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

Wed May 18 08:16:45 CDT 2005

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QUIPS.  Discussion Note 22

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JP = Jim Piat

Re: QUIPS-DIS 21.  http://stderr.org/pipermail/inquiry/2005-May/002687.html
In: QUIPS-DIS.     http://stderr.org/pipermail/inquiry/2005-May/thread.html#2602

Jim,

I attempt to correct a myriad of typos and other infelicities,
hopefully without introducing too many more, and continue.

JP: Seems to me a symbol rooted in neither a material icon,
    index, or community habit of use is pure indeed!  That's
    a plane of existence -- principles built of airy nothings --
    I can not conceive.  To me interpreting the expression
    "pure symbol" in this fashion would be an example of
    the logical absurdity of taking things to extremes --
    such as trying to remove the body from mind or vice versa.
    Genuine triads, no matter how pure of body and mind, do at
    least in principle still incorporate monads and dyads do they
    not (and not merely as a matter of imputation).  I contend that
    it is the fact that symbols do in principle contain reference to
    qualities and correlates which necessitates the imputation of these
    functions when one actually uses symbols devoid of material reminders
    or vestiges of such functions.

JP: But I can't shake the thought that I am still missing your point
    so I don't mean all this so much as a statement of my position
    for the sake of convincing you, but more for the purpose of
    explaining where I'm coming from so that you might better
    be able to show me the error of my ways in terms of the
    point you are trying to make and I'm failing to grasp.

Old, but amended, business:

Among the standard ways of gaining experience
in a novel domain there are these two methods:

   1.  Keep going back to the relevant definitions and/or axioms,
       if you are lucky enough to have any, and try to see what
       you can prove solely from the information given in them.
       This doesn't mean that you close your mind's eyes to the
       hints that come from the admittedly imperfect intuition,
       but you cannot take what that inner voice tells you for
       any brand of established truth.

   2.  Try to construct lots of examples that satisfy the
       definitions and/or axioms, not being afraid to start
       with the simplest constructions that you can arrange,
       and study them for whatever clues to the domain of
       interest that they can provide.

Method 1 would begin by returning to a truly adequate definition like this:

| On the Definition of Logic [Version 1]
|
| Logic will here be defined as 'formal semiotic'.
| A definition of a sign will be given which no more
| refers to human thought than does the definition
| of a line as the place which a particle occupies,
| part by part, during a lapse of time.  Namely,
| a sign is something, 'A', which brings something,
| 'B', its 'interpretant' sign determined or created
| by it, into the same sort of correspondence with
| something, 'C', its 'object', as that in which it
| itself stands to 'C'.  It is from this definition,
| together with a definition of "formal", that I
| deduce mathematically the principles of logic.
| I also make a historical review of all the
| definitions and conceptions of logic, and show,
| not merely that my definition is no novelty, but
| that my non-psychological conception of logic has
| 'virtually' been quite generally held, though not
| generally recognized.  (CSP, NEM 4, 20-21).
|
| On the Definition of Logic [Version 2]
|
| Logic is 'formal semiotic'.  A sign is something,
| 'A', which brings something, 'B', its 'interpretant'
| sign, determined or created by it, into the same
| sort of correspondence (or a lower implied sort)
| with something, 'C', its 'object', as that in
| which itself stands to 'C'.  This definition no
| more involves any reference to human thought than
| does the definition of a line as the place within
| which a particle lies during a lapse of time.
| It is from this definition that I deduce the
| principles of logic by mathematical reasoning,
| and by mathematical reasoning that, I aver, will
| support criticism of Weierstrassian severity, and
| that is perfectly evident.  The word "formal" in
| the definition is also defined.  (CSP, NEM 4, 54).
|
| C.S. Peirce, [Parts of Carnegie Application], L75 (15 Jul 1902), pp. 13-73 in:
| Carolyn Eisele (ed.), 'The New Elements of Mathematics by Charles S. Peirce,
| Volume 4, Mathematical Philosophy', Mouton, The Hague, 1976.
|
| http://members.door.net/arisbe/menu/library/bycsp/l75/l75.htm

Method 2 would start from the same sort of definition, but would
then resort to a more constructive, less deductive way of working.
We might try to see if we could construct simple examples of iconic,
indexical, and purely symbolic sign relations.  If it's not possible
to have such a thing as the last example, as some people claim, then
we ought to be able to see why in the unsuccess of the quest for one.
At any rate, we will usually clarify our conception of the domain in
the process of working through the issues that arise along the way.

