1. peirce and duration
2. Re: Identity & Teridentity
3. Re: Identity & Teridentity
4. Re: Late Gothic Architecture
5. John Rawls, Philosopher, RIP
6. Re: peirce and duration
7. Re: peirce and duration
8. Forms of sociality, the play of musement, and the community of
inquiry
9. CG course
10. Re: peirce and duration
11. Re: Identity & Teridentity
12. Re: Identity & Teridentity
13. Re: Reductions Among Relations
14. Re: McGinn on Popper
15. Re: Reductions Among Relations
16. Re: Identity & Teridentity
17. Triadic relation without mind ?
18. =?ISO-8859-1?Q?Peirce=27s?= philosophy of logical notation
19. Re: Identity & Teridentity
20. Re: Identity & Teridentity
21. Re: Identity & Teridentity
22. Re: Identity & Teridentity: to Howard
23. Re: Identity & Teridentity
24. Peirce, Leibniz and neoPlatonism
25. Re: Identity & Teridentity
26. Re: Identity & Teridentity
27. Re: Peirce, Leibniz and neoPlatonism

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

Subject: peirce and duration
From: gsykes[…]zip.com.au (geoffrey sykes)
Date: Tue, 26 Nov 2002 17:07:24 +1100
X-Message-Number: 1

Roger.

A good question.

Does Deleuze say anything about Peirce in this regard, say in his Cinema books?


Geoffrey




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

Subject: Re: Identity & Teridentity
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Tue, 26 Nov 2002 01:23:03 -0500
X-Message-Number: 2

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

I&T. Note 32

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

JA: A person who does not present the decomposition of a set with respect to sets
is not presenting the decomposition of a relation with respect to relations.

PB: Jon, I did not follow this post of yours, at all.
We have been decomposing 3-ary relations into
2-ary relations and back again, is all.

JA: Who's we?

PB: Database designers & engineers. According to you,
the database we are communicating through does not
implement relations ...

That's not what I said.

The examples that you have been discussing are all "one row databases" --
one particular sandwich, one particular trip between cities. You have
yet to introduce a single example of a non-trivial relation, much less
decompose it into other relations.

JA: You folks have been discussing nothing but single relation instances.
Thus, you have not even got as far (yet) as talking about relations,
which are SETS of relations instances.

PB: ... but I decompose and recompose n-ary relations losslessly
every day, actually most waking hours, so before accepting
your declaration, I would want an argument.

You do understand that we are talking
about 'unkeyed' relational tables here?
If you are thinking of a k-adic relation
with an extra key, then that is really
a (k+1)-adic relation.

Exercise. Show me a lossless reconstruction
of L_0 and L_1 from their 2-adic projections.

Jon Awbrey

o

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

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

Subject: Re: Identity & Teridentity
From: HGCALLAWAY[…]aol.com
Date: Tue, 26 Nov 2002 02:01:50 EST
X-Message-Number: 3

Gary, Charles, John, Peter, list,

You wrote, Gary, about one of the passages supplied by Charrles,

----quote----------
I would especially like to draw the attention of the list to this passage
near the end of 3.355. It places genuine thirdness "often" within nature
itself. This would suggest to me that teridentity is not just a device of
existential graphs (as Howard has suggested), but of CP: intelligibility, or
reason objectified
----end quote-----

Here follows the Peirce quotation you want to emphasize:

----Quote Peirce---------
Nature herself often supplies the place of the intention of a rational agent
in making a Thirdness genuine and not merely accidental; as when a spark, as
third, falling into a barrel of gunpowder, as first, causes an explosion, as
second. But how does nature do this? By virtue of an intelligible law
according to which she acts. If two forces are combined according to the
parallelogram of forces, their resultant is a real third. Yet any force may,
by the parallelogram of forces, be mathematically resolved into the sum of
two others, in an infinity of different ways. Such components, how-ever, are
mere creations of the mind. What is the difference? As far as one isolated
event goes, there is none; the real forces are no more present in the
resultant than any components that the mathematician may imagine. But what
makes the real forces really there is the general law of nature which calls
for them, and not for any other components of the resultant. Thus,
intelligibility, or reason objectified, is what makes Thirdness genuine.
----end quote------------

The idea here, I take it, is to emphasize thirdness as law, and surely the
concept of natural law plays an important role in Peirce's anti-nominalism.
So, we might expect that looking at the difference between teridentity and
identity (in standard contem-porary treatments) in terms of some relation to
law would help to resolve the appa-rent reduction of teridentity to standard
binary identity in contemporary logic. In a private message, Seth suggested
some similar ideas to me.

Let me repeat, though, the simple idea of the reduction of teridentity. If
the following
can be regarded as a formulation of teridentity,

Ixyz,

Then the idea is that we don't need teridentity, in standard logic, since we
can always just substitute "x=y & y=z" for "Ixyz."

So, the question would seem to be, does the idea of reference to law force us
to accept teridentity in contrast to the proposed alternative? If there is
some law involved in our coming to state or derive a claim making use of
"Ixyz," then it seems that we may employ the same law in deriving a
corresponding claim making use of something on the order of "x=y & y=z."

Consider again my suggestion about how folks may have come to identify the
morning star and the evening star. The idea is that we have some law or
observed regularity governing the movements or orbits of the planets (planets
being, perhaps,
just those heavenly bodies which move against the background of the fixed
stars,
whose relations to each other do not change from night to night). So, the
planets are found to move in particular sorts of orbits, and an orbit has
been calculated, say, for the evening star. On calculating an orbit for the
morning star it is found that the orbits of the morning star and the vening
star fit the same pattern. So, we identify the morning star and the evening
star. In some sense laws or law-like regularities
govern our conclusion that the morning star is the evening star.

But if we have the laws of planetary motion stated in our theory, do we also
need the concept of teridentity in order to identify the morning star and the
evening star? Actually, I don't see how it would help. Though we are guided
by some laws or law-like regularities in coming to identify the morning star
with the evening star, still that identification is a kind of hypotheses
intended to explain the congruence of the orbits of the morning star and the
evening star. It is a kind of hypothesis, in relation to the evidence
accumulated before the identification is made, and it is a kind of hypothesis
which might call for further checking. While accepting some role for law or
prior accepted generalization in the acceptance of the identity statement, it
remains unclear how the concept of teridentity might help make that
connection. If x is the morning star and y is the evening star, then what
could z be in the statement "Ixyz"? It is surely not the law or
generalization which may have rendered the identi-fication of the morning
star and the evening star plausible. So, whatever z may be, if "Ixyz" is
true, then so is "x=y & y=z."

So, I do not see how thirdness as law could be brought in here to argue for
teri-dentity in contrast to the proposed or apparent reduction of it. I
continue to think that the notion of teridentity may be connected with some
particularities of Peirce's system of graphs which we are yet to explore in
sufficient detail.

Howard

H.G. Callaway
(hgcallaway[…]aol.com)

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

Subject: Re: Late Gothic Architecture
From: HGCALLAWAY[…]aol.com
Date: Tue, 26 Nov 2002 02:13:00 EST
X-Message-Number: 4

Peirce-l,

A correspondent replies:

----quote---------
BTW, I recall with some amusement a 1950s Hammer Production movie starring
Vincent Price, in which the haunted structure had a Frank Lloyd Wright
prairie- school exterior with a high Victorian/neo-Gothic interior.
----end quote----

Though the message came to me privately, I thought this much of it too rich
not to share with the list.

