PEIRCE-L Digest for Wednesday, November 20, 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. Williams on Truth, Truthfulness, and History
2. RE: Identity, att: Cathy
3. Re: pynchon and peirce
4. re: pynchon and peirce
5. [Fwd: Seminar on Logic and Games]
6. Re: Critique Of Functional Reason
7. Re: Critique Of Functional Reason
8. Re: Critique Of Functional Reason
9. RE: Identity, att: Cathy
10. Re: Identity
11. Re: pynchon and peirce
12. computational mechanics and peirce
13. Re: computational mechanics and peirce
14. Re: Limited Mark Universes
15. Re: pynchon and peirce [and Santayana?]
16. Santayana and literary studies
17. RE: pynchon and peirce
18. Re: pynchon and peirce [and Santayana?]
19. Re: Identity and Teridentity: to Bernard (fwd)
20. Re: computational mechanics and peirce
21. Re: pynchon and peirce [and Santayana?]
22. Re: Hermeneutic Equivalence Classes
23. RE: pynchon and peirce
24. RE: pynchon and peirce
25. prigogine and peirce
26. Re: prigogine and peirce
27. Manifolds of Sensuous Impressions
28. Re: Hermeneutic Equivalence Classes


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

Subject: Williams on Truth, Truthfulness, and History
From:
HGCALLAWAY[…]aol.com
Date: Wed, 20 Nov 2002 03:03:24 EST
X-Message-Number: 1

Peirce-l,

In amongst some progress on various topics, I want to recommend again that
readers of the list take a look at an article by Bernard Williams, of Oxford
University and UC Berkeley, which recently appeared in the London Review of
Books. The full article is available to subscribers on-line at the following
address: <
http://www.lrb.co.uk/v24/will03_.html>. (Without a subscription,
you just get the opening paragraph or so.) The article draws from Williams'
new book, titled _Truth and Truthfulness_, and it addresses not only these
important topics, in a way which readers of the Peirce-l should find chiefly
congenial, but also the role of history for philosophy --and some related
topics.

I am reminded of the Emersonian theme of compensation. There is a just
compen-sation, as Emerson has it, for truth and truthfulness, but also for
their want and lack.
I can hardly think that Peirce would have missed this point in Emerson, and
it may well explain some of Peirce's emphasis on the centrality of truth.

H.G. Callaway
(
hgcallaway[…]aol.com)

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

Subject: RE: Identity, att: Cathy
From: "Seth Sharpless" <
seth.sharpless[…]colorado.edu>
Date: Wed, 20 Nov 2002 01:04:32 -0700
X-Message-Number: 2

Cathy wrote: "And the long 1885 quote is about the
indiscernibility of identicals only."


Are you sure? Note in the 1885 quote: "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. The other
property is that if everything which is true of i is true
of j, then i and j are identical."

Isn't the "other property" the identity of indiscernibles?
(Well, almost. He obviously slipped, intending the protasis
to be "if everything which is true of i is true of j _and_
everything which is true of j is true of i, then i and j
are identical.")

Also, on your point about relativizing precisification to
a language community, I'm not sure you can render that
compatible with what Peirce actually says. This point
has bothered me for a long time in connection with his
concept of an ultimate interpretant. It seems to me that
Peirce, in his effort to make a universal definition of
'sign', has trouble distinguishing between conventional
meaning of an expression, or the meaning which a
speaker intends when she utters the expression, or the
meaning which a human interpreter gives to an expression,
and ultimate Truth. In "New Elements" 1904, Peirce wrote:
"The 'Truth', the fact that is not abstracted but complete,
is the ultimate interpretant of every sign."
I think this was discussed in a July, 2000 thread on
Ultimate Interpretants (which unfortunately I allowed to
get offtrack on to the subject of infinite regress).
Seth


-----Original Message-----
From: Cathy Legg [mailto:clegg[…]cyc.com]
Sent: Tuesday, November 19, 2002 10:32 PM
To: Peirce Discussion Forum
Subject: [peirce-l] Re: Tone, Token, Type

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.


---
Message from peirce-l forum to subscriber
Seth.Sharpless[…]colorado.edu
To unsubscribe send a blank email to:
leave-peirce-l-16605B[…]lyris.ttu.edu


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

Subject: Re: pynchon and peirce
From: "Arnold Shepperson" <
Sheppers[…]nu.ac.za>
Date: Wed, 20 Nov 2002 11:00:49 +0200
X-Message-Number: 3

Victoria

Welcome to Peirce-L, and may your association with the list be long,
fruitful, and challenging.

I majored in English Lit back in the late 1980s, but my focus had
always been on the `realist' novel form that included Dickens, Gaskell,
Eliot, and all the other State of England-related works that one could
associate with South Africans like Nadine Gordimer, or more challenging
stuff like that of JM Coetzee. In short, I didn't `get' my Lit thru the
likes of Pynchon, and it rather challenges my view that one can indeed
relate a realist like Peirce with a post-modern novelist like Pynchon!
Thus does not mean to say, however, that some serious inquiry could
emerge from this, and I for one would be intrigued by what comes out of
your query.

Cheers

Arnold Shepperson
Culture, Communication, and Media Studies
University of Natal
Durban 4041
South Africa


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

Subject: re: pynchon and peirce
From: Jon Awbrey <
jawbrey[…]oakland.edu>
Date: Wed, 20 Nov 2002 08:01:48 -0500
X-Message-Number: 4

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

dear v,

long time no c. can you tell us what you mean by
computational mechanics & narratology and how you
see these as being related?

yours truly,

jon awbrey,
taxonomic taxidermist

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


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

Subject: [Fwd: Seminar on Logic and Games]
From: Jon Awbrey <
jawbrey[…]oakland.edu>
Date: Wed, 20 Nov 2002 08:40:50 -0500
X-Message-Number: 5

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

topic of potential interest ...

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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Subject: Seminar on Logic and Games
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Seminar on Logic and Games

Joel Spencer

Courant Institute - NYU

"The Ehrenfeucht Game on Random Structures"

Monday, November 25, 11 AM to 12:30 PM

Room 9207, CUNY Graduate Center
365 Fifth Avenue
(Fifth Ave and 34th Street)

Abstract: The Ehrenfeucht Game allows a combinatorialist to
show that two models have the same first order properties up
to a given quantifier depth. When applied to random models
it allows one to show a Zero-One Law. How large must n=n(k)
be so that with high probability the Duplicator wins the k
move Ehrenfeucht game? This notion, dubbed tenacity, allows
an analytic exploration of the strength of a Zero-One Law.
Key examples are the random graph G(n,p) (for a variety of
p=p(n)) and the random circular (to avoid edge effects)
bit string U(n,p).

--------------5721671580487F461D8D8530--


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

Subject: Re: Critique Of Functional Reason
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Wed, 20 Nov 2002 08:48:35 -0500
X-Message-Number: 6

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

CFR. Note 15

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

I have presented my thesis and my inquiry:

| Thesis. Mathematics and its applications in physics
| and the other special sciences are serving moderately
| successfully to describe the world as we know it today,
| while logic lags behind in a largely ineffectual state.
|
| Inquiry. Why is this?

I have sketched the outlines of a diagnosis,
a syndrome suggestive of retinal detachment,
affecting the stereoscopy of data and logic.

Still ...

The diagnosis of a severe disorder can hardly be useful,
much less welcome, if it is delivered in the absence of
some orderly array of differential indications, issuing
in the prescription of measures to be taken toward the
remedy of the presenting and the underlying conditions.

