PEIRCE-L Digest for Tuesday, November 19, 2002

PEIRCE-L Digest for Tuesday, November 19, 2002.

NOTE: This record of what has been posted to PEIRCE-L
has been nodified by omission of redundant quotations in
the messages. both for legibility and to save space.
-- Joseph Ransdell, PEIRCE-L manager/owner]

1. Call for papers - Pragmatist Epistemology
2. Re: Tone, Token, Type
3. Re: Tone, Token, Type
4. Re: Tone, Token, Type
5. Re: Limited Mark Universes
6. pynchon and peirce
7. Re: Limited Mark Universes
8. Re: Identity and Teridentity: to Bernard
9. Re: Tone, Token, Type

----------------------------------------------------------------------

Subject: Call for papers - Pragmatist Epistemology
From: Pierre Edouard BOUR <Pierre.Edouard.Bour[…]univ-nancy2.fr>
Date: Tue, 19 Nov 2002 14:19:01 +0100
X-Message-Number: 1

<html>
Dear co-listers, 
 
Please find below a call for papers for Philosophi[…] Scienti[…]e, the
Henri Poincar=E9 Archives' electronic journal. Given the theme of this
issue, I think it might be of some interest for some people on the list.
 
Though the annoucement will be made on other discussion lists, I hope
some of you can communicate the information around. That would surely be
consistent with Peirce's claim that science is a collective task.
 
Best regards, 
 
Pierre Edouard BOUR 
<hr>
 
Call for papers : "Pragmatist epistemology" - Philosophi[…]
Scienti[…]e - Volume 2 (2003) 
Like other areas of philosophy,
epistemology is an open field influenced by various philosophical trends.
Scientific developments dating from the
19th
Century, in the natural sciences or the social sciences, as well as in
mathematics and logic, contributed to the emergence of new philosophical
approaches. One example of this may be seen in the crucial role played by
foundational questions about mathematics in phenomenology and analytic
philosophy. Pragmatism, founded in the 1870=92s, is no exception, and this
volume takes for its object the characterization of =93pragmatist
epistemology=94. 
Beginning with Peirce and James, philosophers have claimed to draw
inspiration from pragmatism: for example, the second Wittgenstein, Jaakko
Hintikka, Susan Haack, Hilary Putnam or Karl Otto Apel. But one could
also consider the many opponents  like Russell or Quine  who
have shown the importance of pragmatism in the philosophical discussion
of the sciences. This volume aims at discovering, if not common theses,
at least some kind of a common inspiration, a =93method of thinking=94. The
texts may be structured around the following themes: 
* Traditions, relations, differences 
* Conceptual innovations and interpretations 
* Criticism and controversy 
* Contemporary relevance 
* Prospects 
 
The deadline for text submission is April 15th 2003. For
further information, please refer to the relevant page on the journal=92s
website, at the following address: 
<div align=3D"center"><a=
href=3D"http://philosophiascientiae.free.fr/pepscall.html"=
eudora=3D"autourl">http://philosophiascientiae.free.fr/pepscall.html <br=
>
</a></div>
or contact Pierre Edouard Bour at:
Pierre.Edouard.Bour[…]univ-nancy2.fr 
The Public[…]tions
Electroniques de Philosophi[…] Scienti[…]e, is a free online journal,
edited by the Henri Poincar=E9 Archives (Universit=E9 Nancy 2 - UMR 7117
CNRS), dedicated to history and philosophy of science. For access to the
journal=92s website, see: 
<div align=3D"center"><a=
href=3D"http://philosophiascientiae.free.fr/indexeng.html"=
eudora=3D"autourl">http://philosophiascientiae.free.fr/indexeng.html 
</a></div>
</html>

----------------------------------------------------------------------

Subject: Re: Tone, Token, Type
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Tue, 19 Nov 2002 08:16:14 -0500
X-Message-Number: 2

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

SS: To put the whole story in a nutshell (which necessarily distorts it a bit),
recall that in the history of philosophy, there have been two main contenders
as criteria of identity for existents: essential properties and spatio-temporal
continuity. Peirce's 1870 view clearly falls into the former group, identity of
existents always being in respect of some property. Peirce's later view appears
to fall in the latter group, allowing entities that are completely indiscernable
at one time, even occupying the same space at that time, to be distinct, because
they are in spatio-temporal continuity with entities occupying different places
at another time.