Howard

H.G. Callaway
(hgcallaway[…]aol.com)

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

Subject: John Rawls, Philosopher, RIP
From: HGCALLAWAY[…]aol.com
Date: Tue, 26 Nov 2002 05:39:10 EST
X-Message-Number: 5

Peirce-l,

I've just seen a note from Robert Talissee, as follows:

----quote--------
John Rawls passed this weekend. Sad news. A memorial
is being planned for next month.
--Bob Talisse
----end quote---

The following I took from the notice published in the Boston Globe:

---quote------------
John Rawls

James Bryant Conant University Professor Emeritus, Harvard, died at his home,
Nov. 24, 2002 in Lexington, MA. Survived by his wife ... [and] ...children
...[and] grandchildren. A Memorial Service will be held Tues., Dec. 3, 2002
at 9:30 a.m. in the First Parish Unitarian Universalist Church, Harrington
Rd. on the Battlegreen, Lexington. Interment at Mt. Auburn Cemetery,
Cambridge. There will be a Memorial Celebration at Harvard University of John
Rawls' life and work to be arranged and announced at a later date. In lieu of
flowers, contributions may be made in John Rawls' name to Amnesty
International, Attn.: Memorial Gifts, 322 8th Ave., NY, NY 10001 or to the
John Rawls Memorial Fund at the Cary Memorial Library Foundation, 1605 Mass.
Ave., Lexington, MA 02420. Anderson
----end quote----------

Howard

H.G. Callaway
(hgcallaway[…]aol.com)

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

Subject: Re: peirce and duration
From: "Arnold Shepperson" <Sheppers[…]nu.ac.za>
Date: Tue, 26 Nov 2002 13:09:52 +0200
X-Message-Number: 6

Roger

I had a look thru the CP and the Robin Catalogue for items that might
have offered something in response to your query. I came up with the
following from Robin:

>> Quote Robin Catalogue
MS 138. Analysis of Time
A. MS., notebook, n.p., begun c.1904-05 with two entries dated August
13, 1908.
Four given rays may be crossed by how many rays? The analysis of the
Four-ray problem requires a consideration of continuity which in its
primitive, i.e., simple, sense has the form of time. Time as a
determination of actuality (later see annotation CSP dissents).
Definition of terms, e.g., instant, gradations. "I will not take up more
of this book with the subject of discrete quantity But I refer to a
similar book labelled 'All Pure Quantity merely ordinal' [MS. 224] for
more about it."

MS 141. On Topical Geometry, in General (T)
A. MS., G-undated-12, pp. 1-14, 4-8, 4-7, 5-7, 5, 9, 13.
Published, in part, as 7.524-538, except 534n4 and 535n6. Omitted from
publication is a discussion of the Kainopythagorean Categories centering
in the view that there are but three and that there can be no element in
experience not included in the three.

MS 390. Chapter IV. The Conception of Time essential in Logic
A. MS., n.p., July 1, 1873, 4 pp.
The conception of a logical mind presupposes a temporal sequence among
ideas, for every mind which passes from doubt to belief involves ideas
which follow one another in time. The flow of time is not by discrete
steps, but is continuous. "Continuum" defined.

MS 391. Chapter IV. The Conception of Time essential in Logic
A. MS., n.p., July 2, 1873, 8 pp.
MS. 391 is an expanded version of MS. 390.

MS 443. Causation and Force (TC)
A. MS., G-1898-1, pp. 1-35, plus discarded pp. 13-15, 13-14, 20, 28,
and 2 pp. with the titles "Time and Causation" (TC) and "Time and
Causality."
Published in three places in the following order: 6.66-81; 7.518-523;
6.82-72. Only the introductory first paragraph was deleted.

MS 740. Appendix No. 2
A. MS., n.p., n.d., 43 pp.
The hypothetic and sensational character of simple conceptions: The
Kantian position on space and time is analyzed. Difference in time is a
quantitative, continuous, commutative ground of disquiparance;
difference in space is a quantitative, continuous, noncommutative ground
of disquiparance.

MS 944. Jottings for 8 Lectures (D8)
A. MS., n.p., n.d., 2 pp. (two attempts); plus a typed copy.
Hegel and CSP mean nearly the same thing by existence. CSP can almost
accept Hegel's definition as the immediate unity of reflection-into-self
and reflection-into-another (his reservation concerns reflection). Hegel
misplaces existence by putting it under the first part of his
Encyclopaedia (Logic) and under the second division (Wesen), whereas he
places time under the second part (Nature). For CSP, time would first
have had to be organized before nature could have begun.

MS 1171. [Century Dictionary Supplement]
A. MS., n.p., n.d., 3 pp.
Definitions of "conceptual time" and "conceptual space."
End Robin <<

In the CP I got the following from 7.536:

>> 7.536. It remains to be shown that this element is the third
Kainopythagorean category. All flow of time involves learning; and all
learning involves the flow of time. Now no continuum can be apprehended
except by a mental generation of it, by thinking of something as moving
through it, or in some way equivalent to this, and founded upon it. For
a mere dull staring at a superficies does not involve the positive
apprehension of continuity. All that is given in such staring is a
feeling which serves as a sign that the object might be apprehended as a
continuum. Thus, all apprehension of continuity involves a consciousness
of learning. In the next place, all learning is virtually reasoning;
that is to say, if not reasoning, it only differs therefrom in being too
low in consciousness to be controllable and in consequently not being
subject to criticism as good or bad, -- no doubt, a most important
distinction for logical purposes, but not affecting the nature of the
elements of experience that it contains. In order to convince ourselves
that all learning is virtually reasoning, we have only to reflect that
the mere experience of a sense-reaction is not learning. That is only
something from which something can be learned, by interpreting it. The
interpretation is the learning. If it is objected that there must be a
first thing learned, I reply that this is like saying that there must be
a first rational fraction, in the order of magnitudes, greater than
zero. There is no minimum time that an experience of learning must
occupy. At least, we do not conceive it so, in conceiving time as
continuous; for every flow of time, however short, is an experience of
learning. It may be replied that this only shows that not all learning
is reasoning, inasmuch as every train of reasoning whatever consists of
a finite number of discrete steps. But my rejoinder is that if by an
argument we mean an attempt to state a step in reasoning, then the
simplest step in reasoning is incapable of being completely stated by
any finite series of arguments. For every step in reasoning has a
premiss, P, and a conclusion, C; and the reasoning consists in the
perception that if P is found true as it has been found true, then must
C be always or mostly true; and this "must" means that not only [is] C
true (or probable) unless P is false (or not found true in the way
supposed) but that every analogous premiss and conclusion are in the
same relation. That is to say, in the reasoning we observe that P has a
certain general character and C is related to it in a certain general
way, and further that given any proposition whatever of that general
character, the proposition related to it in that general way is true
unless the former proposition is false; whence it necessarily follows of
C and P, that either the former is true or the latter is false. But this
is a second argument involved in the reasoning. For the first argument
was

P is true,
Hence, C must be true;

while the second argument is

P has a general character P' and C has a relation r to P;

But given any proposition having the character P', the
proposition having the relation r to it is true unless the former is
false;

Hence, C is true unless P is false.

