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

[Jon Awbrey]

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FOLG.  Discussion Note 8

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JA = Jon Awbrey
JR = Joe Ransdell

Re: FOLG-DIS 7.  http://stderr.org/pipermail/inquiry/2005-October/003143.html
In: FOLG-DIS.    http://stderr.org/pipermail/inquiry/2005-October/thread.html#3135

Joe, Peirce List,

JR: But can that reasonably be supposed to be, implicitly, Peirce's view?
    I think not so I began by pointing out that the difference between
    his Existental Graphs and his earlier Entitative Graphs was not
    simply a matter of interchanging T's for F's and conversely in
    the interpretation of it but entailed rather a fundamental
    difference in the conception of the sheet of assertion and
    the corresponding function of the universe of discourse.
    I do not see how that allows any logical room for the
    more abstract level of the "pure" symbol you seem to
    want to posit, which would be represented in your 
    formalism of "rooted trees, well-formed strings of
    parentheses, or finite sets of non-intersecting
    simple closed curves in the plane".

JR: And I pointed out that Peirce himself did not seem to regard the
    Sheet of Assertion as you do, as a "tabula rasa" of complete
    indeterminacy, as you characterized it, but rather as itself
    a graph, and hence as a symbol in the same sense in which
    a symbol inscribed upon it is a symbol, i.e. there is no
    implicit recognition on his part of a pure symbolism
    which your notation is supposed to represent:
    Existential Graphs and Entitative Graphs are
    not alternative special interpretations of
    a more abstract logical formalism.

I consider Peirce's work on logical graphs within the full context of his
work on logic in general, as many of his later ideas are already marked
in the earliest and middle papers.  Some of us have also been working
through the "Utter Indetermination" theme in the "New Elements", and
almost everything you say about that is contradicted by what Peirce
says there.  No doubt we'll have opportunuities to go through all
of this again sometime, but for now I must get on to new fields.

I fear that your predisposition to gloss over certain themes in
Peirce's work has perhaps prevented you from paying close enough
attention to all of the reading and discussion that we undertook
in regard to the "Amphecks", the "Kaina Stoicheia"/"New Elements",
and the "Qualitative Logic" texts.  Just by way of a random sample:

| For an algebra is a language with a code of formal rules
| for the transformation of expressions, by which we are
| enabled to draw conclusions without the trouble of
| attending to the meaning of the language we use.
|
| C.S. Peirce, "Qualitative Logic", NEM 4, 107
|
| C.S. Peirce, "Qualitative Logic", MS 736, pp. 101-115 in:
| Carolyn Eisele (ed.), 'The New Elements of Mathematics by
| Charles S. Peirce, Volume 4, Mathematical Philosophy',
| Mouton, The Hague, 1976.
|
| Cf. C.S. Peirce, "Qualitative Logic", MS 582 (Fall-Winter 1886), pp. 323-371 in:
|'Writings of Charles S. Peirce:  A Chronological Edition, Volume 5, 1884-1886',
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1993.

Boole, De Morgan, Hamilton, Peirce, and their ilk all understood
the uses of "uninterpreted formal operations" (UFO's).  Early in
the 20th century, of course, the usual suspects distortured this
into the usual cliches about "meaningless ideal symbols" (MIS's),
utterly obscuring the fact that UFO's are excessively meaningful
symbols, subject to a veritable plethora of interpretations, and
nothing at all like deficiently meaningless symbols.  But before
that came to pass, the themes of duality, formal symmetry, along
with the uses of operator variables, were standard tools of 19th
century mathematics, from projective geometry, group theory, and
linear algebra, to that 19th century specialty, invariant theory.

In "The Simplest Mathematics", that I did my senior thesis on in
1976, Peirce systematically explored these notions, going so far
as contemplating what would be the formal consequences of taking
the blank connective or the unmarked operation of application to
represent any one of the sixteen possible dyadic truth functions.
As a simple example of this, recall that Peirce's 1880 "Ampheck"
paper employs a convention that the simple co-inscription of two
proposition letters symbolizes that both propositions are denied.

All of these ideas went into his late work on logical graphs,
and all of them represent important insights that are not to
be obliterated by anything written there.  It is the natural
course, if only for the sake of exposition, to adopt a fixed
interpretation of logical symbols, but the important idea in
all of this work is that the interpretation of symbols takes
place over many stages.

Jon Awbrey

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