SS: Recall how this discussion of identity started. I said that
I would have expected Peirce to take a "realists" position:

SS: quoting from SS post of 11/9/02, 10:39 AM:

| ... namely, that identity is always in respect to some universal
| or type. For example, a is the same as b with respect to color,
| or size, or personhood (the same "person" as), etc. Then what has
| been called (since Aristotle) "numerical identity" could be regarded
| as a "degenerate" form of relative identity, in which a is the same as b
| in 'every' respect. This would make Leibniz's law of indiscernables true
| for numerical identity but not for identity simpliciter, since a could be
| identical to b in one respect and different in another.

SS: Only I found, on reading Peirce, seemingly conflicted statements that
prevented me from confirming this hypothesis and indeed,prevented me
from forming a clear idea of Peirce's theory of identity.

Seth,

I will continue with the reading from Leibniz, which I began for two reasons:
one, to introduce some of the terminology that Peirce was taking for granted
in his writing about such concepts as "composite", "individual", "primitive",
"simple", and so on; two, in order to give an account of Leibniz's principle
as Leibniz was given to write about it.

As far as what you have been writing on this thread,
I find it at the present time to be incommensurable
with any of the meanings that I know for words like
"identity", "realist", "relative", "degenerate", etc.

So let me ask the following questions:

Why do you call the conflating of identity with similarity a "realist" position?
For that matter, why not call your "relative identity" by the name "similarity"?
The use of "relative" in this way, to refer to a universal or an absolute term,
seems to be just begging for trouble. Moreover, it introduces a confound with
all of the other sorts of relativity that might be involved in predication.

Why do you call "numerical identity" the "degenerate" form of "relative identity",
and why do you call your "relative identity" by the name "identity simpliciter"?

You obviously understand that any statement involving a phrase
like "all predicates", "all properties", or "every respect" is
to be regarded with extreme circumspection. Why can you not
accord to Peirce the right that we all assume for ourselves,
to wit, of having to look at it from many different angles?
As I see it, there is (are?) a host of ambiguities lurking
in all these concepts, one that cannot be addressed short
of saying what one means by "all", "every", "predicate",
"property", and "respect".

If one finds even the simplest question, for instance,
whether mass is a "property" of a physical "entity",
one whereof one must be silent, then does it not
appear that the issue of Leibniz's principle is
not so much whether it is true, just yet, as
what in the heceity it means?

Finally, I will just point out that your continuing projection of the
3-fold (tone, token, type) upon the 2-some (particular, universal) is
causing more than a bit of distortion in the texts of Peirce you read.

Jon Awbrey

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

----------------------------------------------------------------------

Subject: Re: Tone, Token, Type
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Tue, 19 Nov 2002 10:30:53 -0500
X-Message-Number: 3

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

JA, citing Peirce's "On a Limited Universe of Marks",
in 'Studies in Logic' (1883, 1983), pp. 182-186,
CP 2.517-531; CE 4, 450-453):

http://suo.ieee.org/ontology/msg03204.html

SS: This passage is opposed to the kind of extensionalism advocated by Quine.
Quine's extensional languages are ones in which classes substitute for
properties and relations, two classes being identical if they have the
same members. In an intensional language, admitting properties as well
as classes, different properties may belong to exactly the same things.
In an intensional language, "a proposition concerning the relations of
two groups of marks is not necessarily equivalent to any proposition
concerning classes of things". Extensional languages, such as the
first-order predicate calculus, or set theory, are adequate for
mathematics, but it is controversial whether the sentences of
ordinary language or the sciences in general can be translated
into such an extensional language sentence for sentence.