Thus, every reasoning involves another reasoning, which in its
turn involves another, and so on ad infinitum. Every reasoning connects
something that has just been learned with knowledge already acquired so
that we thereby learn what has been unknown. It is thus that the present
is so welded to what is just past as to render what is just coming about
inevitable. The consciousness of the present, as the boundary between
past and future, involves them both. Reasoning is a new experience which
involves something old and something hitherto unknown. The past as above
remarked is the ego. My recent past is my uppermost ego; my distant past
is my more generalized ego. The past of the community is our ego. In
attributing a flow of time to unknown events we impute a quasi-ego to
the universe. The present is the immediate representation we are just
learning that brings the future, or non-ego, to be assimilated into the
ego. It is thus seen that learning, or representation, is the third
Kainopythagorean category.
End 7.536

I hope this helps a wee bit. You can find the Robin Catalogue online
at the Peirce Edition Project:

http://www.iupui.edu/~peirce/web/robin/robin.htm

Cheers

Arnold Shepperson

On 26 November you wrote:
>>> roger.dawkins[…]student.unsw.edu.au 11/26/02 02:49am >>>
hello all,

i'm struggling with the following problem, and i'm wondering if anyone
could point me in the direction of a possible solution... william
james
compares peirce's doctrine of being to bergson's creative evolution
(_on
the notion of reality as changing_ 399). my question is, when peirce
is
examining the categories, does he refer explicitly to a pure form of
time
(bergon's duration or deleuze's aion)? obviously, for there to be the
kind
of novelty james is referring to, time cannot be chronological, but
does
peirce ever say as much? is it possible to say that firstness, as a
unique
sheet of assertion (deledalle) is the locus of a pure form of time...?

forgive me if i'm lost totally...

roger.

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

Subject: Re: peirce and duration
From: "Axel Schlotzhauer"
<axel.schlotzhauer[…]philosophie.uni-freiburg.de>
Date: Tue, 26 Nov 2002 13:37:15 +0100
X-Message-Number: 7

I think the following quote given by Arnold Shepperson is
the most helpful:

"MS 944. Jottings for 8 Lectures (D8)
A. MS., n.p., n.d., 2 pp. (two attempts); plus a typed
copy. Hegel and CSP mean nearly the same thing by
existence. CSP can almost accept Hegel's definition as the
immediate unity of reflection-into-self and
reflection-into-another (his reservation concerns
reflection). Hegel misplaces existence by putting it under
the first part of his Encyclopaedia (Logic) and under the
second division (Wesen), whereas he places time under the
second part (Nature). For CSP, time would first have had to
be organized before nature could have begun."

A pure being and time "beyond" the real time and being as
Hegel's classical position of potentiality and new creation
out of it is not the pragmatist position of James I
suppose.
Being is presumably similar for him to his position con-
cerning mind and consciousness: there are streams of being
(consciousness) as a dynamic approach to that phenomenon
and states of being (consciousness) as the static approach
trying to see existence or being not in a flux but as
"objects" of experience although such moments are more
precepts and concepts of awareness and reflection after the
experience. Peirce (1904) contradicted in the latter point
to James.

Both meet I think in stressing the time aspect and its
sequences in first place trying to get for scientific
research the relations in such sequences also as a question
of duration and continuum in the permanent alterations as
scientific laws.

By the Husserl in his phenomenology tried to constitute
time in a primordial experience, influenced by James, but
remained more in the static constitution of a "thing" and
stages in the experience.

I think James refers to Bergsons famous article - I have
not
read it - on the ilan vital (1908) putting such questions
in the form of a life philosophy functionally similar to
the
alterations caused in a time process. But classically that
point and I think Bergson remained in that position that
process is the change from the real to the ideal giving the
heightened experience - I think Bergson is near to the
oceanic feeling of Romain Rolland - of time and space as an
experience from the life force and sensual to the
metaphysical realm. If Bergson stresses this experience of
duration and the sequences in time James I think may see
a similarity to the position of Peirce setting time first
but also his approach. Although being more a classical
idealist Bergson was welcomed in pragmatism also by Mead
and his approaches to the phenomenon of energy and life
force.

Perhaps we may try to get some opinion on the William James
list.

Axel





On Tue, 26 Nov 2002 11:49:32 +1100
Roger Dawkins <roger.dawkins[…]student.unsw.edu.au> wrote:
> hello all,
>
> i'm struggling with the following problem, and i'm
> wondering if anyone
> could point me in the direction of a possible solution...
> william james
> compares peirce's doctrine of being to bergson's creative
> evolution (_on
> the notion of reality as changing_ 399). my question is,
> when peirce is
> examining the categories, does he refer explicitly to a
> pure form of time
> (bergon's duration or deleuze's aion)? obviously, for
> there to be the kind
> of novelty james is referring to, time cannot be
> chronological, but does
> peirce ever say as much? is it possible to say that
> firstness, as a unique
> sheet of assertion (deledalle) is the locus of a pure
> form of time...?
>
> forgive me if i'm lost totally...
>
> roger.
>
>
>
> ---
> Message from peirce-l forum to subscriber
> schlotza[…]uni-freiburg.de
> To unsubscribe send a blank email to:
> leave-peirce-l-9530I[…]lyris.ttu.edu

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

Subject: Forms of sociality, the play of musement, and the community of
inquiry
From: "Arnold Shepperson" <Sheppers[…]nu.ac.za>
Date: Tue, 26 Nov 2002 14:43:08 +0200
X-Message-Number: 8

Listers

My apologies for the overextended cultural-studies type header, but the
following article in the New Yorker just begged for comment on its
relevance for the subject-matters.

http://www.newyorker.com/printable/?critics/021202crbo_books

Cheers

Arnold Shepperson

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

Subject: CG course
From: Gary Richmond <garyrichmond[…]rcn.com>
Date: Tue, 26 Nov 2002 08:34:21 -0500
X-Message-Number: 9


--------------070904070807070309020506
Content-Type: text/plain; charset=us-ascii; format=flowed
Content-Transfer-Encoding: 7bit

Someone recently posted a page from a CG tutorial or course. Can that
person, or someone who has it at hand,
direct me to it as I seem to have misplaced it in my files somewhere.
Thanks.

BYT, Jay Zeman's very valuable paper (it my be his thesis) on EGs is now
on his web page:

http://www.clas.ufl.edu/users/jzeman/

I'd recommend at least the introduction and concluding
paragraphs,"Cleaning Up," to those not familiar with Peirce's
Existential Graphs (the Alpha and Beta forms which were modified by John
Sowa and others into Conceptual Graphs). The
3 chapters take take up the Alpha, Beta, and Gamma (modal) graphs
respectively. I can't completely agree with Jay's conclusions,
which seem to be that that as logics the 3 systems are successes (I
agree with this), while the great modal promise of the
Gamma graphs was probably "doomed from the
start" because of its inherent complexity (this I can't quite agree
with, especially
given the new technological tools evolving in the Semantic Web/
Pragmatic Web initiatives). Since Jay makes some headway
with the Gamma graphs himself, perhaps he meant for Peirce "doomed from
the start" (connecting large packs of tinctured
sheets of assertion, etc.)