New business:

Until a decade ago, when one of my engineering advisors insisted
that I follow the maxim of "Keep It Concrete And Simple" (KICAS),
and come up with the simplest, concrete, non-trivial examples of
sign relations that I could find, I had only considered examples
that arise in logic, which generally have infinite sign domains.

The two examples of finite sign relations that I first came up with
involved a situation that would commonly be thought of as involving
"indexical signs", though it may take some work to clarify how this
relates to Peirce's ideas of indices and indexical signs.  Voi L(A):

Table 1.  Sign Relation L(A) of Interpreter A
o---------------o---------------o---------------o
| Object` ` ` ` | Sign` ` ` ` ` | Interpretant` |
o---------------o---------------o---------------o
| A ` ` ` ` ` ` | "A" ` ` ` ` ` | "A" ` ` ` ` ` |
| A ` ` ` ` ` ` | "A" ` ` ` ` ` | "i" ` ` ` ` ` |
| A ` ` ` ` ` ` | "i" ` ` ` ` ` | "A" ` ` ` ` ` |
| A ` ` ` ` ` ` | "i" ` ` ` ` ` | "i" ` ` ` ` ` |
| B ` ` ` ` ` ` | "B" ` ` ` ` ` | "B" ` ` ` ` ` |
| B ` ` ` ` ` ` | "B" ` ` ` ` ` | "u" ` ` ` ` ` |
| B ` ` ` ` ` ` | "u" ` ` ` ` ` | "B" ` ` ` ` ` |
| B ` ` ` ` ` ` | "u" ` ` ` ` ` | "u" ` ` ` ` ` |
o---------------o---------------o---------------o

Table 2.  Sign Relation L(B) of Interpreter B
o---------------o---------------o---------------o
| Object` ` ` ` | Sign` ` ` ` ` | Interpretant` |
o---------------o---------------o---------------o
| A ` ` ` ` ` ` | "A" ` ` ` ` ` | "A" ` ` ` ` ` |
| A ` ` ` ` ` ` | "A" ` ` ` ` ` | "u" ` ` ` ` ` |
| A ` ` ` ` ` ` | "u" ` ` ` ` ` | "A" ` ` ` ` ` |
| A ` ` ` ` ` ` | "u" ` ` ` ` ` | "u" ` ` ` ` ` |
| B ` ` ` ` ` ` | "B" ` ` ` ` ` | "B" ` ` ` ` ` |
| B ` ` ` ` ` ` | "B" ` ` ` ` ` | "i" ` ` ` ` ` |
| B ` ` ` ` ` ` | "i" ` ` ` ` ` | "B" ` ` ` ` ` |
| B ` ` ` ` ` ` | "i" ` ` ` ` ` | "i" ` ` ` ` ` |
o---------------o---------------o---------------o

The "i" is a nickname for the pronoun "I" and
the "u" is a nickname for the pronoun "you".

To write these in the "sets as sums" way
that Peirce often wrote k-adic relations:

L(A) = A:"A":"A" + A:"A":"i" + A:"i":"A" + A:"i":"i" +
       B:"B":"B" + B:"B":"u" + B:"u":"B" + B:"u":"u"

L(B) = A:"A":"A" + A:"A":"u" + A:"u":"A" + A:"u":"u" +
       B:"B":"B" + B:"B":"i" + B:"i":"B" + B:"i":"i"

Okay, for now, I need to go plop my mind's eyes in a glass of cold water.

Jon Awbrey

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