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

[Jon Awbrey]

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QUIPS.  Discussion Note 26

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JA = Jon Awbrey
JW = Jim Willgoose
KM = Kirsti Määttänen

Re: QUIPS-DIS 15.  http://stderr.org/pipermail/inquiry/2005-May/002680.html
In: QUIPS-DIS.     http://stderr.org/pipermail/inquiry/2005-May/thread.html#2602

KM: When I first posed the question:

KM: How does "of" (Peirce's example of a pure symbol)
    bear information about an object?  What kind of
    an object would it be? 

KM: to Jon, I imagined it to be an unanswerable question.
    And and that an attempt to answer this question would
    make it clear that it is so.  What I had in mind then,
    was something in line with what Jim Willgoose brought up: 

JW: a sign's relation to itself makes
    no reference to a sign's relation
    to an object 

KM: To my surprise Jon did construe an object,
    but I could not make head or tail of it.
    So, being unable to follow Jon's line of
    thought, I decided to see whether I could
    follow that of Peirce's, in the context in
    question, CP 4.447.  No problem with that. 

KM: Now Jon wrote: 

JA: That is what the "pure original"/"base replica" distinction
    is all about, and it's never been what I was talking about
    in this matter, nor is it what Peirce is talking about in
    CP 4.447. 

KM: I won't argue the least with Jon's claims on what he has
    been having in mind.  But then I don't know who has been
    talking about "pure original/"base replica" distinction.

Kirsti,

The conglomeration "pure original/"base replica" is of course
a portmanteau cobbled together by way of collecting the many
connotations that various folks have loaded onto my original
question, and since I never saw the relevance of this line
of interpretation, I'm merely collecting its accoutrements
without quite gathering what is in their minds, either.
In the immediate number/numeral context I did toss in
the pun "base" as a way of alluding to the fact that
numerals are dependent on a base of representation
that does not affect the numbers themselves.

KM: Definitely not me.  What I was talking about in my response
    was the mode of being of pure symbols, which was the question
    Peirce was talking about in CP 4.447.  Which, in turn, lead into
    the question of the nature of the relation between a habit and an
    instant, and/or a conventional sign and a replica.  Which does not,
    to my mind, come down simply as "pure original"/"base replica"
    distinction.  Too much is left out here, for the alleged sake
    of simplicity, I guess.

Which is precisely my point.  Again, I think that there was a fairly clear
sense of the word "pure" that Peirce was using in the term "pure symbol",
as he used it in this context.  I have since subscrbed it as "pure_sym"
to distinguish it from the host of other senses that have since been
nominated as candidates for the canonical interpretation.  At last
count, we had at least these:

   1.  Pure_Sym => unincorporated, uninvoluted

   2.  Pure_Sec => second intentional something or other

   3.  Pure_Syn => syncategorematic symbol

   4.  Pure_Oid => original versus replica

   5.  Pure_Iso => isolated

   6.  Pure_99.44% => pure soap

As an interpretation of what Peirce is saying at CP 4.447,
I can only speak for the first of this slate of candidates.

KM: There seems to be a confusing crossing of (at least)
    two lines of discussion here.  One of them (the earlier
    one, with Jon, Joe, and Gary) was on the question whether
    there are pure symbols.  Now this is a question presupposing
    a yes/no answer.  Before proceeding to offer an answer to the
    question, it must be assured that the question is understood
    well-enough.  What this line of proceeding brought up, was
    that the question must be made more definite, that is it
    must be decided whether it is understood as a question
    concerning being, or a question concerning existence. 

KM: Peirce is quite clear with this in CP 4.447. 

CSP: | a conventional sign is neither a mass of ink on
     | a piece of paper or any other individual existence,
     | nor is it an image present to consciousness, but is
     | a special habit or rule of interpretation and consists
     | precisely in the fact that certain sorts of ink spots --
     | which I call its replicas -- will have certain effects
     | on the conduct, mental and bodily, of the interpreter.

KM: I can see no real disagreement about this amongst the discussants. --
    But the attempt to construe an object of a pure symbol proceeds from
    a different kind of question, a question taking (provisionally) for
    granted that there are pure symbols.  And asking:  If there are pure
    symbols, of the kind Peirce gives three examples in CP 4.447. 

It is with this question that Jon suggests that: 

JA: Instead of thinking about any and all symbols, then, let us think 
    about numerals, the symbols that denote numbers. For simplicity 
    let us think about the natural numbers: N = {0, 1, 2, 3, ...}. 
    Instead of the symbols "and", "or", "of", let us think about 
    the various symbols for multiplication, addition, involution 
    on the natural numbers N. In this Ascii text, these would 
    be the symbols "*", "+", "^", respectively.

This part of the discussion was an attempt to clarify the
distinction between pure_sym and pure_oid by reverting to
a simpler seeting where similar dimensions come into play.

KM: And proceeds to construe objects of these kinds of
    pure symbols, ending up with suggesting that we then: 

JA: ... try to look [CP 4.447] with fresh eyes: 

KM: Not being a mathematician, I cant say whether the following makes sense: 

JA: In this setting we can ask what sorts of objects do the symbols 
    "*", "+", "^" denote, and we get the context-definite answers 
    that they denote particular formal objects that we can think 
    of as 3-adic relations. 

KM: But that much I can say, that this is definitely quite
    far from what Peirce in CP 4.447 had in mind.  Still,
    I find it most enlightening to consider these examples.

I'm glad that your lack of telepathic powers
is limited solely to the contents if my mind.
But when it comes to the more earthly skills
of telegraphy, I think that most readers of
Peirce's logical work would detect that he
signaled his message loud and clear.

KM: It is trivial whether we use "multiplication" and "addition" or "*" and "+".
    What should be asked here, to follow Peirce's line of thought, is:  What is
    the mode of being of multiplication and addition? 

This sounds like a productive (summative?) line of inquiry.

KM: The answer seems to me quite clear:  The mode of being of multiplication
    and addition (etc) is the special rules or habits acting.  That is:  rules
    or habits of acting mentally or mentally AND bodily, i.e. using a paper and
    a pencil -- Which, by the way is the core to clearing up the various confusions
    in mind/body problem. 

KM: What is most essential to the mode of being of mathematics?
    Mathematical objects are definitely not the most essential,
    but the various rules involved in doing mathematics.
    No one becomes a mathematician by reading only, the
    doing part is what makes one a mathematician.  That
    is what makes the conventions (the rules) in the
    tradition embodied habits of individuals, worthy
    to be called mathematicians.

Just so.

KM: If anyone can provide a scan of Escher's picture of a hand drawing a hand
    being drawn by that hand, it would be most illuminating here, I think.

I know the picture:

EDH.  Escher, "Drawing Hands", 1948
EDH.  www.printsplus.biz/online-store/scstore/p-47316.html

KM: I'm aware that the discussion has gone on after the
    mail I'm responding now.  I apologize for not being
    able to keep up with the swift pace of the discussion.

Same here ...

Jon Awbrey

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