Gary




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

Subject: Re: peirce and duration
From: Frances Catherine Kelly <frances.kelly[…]sympatico.ca>
Date: Tue, 26 Nov 2002 09:36:13 -0500
X-Message-Number: 10

Frances replies to Roger and others...

If we take Peirce back to the primordial stuff of the world, before the body of
god and the sign or word of god to the mind of god, then what is left of all
the continua such as energy or space or time that might be is a pure continuum,
be it infinite time or the mind of god, or both running along simultaneously.
This pure continuum would likely be the category of nomenal zeroness, acting as
an empty class holder ready to be used in some real way. As it is understood by
me, the ideal in the Peircean reality of action is continuity. Things however
continue by dispositional tendencies, and not as the result of mechanical
determinations caused by some agent of design like a god.

Peirce clearly tended to reduce things to ever more essential generalities, so
that the beginnings of being is its continuing infinite continuity, which
continuity is the only thing of raw stuff that is sensible to humans or that is
"given" uncontrolled to sense. To the extent that even the basic continuity of
original continua can be sensed, then it is real; which makes the reality of
all stuff a mental but not nominal construct.

Having stated these sweeping opinions of mine, which are based on my memory of
Peircean writings, some search will be conducted to find exact references
related to your specific questions on eternal time and its locus as pure
firstness, but any posted report will have to follow in due course.


Roger Dawkins partly wrote...

> "I'm struggling with the following problem, and I'm wondering if anyone
> could point me in the direction of a possible solution. William James
> compares Peirce's doctrine of being to bergson's creative evolution (on
> the notion of reality as changing 399). My question is, when Peirce is
> examining the categories, does he refer explicitly to a pure form of time
> (Bergon's duration or Deleuze's aion)? Obviously, for there to be the kind
> of novelty James is referring to, time cannot be chronological, but does
> Peirce ever say as much? Is it possible to say that firstness, as a unique
> sheet of assertion (Deledalle) is the locus of a pure form of time ?"




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

Subject: Re: Identity & Teridentity
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Tue, 26 Nov 2002 09:34:04 -0500
X-Message-Number: 11

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

I&T. Note 33

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

HC: Let me repeat, though, the simple idea of the reduction of teridentity.
If the following can be regarded as a formulation of teridentity,

HC: Ixyz,

HC: Then the idea is that we don't need teridentity,
in standard logic, since we can always just
substitute "x=y & y=z" for "Ixyz".

Howard, & All, ...

The very first two quotes that Seth cited on this
topic were concerned with two very different things:

One of them used the technical term "composition" and
one of them used the technical term "containment".

There is no contradiction between these two statements,
because they are talking about two different things.

The first is talking about relational composition,
that Peirce also called "relative multiplication"
or "relative product". In as much as a function
is a special case of a relation, this is a direct
generalization of ordinary functional composition.

Relational composition, with slight modifications
appropriate to the logical use, is analogous to
ordinary matrix multiplication, and Peirce often
represented it this way. In this sense of the
technical term "composition", it is a matter of
definition, not requiring proof, that 3-adic
relations are "indecomposable" to 2-adics.

If anyone should have any doubts as to what Peirce meant
by "relative product" in his earliest papers, or whether
he was still using the same concept later on in his work,
the fundamental analogy between relational "adinities" and
vertex "degrees" (also called "valencies") that is a basic
feature of Existential Graphs should dispell any such doubt.

A reader of Peirce's 1870 "Notation" who recognizes how much of
his technical language comes straight out of Leibniz would know
that the phrase "contained in", as used in the quotation at issue,
invokes a very different concept, that Peirce is here talking about
containment in the 'de inesse' or intensional sense, rather than the
extensional sense. Ignoring many niceties, this is more or less what
you are invoking with formulations of the form "F(x, y) & G(x, y)".

I wish that I knew the capital of ampersand, so that I could help
you to read such schemata the way that Peirce would have read them --
and as any computationally and semiotically sensitive reader could
hardly help but to read them -- beause the "&", in point of its
practical effects, is the biggest darn sign in that whole scheme.
And there is abundant evidence in what Peirce writes that he was
acutely aware that what the "&" evokes is nothing less than, and
nothing simpler than a 3-adic relation, interpretable as applying
either to sentences, to propositions, or to their truth values,
according to the application in question.

Given for free this one 3-adic relation, the one signified by "&",
as a part of one's "logical resource base", along with all of the
other 2-adic relations that one had in store beforehand, one can,
then, of course, construct a number of additional 3-adic relations.
But all of the newfound "generative potency" is tucked away in that
seed of 3-ness that is evoked by the "&".

Jon Awbrey

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

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

Subject: Re: Identity & Teridentity
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Tue, 26 Nov 2002 09:42:20 -0500
X-Message-Number: 12

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

I&T. Note 33

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

[correcting some typos -- JA]

HC: Let me repeat, though, the simple idea of the reduction of teridentity.
If the following can be regarded as a formulation of teridentity,

HC: Ixyz,

HC: Then the idea is that we don't need teridentity,
in standard logic, since we can always just
substitute "x=y & y=z" for "Ixyz".

Howard, & All, ...

The very first two quotes that Seth cited on this
topic were concerned with two very different things:

One of them used the technical term "composition" and
one of them used the technical term "containment".

There is no contradiction between these two statements,
because they are talking about two different things.

The first is talking about relational composition,
that Peirce also called "relative multiplication"
or "relative product". In as much as a function
is a special case of a relation, this is a direct
generalization of ordinary functional composition.

Relational composition, with slight modifications
appropriate to the logical use, is analogous to
ordinary matrix multiplication, and Peirce often
represented it this way. In this sense of the
technical term "composition", it is a matter of
definition, not requiring proof, that 3-adic
relations are "indecomposable" to 2-adics.

If anyone should have any doubts as to what Peirce meant
by "relative product" in his earliest papers, or whether
he was still using the same concept later on in his work,
the fundamental analogy between relational "adinities" and
vertex "degrees" (also called "valencies") that is a basic
feature of Existential Graphs should dispell any such doubt.

A reader of Peirce's 1870 "Notation" who recognizes how much of
his technical language comes straight out of Leibniz would know
that the phrase "contained in", as used in the quotation at issue,
invokes a very different concept, that Peirce is here talking about
containment in the 'de inesse' or intensional sense, rather than the
extensional sense. Ignoring many niceties, this is more or less what
you are invoking with formulations of the form "F(x, y) & G(y, z)".

I wish that I knew the capital of ampersand, so that I could help
you to read such schemata the way that Peirce would have read them --
and as any computationally and semiotically sensitive reader could
hardly help but to read them -- beause the "&", in point of its
practical effects, is the biggest darn sign in that whole scheme.
And there is abundant evidence in what Peirce writes that he was
acutely aware that what the "&" evokes is nothing less than, and
nothing simpler than a 3-adic relation, interpretable as applying
either to sentences, to propositions, or to their truth values,
according to the application in question.

