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

[Jon Awbrey]

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QUIPS.  Discussion Note 16

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JW = Jim Willgoose

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

JW: I think I understand what you are saying (but do not understand
    how the simple/complex distinction comes about in your post).
    By analogy with prime numbers, a pure symbol has only trivial
    factors involved with it (much as "7" can only be divided by
    itself ) as opposed to those symbols which may incorporate
    icons and indices.  Peirce does say "may be interpreted"
    a lot ("Logical Tracts" #2).

Jim,

An artifically simplified problem can hardly be perfect,
that is, cannot have all the features of the problem that
we are really interested in, or else it wouldn't be simpler.
As you observe, we are reasoning by analogy, that is to say,
iconically, and analogies that are not exact isomorphisms are
always partial representations, and they always break if we
push them too far.  There's more than one lesson in that.
For the moment, though, the imperfect analogue will have
served a sufficient purpose if it helps us to separate,
at least in our minds, the original/replica dimension
from the measures of complication, incorporation,
involvement, or whatever word proves most fit,
that we find across the spectrum of symbols.

JW: But then, a pure symbol would appear incapable of interpretation.

Let us examine that.  Peirce does not speak of "meaningless symbols"
as if it were an automatic tautology, and when taxonomenclates the
species of "nonsense", in that imperturbably classifying way of his,
he counts the ways that an imputed symbol can fail to be a symbol.
So if he said, as he did, that words like "and", "or", "of", etc.
are symbols, then he must have been thinking of a selection of
in the light of some canonical interpretation.  If we have some
difficulty with clarifying the meaning of the intended symbols,
then there is a habit that ought to come into play about here,
and that would be the light bulb in the brain that is commonly
known as the pragmatic maxim.

As it happens -- as it almost always happens -- Peirce has done
the homework before assigning it to us, and it was one of my
own earliest adventures in Peirceland to retrace the places
where he explores the various way of providing pragmatic
meanings to the symbols for basic logical operations.
The transcription of those fragments that appear in
the CP gets the prize for the worst mangling of
an original screenplay, but I believe that
Shea Zellweger has since replicated the
original texts somewhere, so maybe I
can look for those.

In the meantime, let's hobble along with the
suggested anlogy to the signs of operations
in natural number arithmetic.

JW: Peirce says they are neither indicative nor iconic and not that
    they may be indicative and/or iconic.  Pure symbols are neither.
    On the other hand, if the suggestion is that n-tuples are the
    formal objects, then how can the symbol be pure?

The suggestion so far is only that certain 3-adic relations
give us 'a' denotation for the symbols in question, that is,
a logical model or an informationally-equivalent object --
whether there can be any such thing as 'the' denotation
is another whole kettle of monkeys.

The fact that the target 3-adic relations are sets of 3-tuples,
and thus are aggregates of their elementary relations, does not
mean that the relations "decompose" in the sense that bears on
their non-incorporate non-involuted status here.  Very roughly
resorting to the analogy again, if I say that 7 is not a prime
because it factors into the sum 1+1+1+1+1+1+1, that is clearly
a misunderstanding of the words "prime" and "factor" as they
are defined in this context.

Exploring this suggestion will give us some experience
with the idea that 3-adic relations can be irreducible
or reducible in several different senses, but there is
yet another reservation about the proceedings so far
that will have to be addressed.  To wit, providing
a logical symbol with a denotative object in the
form of a specific 3-adic relation is not yet
the same thing as reconstructing a suitable
3-adic sign relation in which that symbol
can be said to perform the duties of its
symbolic office.

So that will take a little more work.

JW: Even so, what are the trivial factors involved that are neither
    indicative nor iconic?  (I grant that the type/replica distinction
    does not work well.)  It seems as if you understand a definite context
    is indicated by the pure symbol and that definite context is necessary.
    Does that explain why it is trivial?  (trivial because essential?!)
    I read Peirce as saying that a pure symbol is context-free.
    (especially in contrast to the examples he gives previous
    to "and"/"or."

I didn't quite get what you were asking here.
How do you see the relation of context to
the incorpoartion/involvement question?

Jon Awbrey

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