[Inquiry] Re: Futures Of Logical Graphs -- Discussion

[Jon Awbrey]

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FOLG.  Discussion Note 2

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JA = Jon Awbrey
JR = Joe Ransdell

Re: FOLG-DIS 1.  http://stderr.org/pipermail/inquiry/2005-October/003135.html
In: FOLG-DIS.    http://stderr.org/pipermail/inquiry/2005-October/thread.html#3135

Joe, Peirce List,

I tried to follow the line of reasoning in the following series of statements,
but couldn't quite figure out what you were actually saying and what you were
just assuming in passing.

JR: I suspect that you are right, Jon, in suggesting -- as you seem to be doing --
    that your proposal to replace the concern to understand the philosophical
    implications and use in practice of Peirce's graphical logic (Existential
    Graphs) with your "rooted trees, well-formed strings of parentheses, or
    finite sets of non-intersecting simple closed curves in the plane" will
    not prove to be sufficiently "exciting" to have much future unless you
    show some reason for doing so beyond anything you have shown thus far.

On second reading, I see that there is something about
a "proposal to replace the concern ..." that is being
attributed to me.  Any such proposal is news to me.

JR: Certainly, if it comes to nothing more than enabling you to shore up
    the feeble case you make for your conception of the "pure symbol" as
    an interpretation of what Peirce might mean by that, you shouldn't
    expect people to pay much attention to it.

Apparently the "it" in the antecedent of this contingent proposition
refers to the supposed proposal of the previous segment, to which is
is attached a supposed use for the supposed proposal, the consequent
of all this being that I ought to diminish my expectation of anybody
paying attention to the supposed proposal that I supposedly proposed.

I suppose ...

I just can't figure out what that has to do with what I said.

As far as what Peirce meant by the phrase "pure symbol",
he apparently meant "neither 'iconic' nor 'indicative',
like the words 'and', 'or', 'of', etc."  I believe that
a study of how Peirce regarded such logical symbols is
pertinent to figuring out what he meant in saying this,
and the study of formal systems that Peirce formulated
to define the meanings of such symbols, for instance,
the axiom systems based on the amphecks, along with
the two systems of logical graphs, is a material
part of that inquiry.

Peirce was well aware of the property of duality, deliberately
giving axioms that made it manifest, and he knew, most likely
from the analogous cases in algebra and geometry, exactly what
this implied about the lack of fixity in the meanings defined,
as his explorations of "operator variables" additionally shows.

These details are important because they bear on what a symbol is,
how a symbol works itself into fabric of interpretation, and what
the role of symbols in logic is.  I suspect there is some measure
of philosophical interest in these questions.

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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