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

[Jon Awbrey]

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QUIPS.  Discussion Note 7

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BU = Ben Udell

Re: QUIPS-DIS 5.  http://stderr.org/pipermail/inquiry/2005-May/002606.html
In: QUIPS-DIS.    http://stderr.org/pipermail/inquiry/2005-May/thread.html#2602

BU: I guess I haven't made quite clear that I'm favorable
    to the idea of "and" and "not" etc. as "pure symbols"
    in some sense --  a comparatively innocous sense, i.e.,
    in the sense that they're signs that are only telling
    the interpretant how to handle other signs and are not
    specifying the connotations or denotations of those
    other signs.  One doesn't even need to have read any
    Peirce in order to recognize that symbols like "not",
    "and", "of", etc., are of a special natural kind which
    doesn't include symbols like "red" and "Peirce".  Now,
    the fact that Peirce wrote of "pure symbols" apparently
    only once, takes on different meanings dependently on
    whether his other writings seem to contradict it or
    seem compatible with it.

Ben,

Well, a search of CP is hardly definitive for the statistics of usage --
I haven't even bothered looking through NEM, becuase it never occurred
to me that the particular adjective being used was all that important --
the only thing that I thought he was singling out in these instances
was the fact that the rules of interpretive engagement were somewhat
more succinctly specifiable than in the case of words like "red" and
"Peirce".

BU: That his other remarks seem compatible with it makes it
    less dubious for you to invoke it, it strengthens your
    case comparatively to if his other remarks seemed to
    contradict it.  Another thing that I was getting at
    in discussing whether they "carry" information is
    the question of whether they can be distinguished
    as "pure symbols" through their informational
    properties.

Yes, I think that the important thing is the fact that one or two
of his more general definitions of sign relations appear to cover
all of the other more specialized depictions of their character.
The main thing about these formal symbols is that their forms
are found in the organization of lots and lots of material,
making it useful to treat them in abstraction form those
concrete contents.

BU: Now, I don't know how to do this in terms of
    first-intentional, second-intentional, so I'm
    talking about first-order and second-order
    information.

I don't think it's necessary to drag in second-order anything
simply in order to deal with this level of "zeroth order logic".
I don't know about Aquinas, though I like the way Peirce uses
his idea of "logical reflexion", but it seems that many of the
more nominal thinkers among the Scholastics invoked this stuff
about second intentions as a back-door way of bringing in the
hypostatic abstractions that they couldn't really do without.

BU: What sort of measurement of information do you have in mind?

When it can be quantified, there is the standard AURORAS definition:
"Average Uncertainty Reduction On Receiving A Sign", but Peirce's
ICE formula (Information = Comprehension x Extension) promises
to be more general and apply in more qualitative situations,
if all the details can be worked out.

BU: Going by the usual (as I understand it -- I'm no info theorist),
    if two contingent and mutually independent items "p" and "q"
    are in question, then "pq" has four bits of info.  Apply "not"
    to "pq": "~(pq)" -- then we have a compound which is true in
    three of four cases, and the amount of info is the log of 4/3
    to the base 2, approximately 0.415.  So the "not" takes us
    from 2 bits to 0.415 bits.  Yet we certainly won't say that
    "not" therefore carries negative 1.585 bits.  Instead,
    that's the sense in which I mean that it's not clear
    that "not" carries information so much as operates
    on it.

No, that seems off somehow.  I will see if I can think of an example.

BU: So I figure, this is not information in the sense in which Jon
    is talking about it.  Now, even if we say, that we don't mean
    "information" only in a first-order sense, the question remains
    whether a first-order sense is still helpful in sifting out
    "pure symbols", even if we end up saying that they carry
    information in some other sense.

BU: There also remains the question of what kind of quantifying
    of information you have in mind.  I'm not asking, what fully
    worked out system of quantifying of info do you have in mind,
    as I'm not sure that you need one.  But it would be helpful to
    have some rough notions of what counts as more or less information,
    and how you relate and commensurate information in a word like "not"
    to information in icons, indices, and symbols which direct the mind
    to conjure up icons and indices.

Will think on it.

Jon Awbrey

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