Seth,

I wish that you would try every now and then reading what Peirce writes
without trying to atomize each and every remark, if not the man himself,
according to your true-false checklist of dichotomies, especially since
the most casual reader of Peirce would know that he would consider your
attempt to pit extensions versus intensions (properly "comprehensions")
to be an utterly false and misleading antagonism.

Just reaching into the bean bag of all possible quotations:

| The moment, then, that we pass from nothing and the vacuity of being
| to any content or sphere, we come at once to a composite content and
| sphere. In fact, extension and comprehension -- like space and time --
| are quantities which are not composed of ultimate elements; but
| every part however small is divisible.
|
| The consequence of this fact is that when we wish to enumerate the
| sphere of a term -- a process termed 'division' -- or when we wish
| to run over the content of a term -- a process called 'definition' --
| since we cannot take the elements of our enumeration singly but must
| take them in groups, there is danger that we shall take some element
| twice over, or that we shall omit some. Hence the extension and
| comprehension which we know will be somewhat indeterminate. But
| we must distinguish two kinds of these quantities. If we were to
| subtilize we might make other distinctions but I shall be content
| with two. They are the extension and comprehension relatively to
| our actual knowledge, and what these would be were our knowledge
| perfect.
|
| Logicians have hitherto left the doctrine of extension
| and comprehension in a very imperfect state owing to the
| blinding influence of a psychological treatment of the
| matter. They have, therefore, not made this distinction
| and have reduced the comprehension of a term to what it
| would be if we had no knowledge of fact at all. I mention
| this because if you should come across the matter I am now
| discussing in any book, you would find the matter left in
| quite a different state.
|
| CSP, CE 1, page 462.
|
| Charles Sanders Peirce,
|"The Logic of Science, or, Induction and Hypothesis",
| Lowell Institute Lectures of 1866, pages 357-504 in:
|
|'Writings of Charles S. Peirce: A Chronological Edition',
|'Volume 1, 1857-1866', Peirce Edition Project,
| Indiana University Press, Bloomington, IN, 1982.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

----------------------------------------------------------------------

Subject: Re: Tone, Token, Type
From: "Seth Sharpless" <seth.sharpless[…]colorado.edu>
Date: Tue, 19 Nov 2002 12:41:12 -0700
X-Message-Number: 4

Jon,
I do not have time today to respond to this and your previous
post, setting some questions for me. I shall try to get to it
tomorrow.
Seth

-----Original Message-----
From: Jon Awbrey [mailto:jawbrey[…]oakland.edu]
Sent: Tuesday, November 19, 2002 8:31 AM
To: Peirce Discussion Forum
Subject: [peirce-l] Re: Tone, Token, Type

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

JA, citing Peirce's "On a Limited Universe of Marks",
in 'Studies in Logic' (1883, 1983), pp. 182-186,
CP 2.517-531; CE 4, 450-453):

http://suo.ieee.org/ontology/msg03204.html

SS: This passage is opposed to the kind of extensionalism advocated by
Quine.
Quine's extensional languages are ones in which classes substitute
for
properties and relations, two classes being identical if they have
the
same members. In an intensional language, admitting properties as
well
as classes, different properties may belong to exactly the same
things.
In an intensional language, "a proposition concerning the relations
of
two groups of marks is not necessarily equivalent to any proposition
concerning classes of things". Extensional languages, such as the
first-order predicate calculus, or set theory, are adequate for
mathematics, but it is controversial whether the sentences of
ordinary language or the sciences in general can be translated
into such an extensional language sentence for sentence.

Seth,

I wish that you would try every now and then reading what Peirce writes
without trying to atomize each and every remark, if not the man himself,
according to your true-false checklist of dichotomies, especially since
the most casual reader of Peirce would know that he would consider your
attempt to pit extensions versus intensions (properly "comprehensions")
to be an utterly false and misleading antagonism.