Given for free this one 3-adic relation, the one signified by "&",
as a part of one's "logical resource base", along with all of the
other 2-adic relations that one had in store beforehand, one can,
then, of course, construct a number of additional 3-adic relations.
But all of the newfound "generative potency" is tucked away in that
seed of 3-ness that is evoked by the "&".

Jon Awbrey

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

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

Subject: Re: Reductions Among Relations
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Tue, 26 Nov 2002 16:20:36 -0500
X-Message-Number: 13

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

RAR. Note 13

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

Compositional Analysis of Relations (cont.)

Before we continue with the analysis of the Between relation, let us
take a moment to make sure that we understand the connections between
two topics that may appear at first to be entirely unrelated, namely:

1. A certain use of the logical conjunction, denoted by "&", as it appears
in logical expressions of the form "F(x, y, z) = G(x, y) & H(y, z)",
and that we use to define a 3-adic relation F by means of this "&"
and in terms of a couple of 2-adic relations G and H.

2. The concepts of 2-adic "projection" and "projective determination",
that are invoked in the "weak" notion of "projective reducibility".

Let us begin by drawing ourselves a picture of what is really going on whenever
we formulate a definition of F c XxYxZ via a conjunction of G c XxY and H c YxZ,
as we may choose to do by means of an expression of the following form:

F(x, y, z) = G(x, y) & H(y, z).

Visualize the 3-adic relation F c XxYxZ as a body in XYZ-space,
while G is a figure in XY-space and H is a figure in YZ-space:

o-------------------------------------------------o
| |
| o |
| /|\ |
| / | \ |
| / | \ |
| / | \ |
| / | \ |
| / | \ |
| / | \ |
| o o o |
| |\ / \ /| |
| | \ / F \ / | |
| | \ / * \ / | |
| | \ *** / | |
| | / \//*\\/ \ | |
| | / /// \\\ \ | |
| |/ ///\ /\\\ \| |
| o X /// Y \\\ Z o |
| |\ \/// | \\\/ /| |
| | \ /// | \\\ / | |
| | \ ///\ | /\\\ / | |
| | \/// \ | / \\\/ | |
| | /// \ | / \\\ | |
| | *//\ \ | / /\\* | |
| | */ \ \|/ / \* | |
| X * Y o Y * Z |
| \ G | | H / |
| \ | | / |
| \ | | / |
| \ | | / |
| \ | | / |
| \ | | / |
| \| |/ |
| o o |
| |
o-------------------------------------------------o
Figure 1. Projections of F onto G and H

Back in a sec ...

Jon

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

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

Subject: Re: McGinn on Popper
From: Charles F Rudder <cf_rudder[…]juno.com>
Date: Tue, 26 Nov 2002 15:52:56 -0600
X-Message-Number: 14




RAFE CHAMPION, LIST

Rafe,

This post was delayed longer than I intended. I have been trying to
assemble a patchwork of material from an unpublished manuscript that I
wanted to present as data in an effort to connect what I say here to some
earlier correspondence with Peter Brawley on Pierce and Popper. Having
struggled unsuccessfully to abbreviate my excerpted material in a way
that would cover the bases without bogging readers down in a review of
material with which they already well acquainted, with the exception of
three or four references to and quotations from Bacon and Hume, I finally
deleted the whole mess. The remaining excerpts are still offered as
_data,_ which is to say that despite any appearances to the contrary, my
intention is not didactic.

Rafe Champion writes:

_I am interested in the suggestion that Popper_s political philosophy is
difficult to reconcile with his logic of scientific discovery. The
common feature which Popper identified in his paper 'On the sources of
knowledge and of ignorance' is the non-authoritarian tenor of his
epistemology and his politics. He suggested that traditional epistemology
and traditional political philosophy share an authoritarian structure
which is manifest in the way that the fundamental questions are
formulated. In epistemology, "What is the source of knowledge?" (evidence
versus reason): in politics "Who should rule?". Popper suggested a
different approach, by way of error elimination in the quest for
knowledge, and controlling the power of political rulers so that even bad
ones cannot do too much damage before they are replaced._
End Quote

Without going into details, I will only say here that the root of the
difficulty I have relating Popper_s logic of scientific discovery to his
political philosophy lies in my belief that Popper_s account of the role
of empirical falsifiability and falsification in experimental tests of
scientific hypotheses will not generalize to his account of the roles of
criticism and self-criticism in theoretical arguments. I think that
Popper as much as admits this when he says, _Thus I was led to the idea
of methodological rules and of the fundamental importance of a critical
approach: that is, of an approach which avoided immunizing our theories
against refutation. At the same time, I also realized the opposite; the
value of a dogmatic attitude: somebody had to defend a theory against
criticism or it would succumb too easily, and before it had been able to
make its contribution to the growth of science._ (Objective Knowledge, p.
30.) This, in conjunction with Popper_s acknowledging the theoretical
necessity of accepting nonfalsifiable hypotheses on the strength of
_positive_ arguments: _My thesis is that realism is neither demonstrable
nor refutable. Realism like anything else outside logic and finite
arithmetic is not demonstrable; but while empirical scientific theories
are refutable, realism is not even refutable. . . . But it is arguable,
and the weight of the arguments is overwhelmingly in its favor._
(Objective Knowledge, p. 38.), it seems to me knocks any attempt to
reconcile Popper_s empirical falsification in experimental research with
criticism and self-criticism in theoretical inquiry into a cocked hat.

Rafe C.

_It may be true, as Charles suggested, that there is little new in
Popper_s _evolutionary epistemology_ but it is a salutary corrective to
logical positivism and logical empiricism._
E.Q.

I agree that Popper_s logic of scientific discovery is a valuable
contribution to arguments against mechanical and _data locked_ or _fact
bound_ accounts of the origin and development of scientific hypotheses in
many standard renditions of the scientific method. And, while I am
sympathetic to the role that Popper assigns to criticism and
self-criticism in philosophy and science, I am not as confident as McGinn
seems to be about the unity of Popper_s thought deriving from the
parallel roles of empirical falsifiability in experimental research and
rational criticism in theoretical inquiry.

Rafe C.

_The nature of the influence is difficult to work out because it seems
that Popper was not really aware of Peirce's work until late in life. The
same applied to Duhem; their critiques of induction are practically
identical, but Agassi reported that Popper only read Duhem's major work
in the 1950s._
E.Q.

I agree that unacknowledged influence is difficult if not impossible to
trace. With no additional information and provoked by Popper_s saying,
_Among the few dissenters was Charles Sanders Peirce, the great American
mathematician and physicist, and, I believe, one of the greatest
philosophers of all time._ (Objective Knowledge; _Of Clouds and Clocks,_
p. 212.) it would have been more accurate to have said that I am curious
about how familiar Popper was with Peirce_s work.

