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PEIRCE-L Digest 1291-- February 9-10, 1998
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From PEIRCE-L Forum, Jan 5, 1998, [name of author of message],
"re: Peirce on Teleology"
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Topics covered in this issue include:
1) Re: What is number?
by alan_manning[…]byu.edu (Alan Manning)
2) Re: What is zero? What is number?
by Benoit Favreault
3) Re: Hypostatic Symbols
by Thomas.Riese[…]t-online.de (Thomas Riese)
4) centennial
by "a. reynolds"
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Date: Mon, 09 Feb 1998 15:38:54 -0700
From: alan_manning[…]byu.edu (Alan Manning)
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: What is number?
Message-ID:
I see that George Stickel is one of that relatively small group of people
who really do believe (with Peirce) that thought exists outside human
minds. George writes
>Before human language and community no symbols for the
>numbers existed...But as soon as physical laws became habits, those
>numerical relations were arguments for inertia, gravity, and a host of other
>laws that we take for granted. In this sense the numerical concepts were
>argument within the mind of the universe.
Being attracted by the hypothesis of universal mind myself, I want to go
right along with nearly all that George has said, except that I must stress
that I've been implicitly assuming a subtle but critical distinction in
discussions of number that I don't see George making here. This subtle but
critical distinction is probably causing our inability (so far) to converge
our opinions on this issue. Thus I'd like to make clear and then continue
to insist upon a distinction between _numerical relations themselves_ and
whatever means we might use to *represent*, *interpret*, or *investigate*
numerical relations.
So far, I've been trying to talk about _numerical relations themselves_,
the objects of mathematical study, what the numerals in an equation like 2
+ 3 = 5 or 2 - 2 = 0 really represent. Awhile back somebody asked
whether anybody had an opinion about what numbers were, apart from numerals
we represent them with, and my reply in brief was that these objects of
study are, overall, rhematic indexical legisigns, equivalent linguistically
to pointing words like this, that, these, or those: Thus the phrase
_Three bags full_, is somewhat akin structurally and semantically to the
phrase _These bags full_.
Now consider George Stickel's basic objections and my replies:
QUOTE First, as bits of language, [numbers] are indeed symbols. The
mathematical language employs "3," "three," "III," "tres," "drei," or "=,"
with a third line under the last symbol, plus a host of other symbols to
imply a thirdness. If we choose to use any of those markings to
communicate a concept of three, we employ a symbol. ENDQUOTE
RESPONSE: Surely George is here refering NOT to numerical relations
themselves but rather the media, the means, the methods, in sum, the
SYMBOLS that we (or a thinking universe) might use to *represent*,
*interpret*, or *investigate* numerical relations. Surely though, we have
to agree that there is a distinction between a SYMBOL-- a word,
proposition, or argument-- and the thing represented by a symbol, any thing
such as a physical object or a mental image, a sensation or any other
sub-symbolic sign that might be further named by a word. My cat Neptune is
NOT the word CAT. You may know my cat only by my words, but still, the
actual cat is different from the words I use to describe it. So far, I
think George has been talking about symbols representing (or containing)
numbers, but not numerical relations themselves. The actual numerical
relation represented thereby is NOT the same as the numerical symbol "3" or
the numeral word THREE.
QUOTE Additionally, employing such a notion suggests an argument at some
level, or at the very least, it is a proposition, e.g., "Baa Baa Black
Sheep, have you any wool? Yes sir, yes sir, three bags full." The speaker
is able to use the "three" to verify some number of bags of product, but
only because it is
an "association of general ideas" CP 2.249. ENDQUOTE
RESPONSE: Here I'd make the critical, corollary distinction between a
proposition (or argument), and the component sign-types that are used to
build that proposition. Recall that a proposition is (for Peirce) a
"di-cent" sign, meaning that in the form of the sign itself it has two
essential parts, in this case, a predicate such as BAGS FULL, and an
indexical legisign such as _these_, or, in Stickel's example above,
_three_. These indexical words do indeed contribute to the verification
of the proposition, but they do not (in and of themselves) create an
"association of general ideas". The words _these_ and _three_ are not
evocations of general ideas (in the way that BAGS FULL is), but rather
these words are instructions to the interpreter to ACT, to look around for
objects bearing a particular relation to the speaker and predicate
(NEARBY-PLURALIZE in the case of _these_). The word _three_ is likewise
an instruction to act, to indexically connect each instance of BAGS FULL to
a finger, to a mark on a tally sheet, or any other set of things with the
equivalent x-x-x sequence of object-boundaries).
QUOTE But as soon as physical laws became habits, those numerical
relations were arguments for inertia, gravity, and a host of other laws
that we take for granted....So, it seems to me that numbers are symbols.
However, their degenerative forms (such as a rhematical indexical
legisigns) are permissible as the signs are possibilities or existential in
their relation to an intepretant UNQUOTE
RESPONSE: Again, I'm very, very sympathetic to the idea that numerical
relations are not merely artifacts of human minds, but are inherent in the
real universe and indeed are the product of "thought" or in other words an
evolutionary process exactly analogous to argumentation in and between
human minds. But even so, I have to insist on the distinction between
argument and any component evidence or result of that argument. Any
argument contains (minimally) three propositions, two of evidence and one
of conclusion, but no proposition is by itself an argument. Some argument
may contain or refer to or draw a conclusion about numbers, but it by no
means follows that a number is therefore itself an argument.