Just reaching into the bean bag of all possible quotations:

| The moment, then, that we pass from nothing and the vacuity of being
| to any content or sphere, we come at once to a composite content and
| sphere. In fact, extension and comprehension -- like space and time
--
| are quantities which are not composed of ultimate elements; but
| every part however small is divisible.
|
| The consequence of this fact is that when we wish to enumerate the
| sphere of a term -- a process termed 'division' -- or when we wish
| to run over the content of a term -- a process called 'definition' --
| since we cannot take the elements of our enumeration singly but must
| take them in groups, there is danger that we shall take some element
| twice over, or that we shall omit some. Hence the extension and
| comprehension which we know will be somewhat indeterminate. But
| we must distinguish two kinds of these quantities. If we were to
| subtilize we might make other distinctions but I shall be content
| with two. They are the extension and comprehension relatively to
| our actual knowledge, and what these would be were our knowledge
| perfect.
|
| Logicians have hitherto left the doctrine of extension
| and comprehension in a very imperfect state owing to the
| blinding influence of a psychological treatment of the
| matter. They have, therefore, not made this distinction
| and have reduced the comprehension of a term to what it
| would be if we had no knowledge of fact at all. I mention
| this because if you should come across the matter I am now
| discussing in any book, you would find the matter left in
| quite a different state.
|
| CSP, CE 1, page 462.
|
| Charles Sanders Peirce,
|"The Logic of Science, or, Induction and Hypothesis",
| Lowell Institute Lectures of 1866, pages 357-504 in:
|
|'Writings of Charles S. Peirce: A Chronological Edition',
|'Volume 1, 1857-1866', Peirce Edition Project,
| Indiana University Press, Bloomington, IN, 1982.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

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----------------------------------------------------------------------

Subject: Re: Limited Mark Universes
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Tue, 19 Nov 2002 15:24:11 -0500
X-Message-Number: 5

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

LMU. Note 4

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

There is a little more background material that I ought to fill in,
but I am going to make an initial attempt to paint the Big Picture,
and try to explain in broad terms why I think that Peirce's remarks
on "Limited Mark Universes" (LMU's) are so significant, and how they
anticipate many ideas that I personally did not encounter until the
mid 1980's, in two different fields, cognitive psychology and the
area that is known as "category theory applied to computation".

I am beginning to get a better understanding of the ways that different
thinkers differ in their thinking processes. Peirce was what I think of
as an "exploratory heuristic" (EH) and a "3-adic relational" (3R) thinker.
Thinkers of this sort, a category to which I aspire to aggrandize myself
one day, think in very different ways from those that I am coming to
recognize as "absolute dichotomous" (AD) thinkers.

For example, you can forget all that guff about classifying
languages into "extensional" versus "intensional" brands,
and making some 'auto da fe' to one or the other article
of faith. All the real languages that anybody really
uses in reality have names for things that can be
instances or properties in relation to suitable
other things, not to mention, but they do,
names for these relations themselves.
This is so whether we are talking
logic, math, or normal people.

I think that I will begin from what is closest to me, a problem that
I worked on all through the 1980's, one of the hot topics in AI and
cognitive science at the time, namely, "language acquisition" (LA).
You may remember the analogies that Chomsky pointed out, time and
again, between the problem of "giving a rule to abduction" and
the "poverty of the stimulus" argument for rational grammars,
that is to say, cartesian rationalism and innate grammars.

A large part of the work that I did on this problem reduced me
to working on computational models of formal language learning,
where the formal languages that I could handle from the outset
were very "impoverished" in comparison to natural languages,
but still not entirely trivial, and with many interesting
facets that would repay even a minimalist treatment.

To make a decade-long story as short as I can make it,
here are some of the ideas that gradually worked their
way into my probable density as I errored and trialed:

1. Although it initially looks like a problem of classical induction,
that is to say, forming rules from facts and cases, it turned out
that I could not detach this from more abductive, anticipatory,
or hypothetical forms of concept formation.