So it falls on us to ask ourselves the critical question:
What is the rest of science doing so right that logic is
still stubbornly doing so wrong? For all of the various
other sciences, in the main and in the mean, have passed
through their crises, several and severe, the distempers
of infancy, childhood, adolescence, if not yet maturity,
and they've done so in times not so remote on the scale
of intellectual history to be yet lost to our cultural
memories. They have taken their medicine, and learned
not a few hard lessons from the experience, but logic
lingers on with no show of improvement, sick with its
hangovers from times that we but wish were immemorial.

Well, I've been following a clue all along to what I think might just
be the Rx of choice, a recipe that I've kept in my mind in plain view,
all this time in my present subject line -- if logic is non-functional,
then let's make it functional. And how to do that I will now describe.

I redraw my sketch of the immediate situation,
an icon of the dis-integration that currently
exists between the empirical and the rational
views of the universe, and this time I dab in
a few patches of color from the palette of data
that I gathered in my travels from Omaha to Perth.

Let us now return to the statement that I will mark as "s":

s = "If Perth is 400 miles from Omaha then Perth is in America".

I parse it, at first sight, in the following fashion:

u = "Perth is 400 miles from Omaha",

v = "Perth is in America",

s = ( u ( v )) = not u without v,

s = ( Perth is 400 miles from Omaha ( Perth is in America )).

You have noticed, of course, that I have already forgotten all of
Quine's fine distinctions, which I always do just about two days
after I try to memorize them. I will have to justify it, later.

And here is my picture of the dataset YMMV : {Omaha} -> {Perth}

o-----------------------------------------------------------------------o
| X |
| |
| o---------------o o---------------o |
| / \ / * * * * * \ * * |
| / . * * * * * \ |
| / / \ * * * * * \ * * |
| / / \ * * * * * \ |
| / / \ * * * * * \ * * |
| o o o * * * * * o |
| | | | * * * * * | * * |
| | | | * * * * * | |
| | U | * | V | * * |
| | | | * * * * * | |
| | | | * * * * * | * * |
| o o o * * * * * o |
| \ \ / * * * * * / * * |
| \ \ / * * * * * / |
| \ \ / * * * * * / * * |
| \ . * * * * * / |
| \ / \ * * * * * / * * |
| o---------------o o---------------o |
| |
| 99 = 1 + 80 + 18 |
o-----------------------------------------------------------------------o
Figure 2. Your Mileage May Vary: From Omaha To Perth

Table 3. Your Mileage May Vary: From Omaha To Perth
o----o------------------------------------------------------------------o
| | DE IN KS MN MS ND NV NY VA NB ON |
o----o------------------------------------------------------------------o
| | |
| | - + - + - + - + - + - + - + - + - + - - - - |
| AL | 839 563 892 1203 411 1619 2356 1112 515 1577 1202 |
| | |
| | - + - + - + - + - + - + - + - + - + - - - - |
| AR | 1143 457 337 654 439 1052 1747 1266 1029 1757 1250 |
| | |
| | - + - + - + - + - + - + - + - + - + - - - - |
| GA | 892 670 976 1310 415 1726 2463 1165 569 1635 1260 |
| | |
| | - + - + - + - + - + - + - + - + - + - - - - |
| IL | 823 176 622 758 540 1174 1904 950 665 1452 945 |
| | |
| | - + - + - + - + - + - + - + - + - + - - - - |
| KY | 577 389 958 960 744 1376 2240 825 315 1298 891 |
| | |
| | - + + + - + - + - + - + - + - + - + - - - - |
| MO | 1069 400 403 379 797 844 1595 1134 1012 1542 1035 |
| | |
| | - + - + - + - + - + - + - + - + - + - - - - |
| NE | 1201 598 348 425 893 642 1380 1242 1195 1672 1166 |
| | |
| | - + - + - + - + - + - + - + - + - + - - - - |
| TX | 1317 724 393 925 338 1323 1909 1499 1055 2083 1511 |
| | |
| | - + - + - + - + - + - + - + - + - + - - - - |
| VA | 526 425 994 996 735 1411 2276 774 264 1264 881 |
| | |
o----o------------------------------------------------------------------o

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

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

Subject: Re: Critique Of Functional Reason
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Wed, 20 Nov 2002 09:30:14 -0500
X-Message-Number: 7

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

CFR. Note 16

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

Sixteen Functions

For future reference, I record here the sixteen propositional forms on
two logical variables, expressed or illustrated in four different ways.
Also, I include two families of convenient nicknames that I frequently
use for these functions: The "F" series codifies the "truth table" of
each proposition as a binary numeral in its subscript. The "f" series
employs as its subscript the decimal equivalent of this binary numeral.