Rather, numerical relations in and of themselves are inherently indexical
rather than symbolic. I mean this only in that way that Peirce meant it.
_Indexical_ means that the relation of numbers to objects (whether those
objects be physical things or other numbers) is a matter of action rather
than a matter of habitual generalization (as the _symbol_ CAT is related to
the set of cats by habitual generalization). One proof of this is that
mechanical computers can work with numbers effectively, but no automatic
mechanism to date has been demonstrated to effectively interpret the
conceptual meaning of a word, proposition, or argument in the fullest,
Peircean sense of *interpret* (=dialogue in evolutionary fashion). Some
computational linguists are still trying to reduce genuinely symbolic
language to merely indexical mathematics, but the Peircean analysis
suggests that this project must fail.
And so, I say again that _numerical relations in and of themselves_ are
indexical legisigns. As legisigns, numbers themselves are interpreted by
habit-of-action, but as indices they are connected to objects by action per
se, both in human minds and universal mind. Indexical numerical relations
are not degenerate forms of some higher, symbolic form of "number."
Rhematic Indexical Legisigns (1-2-3) only can "degenerate" from Dicent
Indexical Legisigns (2-2-3, e.g. a action-oriented social signal like a red
light at an intersection, or a coach's signal to a batter to bunt). They
bear no direct (de)generative relationship to symbols in the Peircean
Ten-class system. Development goes in the other direction: Human beings
(and even perhaps universal mind), by evolutionary, hypostatic abstraction,
may develop symbolic predicates, propositions, and arguments *about*
numerical relations, but these signs are of a fundamentally different (and
more advanced) type than numerical relations themselves. The word CAT is
more than my actual cat every could be, but on the other hand, my actual
cat is NOT a degenerate form of the human word.
Alan Manning
------------------------------
Date: Tue, 10 Feb 1998 00:26:48 -0500
From: Benoit Favreault
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: What is zero? What is number?
Message-ID: <34DFE518.25E05695[…]microtec.net>
Cathy Legg
wrote:
> However, I suspect that there is no one answer to this question, but it
> rather depends in what light we are regarding numbers, and to what end.
> (The categories being not things, properties of things, or parts of things,
> but modes of being, as is currently being discussed in another thread.)
>
"Modes of
being" is
a
confusing
expression,
as I
remember
the thread
you refer
to, it as
to be
taken as
"mode of
predication"
("mode de
prédication"
comme nous
l'avait
rappelé M.
Balat). By
the way
this is a
cardinal
idea of
the "New
List..."
(slow
readers
will have
to "fast
forward"
to the 4th
par.)
For the
possibility
for
numbers to
"express"
continuity
I would
suggest
that, for
exemple,
the set(I
insist:
the set)
of Real
numbers is
not a
continuum
(because,
as you
say,
numbers
are points
or
haecceities
which
interrupt
the
continuity)
but could
be
consider
as an Icon
of
continuity.
Wich
simply
means it
can lead
you to the
idea of
continuity
(or, in a
wittgensteinian
way: that
continuity
shows
itself
throught
it)(cf. CP
2.278).
Best...
Benoit
Favreault
Programme
de
doctorat
en
semiologie
Universite
du Quebec
a Montreal
------------------------------
Date: Tue, 10 Feb 1998 12:31:28 +0100
From: Thomas.Riese[…]t-online.de (Thomas Riese)
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: Hypostatic Symbols
Message-ID:
Cathy, you wrote:
> On Fri, 6 Feb 1998 Bill Everdell wrote (slightly subversively):
>
> > To which I cannot resist appending the poem by Hughes Mearns which
> > illustrates so many of my classes and sums up so much of ontology for me:
> >
> > As I was sitting in my chair
> > I knew the bottom wasn't there
> > Nor legs nor back; but I just sat
> > Ignoring little things like that
>
> - which moves me to add a poem by a gifted poet from my hometown of
> Melbourne which expresses a very similar idea:
>
> "Come sit down beside me", I said to myself,
> And although it doesn't make sense,
> I held my own hand in a small sign of trust,
> And together I sat on the fence.
> (Michael Leunig, a classic work from the mid-'80s).
>
> Now *that's* bootstrapping.
Hey Cathy, I didn't guess that this is a subversive hint of your
birthday:-) (I had to think a lot about it:-))
Congratulations!!
Thomas.
------------------------------
Date: Tue, 10 Feb 1998 10:48:29 -0500 (EST)
From: "a. reynolds"
To: peirce-list
Subject: centennial
Message-ID:
Just thought that I would remind people that it was one hundred years ago
today that CSP began his Cambridge lectures titled "Reasoning and the
Logic of Things." These are great lectures, but has anyone else noticed
that within them Peirce has dropped all talk of the `law of mind' and
instead refers to `non-conservative actions.' Does any one know if the
phrase `law of mind' ever recurs again in his writing after the 1893
Monist series?
Andrew
*******************************
Andrew Reynolds
Dept. of Philosophy
University of Western Ontario
London, Ontario
http://publish.uwo.ca/~areynold/
*******************************
------------------------------
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