary substance is this man, this horse, etc. But it could be abstract, a mathematical structure for example.
2. 'Accident' or attribute or quality.
3. Modality, logical quality ('indeed', 'not'), probability, novelty (information), feasibility, optimality, etc. By those I mean mode in its original definition though not usage (see Peirce, CP 2.382 and DPP p. 89) as referring to any qualification of a proposition or its copula, and I expand the idea to include straightforward logical quality - affirmative and negative. Update (3/17/2010). I just found that Peirce leaned that way about modality and logical quality. See "Prolegomena to an Apology for Pragmaticism" (1906) The Monist, v. XVI, n. 4, pp. 492-546, footnote on page 525 (last footnote of CP 4.552). End of update. Obviously I need a distinct technical term for it but I'll make do with "modality" for the time being, though, again, I do not mean it only in the usual sense (necessity, possibility, impossibility, unnecessariness). It is something like a conduit of comprehension (intension) which may qualify the comprehension in terms of fulfillment in some portion or totality of cases, the distribution of the associated denotation, etc.
4. Mathematical relationship ('double of', 'inverted order of', 'indefinite integral of', etc.), particularly as conceived of as object(s)-to-object(s) relationships. In a way, it's like a router or re-router of denotation (or maybe I should say, denotational relationships).

The index represents an object by being connected to it (in the same larger object).
The semblance represents an object by sharing characteristics or qualities with it.
The symbol represents its object by having the same modal properties/relationships.
The proxy represents its object by having the same mathematical relationships in some sense, anyway by making the same "decisions," following the same rules under ongoing observation and experimentation.

So, consider a property which has a 50-50 chance of belonging to any given object in a total population. One side (it could be either side) of a fair coin symbolizes that property in its frequency. Surprising winners symbolize each other, in a sense, irrespectively of resemblance or connection or proxyhood to each other. There is something in common about their situations - not their locations or times, but about the alternatives in which they are involved. Again, not proxyhood: you can't use a fair coin to determine the outcome of an evenly matched two-horse race, but you can consider the fair coin in order to deduce horses' odds on the assumption that the race is evenly matched. And so on. Sometimes the odds overwhelmingly favor a given outcome. Two masses of particles can be proxies for each other if they make the same "decisions" thanks to the law of large numbers when their respective particles are not proxies for each other. These relationships of attribution, distribution, etc., are matters of interpretation, but are not always subjective or matters of mere convention. Implication itself depends on structures or processes of alternatives among cases; meaning is a phenomenon, if you will, of modality. The modalities lead to an effect on interpretation. Sometimes, habitual implications are translated into conventional symbols which have the same value as (are equivalent to) their objects despite disconnection and dissimilarity.

(At one time, Peirce distinguished comprehension or intension from implication; at later times, he seemed to hold that they're more or less the same thing. I need to look further into that. The problem is that comprehension is of characteristics, but Peirce does not seem to take resemblance as a kind of comprehension. And if one either denotes objects ("Seconds") or comprehends characters ("Firsts"), then, in Peirce's system, what mode of sign relation is there to "Thirds" - representation, sign relation, attribution, etc., themselves? It appears that, early on, Peirce would have said implication, but not later on.)

As regards Jakobson's paradigm, it is an alternative among words that could be used in a given place and time. It is not the expression of such an alternative, e.g., "The horse cantered or galloped." Such disjunctive compounds, as well as conjunctive compounds, are alternates forming an alternative or paradigm (if there's some flexibility about the length of the phrase to be chosen). Moreover, logical conjunctions and alternatives all express basically "paradigmatic" rather than syntagmatic relationships, insofar as paradigmatic relations reflect relations of logical quality and modality. (Note: the polyadized variables expression "xyz" is not a logical conjunction like the conjunct propositions expression "pqr", instead it is something else.) When we speak in a second-order way about the first order, then the "and" versus "or" distinction is like that of syntagmatic versus paradigmatic - you use one word (or phrase) AND another AND another, etc., in the syntagmatic relation, and one word (or phrase) OR another OR another in the paradigmatic relation, but the resultant sentence does not thereby express relations of conjunction and alternation. Expressions of logical relations - "She wore a blue or green dress" - "She wore a blue and green dress" - etc., are expressions, explicitations, of options about things, options that also also underlie and help determine paradigmatic relations among words. That said, I'm unsure how best to analogize paradigm (to process? to function?) as I've analogized syntagma to structure. I guess it's not such a shortcut after all.

Do I feel that my idea of symbol is comfortably simple and consistent with my ideas of the other sign kinds yet? Not quite yet.
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