Mc Ginn on Popper

McGinn notes that, _Popper_s aim in proposing his criterion of
falsifiability as a mark of science was to answer what the called the
_demarcation problem_the problem of distinguishing science from
nonscience.__ which McGinn further notes and Popper admitted was
consonant with the logical positivists_ introduction of the
_verifiability principal of meaning_ as a criterion for setting
linguistically meaningful studies in logic and the sciences apart from
linguistically meaningless studies in theology and philosophy. What
McGinn does not tell us is that, according to Popper, the solution of the
demarcation problem depends on finding a valid solution of _Hume_s
Problem._ As Popper saw it, Hume had, (1) convincingly demonstrated that
earlier attempts to solve the logical demarcation problem were seriously
flawed, and (2) proposed an alternative psychological solution that was
also flawed. Popper_s critique of logical positivism is rooted in
Popper_s claims that the Vienna Circle and fellow travelers had ignored
Hume_s successful and devastating critique of earlier attempts to solve
the logical demarcation problem with the result that, (1) they were
repeating errors that Hume had already exposed, and (2) they failed to
address, much less solve, the residual problem, namely, Hume_s failure to
present a viable alternative solution of the demarcation problem. As
Popper puts it in one place:

_Hume must be credited with the formulation of the pure logical problem
of induction and its solutions (and I am proud that, as far as I know, I
was the first to credit him with it). He writes, for example, that we
have no reason to believe, _that those instances, of which we have had no
experience, [are likely to] resemble those, of which we have had
experience._ . . . This, then, in all its purity, is what I have
christened _Hume_s [logical] problem of induction._ Hume_s answer is as
clear as can be: there is no argument of reason which permits an
inference from one case to another, however similar the conditions may
be; and I completely agree with him in this respect. I believe, however,
that Hume is wrong when the thinks that in practice we make such
inferences, on the basis of repetition or habit. I assert that his
psychology is primitive._ (Objective Knowledge, p. 96.)

In sum, Popper argues that despite impressive nineteenth and early
twentieth century developments in the foundations of mathematics,
mathematical logic, and post-Newtonian physics to which a number of
logical positivists were substantial contributors, empiricist and
neo-Kantian epistemology or philosophy of science had stalled out with
Hume and, returning to Hume as its point of departure, needed to be
restarted.

WHAT DEMARCATION PROBLEM?

It is my personal opinion that, rather than adding _paradigm_ to the
honorific terms in technical vocabularies and blaming it on Thomas Kuhn,
we could have benefited by following Kuhn_s lead in proposing a _role for
history_ in contemporary efforts to untangle the whats and whys of
philosophical discourse since C. 1950.

Popper; Objective Knowledge, pp 32 _ 33:

_In my opinion, the greatest scandal of philosophy is that, while all
around us the world of nature perishes_and not the world of nature
alone_philosophers continue to talk, sometimes cleverly and sometimes
not, about the question of whether this world exists. The get involved
in scholasticism, in linguistic puzzles such as, for example, whether or
not there are differences between _being_ and _existing_. (As in
contemporary art, there are no standards in these worlds of philosophy.)
[Popper notes: _I am using the term _scholasticism_ to indicate an
attitude of arguing without a serious problem_an attitude that was by no
means universal among the schoolmen of the Middle Ages._]_

E. Q.

Reflecting, to paraphrase Lyotard, a general climate of intellectual
skepticism and "incredulity" toward medieval "grand narratives" which
also appears, among others, in the writings of Montaigne, Malabranche,
and Pierre Bayle, the works of Bacon and Descartes may be taken as
seventeenth century "reports on knowledge" set out in response to a
post-medieval "legitimation crisis" in the human and physical sciences.
Bacon and Descartes were offended by the academic wrangling among
Scholastic theologians and philosophers that Bacon describes as
contentious, pugnacious, specious and empty. Both took this
contentiousness as prima fascia evidence of the pernicious influence of
an intellectual and academic decadence and degeneracy under which the
sciences since antiquity had regressed. Given their assessments of the
disreputable state into which philosophy (science) had fallen, Bacon and
Descartes saw no alternative to abandoning the scholastic project and its
conclusions altogether in an effort to rebuild from scratch--proceeding
from new and secure foundations to reconstruct the sciences from the
ground up. Bacon and Descartes agreed that the ancients had made a noble
start and significant progress toward laying the ground work for the
rational conduct of human affairs which had been so corrupted by
Scholastic theologians and philosophers that any present and future
continuation of the ancient project required both a recovery of the rigor
of ancient science and a _method_ of inquiry by means of which science
could be distinguished from nonscience and thus avoid the regressive
consequences of repeating the kinds of error into which Scholasticism
had fallen.

Because Popper took Hume_s critique of earlier attempts to distinguish
science from nonscience and, hence, the problem itself, as unproblematic,
Popper_s unproblematic includes what Hume took as unproblematic and
problematic in the works of his predecessors, principal among which,
given Hume_s empiricist proclivities, were Francis Bacon and the Baconian
legacy. We must look (among others) to Descartes and Bacon for Hume_s
demarcation problem, and to Bacon for what Hume saw as problematic in
earlier efforts to solve the problem. Popper_s _demarcation problem_ is
Descartes_ and Bacon_s _demarcation problem,__to set out a criterion for
distinguishing genuine science from contemporary residues of Scholastic
pseudo-science_which Popper, who along with Hume rejected Cartesian a
priori rationalism, claims Hume successfully showed that Bacon failed to
solve.

McGinn says, _The simple fact is that induction is deeply embedded in
science and common sense, and there is no convincing reason why we should
declare it irrational._ Here it seems to me that McGinn misses Popper_s
point. Popper does not claim that [logical] induction is irrational;
Popper claims that [logical] induction does not occur. Popper sees
attempts to explain and defend the logical validity of scientific
theories inductively as erroneous which is not in itself irrational.
According to Popper, the progress of empirical science is a consequence
of _error elimination,_ which is to say that error which is inherent and
inevitable in the conjectures that are included in rational problem
solving is inherent and inevitable in rationality. From Popper_s point
of view, the only irrationality associated with induction is the
irrational refusal to admit its logical refutation_to admit an instance
of error elimination.

McGinn goes on to say that, _there is something contrived and artificial
about setting up an opposition here: for falsifying a statement is
equivalent to verifying its negation. If I make an observation that that
falsifies the statement that Jones is in the next room (I go there and
have a look), I thereby verify the statement that Jones is not in the
next room._ Here again, I believe McGinn misses Popper_s point.
Following Hume, Popper does not deny that propositions referring to
singular objects and occasions or specific points in space and time (A
specific individual, Jones, is in a specific place, the next room, now.)
are empirically verifiable. What Popper denies is that general
propositions are empirically/experimentally verifiable (Some individual
will always be in the next room at a certain time.) Popper_s claim,
again following Hume, is that, however often it is repeated, having a
look into the next room and finding an individual present at the
designated time cannot be logically construed as evidence that an
individual will be found on all future instances. If, however, on only
one occasion the room is empty at the designated time, then, according to
Popper, (a) an empirically verifiable singular proposition is true, and
(b) the true singular proposition contradicts, and, hence, falsifies the
general proposition. [Peirce addresses, and Popper does not, in
considerable detail the nature of and relations between _singular
propositions,_ and _particular,_ and _universal_ general propositions
that are germane to McGinn_s references to the facticity of London, H2O
molecules, and boiling points.] That is, believing that the general
proposition _Some individual will always . . ._ is false because a
singular proposition is true is not to believe that a _generalization_ is
true. That the room is found empty on one occasion, does not, for
instance, falsify or say anything else about the general assertion that
some individual is usually present in the room at the designated time_the
falsification of which would require establishing a criterion for
_usually_ and comparing the ratio of _absents_ to observations to the
ratio of _presents_ to observations. That is, statements of
probabilities are not _Popperian falsifiable_ which I see as a weakness
in Popper_s thesis that McGinn does not address.