2. Instead of just the extensions and the intensions of concepts
(I had not yet clued into comprehensions at that time), there
was another sort of relation between data and concepts that
I was forced to consider, on account of what many call the
"generative property" of any non-trivial language, or what
is just about the same thing, the circumstance that the
language learner, by the very nature of the task, does
not have the whole extension of a language or any of
its grammatical categories, but at every stage of
the game has only a finite experiential record
of the instances that fall under the putative,
contingent, and ever hypothetical, concepts.

This last aspect of the problem led me to recognize the importance of the
sampling relation, which reminded me, via some vague or vagrant memory,
of Aristotle's "enumerative induction", and so I came to call this
relation between the data and the concept the "enumeration" of
the concept, and extension and intension makes three.

Have to break here ...

Jon Awbrey

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

----------------------------------------------------------------------

Subject: pynchon and peirce
From: Victoria N. Alexander <alexander[…]dactyl.org>
Date: Tue, 19 Nov 2002 21:01:15 -0500
X-Message-Number: 6

Hello All

I've recently joined the list. I would like to announce my current
research focus, as a way of fishing for any comments anyone might want
to make. (I hope that this will give me a quick introduction to forum
participants.) I'm working on Peirce's view of final causality and
relating it to work being done today in theoretical physics,
particularly a field known as "computational mechanics." I know and
admire Pape's and Short's papers.

But my interest in Peirce stems from Narratology, and at present I have
a question that concerns literature. If anyone can point out any
research explicitly relating Peirce to postmodern novelist Thomas
Pynchon, I would appreciate it. A thorough search through a number of
archives has turned up surprisingly little. Thanks for your time.

Victoria Alexander, Ph.D.

----------------------------------------------------------------------

Subject: Re: Limited Mark Universes
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Tue, 19 Nov 2002 22:18:03 -0500
X-Message-Number: 7

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

LMU. Note 5

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Peirce came into this arena with a question about "how science works",
and he took off from a standard sort of Kantian platform that permits
you to get started by just going ahead and accepting the evident fact,
the apparent phenomenon, or the provisional hypothesis that science,
as we do it, but not necessarily as we know it, does work, and then
to move on to the next question, to wit: What are the conditions
for the possibility of science working?

I walked into this theatre with a problem about language learning, and
had very little acquaintance and a whole lot of wrong ideas about Kant.

But there is a natural analogy between the task of scientific knowing
and the task of language acquisition, as Newton clearly recognized in
the guise of his metaphor about science as the decoding of nature's
cryptographic laws.

So I will start out by explaining a very simple sort of language acquisition task.
One of the first obstacles that we run into is this huge gulf between all of the
realistic examples and all of the sorts of examples that one can discuss in the
beginning, the fact that all of the motive settings are very complex indeed
and all of the simple set-pieces are very simple indeed.

So I will beg you to use your imagination.

Okay, enough preamble.

An "alphabet" (or a "lexicon") is a finite set A.

The "kleene star" A* of the alphabet A
is the set of all finite sequences that
can be formed out of the elements of A.
We call these "strings" or "sequences".
Note that A* includes the empty string.

A "formal language" L over the alphabet A is an arbitrary subset of A*,
thus L c A*. Depending on the setting, the strings or sequences of L
are called "L-words", "L-strands", or "L-sentences", in one locution,
or "words of L", "strands of L", or "sentences of L", in another.
Whenever there is only one language under discussion, or when
it is otherwise clear, the obvious abridgements may be used.

Enough for today ...