o-----------------------------o-----------------------------o
| | |
| F_0000 | f_0 |
| | |
| 1 + | |
| | |
| | |
| 0 --->o---o---o---o---o---> | ( ) |
| | |
| uv = 10, 11, 01, 00 | |
| | |
| o----------------o | |
| | X /\ /\ | | |
| | / \/ \ | | |
| | / /\ \ | | |
| | / U / \ V \ | | |
| | \ \ / / | | |
| | \ \/ / | | o |
| | \ /\ / | | | |
| | \/ \/ | | | |
| o----------------o | @ |
| | |
o-----------------------------o-----------------------------o
| | |
| F_0001 | f_1 |
| | |
| 1 + o---o | |
| |%%%| | |
| |%%%| | |
| 0 --->o---o---o---o o---> | (u) (v) |
| | |
| uv = 10, 11, 01, 00 | |
| | |
| o----------------o | |
| |%X%%%/\%%/\%%%%%| | |
| |%%%%/ \/ \%%%%| | |
| |%%%/ /\ \%%%| | |
| |%%/ U / \ V \%%| | |
| |%%\ \ / /%%| | u v |
| |%%%\ \/ /%%%| | o o |
| |%%%%\ /\ /%%%%| | \ / |
| |%%%%%\/ \/%%%%%| | \ / |
| o----------------o | @ |
| | |
o-----------------------------o-----------------------------o
| | |
| F_0010 | f_2 |
| | |
| 1 + o---o | |
| |%%%| | |
| |%%%| | |
| 0 --->o---o---o o---o---> | (u) v |
| | |
| uv = 10, 11, 01, 00 | |
| | |
| o----------------o | |
| | X /\ /\ | | |
| | / \/%%\ | | |
| | / /\%%%\ | | |
| | / U / \%V%\ | | |
| | \ \ /%%%/ | | |
| | \ \/%%%/ | | u o |
| | \ /\%%/ | | | |
| | \/ \/ | | | |
| o----------------o | @ v |
| | |
o-----------------------------o-----------------------------o
| | |
| F_0011 | f_3 |
| | |
| 1 + o---o---o | |
| |%%%%%%%| | |
| |%%%%%%%| | |
| 0 --->o---o---o o---> | (u) |
| | |
| uv = 10, 11, 01, 00 | |
| | |
| o----------------o | |
| |%X%%%/\%%/\%%%%%| | |
| |%%%%/ \/%%\%%%%| | |
| |%%%/ /\%%%\%%%| | |
| |%%/ U / \%V%\%%| | |
| |%%\ \ /%%%/%%| | u |
| |%%%\ \/%%%/%%%| | o |
| |%%%%\ /\%%/%%%%| | | |
| |%%%%%\/%%\/%%%%%| | | |
| o----------------o | @ |
| | |
o-----------------------------o-----------------------------o
| | |
| F_0100 | f_4 |
| | |
| 1 + o---o | |
| |%%%| | |
| |%%%| | |
| 0 --->o o---o---o---o---> | u (v) |
| | |
| uv = 10, 11, 01, 00 | |
| | |
| o----------------o | |
| | X /\ /\ | | |
| | /%%\/ \ | | |
| | /%%%/\ \ | | |
| | /%U%/ \ V \ | | |
| | \%%%\ / / | | |
| | \%%%\/ / | | o v |
| | \%%/\ / | | | |
| | \/ \/ | | | |
| o----------------o | u @ |
| | |
o-----------------------------o-----------------------------o
| | |
| F_0101 | f_5 |
| | |
| 1 + o---o o---o | |
| |%%%| |%%%| | |
| |%%%| |%%%| | |
| 0 --->o o---o---o o---> | (v) |
| | |
| uv = 10, 11, 01, 00 | |
| | |
| o----------------o | |
| |%X%%%/\%%/\%%%%%| | |
| |%%%%/%%\/ \%%%%| | |
| |%%%/%%%/\ \%%%| | |
| |%%/%U%/ \ V \%%| | |
| |%%\%%%\ / /%%| | v |
| |%%%\%%%\/ /%%%| | o |
| |%%%%\%%/\ /%%%%| | | |
| |%%%%%\/%%\/%%%%%| | | |
| o----------------o | @ |
| | |
o-----------------------------o-----------------------------o
| | |
| F_0110 | f_6 |
| | |
| 1 + o---o o---o | |
| |%%%| |%%%| | |
| |%%%| |%%%| | |
| 0 --->o o---o o---o---> | (u , v) |
| | |
| uv = 10, 11, 01, 00 | |
| | |
| o----------------o | |
| | X /\ /\ | | |
| | /%%\/%%\ | | |
| | /%%%/\%%%\ | | |
| | /%U%/ \%V%\ | | |
| | \%%%\ /%%%/ | | u v |
| | \%%%\/%%%/ | | o-----o |
| | \%%/\%%/ | | \ / |
| | \/ \/ | | \ / |
| o----------------o | @ |
| | |
o-----------------------------o-----------------------------o
| | |
| F_0111 | f_7 |
| | |
| 1 + o---o o---o---o | |
| |%%%| |%%%%%%%| | |
| |%%%| |%%%%%%%| | |
| 0 --->o o---o o---> | (u v) |
| | |
| uv = 10, 11, 01, 00 | |
| | |
| o----------------o | |
| |%X%%%/\%%/\%%%%%| | |
| |%%%%/%%\/%%\%%%%| | |
| |%%%/%%%/\%%%\%%%| | |
| |%%/%U%/ \%V%\%%| | |
| |%%\%%%\ /%%%/%%| | u v |
| |%%%\%%%\/%%%/%%%| | o |
| |%%%%\%%/\%%/%%%%| | | |
| |%%%%%\/%%\/%%%%%| | | |
| o----------------o | @ |
| | |
o-----------------------------o-----------------------------o
| | |
| F_1000 | f_8 |
| | |
| 1 + o---o | |
| |%%%| | |
| |%%%| | |
| 0 --->o---o o---o---o---> | u v |
| | |
| uv = 10, 11, 01, 00 | |
| | |
| o----------------o | |
| | X /\ /\ | | |
| | / \/ \ | | |
| | / /\ \ | | |
| | / U /%%\ V \ | | |
| | \ \%%/ / | | |
| | \ \/ / | | |
| | \ /\ / | | |
| | \/ \/ | | u v |
| o----------------o | @ |
| | |
o-----------------------------o-----------------------------o
| | |
| F_1001 | f_9 |
| | |
| 1 + o---o o---o | |
| |%%%| |%%%| | |
| |%%%| |%%%| | |
| 0 --->o---o o---o o---> | ((u , v)) |
| | |
| uv = 10, 11, 01, 00 | |
| | |
| o----------------o | |
| |%X%%%/\%%/\%%%%%| | |
| |%%%%/ \/ \%%%%| | u v |
| |%%%/ /\ \%%%| | o-----o |
| |%%/ U /%%\ V \%%| | \ / |
| |%%\ \%%/ /%%| | \ / |
| |%%%\ \/ /%%%| | o |
| |%%%%\ /\ /%%%%| | | |
| |%%%%%\/%%\/%%%%%| | | |
| o----------------o | @ |
| | |
o-----------------------------o-----------------------------o
| | |
| F_1010 | f_10 |
| | |
| 1 + o---o---o | |
| |%%%%%%%| | |
| |%%%%%%%| | |
| 0 --->o---o o---o---> | v |
| | |
| uv = 10, 11, 01, 00 | |
| | |
| o----------------o | |
| | X /\ /\ | | |
| | / \/%%\ | | |
| | / /\%%%\ | | |
| | / U /%%\%V%\ | | |
| | \ \%%/%%%/ | | |
| | \ \/%%%/ | | |
| | \ /\%%/ | | |
| | \/ \/ | | v |
| o----------------o | @ |
| | |
o-----------------------------o-----------------------------o
| | |
| F_1011 | f_11 |
| | |
| 1 + o---o---o---o | |
| |%%%%%%%%%%%| | |
| |%%%%%%%%%%%| | |
| 0 --->o---o o---> | (u (v)) |
| | |
| uv = 10, 11, 01, 00 | |
| | |
| o----------------o | |
| |%X%%%/\%%/\%%%%%| | |
| |%%%%/ \/%%\%%%%| | |
| |%%%/ /\%%%\%%%| | v o |
| |%%/ U /%%\%V%\%%| | | |
| |%%\ \%%/%%%/%%| | | |
| |%%%\ \/%%%/%%%| | u o |
| |%%%%\ /\%%/%%%%| | | |
| |%%%%%\/%%\/%%%%%| | | |
| o----------------o | @ |
| | |
o-----------------------------o-----------------------------o
| | |
| F_1100 | f_12 |
| | |
| 1 + o---o---o | |
| |%%%%%%%| | |
| |%%%%%%%| | |
| 0 --->o o---o---o---> | u |
| | |
| uv = 10, 11, 01, 00 | |
| | |
| o----------------o | |
| | X /\ /\ | | |
| | /%%\/ \ | | |
| | /%%%/\ \ | | |
| | /%U%/%%\ V \ | | |
| | \%%%\%%/ / | | |
| | \%%%\/ / | | |
| | \%%/\ / | | |
| | \/ \/ | | u |
| o----------------o | @ |
| | |
o-----------------------------o-----------------------------o
| | |
| F_1101 | f_13 |
| | |
| 1 + o---o---o o---o | |
| |%%%%%%%| |%%%| | |
| |%%%%%%%| |%%%| | |
| 0 --->o o---o o---> | ((u) v) |
| | |
| uv = 10, 11, 01, 00 | |
| | |
| o----------------o | |
| |%X%%%/\%%/\%%%%%| | |
| |%%%%/%%\/ \%%%%| | |
| |%%%/%%%/\ \%%%| | u o |
| |%%/%U%/%%\ V \%%| | | |
| |%%\%%%\%%/ /%%| | | |
| |%%%\%%%\/ /%%%| | v o |
| |%%%%\%%/\ /%%%%| | | |
| |%%%%%\/%%\/%%%%%| | | |
| o----------------o | @ |
| | |
o-----------------------------o-----------------------------o
| | |
| F_1110 | f_14 |
| | |
| 1 + o---o---o---o | |
| |%%%%%%%%%%%| | |
| |%%%%%%%%%%%| | |
| 0 --->o o---o---> | ((u) (v)) |
| | |
| uv = 10, 11, 01, 00 | |
| | |
| o----------------o | |
| | X /\ /\ | | |
| | /%%\/%%\ | | u v |
| | /%%%/\%%%\ | | o o |
| | /%U%/%%\%V%\ | | \ / |
| | \%%%\%%/%%%/ | | \ / |
| | \%%%\/%%%/ | | o |
| | \%%/\%%/ | | | |
| | \/ \/ | | | |
| o----------------o | @ |
| | |
o-----------------------------o-----------------------------o
| | |
| F_1111 | f_15 |
| | |
| 1 + o---o---o---o---o | |
| |%%%%%%%%%%%%%%%| | |
| |%%%%%%%%%%%%%%%| | |
| 0 --->o o---> | (( )) |
| | |
| uv = 10, 11, 01, 00 | |
| | |
| o----------------o | |
| |%X%%%/\%%/\%%%%%| | |
| |%%%%/%%\/%%\%%%%| | |
| |%%%/%%%/\%%%\%%%| | |
| |%%/%U%/%%\%V%\%%| | |
| |%%\%%%\%%/%%%/%%| | |
| |%%%\%%%\/%%%/%%%| | |
| |%%%%\%%/\%%/%%%%| | |
| |%%%%%\/%%\/%%%%%| | |
| o----------------o | @ |
| | |
o-----------------------------o-----------------------------o