Although I agree with McGinn that Popper is wrong in denying the logical
validity of experimental verification of scientific hypotheses, I believe
that McGinn (a) attacks a straw man in attributing to Popper the thesis
that, _observation plays no role in the production of theories as opposed
to their falsification, that all we ever do is conjure up imaginative
problem_solving hypotheses that we go on to try to falsify, and (b)
distorts the role of conjectures or guesses in Popper_s thesis when he
says that _it is absurd to suggest that basic high school science
consists of mere guesses that no one has managed to refute._

Popper never claimed that facts play no role either in the problematic
circumstances that provoke scientific inquiry or in the origin of
scientific theories and hypotheses which they obviously must if they are
to be factually falsifiable. Popper claims, that the origin of
scientific and all other hypotheses is conjectural in the sense that
their plausibility is not contingent on known facts_the same facts may
support the plausibility of any number of theories, and theories my posit
the existence of previously unobserved facts. That is, according to
Popper facts do not dictate theories and, hence, are not valid
pre-experimental criteria for choosing between or among different
theories. According to Popper, the best pre-experimental theories are
the most complex and hence, falsifiable theories; a point with which
McGinn seems to agree in his initial assessment of Popper_s contribution
and later on when he says, _Observation poses a question of explanation,
and creativity gets to work to produce the needed theory._

Neither does Popper claim that the settled conclusions of scientific
inquiry such as those included in basic high school texts are mere
conjectures or guesses. Here it seems to me that McGinn distorts Popper
as a consequence of a failure to address what Popper calls _Hume_s
problem_ and his alleged successful solution of Hume_s problem. Popper
claims that his original contribution to experimental logic consisted
first of an augmentation of Hume_s logical argument in which Popper
argues that the empirical falsification of scientific theories and
hypotheses is deductively valid, and second of an alternative to Hume_s
unsatisfactory attempt to solve the _demarcation problem_ by
demonstrating that the logical or non-psychological status of standing
scientific theories is rigorously unfalsified. As noted above, according
to Popper, Hume correctly pointed out that no consequences of careful and
extensive empirical testing can be strictly said to _verify_ scientific
theories and hypotheses, which for Popper and Hume would mean to
demonstrate necessary connections between empirical antecedents and
consequents.

Hume agreed with Bacon that the object of scientific inquiry was to
discover _formal causes_ or general _natural laws_ or _constant
connections_ between singular objects and events that determine the
present arrangements and future consequences of present arrangements of
singular objects and events and juxtapositions of or contiguous
connections between singular objects and events (_material_ and
_efficient_ causes). That is, the causal relation that concerned Bacon
and Hume was between formal and efficient causes under which, relative to
formal causes or natural laws, efficient causes were _effects._ As Bacon
puts it in one place:

_Now if a man's knowledge be confined to the efficient and material
causes [sense data] (which are unstable causes, and merely vehicles, or
causes which convey the form in certain cases), he may arrive at new
discoveries in reference to substances in some degree similar to one
another, and selected before hand; but he does not touch the deepest
boundaries of things. But whosoever is acquainted with forms [formal
causes], embraces the unity of nature in substances most unlike; and is
therefore to detect and bring to light things never yet done, and such as
neither the vicissitudes of nature, nor industry in experimenting, nor
accident itself, would have brought into act, and which would never have
occurred to the thought of man. From the discovery of forms therefore
results truth in speculation and freedom in operation._ [Bacon_s
acknowledging the reality of generals or laws puts him much closer to
what Peirce calls Scholastic Realism than Hume whose position is
radically nominalistic.]
E.Q.

But, Hume disagreed with Bacon's claim that the existence of formal
causes was inductively verifiable. We do, Hume admits, think and act as
if our experience of particular connections accessible to the senses is
constant, but, contrary to Bacon, Hume argues that no chain of reasoning
warrants such thought and action. Our senses inform us of the existence
of particular things like bread and billiard balls and of particular
qualities of things such as color, weight, and consistency. We also
perceive the actual motion and juxtaposition of bodies and the temporal
sequence of movement and contact between bodies. We do not, however,
perceive and, hence, can not except by a mental or abstract inference,
conceive any force or power which "would carry on a moving body for ever
in a continual change of place, and which bodies would never lose by
communicating it to others." We can trust past experience of particular
things and connections at specific points and instants in space and time:
"as to past experience, it can be allowed to give direct and certain
information of those precise objects only, and that precise period of
time, which fell under its cognizance." But, "why this experience should
be extended to future times and other objects"; that is, what evidence or
reason justifies the expectation that future experience of objects,
connections, and their consequences will remain similar to past objects,
connections, and consequences, is Hume's question.

The propositions, "I have found that such an object has always been
attended with such an effect." and "I foresee, other objects, which are,
in appearance, similar, will be attended by similar effects." are, Hume
notes, "far from being the same". Hume admits that consequents like _I
foresee such and so . . ._ are appropriately inferred from antecedents
like _I have found that such and so . . ._ , that is, apart from past
experience there is no reasonable means of anticipating future
experience. Experience reveals recurrent similarities among ideas of
objects and the consequences of their conjunction which psychologically
induce us to believe that in the future the conjunctions of similar
objects will have similar consequences: "In reality, all arguments from
experience are founded on the similarity which we discover among natural
objects, and by which we are induced to expect effects similar to those
which we have found to follow from such objects." But, Hume argues,
inferences from past to future can not be made by a consistent chain of
reasoning. There is always a "missing link", or, as Hume puts it, the
absence of a medium, "which may enable the mind to draw such an
inference, if indeed it be drawn by reasoning and argument." Bacon,
Locke, and presumably Newton to the contrary, Hume's conclusion
concerning knowledge of, in contrast to beliefs about, matters of fact is
that inductive logical proofs of constant or necessary connections
between matters of fact are impossible, and in actuality do not occur.

Hume claims to be able to identify in observation and memory of matters
of fact only ideas of resemblance and contiguity, while ideas of constant
connections go beyond experience of matters of fact. Consequently, the
experiential evidence that past conjunctions of similar objects have had
similar consequences can not justify the logical conclusion "therefore,
experience of future conjunctions of objects similar to past objects will
have similar consequences." or the logically equivalent inference "if
past experiences of the conjunction of similar objects have had similar
consequences, then future experiences of objects similar to past objects
will have similar consequences." Hume_s "missing link" or "medium" is
that which justifies the transitive relation indicated by "therefore" or
"if--then". Ideas of matters of fact being confined to relations of
resemblance and contiguity, no valid logical inference will justify the
assertion of any constant transitive relation or continuity between past
and future resemblances. Contiguity, the relation between objects in the
antecedent, does not resemble transitivity which is the relation between
terms in the consequent, and the mere resemblance or similarity between
ideas of objects and events does not empirically eliminate, or provide
the necessary conditions for logically eliminating, the possible
existence of scientifically significant dissimilarities between ideas of
objects and events. In short, Hume argues, at no point in the conduct of
scientific inquiry do we have access to any empirical, experimental, or
logical means of proving that the consequences of future observation and
experimentation will not contradict beliefs and expectations based on
past observations and experiments.

