#### Re: Logical Graphs, Iconicity, Interpretation

johncm22

Jon

The quote you have given does not match the standard Peircean trichotomy of icon, index, symbol.
See this quote from CP 4.448

"A sign, or, to use a more general and more definite term, a representamen, is of one or other of three kinds:†1 it is either an icon, an index, or a symbol. An icon is a representamen of what it represents and for the mind that interprets it as such, by virtue of its being an immediate image, that is to say by virtue of characters which belong to it in itself as a sensible object, and which it would possess just the same were there no object in nature that it resembled, and though it never were interpreted as a sign. It is of the nature of an appearance, and as such, strictly speaking, exists only in consciousness, although for convenience in ordinary parlance and when extreme precision is not called for, we extend the term icon to the outward objects which excite in consciousness the image itself. A geometrical diagram is a good example of an icon. A pure icon can convey no positive or factual information; for it affords no assurance that there is any such thing in nature. But it is of the utmost value for enabling its interpreter to study what would be the character of such an object in case any such did exist. Geometry sufficiently illustrates that. Of a completely opposite nature is the kind of representamen termed an index. This is a real thing or fact which is a sign of its object by virtue of being connected with it as a matter of fact and by also forcibly intruding upon the mind, quite regardless of its being interpreted as a sign. It may simply serve to identify its object and assure us of its existence and presence. But very often the nature of the factual connexion of the index with its object is such as to excite in consciousness an image of some features of the object, and in that way affords evidence from which positive assurance as to truth of fact may be drawn. A photograph, for example, not only excites an image, has an appearance, but, owing to its optical connexion with the object, is evidence that that appearance corresponds to a reality. A symbol is a representamen whose special significance or fitness to represent just what it does represent lies in nothing but the very fact of there being a habit, disposition, or other effective general rule that it will be so interpreted. Take, for example, the word “man.” These three letters are not in the least like a man; nor is the sound with which they are associated. Neither is the word existentially connected with any man as an index. It cannot be so, since the word is not an existence at all. The word does not consist of three films of ink. If the word “man” occurs hundreds of times in a book of which myriads of copies are printed, all those millions of triplets of patches of ink are embodiments of one and the same word. I call each of those embodiments a replica of the symbol. This shows that the word is not a thing. What is its nature? It consists in the really working general rule that three such patches seen by a person who knows English will effect his conduct and thoughts according to a rule. Thus the mode of being of the symbol is different from that of the icon and from that of the index. An icon has such being as belongs to past experience. It exists only as an image in the mind. An index has the being of present experience. The being of a symbol consists in the real fact that something surely will be experienced if certain conditions be satisfied. Namely, it will influence the thought and conduct of its interpreter. Every word is a symbol. Every sentence is a symbol. Every book is a symbol. Every representamen depending upon conventions is a symbol. Just as a photograph is an index having an icon incorporated into it, that is, excited in the mind by its force, so a symbol may have an icon or an index incorporated into it, that is, the active law that it is may require its interpretation to involve the calling up of an image, or a composite photograph of many images of past experiences, as ordinary common nouns and verbs do; or it may require its interpretation to refer to the actual surrounding circumstances of the occasion of its embodiment, like such words as that, this, I, you, which, here, now, yonder, etc. Or it may be pure symbol, neither iconic nor indicative, like the words and, or, of, etc."

Your one seems to have icons, and then two different kinds of symbols with no indexes.

Would you like to comment or explain

Thanks

John

On Mon, 4 Oct 2021 at 22:20, Jon Awbrey <jawbrey@...> wrote:
Cf: Logical Graphs, Iconicity, Interpretation • 2
https://inquiryintoinquiry.com/2021/10/04/logical-graphs-iconicity-interpretation-2/

<QUOTE C.S. Peirce>

In the first place there are likenesses or copies — such as statues,
pictures, emblems, hieroglyphics, and the like.  Such representations
stand for their objects only so far as they have an actual resemblance
to them — that is agree with them in some characters.  The peculiarity
of such representations is that they do not determine their objects —
they stand for anything more or less;  for they stand for whatever
they resemble and they resemble everything more or less.

The second kind of representations are such as are set up by
a convention of men or a decree of God.  Such are tallies,
proper names, &c.  The peculiarity of these conventional
signs is that they represent no character of their objects.
Likenesses denote nothing in particular;  conventional signs
connote nothing in particular.

The third and last kind of representations are symbols or general
representations.  They connote attributes and so connote them as
to determine what they denote.  To this class belong all words
and all conceptions.  Most combinations of words are also symbols.
A proposition, an argument, even a whole book may be, and should be,
a single symbol.

C.S. Peirce (1866), Lowell Lecture 7, CE 1, 467–468
( https://oeis.org/wiki/Semeiotic#Types_of_signs )
</QUOTE>

All,

The Table in the previous post can now be sorted to bring out the
“family resemblances”, likenesses, or symmetries among logical graphs
and the boolean functions they denote, where the “orbits” or similarity
classes are determined by the dual interpretation of logical graphs.

Performing the sort produces the following Table.  As we have
seen in previous discussions, there are 10 orbits in all,
4 orbits of 1 point each and 6 orbits of 2 points each.

Table 2.  Boolean Functions and Logical Graphs on Two Variables • Orbit Order
https://inquiryintoinquiry.files.wordpress.com/2021/10/boolean-functions-and-logical-graphs-on-two-variables-e280a2-orbit-order.png

Resources
=========

• Logic Syllabus ( https://oeis.org/wiki/Logic_Syllabus )
• Logical Graphs ( https://oeis.org/wiki/Logical_Graphs )

Regards,

Jon

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