Robert, list,
 
Robert's "The Syntax of a Class of Signs" (scroll down to see) is interesting. Robert might helpfully clarify a few things.
 
1. Robert's conclusion is "We can define the syntax of a classe of signs as the part of the lattice of the ten classes of signs situated below this class. Then, the complete lattice appears as the grammar of signs." At least at first glance, given that the foregoing discussion was about the syntaxes of classes of signs, shouldn't the conclusion be "... Then the complete lattice appears as the *syntax* of signs" [emphasis added] ? I don't know how Peirce defined "grammar." In looking around the Web, the definitions oftenest mention grammar as involving morphology and syntax. It's not clear to me that the lattice accommodates all such distinctions as those involving kinds of hypoicons (images, diagrams, metaphors), etc. If the lattice doesn't accommodate their distinctions, then Robert might want to call that "morphology" and thus confine the lattice to syntax. I'm improvising here, though, so I don't know what I'll think about it tomorrow. Meanwhile, The Century Dictionary gives for "grammar" http://www.leoyan.com/century-dictionary.com/03/index03.djvu?djvuopts&page=819:
 
66~~~~~~~~~~
1. A systematic account of the usages of a language, as regards especially the parts of speech it distinguishes, the forms and uses of infiected words, and the combinations of words into sentences; hence, also, a similar account of a group of languages, or of all languages or language in general, so far as these admit a common treatment. The formerly current classification of the subjects of grammar as fivefold, namely, _orthography_, _orthoëpy_, _etymology_, _syntax_, and _prosody_, is heterogeneous and obsolescent. The first and last do not belong really to grmnmar, though often for convenience included in the text-books of grammar; _orthoëpy_ is properly phonology or phonetics, an account of the system of sounds used by a language and of their combinations; and _etymology_ is improperly used for an account of the parts of speech mid their inflections. See these words. Abbreviated _gram._
[examples]
2. Grammatical statements viewed as the rules of a language to which speakers or writers must conform; propriety of linguistic usage; accepted or correct mode of speech or writing.
[examples]
3. A treatise on grammar. Hence--4. An account of the elements of any branch of knowledge, prepared for teaching or learning; an outline or sketch of the principles of a subject: as, a grammar of geography; a grammar of art.--5. The formal principles of any science; a system of rules to be observed in the putting together of any kind of elements.
[examples]
Comparative grammar, grammatical treatment of a number of languages, compariug their phenomena in order to derive knowledge of their relations and history or to deduce general principles of language.
~~~~~~~~~~99
 
2. The thought that, by Robert's standard, the syntax of arguments is the same thing as "the grammar [or syntax] of signs," got me to thinking about the qualisign at the other extreme. The qualisign would just be by itself. Can that be right? This may be a question of phrasing. The qualisign has, in Robert's sense, minimal syntax proper to it, but the qualisign is involved in the syntax of all other signs. So, one might distinguish between, for instance, the syntax of the involvent dicisign and the syntax of the involute dicisign.
 
3. Is Robert saying that the lattice contains all the distinct information needed to generate the essentials of a paragraph like the one which he quotes from Peirce? Are all such conceptions as those of the replica adequately implied?  Now, I don't know whether he would be going too far with such claims.  But I'm wondering whether that's basically what Robert is claiming.
 
Incidentally, I recreated the graphic images as monochrome bitmaps, which Marty is free to use without attribution if he wants them. I recreated them because I assumed that the originals were the cause of his rtf (rich text file)'s being so large (around 850KB). But then I found that, in fact, his graphic images are quite low-KB -- jpgs ranging from 3KB to 11KB.  However, the rtf stored them in a way that made the file very large. I guess that's what rtfs do. Replacement with the monochrome bitmaps reduced the rtf filesize from around 850KB to around 72KB. The monochrome bitmaps themselves are 0.842KB, 2.21KB, & 3.38KB.
 
Best, Ben Udell

THE SYNTAX OF A CLASS OF SIGNS [Robert Marty].

http://www.univ-perp.fr/see/rch/lts/marty/lattices/Lattice-CP.rtf
[Marty also directs attention to http://www.univ-perp.fr/see/rch/lts/marty/lattices/Lattice-CP.rtf ]

On two occasions in the texts on the ten classes of signs 2-254 to 2-263 Peirce talk of the syntax of a class :

First in 2-257 concerning the Dicent Sinsign [ 2® 2® 2 ] he write :

"Such a Sign must involve an Iconic Sinsign [ 2® 1® 1 ] to embody the information and a Rhematic Indexical Sinsign [ 2® 2® 1 ] to indicate the Object to which the information refers. [….]

But the mode of combination, or Syntax, of these two must also be significant."

Remember that the logical presuppositions relationships between the three classes are the following :

I consider because is the only reasonnable abduction that this diagram bring to light what Peirce evoke when he use the term "syntax" and represent the syntax of these class.

Second in 2-262 concerning the Dicent Symbol [ 3® 3® 2 ] he write :

"The dicent symbol [ 3® 3® 2 ] or ordinary Proposition, is a sign connected with its object by an association of general ideas, and acting like a Rhematic Symbol [ 3® 3® 1 ] , except that its intended interpretant represents the Dicent Symbol [ 3® 3® 2 ] as being, in respect to what it signifies, really affected [ 2 ] by its Object, so that the existence [ 2 ] or law [ 3 ] which it calls to mind must be actually connected with the indicated Object. Thus, the intended Interpretant looks upon the Dicent Symbol [ 3® 3® 2 ] as a Dicent Indexical Legisign [ 3® 2® 2 ] ; and if it be true, it does partake of this nature, although this does not represent its whole nature. Like the Rhematic Symbol [ 3® 3® 1 ] , it is necessarily a Legisign. Like the Dicent Sinsign [ 2® 2® 2 ] it is composite inasmuch as it necessarily involves a Rhematic Symbol [ 3® 3® 1 ] (and thus is for its Interpretant an Iconic Legisign [ 3® 1® 1 ] ) to express its information and a Rhematic Indexical Legisign [ 3® 2® 1 ] to indicate the subject of that information. But its Syntax of these is significant. The Replica of the Dicent Symbol [ 3® 3® 2 ] is a Dicent Sinsign [ 2® 2® 2 ]of a peculiar kind. This is easily seen to be true when the information the Dicent Symbol [ 3® 3® 2 ] conveys is of actual fact. When that information is of a real law, it is not true in the same fullness. For a Dicent Sinsign [ 2® 2® 2 ]cannot convey information of law. It is, therefore, true of the Replica of such a Dicent Symbol [ 3® 3® 2 ]only in so far as the law has its being in instances.

The corresponding diagram is the following :

We can complete this diagram with the other classes and their relations ( logical presuppositions) :

One can notice that we obtain the part of the lattice of the ten classes of signs situated below the dicent symbol . Here also we can consider that we have the syntax of the dicent symbol.

Conclusion :

We can define the syntax of a classe of signs as the part of the lattice of the ten classes of signs situated below this class.

Then, the complete lattice appears as the grammar of signs.

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