Jon Awbrey

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

----------------------------------------------------------------------

Subject: Re: Identity and Teridentity: to Bernard
From: Cathy Legg <clegg[…]cyc.com>
Date: Tue, 19 Nov 2002 22:57:38 -0600 (CST)
X-Message-Number: 8

On Sat, 16 Nov 2002, Bernard Morand wrote:

> At 19:28 15/11/02 -0600, you wrote:
> >Salut Bernard!
>
> Bonjour Cathy,
> Tr=E8s heureux de converser avec vous de nouveau. Je vois au titre
> d'ontologiste que vous mettez dans votre signature (ainsi que votre tra=
vail
> dans le Cyc) que nous aurions beaucoup de choses =E0 nous dire et peut =
=EAtre
> quelques diff=E9rences :

Indeed! Feel free to interrogate or challenge me on this if you wish.

> >On Thu, 14 Nov 2002, Bernard Morand wrote:
> >
> > > Thanks for your thoughtful responses. I apologize for taking the oc=
casion
> > > of the discussion in order to try to clarify something which bother=
ed me
> > > for a long time and thus making some kind of diversion in the threa=
d.
> > > I would have better to make explicit the matter. First, I am not a
> > > professional logician. I never managed to understand the usual acco=
unt
> > > repeated in many books and by several authors (J. Sowa for example)=
who
> > > tell us that on the whole Peirce's logic is nothing but the modern=
first
> > > order logic put in another dress. Such a statement is often followe=
d by the
> > > idea that he was the inventor of the quantifiers, a reference to EG=
, and so
> > > on. But when I come to read his work on the algebra of logic for ex=
ample, I
> > > can't equate it with FOL. Thus I am lead to thing that a) I have no=
t
> > > understood Peirce's logic or b) I have not understood propositional=
logics
> > > or c) the previous statements are false. One key point among others=
is I
> > > think, what is at stake with the quantification.
> >
> >My understanding is that Peirce's alpha graphs are equivalent to
> >the propositional calculus and his beta graphs are equivalent to first
> >order predicate calculus with identity (so Sowa et al are right in tha=
t
> >respect).
>
> This is precisely what I am strongly doubting of. All seems to work as =
if
> people read (and sometimes not read at all) Peirce through the glasses =
of
> contemporary logic. So they believe that they find it into Peirce. He i=
s
> such an original thinker that we have to take what he wrote for what h=
e
> really said. Trying to make from the beginning an account of his work i=
n
> terms of what has been believed later often ends in misinterpretations.

I believe this also.

> Among several reasons of such a method, there is the fact that he makes=
his
> own precise terminology and overall his whole philosophy. But you know =
that
> better than me. As to his work in logics, Sowa himself recognizes a spe=
cial
> place to Peirce: the boolean tradition. Who nowadays in logics refers t=
o
> such a tradition ? Quite nobody I think. Who nowadays is really working
> logics with the same strong relationship to philosophy ? Few people I
> think. Who nowadays makes in logics the same relationship to mathematic=
s as
> himself, a relationship that sounds wholly old-fashioned to contemporar=
y
> ears ?

True

>These are my reasons to suspect that, without proof of the contrary,
> the so called equivalencies are not such. A last example, he would have
> been horrified to call his logic a calculus.

Ok, but can you give me an example of something which is expressable by,
say the alpha graphs and not propositional (ahem!) 'logic', or by the bet=
a
graphs and not predicate logic? What is the pragmatic different between
the two? Your discussion with Ben re. 'variables' vs 'indices' might, I
guess, be heading in this direction, but can you give me something more
specific?

By the way, I really agree with what you said there re. "we can't start
logic with a list of already-identified objects". I think this connects u=
p
with what Seth was saying earlier also.

Amities,

Cathy.

> >In his gamma graphs, however, he broaches the topic of modal
> >logic and goes beyond FOL. However this system, unlike the others, was
> >never finished. I tried to read of some his writings on the gamma grap=
hs
> >at one stage and found it really difficult. He experiments with lots o=
f
> >creative ideas - e.g. different colours, different textures (e.g. fur(=
!)),
> >cutting the page and writing things on the back, cutting the page and
> >throwing pieces away, a slew of different pages each with a small chan=
ge
> >(like the 'cartoons' we used to draw as children and make them move by
> >flipping the pages) to see thought in action...Jay Zeman has a paper o=
n
> >it all which is quite informative. (I think that might be in the Natha=
n
> >Houser volume as well...?)
>
> Yes it is "Peirce and Philo". As to the subject of modal logic, the pro=
ject
> of "seeing thought in action", making material objects and devices in o=
rder
> to study the process of reasoning would probably receive some smiles he=
re
> and there. Nobody used to work like that because the idea that logic is=
in
> need of the experimental method is quite incomprehensible at the moment.
>
> Amiti=E9s
>
> Bernard
>
>
> ---
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>

