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

[Jon Awbrey]

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QUIPS.  Discussion Note 18

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Re: QUIPS-DIS 16.  http://stderr.org/pipermail/inquiry/2005-May/002681.html
In: QUIPS-DIS.     http://stderr.org/pipermail/inquiry/2005-May/thread.html#2602

JW: Unlike previous examples given in the text cited (4.447),
    pure symbols must incorporate or involve other symbols.

Jim,

No, a symbol may have, and a pure symbol may have,
but none of them need have any such incorporations
or involvements in order to have independent meaning.
It is indeed one of the penetrating powers of Peirce's
pragmatic semiotics to have recognized this possibility.
The settings in which this possibility is best actualized
and becomes most evident are precisely in his two systems
of logical graphs, namely, the entitative graphs that are
partly exposited in his essay on "Qualitative Logic", and
the existential graphs that we have noted here previously.

I hope to get to this, all in good time,
but I will have to pause for the moment.

JW: All the other examples are "dressed".  Unlike common nouns,
    verbs, and the list of symbols that have obvious indices
    or icons, pure symbols are "naked".  They can only "dress"
    themselves by being incorporated into a more complex symbol.
    By analogy (as you say imperfect), much like the factoring
    of the number 7, a pure symbol is trivial ("naked") until
    combined with arithmetic operations.  But it is no more
    or less trivial than any other number (except zero) when
    generated inductively by the number axioms.  Thus, I see
    pure symbols as context-free when treated in isolation.
    Didn't the Medievals straghten some of this out when
    they spoke of syncategorematic expressions?

My unrefreshed consciousness blurs at the first part of this paragraph,
but the fact that the "syncat dodge" was mostly resorted to by medieval
nominalists should also give you pause at this point.  At any rate, it
was definitely not Peirce's main way of interpreting logical operators.

Jon Awbrey

Incidental Musement:

Cosma's Notebook, "Semiotics" (and Syncategores)
http://cscs.umich.edu/~crshalizi/notebooks/semiotics.html

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