In what sense is a phoneme like a Platonic form?

[jkpate]

Zaba, what you wrote is basically my understanding. I'd take it further and say there are several ways of analyzing language into "signs." When we study syntax, we are concerned with signs whose signified is grammatical relations and whose signifier is a string of words (or lemmas and paradigms). When we study sociophonetics, we are concerned with signs whose signified is, say, socioeconomic class and whose signifiers are, say, talker-specific vowel spaces. However, I don't know whether Saussure would agree with this view.

(By the way, this is one reason I like information theory as an approach to language. In information theory, the "signs" are called "codewords," the "signifieds" are called "messages," and the signifiers are called "signals").

[MalFet]

Yep, looks good!

And, as a bonus, you're intuiting (and jkpate is elaborating on) a very interesting dimension to this all, which is that any particular speech event can and often must be analyzed in multiple dimensions simultaneously to be intelligible. In other words, a sound can be a phonological sign, a semantic sign, a sociolinguistic sign, a pragmatic sign, etc. all at the same time.

Saussure was certainly aware of this, but his analysis was fairly limited. Figuring out how to account for this simultaneity has been a major focus of linguistic and semiotic theory ever since. The generativists have mostly dodged the issue by postulating module independence, Relevance Theory and the Information Theory folks have focused on communicative intention, semiotics has elaborated the dyadic sign to include a third dimension, and I'm sure there are other major approaches I'm just not familiar with.

[zaba]

FROM A SEMANTIC PERSPECTIVE:
0. The "sign" is a unit with two sides:
1. signified is the material thing in the world that (2) points to
2. signifier is the ideational thing: the language used to point to (1)

The signifier for this sign is both phonetic sequence and phonemes, right?

[zaba]

Is it crazy to think of it as a kind of chain? I guess I'm pushing it... but it's elegant insofar as it gets from semantics to distinctive features of phonemes, which is sorta cool.

FROM A SEMANTIC PERSPECTIVE:
0. The "sign" is a unit with two sides:
1. signified is the material thing in the world that (2) points to
2. signifier is the ideational thing: the language used to point to (1)

2. FROM  A SPEECH SOUND PERSPECTIVE:
2a. The signifier itself is a kind of "sign" with two sides of its own:
2b. signified is the material thing: phonetic sequence [sound]
2c. signifier is the ideational thing: phonemes & distinctive features [category]

2c. FROM A PHONEMIC PERSPECTIVE
2ci. The signifier = the phoneme
2cii. the signified is the material-like component represented by distinctive features
2ciii. The signifier is the ideational thing: the phoneme itself

[jkpate]

I'm not sure that "chain" is the right technical term, but I think the basic idea is reasonable. If we have a variable for everything that can be either a signifier or a signified (or both), we can indicate what the signs are by drawing a black square for each sign instance and then drawing lines between the square and the signified and signifier variables that participate in the sign instance. So for example we could have a string of "phoneme" variables, a string of "word" variables, and a string of "phrase" variables. To indicate that /kæt/ signifies the word "cat", we draw a black square between them, and draw a line from the square to the "cat" word variable, and from the square to the /k/ /æ/ /t/ phoneme variables.  Similarly, we could have a "the" word variable, and an "NP" syntactic variable, and indicate that "the cat" signifies a noun phrase by putting another square between them and then drawing lines from each of "NP", "the", and "cat" to that square. So we have one black square for each sign, and it connects to variables that are part of either the signified or the signifier of that sign.

If we do this, we'll be drawing a factor graph for the syntax and word segmentation of the phoneme string. Factor graphs are used in information theory to devise near-optimal codes, and are used in probability theory to define structured probability distributions over a given set of variables (in fact, those end up being the same thing). And there's no reason, in principle, not to include semantic, pragmatic, social, or other variables. And if you decide you want to explore some non-modular correspondence, such as an influence of social variables about interlocutor identity on syntactic ambiguity resolution, you can just draw a line between the relevant indexical variables and one or more "sign" squares whose signified is syntactic.

So probabilistic models of language structure embody your intuition that there are series of signs that "feed into" each other, and provide a natural framework for formulating and evaluating hypotheses about what the signs are. Of course, actually implementing and running these models takes a lot of effort, especially if you want to include lots of "cross-module" correspondences.

[MalFet]

I'd hesitate to use the term "chain" for two reasons. First, when you start looking at actually interpretive process, the matter gets very complicated very quickly. There's a lot of good work on this in (for example) gestalt psychology. Second, the idea of chained signs is a technical term of art in some fields of semiotics, where it has a very particular meaning that's probably not identical to what you intend.

But, as far as your actual description goes, I suspect that's more or less accurate.