Ben, Jim and list,
My understanding of the problem opened by Peirce's use of subindices or hyposemes seems to be quite different from your's. So I try to give my idea of it below, being accepted that I think this not to be secondary problem in Peirce's sign theory because he also used the same distinction for icons (hypoicons) as Frances  Kelly recalls it in another post.

Ben summarizes the problem this way when he writes (in part) in reply to Jim:
Now here, then, is what you cannot reconcile:
 
From "A Letter to Lady Welby," SS 33, 1904:
66~~~~~~~
"I define an Index as a sign determined by its dynamic object by virtue of being in a real relation to it. Such is a Proper Name (a legisign); such is the occurrence of a symptom of a disease (the symptom itself is a legisign, a general type of a definite character. The occurrence in a particular case is a sinsign).
~~~~~~~99
 
YET:
 
1903 ('A Syllabus of Certain Topics of Logic', EP 2:274) he says of subindices / hyposemes (click on "subindex" in the sidebar at the Commens Dictionary):
66~~~~~~~
_Subindices_ or _hyposemes_ are signs which are rendered such principally by an actual connection with their objects. Thus a proper name, [a] personal demonstrative, or relative pronoun or the letter attached to a diagram, denotes what it does owing to a real connection with its object but none of these is an Index, since it is not an individual.
~~~~~~~99
 
You will note that in the 1903 he says, specifically, that a proper name IS a subindex and ISN'T an index "since it is not an invidual."  Peirce is very clear on that point.
 
My reading of this is that despite Peirce is saying that a proper name, a personal demonstrative, etc. are not indices because they lack of individuality, he is NOT saying at the same time that they would be subindices or hyposemes. May be Ben is mislead by equating "real" with "actual". The first sentence only states to my sense a character of subindices, namely Actuality of a Connection.The second sentence states -INDEPENDENTLY-  that in order to be an Index, individuality is required.
Now, the two sentences are related by "Thus", which means I think that if we consider that subindices are some kinds of indices, yet they need to be individuals as well as actually connected to their objects.
But nothing implies here that a proper name is a subindex. On the contrary, not being an index  he cannot be a fortiori a subindex.

BEN:
Yet in the other, the 1904, he says that a proper name, in the sense of a legisign, _is_ an index.
 
The point is that Peirce is _varying_ over time. That's what I was tracing the series of quotes. In the 1904, an Index can be a legisign or a sinsign. That means it can be general or singular.
I doubt for the time being Peirce is varying here. There is a recurrent shorthand that perverts our reasoning. It consists in assimilating the relation sign-object into a kind of sign (this I had  already said at the time of the "pure symbols" discussion). Strictly speaking saying that a sign is an index is a metonymy (which Peirce uses often too). The first trichotomy , the sign in itself, allow a sign to be either a qualisign, or a sinsign, or a legisign. It is only after that that either of them (except the qualisign) can be considered as an index for example. If there is a change in Peirce's analysis of signs starting from the Syllabus of 1903, it is in the "invention" of the first trichotomy. Perhaps it would be safer not to say as Ben does that an Index can be a legisign (general) or a sinsign (singular) but the converse: a legisign and a sinsign can be both indices (among other things).

Now, what about subindices and other hyposemes? I am not sure at all. But as it is suggested by the etymology they  seem to me to be species of index, this latter being their genus. At first sight this could apply indifferently to sinsigns and legisigns, being admitted if we follow Peirce that the supplementary indexical character lies in the actuality of their connection to their objects. Now, this does not prevent the question I hear Ben uttering behind his computer screen: does legisigns (or generals) can have actual connections to their objects or does this property can apply only to singulars?

Hoping to have not enfonce des portes ouvertes.

Bernard

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