[Inquiry] Re: Futures Of Logical Graphs -- Discussion

[Jon Awbrey]

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FOLG.  Discussion Note 28

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GR = Gary Richmond

Re: FOLG-DIS 27.  http://stderr.org/pipermail/inquiry/2005-November/003182.html
In: FOLG-DIS.     http://stderr.org/pipermail/inquiry/2005-November/thread.html#3167

Gary, Peirce List,

Thanks for the able summary of many issues indicental to our present topic.
I will put off consideration of the line of identity, indeed, any question
of the Peirce's Beta level or the logic of relations proper, until such time
as we get a solid grip on the Alpha level or the logic of simple propositions.

I do not understand your perception that Peirce uses "pure symbol" loosely
in what I have labelled as Statement 1 -- as a negation of a long list of
predicates, its meaning is rather unusually definite.  But the relations
of looseness to purity are the stuff of many a thrilling story, so I'll
let it go.  As to the relation of perfection to purity, an overlapping
but still engaging genre, I never did see any problem, since the near
synonym of "perfect" is "complete", and there was never any question
that complete signs, and thus complex signs, were any brand of pure.

I do agree that the sense of pure in Statement 1 seems to be different
from the sense of pure that is used in contrast with replicas of signs --
I think the latter dimension is akin to "abstract" versus "concrete",
"type" versus "token", "rule" versus "case", and similar such senses.
Though interesting in its own right, I think this issue is understood
by most folks, myself anyway, and quite independent of the other issue.

I have already collected a long list of passages from Peirce
on what exactly he meant by second intentions, but once again,
I think that is probably purely incidental to the other matter.

Then again ...

Jon Awbrey

GR: It appears to me that Peirce uses the expression "pure symbol" rather loosely
    when one compares the relevant passage Jon quoted with the one following (which
    he did not).  In the former passage Peirce comments that "a symbol may have an
    icon or an index incorporated into it" and provides such examples as a common
    noun -- say, "man" -- to illustrate iconic incorporation ("a composite photograph
    of many images of past experiences") and such words as demonstrative pronouns--say,
    "this"--as an example of indexical incorporation (that is, referring "to the actual
    surrounding circumstances of the occasion of its embodiment)", and he concludes the
    paragraph with his suggestion that there are "pure symbols" ("neither iconic nor
    indicative, like the words and, or, of, etc".)

GR: But in the passage immediately following this one Peirce comments that
    "the most perfect of signs are those in which the iconic, indicative,
    and symbolic characters are blended as equally as possible" and gives
    as an "interesting example" of this type of sign the line of identity
    (he goes on later to show how it includes beyond its symbolic character
    "the nature of an index" while on the other hand it is "in the highest
    degree iconic" (these quotes from a segment of 4.448  not here given).
    Peirce writes:.

| As a conventional sign, it [the line of identity] is a symbol;
| and the symbolic character, when present in a sign, is of its
| nature predominant over the others.  The line of identity is
| not, however, arbitrarily conventional nor purely conventional.
| Consider any portion of it taken arbitrarily ... and it is an
| ordinary graph .... But when we consider the ... connexion of
| this portion with a next adjacent portion, although the two
| together make up the same graph, yet the identification of
| the something, to which the hook of the one refers, with
| the something, to which the hook of the other refers, is
| beyond the power of any graph to effect, since a graph,
| as a symbol, is of the nature of a law, and is therefore
| general, while here there must be an identification of
| individuals.  This identification is effected not by
| the pure symbol, but by its replica which is a thing.
|
| C.S. Peirce, 'Collected Papers', CP 4.448 

GR: Note especially the last sentence here states that "This identification
    is effected not by the pure symbol, but by its replica which is a thing."
    Now Peirce's use of "pure symbol" in this sentence seems clearly different
    from that in the paragraph preceding (with its examples of "and, or, of,
    etc.") for he has just identified the line of identity as an example of
    "the most perfect" kind of sign which blends "the iconic, indexical, and
    symbolic characters."  A hint as to a possible resolution of this problem
    is given, I believe, in his explicit reference to the replica.  He writes
    {albeit in specific reference to assertion) just a couple of paragraphs
    later that:

| ... no assertion can be constructed out of pure symbols alone.
| Indeed, the pure symbols are immutable, and it is not them that
| are joined together by the syntax of the sentence, but occurrences
| of them -- replicas of them.  My aim is to use the term "graph" for
| a graph-symbol, although I dare say I sometimes lapse into using it
| for a graph-replica.  [emphasis added]
|
| C.S. Peirce, 'Collected Papers', CP 4.500 

GR: Well, it may be that Peirce's use(s) of the expression "pure symbol"
    also reveal a kind of "lapse" (or, more generously, a groping towards
    an adequate terminology for some vexing semeiotic concepts), but I'm
    afraid I haven't any time to get into this at present and offer this
    half-baked thought (but especially the passages above and another
    immediately below my signature) for your consideration. 

| Every symbol is an ens rationis, because it consists in a habit, in a regularity;
| now every regularity consists in the future conditional occurrence of facts not
| themselves that regularity.  Many important truths are expressed by propositions
| which relate directly to symbols or to ideal objects of symbols, not to realities.
| If we say that two walls collide, we express a real relation between them, meaning
| by a real relation one which involves the existence of its correlates.  If we say
| that a ball is red, we express a positive quality of feeling really connected with
| the ball.  But if we say that the ball is not blue, we simply express -- as far as
| the direct expression goes -- a relation of inapplicability between the predicate
| blue, and the ball or the sign of it.  So it is with every negation.  Now it has
| already been shown that every universal proposition involves a negation, at least
| when it is expressed as an existential graph.  On the other hand, almost every
| graph expressing a proposition not universal has a line of identity.  But identity,
| though expressed by the line as a dyadic relation, is not a relation between two
| things, but between two representamens of the same thing.
|
| Every rhema whose blanks may be filled by signs of ordinary individuals,
| but which signifies only what is true of symbols of those individuals,
| without any reference to qualities of sense, is termed a rhema of
| second intention.  For second intention is thought about thought
| as symbol. Second intentions and certain entia rationis demand
| the special attention of the logician.
|
| C.S. Peirce, 'Collected Papers', CP 4.464-465

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