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

[Jon Awbrey]

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QUIPS.  Discussion Note 4

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BU = Ben Udell

Ben,

Remarks interspered below.

BU: I still find the argument confusing.  Although Peirce appears only once
    to have spoken of "pure symbols", it doesn't seem to contradict what he
    says elsewhere about the suitedness of symbols to be involved with icons
    and indices.

In that context, Peirce used the term "pure symbols" and followed it
with a list of examples that we may suppose was meant to clarify the
sense intended in that context.  Any reader of his logical work from
1870 on would recognize the list that he gave as the first few items
of a natural kind.  If he had meant "pure" in the sense of "type" as
opposed to "token", then any random list of symbols, indeed, any old
list of signs would have worked just as well, since all things except
haecceities have their typical along with their instantial features.

BU: Words like "and" help make complex symbols
    chock full of connotation and designation.

Yes, but don't forget that all symbols have
denotations and connotations of their own.
In other words, it does not take an icon
to get a connotation or an index to get
a denotation.  In Peirce's rough rubric
of the early years, symbols denote by
connoting.

| We are already familiar with the distinction between the extension and
| comprehension of terms.  A term has comprehension in virtue of having
| a meaning and has extension in virtue of being applicable to objects.
| The meaning of a term is called its 'connotation';  its applicability
| to things its 'denotation'.  Every symbol 'denotes' by 'connoting'.
| A representation which 'denotes' without connoting is a mere 'sign'.
| If it 'connotes' without thereby 'denoting', it is a mere copy.
|
| C.S. Peirce, 'Chronological Edition', CE 1, 272
|
| Charles Sanders Peirce, "On the Logic of Science",
| Harvard University Lectures of 1865, pages 161-302 in:
|
|'Writings of Charles S. Peirce:  A Chronological Edition',
|'Volume 1, 1857-1866', Peirce Edition Project,
| Indiana University Press, Bloomington, IN, 1982.

BU: It seems natural -- words like "and" and "not" are so many routings,
    reroutings, and complexifications of the copula that combines subject
    with predicate.  We may get to the conception of "and" only through
    imagery and experience of accompaniments, but the logical conception
    is more general than that of "with" or "in company together" (e.g.,
    "Keats and Chapman invested their remaining funds in a goose fair")
    and is logically definable such that we can pull the conceptual ladder
    up after ourselves as long as we're not closing all mental doors to the
    qualitative and to the concrete -- there's something already there which
    "and" represents, like an orbit which we can reach, and this "orbit" is
    what I take Jon to mean by the "formal constraint which a symbol places
    on its domains", which one might reasonably want to study apart from
    indexical or iconic ladders to it, without any need to deny those
    ladders' existences and neededness (the need for concrete analogies
    to abstract ideas is familiar enough). 

As far as natural languages go, even the simplest words,
like "and" and so on, will have many divergent meanings,
as one discovers by collecting enough examples of their
use in everyday contexts, but as far logic goes, we can
give fairly precise meanings to these sorts of logical
symbols, for example, in the case of "and" we can say
that it denotes a 3-adic relation among truth values,
specifically, this one:  {t:t:t, f:t:f, f:f:t, f:f:f}.
Here the relate is the truth value that results from
the logical conjunction of the truth values of the
first and second correlates.

BU: On the other hand, what sort of first-order information
    does a logical operator like "and" carry?  It seem more
    an operator on information than like information itself.
    Likewise words like "or" and "not".  This is related to
    the question of how one gets information-theoretically
    at the "psychological novelty" or "novel aspect" of a
    deductive conclusion.  There's no information in that
    conclusion except in a second-order sense, i.e., in
    the relatively novel combination of signs.  But this
    is the very viewpoint from which we seem confronted
    with second-order indexicality and second-order
    iconicity, though one might argue that this is
    just the level of qualisigns, not of the truly
    general legisign, which (according to Joe as
    versus Tom Short) is essentially the sign's
    acceptation, not merely the repeatedly
    instantiable form of a sign.

Not sure I got this part.

Have to break here ...

Jon Awbrey

BU: On the other hand, if the *bearing* or *carrying* of first-order information
    by a sign like "and" or "not" is questionable, then, still, what about a sign
    like "+"?  It does seem to tell us info, for instance in "5+7", that none of
    the 5 are among the 7.  Perhaps the "of" in "sum of" doesn't carry information
    but only operates on information?  Whatever the case there, still, more generally,
    mathematics does involve uncertainties, and does not seem to reduce to deductive
    logic.  But then to top it off, Jon sounds like he's hinting that he thinks that
    maybe symbols could denote or connote somewhat arbitrary things -- qualities or
    concrete things -- without indexical or iconic aid -- as if the "orbits" or
    "formal constraints" may reach much farther into the everyday idiosyncratic
    than is usually imagined.  Or instead perhaps Jon has only logical operators
    in mind?  Or only logical and mathematical objects?  But, in the case of
    mathematical objects, how will mathematical information be conveyed without
    the aid of mathematical diagrams (icons)?  Then again, Jon may mean mainly
    that the most general definitions of signs do not themselves compel symbols
    to be involved with icons and indices and that he is unsure and curious just
    where that leads, even if he grants that the natural way of symbols, in Peirce's
    view and in truth, is involvement with icons and indices.

BU: Anyway, if I sound confused, it's because I am.

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