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

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

Subject: Re: Critique Of Functional Reason
From: Jon Awbrey <
jawbrey[…]oakland.edu>
Date: Wed, 20 Nov 2002 09:48:02 -0500
X-Message-Number: 8

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

CFR. Note 17

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

One of the ways that we might build stronger and more realistic bonds
between our DB's and our KB's is by looking at the ways that constant
propositions in real-world theories and contingent propositions in
real-world factual assertions are "supported by" the sorts of data,
that is, actual measurements and empirical observations, that we
put in real-world databases.

From what I remember of the "real world",
it had to do with propositions like this:

1. If health care service provider J
assigns patient K to stereotype L,
then K will get quality-of-care M.

2. The prevalence of low birth weight babies
in health care underserved populations is
not just a fluke, but can be accounted to
the effects of lower quality health care.

Stuff like that ...

At this particular juncture I appear to be
stuck with Quine's slightly hokey example:

q = "If Perth is 400 miles from Omaha then Perth is in America".

Still, Quine's example does have non-trivial logical structure,
one that is even a little bit analogous to case number 1 above,
say, under the following transformation: J = Omaha, K = Perth,
L = 400 miles distant, and "care of quality M" = "in America".

The relationship through which a database "supports" a proposition is,
strange to say, a model-theoretic relationship. Indeed, there is good
reason to express the fact that DB(MapQuest) supports the proposition q
by writing out a symbolic formula of the following form:

DB(MQ) |= q.

The reason that this seems so "strange to say" is not the fault
of the claim itself, but due to the way that model theory seems
to have lost its way since it first set out, and even abandoned
almost altogether its initial attachment to notions of evidence
and rational grounds, all in the time since it began to take on
more formal airs.

Jon Awbrey

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

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

Subject: RE: Identity, att: Cathy
From:
HGCALLAWAY[…]aol.com
Date: Wed, 20 Nov 2002 10:32:52 EST
X-Message-Number: 9

Seth & list,

It struck me as somewhat curious that you have continued returning to the
identitiy of indiscernibles, as contrasted with the indiscernibility of
identicals. I've been wondering what you are getting at. Perhaps you have in
mind something to do with the pragmatic principle?

You wrote:

<< Are you sure? Note in the 1885 quote: "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. The other
property is that if everything which is true of i is true
of j, then i and j are identical.">>

So, the point is that Peirce seems to be taking up both claims. Notice here,
by the way, that "i" and "j" seem to function as something like variables. We
consider what must follow if i and j are identical, e.g., without knowing or
asserting that they are. So, if we imagine that we use "i" and "j" to
actually talk about things, then it would have to be that we could talk about
them just the same, whether or not they are identical; and the reference of
any terms so used must be to that degree indefinite. Likewise with the claim
that if everything true or i is also true of j and vice versa, then i=j,
though that might seem to be more difficult to establish.

You continue:

Isn't the "other property" the identity of indiscernibles?
(Well, almost. He obviously slipped, intending the protasis
to be "if everything which is true of i is true of j _and_
everything which is true of j is true of i, then i and j
are identical.") >>

O.k. --but what is your interest in the identity of indiscrernibles here?
Surely we might often have occasion to identify A and B, without checking on
every possible difference --which would seem to be an unending task. Often,
people are satisfied with crucial or predicted measurements as a good
indication of identity. As regards the morning star and the evening star,
say, I imagine someone projecting the orbit of the morning star and finding
on observation, that the orbit of the evening star fits the prediction.
Confirming a quantified prediction is often sufficient.

Is there some other connected issue you have in mind to explore?

Howard

H.G. Callaway
(
hgcallaway[…]aol.com)

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

Subject: Re: Identity
From: Jon Awbrey <
jawbrey[…]oakland.edu>
Date: Wed, 20 Nov 2002 11:11:03 -0500
X-Message-Number: 10

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

SS: Cathy wrote: "And the long 1885 quote is about
the indiscernibility of identicals only."

SS: Are you sure? Note in the 1885 quote: "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. The other property is that if
everything which is true of i is true of j, then i and j are
identical."

SS: Isn't the "other property" the identity of indiscernibles?
(Well, almost. He obviously slipped, intending the protasis
to be "if everything which is true of i is true of j 'and'
everything which is true of j is true of i, then i and j
are identical".)

seth,

if "i" and "j" are individual terms, then they are determinate
on all of the properties that are available in the discussion.
if j has all of the properties of i, and if i is determinate
on all of the available properties, then, as an atom, j = i.

this assumes, as taken for granted in this context, that the "universe of marks"
is closed under negation, that is, if A is property then ~A is a property, and,
of course, if A is false of x then ~A is true of x. hence, the peculiarity.

jon

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

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

Subject: Re: pynchon and peirce
From: Victoria N. Alexander <
alexander[…]dactyl.org>
Date: Wed, 20 Nov 2002 12:06:15 -0500
X-Message-Number: 11

Dear Arnold,

As you are no doubt aware, many literary theorists have attempted to
argue that Peirce is "postmodern," that his semiotics in some sense
defines what postmodernism is. (I disagree with most of these readings.)
Links between Pynchon and Peirce's semiotics have been made, but if I
can show a stronger link or rather a different kind of link, then
deconstructionists will have to revise their notions of what
postmodernism is since Pynchon texts have certainly contributed to that
definition. My interpretation of postmodernism as constructive rather
than deconstructive agrees more or less with those found in the
collection of essays entitled _Founders of Constructive Postmodern
Philosophy: Peirce, James, Bergson, Whitehead, and Hartshorne_ (1993)

Victoria Alexander

On Wednesday, November 20, 2002, at 04:00 AM, Arnold Shepperson wrote:

> Victoria
>
> Welcome to Peirce-L, and may your association with the list be long,
> fruitful, and challenging.
>
> I majored in English Lit back in the late 1980s, but my focus had
> always been on the `realist' novel form that included Dickens, Gaskell,
> Eliot, and all the other State of England-related works that one could
> associate with South Africans like Nadine Gordimer, or more challenging
> stuff like that of JM Coetzee. In short, I didn't `get' my Lit thru the
> likes of Pynchon, and it rather challenges my view that one can indeed
> relate a realist like Peirce with a post-modern novelist like Pynchon!
> Thus does not mean to say, however, that some serious inquiry could
> emerge from this, and I for one would be intrigued by what comes out of
> your query.
>
> Cheers
>
> Arnold Shepperson
> Culture, Communication, and Media Studies
> University of Natal
> Durban 4041
> South Africa
>
> ---
> Message from peirce-l forum to subscriber
alexander[…]dactyl.org
> To unsubscribe send a blank email to: leave-peirce-
>
l-527695M[…]lyris.ttu.edu
>


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

Subject: computational mechanics and peirce
From: Victoria N. Alexander <
alexander[…]dactyl.org>
Date: Wed, 20 Nov 2002 12:11:51 -0500
X-Message-Number: 12

Several have asked for information on "computational mechanics" and an
explanation as to how it might relate to Peirce. I don't mind sharing my
research with every one since computational mechanics is the discovery
of my former colleague, James Crutchfield, I'm happy to encourage any
and all interest in that area. (Crutchfield was one of the original
investigators of deterministic chaos in the late 70s early 80s.) If you
do find this useful, please pay me the compliment of a footnote.

As the name implies, computation mechanics might be considered an
improvement on statistical mechanics. It takes into consideration not
just the statistical measure of order/disorder in a system but its
measure of "structural complexity." While statistical mechanics depends
upon a linear analysis of a system, computational mechanics is concerned
with a system's nonlinear properties. Peirce's interest in feedback may
make him an early predecessor of nonlinear dynamics, or at least makes
it seem as if the quality of his thought would have been receptive to
nonlinear dynamics. A comparison can be made to Peirce's semiotics
insofar as computational mechanics does not attempt to derive a model of
a system based on a data stream. Instead it takes successive models and
derives a metamodel based the changes in the causal architecture from
model to model. Thus, the metamodel is derived from the system itself,
not imposed by an observer as a model based on a data stream is.
Computational mechanics theorists claim they can defend the "relative
objectivity" of the metamodel. The metamodel provides the rule or
procedure that actually reproduces the pattern of which it is the
metamodel. CM is a theory of meaning and interpretation, or as
Crutchfield puts it, it's a "theory of theory building," and with CM the
discovery of the model of any system has become an automated process:
the subjective scientist has been removed from the picture. (Yes, I
realize the implications of that statement, and so does Crutchfield.)
The object of study in CM, I should clarify, is emergent phenomena (both
of self-organization and deterministic chaos) that is, any kind of
epiphenomena.

For further info:
James P. Crutchfield, "Calculi of Emergence: Computation, Dynamics, and
Induction," Physica D 75 (1994): 11-54.

My research can be found at
short talk:
http://www.dactyl.org/directors/vna/conf/dichotomies.html
dissertation:
http://www.dactyl.org/directors/vna/Narrative_Telos.htm
Search the document for "Crutchfield."

CM relates to Narratology insofar as it provides a theory of the theory
of narrative meaning.
Victoria Alexander

ps Would anyone be interested in reading and possibly commenting on my
article on Peirce and Pynchon before it goes into _Pynchon Notes_?

On Tuesday, November 19, 2002, at 09:01 PM, Victoria N. Alexander wrote:

> 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.
>
>
> ---
> Message from peirce-l forum to subscriber
alexander[…]dactyl.org
> To unsubscribe send a blank email to: leave-peirce-
>
l-527695M[…]lyris.ttu.edu
>


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

Subject: Re: computational mechanics and peirce
From: Kenneth Ketner <
b9oky[…]TTACS.TTU.EDU>
Date: Wed, 20 Nov 2002 11:28:33 -0600
X-Message-Number: 13

I am interested in your article. thanks

Victoria N. Alexander wrote:

>
> My research can be found at
> short talk:
http://www.dactyl.org/directors/vna/conf/dichotomies.html
> dissertation:
http://www.dactyl.org/directors/vna/Narrative_Telos.htm
> Search the document for "Crutchfield."
>
> CM relates to Narratology insofar as it provides a theory of the
> theory of narrative meaning.
> Victoria Alexander
>
> ps Would anyone be interested in reading and possibly commenting on my
> article on Peirce and Pynchon before it goes into _Pynchon Notes_?
>
>

--
Kenneth L. Ketner
Paul Whitfield Horn Professor
Institute for Studies in Pragmaticism
Texas Tech University
Charles Sanders Peirce Interdisciplinary Professor
School of Nursing
Texas Tech University Health Sciences Center
Lubbock, TX 79409-0002
806 742 3128
Office email:
b9oky[…]ttacs.ttu.edu
Home email:
ketner[…]arisbeassociates.com
Office website:
http://www.pragmaticism.net
Personal website:
http://www.wyttynys.net




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

Subject: Re: Limited Mark Universes
From: Jon Awbrey <
jawbrey[…]oakland.edu>
Date: Wed, 20 Nov 2002 12:40:59 -0500
X-Message-Number: 14

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

LMU. Note 6

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

| By their fruit flies ye shall know them.
|
| ~~ Pragmatic definition of a geneticist.

To be a language, formally speaking, L c A*, is to embody
a distinction between the strings or sequences of A* that
are in L and those that aren't. There are two exceptions,
or degenerate cases, if one prefers to view them that way,
two languages that draw no distinction in the space of A*.
These are the "empty language" L_0 = {}, so empty that it
fails to contain even so much as the empty string <>, and
the "total language" L_1 = A*.

Some would say that we are only doing syntax as this point,
but others say that the semantic and pragmatic dimensions
cannot be reduced to zero magnitudes, even in this frame.
For example it is possible to see in the present setting --
others would say "read into the present scene" -- a bit,
yes, exactly one bit, of semantic meaning and pragmatic
motive, namely the Peircean arrow from the nonsense of
non-L to the sense of L, except for the non-orientable
cases, of course.

Jon Awbrey

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

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

Subject: Re: pynchon and peirce [and Santayana?]
From: Mark Crosby <
Crosby_M[…]rocketmail.com>
Date: Wed, 20 Nov 2002 10:15:55 -0800 (PST)
X-Message-Number: 15

Hi, I know next to nothing about literary criticism
and the semiologies involved, but have just started to
read a bit of George Santayana. Is Santayana studied
'at all' (beyond, perhaps, a handful of specialists)
in literary criticism today?

Santayana, of course, was at Harvard when Peirce was
lecturing there early in the last century. Does anyone
know if Santayana himself or anyone else has ever
explicated how much of Peirce's semiotic Santayana
might have used in his own work, whether literary,
philosophical or political?

Per Thomas Alexander's wonderful 1993 article,
"Santayana's Unbearable Lightness of Being: Aesthetics
as a Prelude to Ontology" in _Overhead in Seville:
Bulletin of the Santayana Society_ at
http://www.math.uwaterloo.ca/~kerrlaws/Santayana/Bulletin/s1_93.htm
it seems that Santayana and John Dewey were sometime
sparring partners.. Alexander suggests in that article
that "Dewey and Santayana will emerge as truly
'postmodern philosophers', a term which I am sure
makes Santayana's shade in Limbo wince in disgust".
However, as Victoria suggests (I think) there could be
a constructive sense of 'postmodern' (maybe in the
sense of overcoming the errors of 'modernity'?)

With that sort of understanding of 'postmodernist' in
mind, if Peirce might play a role in such a
constructive undertaking, might not Santayana also
have a critical role to play?