--=20

-------------------------------------------------------------------------=
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Cathy Legg, Phd Cycorp, Inc.
Ontologist 3721 Executive Center Dr., ste 100
www.cyc.com Austin, TX 78731-1615

download OpenCyc at http://www.opencyc.org
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----------------------------------------------------------------------

Subject: Re: Tone, Token, Type
From: Cathy Legg <clegg[…]cyc.com>
Date: Tue, 19 Nov 2002 23:31:43 -0600 (CST)
X-Message-Number: 9

On Fri, 15 Nov 2002, Seth Sharpless wrote:

> Cathy Legg referred to the following quotes:
> ----------------from Peirce-------------------------
> > 1885 Affirming Leibniz's principle
> > ---------------------------------
> > But this relation of identity has peculiar properties. The first is
> > that i and j are identical, whatever is true of i is true of j.... The
>
> > other property is that if everything which is true of i is true of j,
> > then i and j are identical.
> > ----------------------------------
> >
> > 1896-7 Denying Leibniz's principle.
> > --------------------------------
> > Two drops of water retain each its identity and opposition to the
> > other no matter in what or in how many respects they are alike. Even
> > could they interpenetrate one another like optical images (which are
> > also individual), they would nevertheless react, though perhaps not at
>
> > that moment, and by virtue of that reaction would retain their
> > identities. CP1.456 (1896)
> >
> > They are like two ideal rain drops, distinct but not different.
> > Leibniz's "principle of indiscernibles" is all nonsense. No doubt, all
>
> > things differ; but there is no logical necessity for it. CP 4.311
> > (1897)
> > -----------end of Peirce quotes---------------------
>
> ---------Cathy commented-----------------------
> I wonder whether one might reconcile these two quotes by arguing that in
> the former Peirce is speaking qua formal logician (note that he is
> speaking only of an 'i' and a 'j') and in the latter qua metaphysician.
> Subjects in formal logic might perhaps have no reality except the
> preperties explicitly ascribed to them, which is obviously not the case
> for real things...?
>
> I would need to see the larger contexts from which these quotes were
> taken to see if this was on the right track, though, and what exactly
> was going on in these two quotes.
> -----------end of quote from Cathy--------------
>
> I apologize for omitting a paragraph reference for the first quote.
> Here it is in its entirety:
> -----------------quote from Peirce
> CP3.398. (1885) Let us now consider the logic of terms taken in
> collective senses. Our notation, so far as we have developed it, does
> not show us even how to express that two indices, i and j, denote one
> and the same thing. We may adopt a special token of second intention,
> say 1, to express identity, and may write 1[i j]. But this relation of
> identity has peculiar properties. The first is that if i and j are
> identical, whatever is true of i is true of j. This may be written
>
> p[i]p[j]{~1[i j]+~x[i]+x[j]}.
>
> The use of the general index of a token, x, here, shows that the formula
> is iconical. The other property is that if everything which is true of i
> is true of j, then i and j are identical. This is most naturally written
> as follows: Let the token, q, signify the relation of a quality,
> character, fact, or predicate to its subject. Then the property we
> desire to express is
>
> p[i]p[j]S[k](1[i j]+~q[k i]q[k j]).
>
> And identity is defined thus
>
> 1[i j] = p[k](q[k i]q[k j]+~q[k i]~q[k j]).
>
> That is, to say that things are identical is to say that every predicate
> is true of both or false of both. It may seem circuitous to introduce
> the idea of a quality to express identity; but that impression will be
> modified by reflecting that q[k i]q[j k] merely means that i and j are
> both within the class or collection k. If we please, we can dispense
> with the token q, by using the index of a token and by referring to this
> in the Quantifier just as subjacent indices are referred to. That is to
> say,
>
> we may write 1[i j] = p[x](x[i]x[j]+~x[i]~x[j]).
> --------------------end of CP3.398 quote--------------
>
> It is true, Cathy, that he is speaking as a logician, and that 'i' and
> 'j' are indices, and 1[ij] means that they denote the same thing, but I
> do not see how that helps you to escape the affirmation of Leibniz's
> principle. It is to say that John and Joe (if John were denoted by 'i'
> and Joe by 'j') have the same properties. His statement, "to say that
> things are identical is to say that every predicate is true of both or
> false of both," is blunt enough. And this is not a new tune for Peirce.
> Consider, for example, his 1873 comment, "If a and b have the same
> predicates (in true propositions) then there is no difference between a
> and b, so far as the objects they name are concerned (MS229)." Treating
> identity as a relation in second intentions, asserting in effect that
> two tokens name the same thing, does not allow one to wiggle out of the
> fact that it is the things named that are claimed by Peirce to have the
> same properties, not the names themselves.
>
Thanks for the rest of the 1897 quote. As I read the 1897 quote, though,
he's not denying the indiscernibility of identicals, only the identtity
of indiscernibles. And the long 1885 quote is about the
indiscernibility of identicals only.

