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

Jon Awbrey jawbrey at att.net
Sun May 22 22:16:27 CDT 2005 

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QUIPS.  Discussion Note 31

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JA = Jon Awbrey
KM = Kirsti Määttänen

Re: QUIPS-DIS 26.  http://stderr.org/pipermail/inquiry/2005-May/002692.html
In: QUIPS-DIS.     http://stderr.org/pipermail/inquiry/2005-May/thread.html#2602

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. 

KM: 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.

KM: 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.

JA: 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.

JA: I'm glad that your lack of telepathic powers
    is limited solely to the contents of my mind.

KM: Hah! -- Perhaps better put it this way:  with your telegraphy in
    this issue I have quite often felt a pressing NEED of possessing
    telepathic powers.  Whilst with CP 4.447 no such pressure arises.
    Which, of course, is not to claim that I understand it something
    like fully or anything like that.

JA: 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: Well, then I most certainly am not one the 'most readers'.
    But if the message is loud and clear, why not provide the
    quotes where the message is explicated?

By way of introduction to Peirce's logical work,
I can recommend no better introduction than his
"Logic of Relatives" of 1870, early sections of
which, along with my comments, are copied here:

LOR.  Logic Of Relatives

00.  http://stderr.org/pipermail/inquiry/2004-November/thread.html#1750
01.  http://stderr.org/pipermail/inquiry/2004-November/001750.html
02.  http://stderr.org/pipermail/inquiry/2004-November/001751.html
03.  http://stderr.org/pipermail/inquiry/2004-November/001752.html
04.  http://stderr.org/pipermail/inquiry/2004-November/001753.html
05.  http://stderr.org/pipermail/inquiry/2004-November/001754.html
06.  http://stderr.org/pipermail/inquiry/2004-November/001760.html
07.  http://stderr.org/pipermail/inquiry/2004-November/001769.html
08.  http://stderr.org/pipermail/inquiry/2004-November/001774.html
09.  http://stderr.org/pipermail/inquiry/2004-November/001783.html
10.  http://stderr.org/pipermail/inquiry/2004-November/001794.html
11.  http://stderr.org/pipermail/inquiry/2004-November/001812.html
12.  http://stderr.org/pipermail/inquiry/2004-November/001842.html

LOR-COM.  Logic Of Relatives -- Commentary

00.     http://stderr.org/pipermail/inquiry/2004-November/thread.html#1755
01.     http://stderr.org/pipermail/inquiry/2004-November/001755.html
02.     http://stderr.org/pipermail/inquiry/2004-November/001756.html
03.     http://stderr.org/pipermail/inquiry/2004-November/001757.html
04.     http://stderr.org/pipermail/inquiry/2004-November/001758.html
05.     http://stderr.org/pipermail/inquiry/2004-November/001759.html
06.     http://stderr.org/pipermail/inquiry/2004-November/001761.html
07.     http://stderr.org/pipermail/inquiry/2004-November/001770.html
08.1.   http://stderr.org/pipermail/inquiry/2004-November/001775.html
08.2.   http://stderr.org/pipermail/inquiry/2004-November/001776.html
08.3.   http://stderr.org/pipermail/inquiry/2004-November/001777.html
08.4.   http://stderr.org/pipermail/inquiry/2004-November/001778.html
08.5.   http://stderr.org/pipermail/inquiry/2004-November/001781.html
08.6.   http://stderr.org/pipermail/inquiry/2004-November/001782.html
09.1.   http://stderr.org/pipermail/inquiry/2004-November/001787.html
09.2.   http://stderr.org/pipermail/inquiry/2004-November/001788.html
09.3.   http://stderr.org/pipermail/inquiry/2004-November/001789.html
09.4.   http://stderr.org/pipermail/inquiry/2004-November/001790.html
09.5.   http://stderr.org/pipermail/inquiry/2004-November/001791.html
09.6.   http://stderr.org/pipermail/inquiry/2004-November/001792.html
09.7.   http://stderr.org/pipermail/inquiry/2004-November/001793.html
10.01.  http://stderr.org/pipermail/inquiry/2004-November/001795.html
10.02.  http://stderr.org/pipermail/inquiry/2004-November/001796.html
10.03.  http://stderr.org/pipermail/inquiry/2004-November/001797.html
10.04.  http://stderr.org/pipermail/inquiry/2004-November/001798.html
10.05.  http://stderr.org/pipermail/inquiry/2004-November/001799.html
10.06.  http://stderr.org/pipermail/inquiry/2004-November/001800.html
10.07.  http://stderr.org/pipermail/inquiry/2004-November/001801.html
10.08.  http://stderr.org/pipermail/inquiry/2004-November/001802.html
10.09.  http://stderr.org/pipermail/inquiry/2004-November/001803.html
10.10.  http://stderr.org/pipermail/inquiry/2004-November/001804.html
10.11.  http://stderr.org/pipermail/inquiry/2004-November/001805.html
11.01.  http://stderr.org/pipermail/inquiry/2004-November/001813.html
11.02.  http://stderr.org/pipermail/inquiry/2004-November/001814.html
11.03.  http://stderr.org/pipermail/inquiry/2004-November/001815.html
11.04.  http://stderr.org/pipermail/inquiry/2004-November/001816.html
11.05.  http://stderr.org/pipermail/inquiry/2004-November/001817.html
11.06.  http://stderr.org/pipermail/inquiry/2004-November/001818.html
11.07.  http://stderr.org/pipermail/inquiry/2004-November/001819.html
11.08.  http://stderr.org/pipermail/inquiry/2004-November/001820.html
11.09.  http://stderr.org/pipermail/inquiry/2004-November/001821.html
11.10.  http://stderr.org/pipermail/inquiry/2004-November/001822.html
11.11.  http://stderr.org/pipermail/inquiry/2004-November/001823.html
11.12.  http://stderr.org/pipermail/inquiry/2004-November/001824.html
11.13.  http://stderr.org/pipermail/inquiry/2004-November/001825.html
11.14.  http://stderr.org/pipermail/inquiry/2004-November/001826.html
11.15.  http://stderr.org/pipermail/inquiry/2004-November/001827.html
11.16.  http://stderr.org/pipermail/inquiry/2004-November/001828.html
11.17.  http://stderr.org/pipermail/inquiry/2004-November/001829.html
11.18.  http://stderr.org/pipermail/inquiry/2004-November/001830.html
11.19.  http://stderr.org/pipermail/inquiry/2004-November/001831.html
11.20.  http://stderr.org/pipermail/inquiry/2004-November/001832.html
11.21.  http://stderr.org/pipermail/inquiry/2004-November/001833.html
11.22.  http://stderr.org/pipermail/inquiry/2004-November/001834.html
11.23.  http://stderr.org/pipermail/inquiry/2004-November/001835.html
11.24.  http://stderr.org/pipermail/inquiry/2004-November/001836.html
12.     http://stderr.org/pipermail/inquiry/2004-November/001843.html

I would be pleased to discuss this material
with you if you have any questions about it.

Jon Awbrey

Incidental Musement:

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

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