Any clues along these lines would be appreciated,
Mark

--- "Victoria N. Alexander" <
alexander[…]dactyl.org>
wrote:
> Dear Arnold,
>
> As you are no doubt aware, many literary theorists
> have attempted to argue that Peirce is "postmodern,"
> that his semiotics in some sense defines what
> postmodernism is. (I disagree with most of these
> readings.)
> Links between Pynchon and Peirce's semiotics have
> been made, but if I can show a stronger link or
> rather a different kind of link, then
> deconstructionists will have to revise their notions
> of what postmodernism is since Pynchon texts have
> certainly contributed to that definition. My
> interpretation of postmodernism as constructive
> rather than deconstructive agrees more or less with
> those found in the collection of essays entitled
> _Founders of Constructive Postmodern Philosophy:
> Peirce, James, Bergson, Whitehead, and Hartshorne_
(1993)
>
> Victoria Alexander
>
> On Wednesday, November 20, 2002, at 04:00 AM,
> Arnold Shepperson wrote:
>
> > Victoria
> >
> > Welcome to Peirce-L, and may your association with
> > the list be long, fruitful, and challenging.
> >
> > I majored in English Lit back in the late 1980s,
> > but my focus had always been on the `realist'
novel
> > form that included Dickens, Gaskell, Eliot, and
> > all the other State of England-related works that
> > one could associate with South Africans like
> > Nadine Gordimer, or more challenging stuff like
> > that of JM Coetzee. In short, I didn't `get' my
> > Lit thru the likes of Pynchon, and it rather
> > challenges my view that one can indeed relate a
> > realist like Peirce with a post-modern novelist
> > like Pynchon!
> > Thus does not mean to say, however, that some
> > serious inquiry could emerge from this, and I for
> > one would be intrigued by what comes out of
> > your query.
> >
> > Cheers
> >
> > Arnold Shepperson
> > Culture, Communication, and Media Studies
> > University of Natal
> > Durban 4041
> > South Africa


__________________________________________________
Do you Yahoo!?
Yahoo! Web Hosting - Let the expert host your site
http://webhosting.yahoo.com


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

Subject: Santayana and literary studies
From: "Victoria N. Alexander" <
alexander[…]dactyl.org>
Date: Wed, 20 Nov 2002 13:42:41 -0500
X-Message-Number: 16



Mark Crosby wrote:

> Hi, I know next to nothing about literary criticism
> and the semiologies involved, but have just started to
> read a bit of George Santayana. Is Santayana studied
> 'at all' (beyond, perhaps, a handful of specialists)
> in literary criticism today?
>


The influence of Santayana on poet Wallace Stevens is pretty well
researched. In many of these writings, one will find references to
Peirce as well, another great influence of Stevens. Many Stevens critics
would also support an

understanding of his "postmodernist" project as a constructive undertaking.


Victoria Alexander


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

Subject: RE: pynchon and peirce
From: "Benjamin Udell" <
budell[…]hdgonline.net>
Date: Tue, 19 Nov 2002 22:31:42 -0500
X-Message-Number: 17

Welcome, Victoria, to peirce-l!

I've no idea about Pynchon. For whatever it may be worth, the two =
literary, though not particularly narrational, connections with Peirce =
that I'm aware of are:

"Cutpurse Philosopher", a page-&-a-half essay by Edward Dahlberg, =
collected in his _Alms for Oblivion_. The title refers not to Peirce but =
to a friend of Peirce's.

_Bottom: On Shakespeare_ by Louis Zukofsky which quotes from Peirce at =
some points.

It would be interesting if there were a list or index of literary =
references to Peirce.

Best,
Ben Udell

=20
Body: 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.
=20


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

Subject: Re: pynchon and peirce [and Santayana?]
From:
HGCALLAWAY[…]aol.com
Date: Wed, 20 Nov 2002 15:11:35 EST
X-Message-Number: 18

Mark Crosby wrote:

<< Hi, I know next to nothing about literary criticism
and the semiologies involved, but have just started to
read a bit of George Santayana. Is Santayana studied
'at all' (beyond, perhaps, a handful of specialists)
in literary criticism today?
>>

At the risk of possibly going on to showing my ignorance of pynchon and too
much of literary criticism (in spite of having a sometimes lively interest
for aesthetics and art), I would mention here that our text book, Stroh and
Callaway, _American Ethics_, University Press of America, 2000, contains a
final Chapter partly focused on Santayana with 4 selections --including "The
Genteel Tradition." My colleague Stroh is something of a Santayana
specialist, having done a dissertation at Prince-ton on Santayana. In any
case, sorting out some of Santayana and his relationship to other figures in
American philosophy is something we had to do in putting to-gether our book.

I believe I read the piece you mention by Tom Alexander, though this was some
time ago. I do think that Santayana is important to American philosophy and
some of its development during the 20th century. So, I would like to hear
more about other views of Santayana --and his relation to Peirce of course.

A "constructive" or maybe reconstructive "post-modernism" certainly sounds
better than a deconstructive version. Perhaps some would speak of
reconstructing moder-nity? Would that be equally acceptable? (Perhaps it
depends on what is meant by "modernity.")

Howard

H.G. Callaway
(
hgcallaway[…]aol.com)

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

Subject: Re: Identity and Teridentity: to Bernard (fwd)
From: Cathy Legg <
clegg[…]cyc.com>
Date: Wed, 20 Nov 2002 14:51:52 -0600 (CST)
X-Message-Number: 19

This message, which I sent last night, didn't come through to the list as
far as I can tell, so I'm sending it again. Apologies to anyone who
receives it twice.

Cathy.

---------- Forwarded message ----------
Date: Tue, 19 Nov 2002 22:57:38 -0600 (CST)
From: Cathy Legg <
clegg[…]cyc.com>
To: Peirce Discussion Forum <
peirce-l[…]lyris.acs.ttu.edu>
Subject: Re: [peirce-l] Re: Identity and Teridentity: to Bernard

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
>
>
> ---
> Message from peirce-l forum to subscriber
clegg[…]cyc.com
> To unsubscribe send a blank email to:
leave-peirce-l-60869T[…]lyris.ttu.e=
du
>

--=20

-------------------------------------------------------------------------=
-
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
-------------------------------------------------------------------------=
-




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

Subject: Re: computational mechanics and peirce
From: Inna Semetsky <
innasense[…]mac.com>
Date: Wed, 20 Nov 2002 13:49:08 -0800 (PST)
X-Message-Number: 20

Thanks for informative email, Victoria. Indeed, Prigogine himself acknowledeged his debt to Peirce in his "New Science of chaos". Later this connection has been picked up by Joseph Brent--although i dont know if he found prigogine's reference to peirce or realized himself that they speak the same language.
I remember we've discussed earler complex causal relations on this list with regard to the dynamics of intentional action and the concept of self-cause. I have a chapter in my dissertation on communication and self-cause, that is the necessity of multileveled causal relations as a prrecondition for emergence, top-down AND bottom-up.
inna

On Thursday, Nov 21, 2002, at 04:11AM, Victoria N. Alexander <
alexander[…]dactyl.org> wrote:

