[Inquiry] Re: Questions Involving Pure Symbols -- Discussion

[Jon Awbrey]

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QUIPS.  Discussion Note 11

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JA = Jon Awbrey
JR = Joe Ransdell

JA: As a person who has taken a special interest in graphical syntaxes for logic,
    including most especially Peirce's, for almost 40 years now, I am gratified
    to see them getting some general attention.  Some of the most characteristic,
    distinctive, insightful, and farsighted features of Peirce's whole approach
    to logic can be found with especial saliency in these graph-theoretic forms.

JA: In its bearing on the existence of pure symbols, the conclusion is the same.
    There are such things as symbols that do not incorporate icons and indices
    in their basic function as symbols, indeed, some of the most genuine types
    of signs, in the sense that that their interpretation is wholly independent
    of anything but the fact that they do get interpreted to mean what they do,
    are most saliently evident in Peirce's graphical syntaxes for logic.

JR: All symbols without exception are wholly independent of anything but the fact,
    if it is a fact, that they will be interpreted to mean what they do.  That is
    what distinguishes them from icons and indices.  This does not distinguish a
    class of supposedly pure symbols which do not depend upon icons and indices
    to do what they do as symbols.

Joe,

That's what "wholly independent" means -- not depending, among other things,
on the existence of any sign but the interpretant sign of the same object.
Since no one, I think, is saying that a symbol is necessarily also an
icon or index, and since the only other sign that is demanded by the
definition of a sign relation is the sign's interpretant sign, and
since there is nothing in the definition that demands that the
interpretant sign must be an icon or an index, where are these
other signs suppose to come from?  That can only happen in
the case of compound signs, like propositions, which are
able to make "independent" references to objects and
qualities.

JA: The fact that composite and hybrid symbols exist
    does not imply that pure symbols do not exist.

JR: No one has talked about "composite and hybrid symbols" in this
    connection, and you have no right to insinuate the idea that
    there is some dispute about whether or not there are symbols
    which are neither composite nor hybrid, whatever these terms
    might be construed as meaning.

Peirce is constantly talking about compounded signs and the combinations
of signs into complex signs.  These are considerations of complexity that
make sense with regard to signs taken at any level or abstraction, from
the most abstract form and type to the most concrete replica and token,
though it's true that we cannot always translate a form of complexity
at one level into a corresponding form of complexity at another level.
And it is with regard to these complex signs that Peirce speaks of
symbols that do "incorporate" or "involve" other kinds of signs.

Peirce also speaks of signs that combine the characters of several species
of signs, and words like "hybrid" or "mixed" seems convenient for these,
as he follows Aristotle in referring to mixed syllogisms and the like.
Anyone is free to suggest other terms, but the basic idea remains.

JA: The fact that compostite and hybrid symbols are
    important and interesting does not imply that
    pure symbols are not important or interesting.

JR: This is desperation argumentation.
    You are not strengthening your case
    with diversionary moves like this.

I am simply describing a form of argumentation
that has been resorted to in recent discussions,
and observing that it is not a valid argument.

JR: The fact that pure symbols combine with all types of signs
    to form complex types of expressions with their own types
    of informative meaning does not mean that the pure symbols
    which are thus combined do not have their own connotations
    and denotations.

JR: And I repeat what I just said above.  If you want to make your
    case you will have to explain how symbols can denote anything
    or connote anything without dependence on indexical or iconic
    sign functions.

A sufficient explanation is already implicit in the very definition
of a sign relation, since it says exactly what it means to be a sign.
It specifies the conditions that must be satisfied in order for a sign
to have a reference to objects and a reference to interpretant signs,
and if there is any sense to be had in the concepts of denotation
and connotation, then they must be defined in terms of that,
and not the other way around.

JR: Symbols are rules or laws.  How can they be actualized in instances
    in which they are actually operative without involving indexicality
    or iconicity?  My guess is that the fallacy in your thinking on this
    roots in a confusion which involves regarding symbols as SUBJECT TO
    law or rule rather than as BEING laws or rules, but there is something
    that is subverting your thinking on this, Jon.  The evidence for this is
    in the kind of argumentation you are resorting to.

When we say "the symbol is the law", we are engaging in a figure of speech
that is known as metonymy.  It has its uses, but the fact is that Peirce
does not consistently maintain this manner of speaking, nor does anyone.
Nor is it possible to do so without the creation of endless confusion.

Jon Awbrey

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