> On the shift from identity as a dyadic relation (1896) to tridentity
> (1903 or thereabouts), Cathy wrote: "It does sound here as though he
> changed his mind. I am surprised he is saying that identity is
> essentially a dual relation so late."
>
> Well, I extracted the 1896 date from Collected Papers, which is an
> unreliable way of dating I think. Is it your impression that Peirce had
> worked out the tridentity theory by 1892? Is there evidence for that?

Not to hand, alas.

I did as promised look up the intro to Burch's "A Peircean Reduction
Thesis" and couldn't find any mention of Quine's reduction proof, so
there goes that theory. I then looked through Burch's 2 papers from the
Houser volume (and also a paper by Jacqueline Brunning on teridentity
which is very good ("Genuine Triads and Teridentity") and couldn't find
any mention. I know it is out there somewhere!!.

> Thanks, Cathy. By the way, I thought your paper on growth of
> meaning over time was super... especially in its neat summing up of 20th
> century issues in analytic philosophy, each in a word or two..

Oh - thanks for reading it!

> Masterful! But I do have some reservations about your main thesis
> there. Is it your contention that, say, the English expression, "Dinner
> is served," has one ultimately correct meaning, which after many
> generations English users will tend to converge on? That is, do
> ordinary conventional words have, so to speak, a "natural meaning," one
> which God knows, and generations of Englishmen may finally come close to
> discerning, God willing.

Yes this objection comes up fairly often when I give the paper. I don't
think Peirce is committed to the claim that every word ever used by homo
sapiens will wind up at 'the end of inquiry' perfectly precisified - just
that the general tendency in sign-use over time is for signs to become
*more* precisified. Peirce said "Think how much more 'planet' means now
than in the time of Hipparchus". Well, analogously, think how much more
'dinner' means now than in the time of...(grabbing some berries and
stuffing them in your mouth. Cave-man time) But there might be limits to
the precisification this particular sign admits of, and, who knows, it
might even drop by the wayside entirely one day (like "going a Maying"
seems to have), if human life changes significantly.

> It has been a while since I looked at your
> paper, so I may have it wrong, but I remember thinking something like
> this when I read it. Has it already been published?

I got a promise from a journal that they would look at it again if I
resubmitted it with changes about a year ago, though I don't think they
were wildly keen on it. I should send it back soon, I guess.

Regards,
Cathy.

---

END OF DIGEST 11-19-02

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