[Inquiry] Re: Pure Symbols -- Discussion

[Jon Awbrey]

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PS.  Discussion Note 17

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JR = Joe Ransdell
JA = Jon Awbrey

Re: PS-DIS 08.  http://stderr.org/pipermail/inquiry/2005-March/002477.html  
Cf: PS-DIS 10.  http://stderr.org/pipermail/inquiry/2005-March/002479.html
In: PS-DIS.     http://stderr.org/pipermail/inquiry/2005-March/thread.html#2466
 
JR: Let me restate my answer as you may not
    catch my point given the way I phrased it.

Joe,

I have already made one answer to this in Discussion Note 10 on this thread.
I am quite familiar with the syncat dodge as it is was frequently exploited
by logicist-syntacticist folks on the SUO List to dismiss Peircean insights
and even some points where Tarski sided in spirit with Peirce against Quine.

The short answer is that Peirce treated the symbols for logical operators as
referential in force, on a par with any other symbols that have an independent
denotation in their own right.  Examples of this are abundant and pervasive all
throughout his logical work.  Your invocations of higher intentional symbols and
the pragmatic maxim will not avail you in this, indeed, one route to deriving the
referential semantics for logical operator symbols is precisely through these means.

One other point, in your comments below,
you seem to be conflating referential
with indexical at several points --
they are not identical notions.

Again, your assumption that "we are talking about symbols sufficiently complete
to be bearers of assertive force" is not a shared assumption.  Assuming that is
tantamount to assuming that we are talking about propositions, more properly,
expressions of propositions commonly known as "sentences".  This is beside
the point, since I have never claimed that sentences (or books, or people)
are pure symbols.

Jon Awbrey

JR: And doesn't the Existential Graph system contain icons
    of very abstract logical symbols, such as containment,
    exclusion, inclusion, etc.?  That is, doesn't Peirce
    himself regard the graphical figures as iconic of
    those relations, that being why he prefers it
    to other notations that are not so iconic?

JR:  In response to this you say:

JA:  The question under consideration is whether there are such things as pure symbols,
     involving in their function as symbols, per se, no iconic or indicial properties.

JR: That is the topic I am addressing.  My answer is no, there are no such symbols.
    That cannot be what he meant by "pure symbols".   I responded in an earlier
    message to the idea of "pure symbols" saying, in effect, that one can see
    why Peirce would have thought it worthwhile to distinguish symbols into
    the "pure" and whatever the proper contrary of that would be ("impure"
    or perhaps "less pure"), even though there there can be no such thing
    as pure symbols that are absolutely pure, if that means devoid of
    dependence on icons and indices in order to perform their function
    as symbols.  The motivation for distinguishing the two types of
    symbols was explained by me in terms of the scholastic distinction
    between syncategorematic terms (roughly the equivalent of logical
    connectives and the like) and categorematic terms (all other symbols,
    which include both descriptive terms such as common nouns, verbs,
    adjectives, adverbs, on the one hand, and terms having a referential
    function, like proper names, pronouns, and other kinds of indicators.
    From his examples of pure icons I take it that he meant, roughly, what
    was meant in using the word "syn-categorematic"  for words which were
    so-called because they are auxiliary in character, their peculiar function
    being to assist categorematic terms in such a way that, occurring with them,
    complete assertions could be made.  Their purity is not, in other words,
    owing to their absolute disconnection from iconic and indexical functions
    but from the indirectness of their connection with these functions, which
    depends upon their immediate connection with categorematic words, which have
    a direct relationship to the iconic and the indexical.  The wording of his
    description of the pure symbol, as it is stated in contrast with what seem
    to be two rather obviously distinct types of impure or less than pure symbols,
    those that have patent descriptive meaning and those that seem to function
    instead primarily as referential, suggested this to me to begin with.
    I then went on to say that although the auxiliary function of the pure
    symbols was enough in itself to explain why he would call them "pure"
    while at the same time going on to talk about what would appear to be
    an example of a pure symbol -- the line of identity -- as being not only
    symbolic but being in itself iconic and indexical as well, which clearly
    precludes construing "pure" as meaning "having nothing to do with iconicity
    or indexicality", it is also possible that he would have thought of impure
    symbols as being second intentional.  Now supposing that he did, the further
    possibility then suggests itself that he would have regarded such symbols as
    having direct but usually ignored iconic and indexical functions as well in
    their relationship to first intentional symbols, such as categorematic terms.
    When we note that the very discussion in question is in fact about the nonobvious
    but (he claims) quite real iconic and indexical properties associated with that
    symbolic sign, it seems plausible to say that its symbolic function is not merely
    being completed via its indirect relation to iconicity and indexicality, through
    their relation to the first intentions which are its object, but directly as well,
    in its own right as second intentional.  However, this is simply a further suggestion
    as regards how the pure symbol can be understood as essentially dependent in its
    functioning on iconic and indexical elements.

JA: The questions of whether there may be, in addition,
    icons of these symbols, and whether these putative
    "icons of symbols" may have virtues that one might
    prefer for this or that conceivable purpose under
    heaven -- these are of course interesting topics,
    but not the main question at issue here.

JR: I am not concerned with icons of symbols, whatever that might be construed
    as meaning, but with the functioning of symbols, pure and impure, which --
    I am saying -- always involves iconic and referential functions, i.e.
    assuming we are talking about symbols sufficiently complete to be
    bearers of assertive force.  I understand the pragmatic maxim to
    be based on the idea that you only have a pseudo-symbol if you
    cannot supply an account of how it is supposed to function in
    coordinating the indexical and iconic functions, which provide
    the means for identification of the subject of the assertion and
    the content of the expectation associated with the actual interaction
    based on the realilzation of the indexical function.   The pragmatic maxim
    says, in effect, that the given symbol means the experimental/observational
    consequences (conditional relationships) associated with its use, and these
    consequentia involve indexicality in their antecedents and iconicity in their
    consequents respectively.  This is essential to any symbol as such, symbols
    have a coordinating function relative to icon and indices.  Apart from that
    they are meaningless verbiage and not really symbols at all.

JR: Finally, my point was that there is no reason to believe
    that formalistic doings are somehow exempt from the maxim,
    though it is certainly possible that some formalism is doing
    nothing whatever because the formalists mistakenly think they
    are flying on wings requiring no interaction with such mundane
    nuisances as air.

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