>Several have asked for information on "computational mechanics" and an
>explanation as to how it might relate to Peirce. I don't mind sharing my
>research with every one since computational mechanics is the discovery
>of my former colleague, James Crutchfield, I'm happy to encourage any
>and all interest in that area. (Crutchfield was one of the original
>investigators of deterministic chaos in the late 70s early 80s.) If you
>do find this useful, please pay me the compliment of a footnote.
>
>As the name implies, computation mechanics might be considered an
>improvement on statistical mechanics. It takes into consideration not
>just the statistical measure of order/disorder in a system but its
>measure of "structural complexity." While statistical mechanics depends
>upon a linear analysis of a system, computational mechanics is concerned
>with a system's nonlinear properties. Peirce's interest in feedback may
>make him an early predecessor of nonlinear dynamics, or at least makes
>it seem as if the quality of his thought would have been receptive to
>nonlinear dynamics. A comparison can be made to Peirce's semiotics
>insofar as computational mechanics does not attempt to derive a model of
>a system based on a data stream. Instead it takes successive models and
>derives a metamodel based the changes in the causal architecture from
>model to model. Thus, the metamodel is derived from the system itself,
>not imposed by an observer as a model based on a data stream is.
>Computational mechanics theorists claim they can defend the "relative
>objectivity" of the metamodel. The metamodel provides the rule or
>procedure that actually reproduces the pattern of which it is the
>metamodel. CM is a theory of meaning and interpretation, or as
>Crutchfield puts it, it's a "theory of theory building," and with CM the
>discovery of the model of any system has become an automated process:
>the subjective scientist has been removed from the picture. (Yes, I
>realize the implications of that statement, and so does Crutchfield.)
>The object of study in CM, I should clarify, is emergent phenomena (both
>of self-organization and deterministic chaos) that is, any kind of
>epiphenomena.
>
>For further info:
>James P. Crutchfield, "Calculi of Emergence: Computation, Dynamics, and
>Induction," Physica D 75 (1994): 11-54.
>
>My research can be found at
>short talk:
http://www.dactyl.org/directors/vna/conf/dichotomies.html
>dissertation:
http://www.dactyl.org/directors/vna/Narrative_Telos.htm
>Search the document for "Crutchfield."
>
>CM relates to Narratology insofar as it provides a theory of the theory
>of narrative meaning.
>Victoria Alexander
>
>ps Would anyone be interested in reading and possibly commenting on my
>article on Peirce and Pynchon before it goes into _Pynchon Notes_?
>
>On Tuesday, November 19, 2002, at 09:01 PM, Victoria N. Alexander wrote:
>
>> 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.
>>
>>
>> ---
>> Message from peirce-l forum to subscriber
alexander[…]dactyl.org
>> To unsubscribe send a blank email to: leave-peirce-
>>
l-527695M[…]lyris.ttu.edu
>>
>
>
>---
>Message from peirce-l forum to subscriber
irs5[…]columbia.edu
>To unsubscribe send a blank email to:
leave-peirce-l-36948S[…]lyris.ttu.edu
>
>


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

Subject: Re: pynchon and peirce [and Santayana?]
From: Mark Crosby <
Crosby_M[…]rocketmail.com>
Date: Wed, 20 Nov 2002 13:57:33 -0800 (PST)
X-Message-Number: 21

Thanks Howard, I think I'm finally going to put your
book on my wish list! Thanks also to Victoria: Wallace
Stevens seems to be a common currency on many
'sides'..

I might add, in 'answer' to my own query, that Nathan
Houser wrote an article, "Santayana's Peirce", in the
1990 _Overheard in Seville: Bulletin of the Santayana
Society_ -- most of that volume was devoted to Peirce
and Santayana. Unfortunately (for me) the articles in
this journal are only available online from 1993 on..

Another link that might be of interest to this
community is Henry Samuel Levinson's 1994 article
"Santayana and Making Claims on the Spiritual Truth
about Matters of Fact" at
http://www.math.uwaterloo.ca/~kerrlaws/Santayana/Bulletin/s1_94.htm
which seems to have a good deal to say about "sorting
out some of Santayana and his relationship to other
figures in American philosophy" (but folks here may
also have read this "some time ago" ;) Mark

---
HGCALLAWAY[…]aol.com wrote:
> Mark Crosby wrote:
>
> << Hi, I know next to nothing about literary
> criticism and the semiologies involved, but have
> just started to read a bit of George Santayana. Is
> Santayana studied 'at all' (beyond, perhaps, a
> handful of specialists) in literary criticism today?

> >>
>
> At the risk of possibly going on to showing my
> ignorance of pynchon and too much of literary
> criticism (in spite of having a sometimes lively
> interest for aesthetics and art), I would mention
> here that our text book, Stroh and Callaway,
> _American Ethics_, University Press of America,
> 2000, contains a final Chapter partly focused on
> Santayana with 4 selections --including "The
> Genteel Tradition." My colleague Stroh is something
> of a Santayana specialist, having done a
> dissertation at Prince-ton on Santayana. In any
> case, sorting out some of Santayana and his
> relationship to other figures in American philosophy
> is something we had to do in putting to-gether our
book.
>
> I believe I read the piece you mention by Tom
> Alexander, though this was some time ago. I do think
> that Santayana is important to American philosophy
> and some of its development during the 20th century.
> So, I would like to hear more about other views of
> Santayana --and his relation to Peirce of course.
>
> A "constructive" or maybe reconstructive
> "post-modernism" certainly sounds better than a
> deconstructive version. Perhaps some would speak of
> reconstructing moder-nity? Would that be equally
> acceptable? (Perhaps it depends on what is meant
> by "modernity.")
>
> Howard
>
> H.G. Callaway
> (
hgcallaway[…]aol.com)


__________________________________________________
Do you Yahoo!?
Yahoo! Web Hosting - Let the expert host your site
http://webhosting.yahoo.com

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

Subject: Re: Hermeneutic Equivalence Classes
From: Jon Awbrey <
jawbrey[…]oakland.edu>
Date: Wed, 20 Nov 2002 18:18:20 -0500
X-Message-Number: 22

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

| Leibniz, "Elements of a Calculus" (cont.)
|
| 14. What we have just said about terms which, in various ways, contain
| or do not contain each other, let us now transfer to their symbolic
| numbers. This is easy, since we said in article 4 that when a term
| helps to constitute another, i.e. when the concept of the term is
| contained in the concept of another, then the symbolic number of
| the constituent term is a factor of the symbolic number to be
| assumed as standing for the term to be constituted; or, what
| is the same, the symbolic number of the term to be constituted
| (i.e. which contains another) is divisible by the symbolic number
| of the constituent term (i.e. which is in the other).
|
| For example, the concept of animal helps to constitute the concept of man,
| and so the symbolic number of animal, 'a' (e.g. 2), together with another
| number 'r' (such as 3), will be a factor of the number 'ar', or 'h' (2 x 3,
| or 6) -- namely, the symbolic number of man. It is therefore necessary
| that the number 'ar' or 'h' (i.e. 6) can be divided by 'a' (i.e. by 2).
|
| Leibniz, 'Logical Papers', p. 21.
|
| Leibniz, G.W., "Elements of a Calculus" (April, 1679),
| G.H.R. Parkinson (ed.), 'Leibniz: Logical Papers', pp. 17-24,
| Oxford University Press, London, UK, 1966. (Couturat, 49-57).

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

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

Subject: RE: pynchon and peirce
From:
gsykes[…]zip.com.au (geoffrey sykes)
Date: Thu, 21 Nov 2002 12:12:45 +1100
X-Message-Number: 23


Benjamin, Victoria and list

One reference. From recollection following is about literature.

Sheriff, J. 1994. Charles Peirce's Guess at the Riddle. Grounds for Human
Significance. Bloomington: Indiana University Press.

Also an essay by same author, "Literary art: Meaning as a Sign of
Possibility". In Colapietro and Olshewsky, T., eds. 1996. Peirce's Doctrine
of Signs. Theory, Applications and Connections. New York: Mouton de Gruyter.

The issue of literature reminds of the interesting list discussion (some
months back) about Peirce and Emerson, late nineteenth century New England
literary culture, and Peirce's varying statements about poetry.

There seem to be many dispersed references to Peirce and postmodernism -
perhaps as many varieties as there are of the latter multi facted "movement"
- and too many to collate here. John Deeley has made a seemingly provocative
argument about the New List 1867 paper and postmodernism - one that seems
well overstated.

By the way, do you know the etymology of the PM term? It seems to be have
coined by the American poet Charles Olson, with specific literary associations.

Regards

Geoffrey Sykes




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

Subject: RE: pynchon and peirce
From: "Benjamin Udell" <
budell[…]hdgonline.net>
Date: Wed, 20 Nov 2002 20:09:49 -0500
X-Message-Number: 24

Geoffrey Sykes: < By the way, do you know the etymology of the PM term? =
It seems to be have coined by the American poet Charles Olson, with =
specific literary associations. >

Well don't just stop there, please tell the story. I had no idea Olson =
did that.

- Best, Ben Udell


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

Subject: prigogine and peirce
From: Victoria N. Alexander <
alexander[…]dactyl.org>
Date: Wed, 20 Nov 2002 20:44:10 -0500
X-Message-Number: 25

Inna,

Prigogine's description of emergent phenomena is a qualitative rather
than a quantitative one. This has long been the "problem" with the
complexity sciences in general and part of the reason why the conception
of emergence has been so easily absorbed by deconstructive
postmodernism. But a quantitative description of emergence would, I
think, fit better with a Peircean form of constructive postmodernism.
This is the hope at least with my work with computational mechanics.

Any more memories of the list's previous discussions of the dynamics of
intentional action would be appreciated, and I would like a link to your
dissertation if one is available.

Victoria

On Wednesday, November 20, 2002, at 04:49 PM, Inna Semetsky wrote:

> Thanks for informative email, Victoria. Indeed, Prigogine himself
> acknowledeged his debt to Peirce in his "New Science of chaos". Later
> this connection has been picked up by Joseph Brent--although i dont
> know if he found prigogine's reference to peirce or realized himself
> that they speak the same language.
> I remember we've discussed earler complex causal relations on this list
> with regard to the dynamics of intentional action and the concept of
> self-cause. I have a chapter in my dissertation on communication and
> self-cause, that is the necessity of multileveled causal relations as a
> prrecondition for emergence, top-down AND bottom-up.
> inna
>
[SEE MESSAGE EARLIER]


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

Subject: Re: prigogine and peirce
From: Inna Semetsky <
innasense[…]mac.com>
Date: Wed, 20 Nov 2002 18:32:30 -0800 (PST)
X-Message-Number: 26

Victoria

i look forward to learning more about this quantitative approach.

I asked you earlier if i may please have full citations of the two authors you mentioned. I wonder if computational mechanics is somehow related to analogue code becoming digital. If so, this problem was of interest to me for years, and still is. Qualitatively, again, it has been addressed by such authors as Emmeche and Hoffmeyer in evolutionary biology (from the semiotic perspective).
The author of action book is Alicia Juarrero, do not remember precise title now, and cannot check at the moment.
The link to my dissertation is available through google search, just type my name. but i think it's only first 20 pages and Peirce may not even be mentioned there yet, he was supplementary to two other, central, phil. figures in my diss.

inna

On Thursday, Nov 21, 2002, at 12:44PM, Victoria N. Alexander <
alexander[…]dactyl.org> wrote:

>Inna,
>
>Prigogine's description of emergent phenomena is a qualitative rather
>than a quantitative one. This has long been the "problem" with the
>complexity sciences in general and part of the reason why the conception
>of emergence has been so easily absorbed by deconstructive
>postmodernism. But a quantitative description of emergence would, I
>think, fit better with a Peircean form of constructive postmodernism.
>This is the hope at least with my work with computational mechanics.
>
>Any more memories of the list's previous discussions of the dynamics of
>intentional action would be appreciated, and I would like a link to your
>dissertation if one is available.
>
>Victoria
>
>On Wednesday, November 20, 2002, at 04:49 PM, Inna Semetsky wrote:
[SEE MESSAGE ABOVE]



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

Subject: Manifolds of Sensuous Impressions
From: Jon Awbrey <
jawbrey[…]oakland.edu>
Date: Wed, 20 Nov 2002 21:40:46 -0500
X-Message-Number: 27

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

MSI. Note 1

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

| 11. On the Hypotheses Which Lie at the Basis of Geometry
|
| On June 10, 1854, Bernhard Riemann delivered his probationary lecture
| as a candidate for an unpaid lectureship at G=F6ttingen. The title of =
the
| paper was "Ueber die Hypothesen welche der Geometrie zu Grunde Liegen".
| It is reported that the lecture won enthusiastic praise from Gauss and
| after its publication in 1867 it won similar praise throughout the
| mathematical world. One of the first to appreciate its importance
| was the English mathematician and friend of the Peirce family,
| William Kingdon Clifford. A first-rate mathematician himself,
| Clifford recognized the great importance of Riemann's lecture
| and in 1873 he translated it into English. It is quite probable
| that Clifford's praise of Riemann's work influenced Peirce's judgment
| of it. Concerning him, Peirce wrote, "Bernhard Riemann is recognized
| by all mathematicians as 'the' highest authority upon the philosophy
| of geometry". Since Peirce's views on the foundations of geometry
| are based on Riemann's, we must examine the latter's theory in
| some detail. (MGM, p. 219).
|
| Murray G. Murphey,
|'The Development of Peirce's Philosophy',
| first published, Harvard University Press, Cambridge, MA, 1961.
| reprinted, Hackett Publishing Company, Indianapolis, IN, 1993.

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

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

Subject: Re: Hermeneutic Equivalence Classes
From: Jon Awbrey <
jawbrey[…]oakland.edu>
Date: Wed, 20 Nov 2002 22:20:18 -0500
X-Message-Number: 28

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

| Leibniz, "Elements of a Calculus" (cont.)
|
| 15. When two terms are coincident, e.g. "man" and "rational animal", then
| their numbers, 'h' and 'ar', are in effect coincident (as 2 x 3 and 6).
| Since, however, the one term contains the other in this way, although
| reciprocally (for "man" contains "rational animal", and nothing besides;
| and "rational animal" contains "man", and nothing besides which is not
| already contained in "man"), it is necessary that the numbers 'h' and
| 'ar' (2 x 3 and 6) should also contain each other. This is the case,
| since they are coincident, and the same number is contained in itself.
|
| Furthermore, it is necessary that the one can be divided by the other,
| which is also the case; for if any number is divided by itself, the
| result is unity. So what we said in the previous article -- that
| when one term contains another the symbolic number of the former
| is divisible by the symbolic number of the latter -- also holds
| in the case of coincident terms.
|
| Leibniz, 'Logical Papers', pp. 21-22.
|
| Leibniz, G.W., "Elements of a Calculus" (April, 1679),
| G.H.R. Parkinson (ed.), 'Leibniz: Logical Papers', pp. 17-24,
| Oxford University Press, London, UK, 1966. (Couturat, 49-57).

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



---

END OF DIGEST 11-20- 02

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Page last modified by B.U. April 28, 2012, earliest in summer 2011 — B.U.

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