Assuming all of the above, Popper argues that Hume failed to see that
because the logical form of theoretical assertions is universal (for
_all_ ____ such and so holds) one empirical contradiction is sufficient
to falsify (_not all_) scientific hypotheses, while the best that can be
said for so called successful observations and experiments is that they
have _survived_ rigorous efforts to falsify them. But, the best that can
be said for the settled results of scientific inquiry, is, according to
Popper, considerably better than what Hume was willing to concede. If,
according to Hume, neither experimental conclusions nor those of "mixed"
hypothetical arguments provide evidence that the conclusions of
theoretical arguments are true--if physics does not consist of
experimentally or hypothetically verifiable ideas of universal scientific
laws--then of what does physics consist and how does it proceed? Hume's
answer to these questions is that physics and other experimental sciences
consists of empirically verifiable ideas of particular objects, their
conjunctions, and temporal sequences of conjunctions at specific points
and instants in space and time conjoined with experimentally and
hypothetically unverifiable abstract ideas of natural laws which we are
psychologically induced to believe:

_What, then, is the conclusion of the whole matter? A simple one;
though, it must be confessed, pretty remote from the common theories of
philosophy. All belief of matter of fact or real existence is derived
merely from some object, presented to the memory or senses, and a
customary conjunction between them and some other object. Or in other
words; having found, in many instances, that any two kinds of objects--
flame and heat, snow and cold--have always been conjoined together; if
flame or snow be presented anew to the senses, the mind is carried by
custom to expect heat or cold, and to believe that such a quality does
exist, and will discover itself upon a nearer approach._


In short, the conclusions of scientific inquiry consist of habitual or
customary beliefs and expectations which are unverifiable inferences from
verifiable past experiences.

Popper sees the survival of rigorous efforts to falsify scientific
hypotheses as a stronger logical case than Hume_s because it makes the
logical warrant for accepting scientific theories and hypotheses _not yet
empirically falsified_ rather than mere psychological habituation. That
is, to any psychologically and sociologically induced confidence and
prestige that may attach to the results of scientific inquiry is added
the _positive_ reason that they have been rigorously tested and remain
unfalsidied. In short, the settled conclusions of scientific
investigation are not _mere_ guesses, but guesses that through an
experimental _winnowing process_ have survived the extinction of other
guesses that did not pass experimental tests.

One final comment on _McGinn on Popper._ McGinn_s claim that, _Popper_s
criterion of falsification can still be applied to such subjects as
history, language translation, and common-sense psychology._ is subject
to the same confusion of the difference between Popper_s empirically
verifiable singular propositions and non-verifiable general propositions.
McGinn_s saying that, _Historical statements can be falsified by the
examination of records and other traces of the past . . ._ refers to
statements like _A person is presently in the next room._ If by history
one means simply a descriptive activity such as compiling records of past
events, then McGinn is correct in saying that history meets Popper_s
criterion for a science. If, however, one takes history, psychology, and
other social sciences as presenting and defending inferential _systems_
like those of Hegel, Marx, and Piaget, it is not clear that history and
the social sciences pass Popper_s test. I would say that for Popper the
primary contemporary form of the _demarcation problem_ is distinguishing
genuine from pseudo _social sciences._

Charles




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

Subject: Re: Reductions Among Relations
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Tue, 26 Nov 2002 18:25:25 -0500
X-Message-Number: 15

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

RAR. Note 14

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

Compositional Analysis of Relations (cont.)

The 2-adic "projections" Proj_XY, Proj_XZ, Proj_YZ, for
any 3-adic relation L c XxYxZ, along with the equivalent
forms of application L_XY, L_XZ, L_YZ, respectively, are
defined as follows:

Proj_XY (L) = L_XY = {<x, y> in XxY : <x, y, z> in L for some z in Z},

Proj_XZ (L) = L_XZ = {<x, z> in XxZ : <x, y, z> in L for some y in Y},

Proj_YZ (L) = L_YZ = {<y, z> in YxZ : <x, y, z> in L for some x in X}.

In light of these definitions, Proj_XY is a mapping
from the space !L!_XYZ of 3-adic relations L c XxYxZ
into the space !L!_XY of 2-adic relations M c XxY, and
similarly, mutatis mutandis, for the other projections.

In mathematics, the inverse relation of a projection is
usually called an "extension", but in view of the ample
confusion that we already have in logic over extensions
and intensions and comprehensions and so on, I will try
to guard against against confusion in this context by
always using the adjective form of "tacit extensions".

The "tacit extensions" TE_XY_Z, TE_XZ_Y, TE_YZ_X,
of the 2-adic relations U c XxY, V c XxZ, W c YxZ,
respectively, can be defined in the following way:

TE_XY_Z (U) = {<x, y, z> : <x, y> in U},

TE_XZ_Y (V) = {<x, y, z> : <x, z> in V},

TE_YZ_X (W) = {<x, y, z> : <y, z> in W}.

It will be clear enough to write TE(U), TE(V), TE(W),
respectively, so long as the contexts are understood.

In our present application, we are making use of
the tacit extension of G c XxY to TE(G) c XxYxZ and
the tacit extension of H c YxZ to TE(H) c XxYxZ, only.

Here are the snapshots:

o-------------------------------------------------o
| |
| o |
| /|\ |
| / | \ |
| / | \ |
| / | \ |
| / | \ |
| / | \ |
| / | * \ |
| o o ** o |
| |\ / \*** /| |
| | \ / *** / | |
| | \ / ***\ / | |
| | \ *** / | |
| | / \*** / \ | |
| | / *** / \ | |
| |/ ***\ / \| |
| o X /** Y Z o |
| |\ \//* | / /| |
| | \ /// | / / | |
| | \ ///\ | / / | |
| | \ /// \ | / / | |
| | \/// \ | / / | |
| | /\/ \ | / / | |
| | *//\ \|/ / * | |
| X */ Y o Y * Z |
| \ * | | * / |
| \ G | | H / |
| \ | | / |
| \ | | / |
| \ | | / |
| \ | | / |
| \| |/ |
| o o |
| |
o-------------------------------------------------o
Figure 2. Tacit Extension of G to X x Y x Z

o-------------------------------------------------o
| |
| o |
| /|\ |
| / | \ |
| / | \ |
| / | \ |
| / | \ |
| / | \ |
| / * | \ |
| o ** o o |
| |\ ***/ \ /| |
| | \ *** \ / | |
| | \ /*** \ / | |
| | \ *** / | |
| | / \ ***/ \ | |
| | / \ *** \ | |
| |/ \ /*** \| |
| o X Y **\ Z o |
| |\ \ | *\\/ /| |
| | \ \ | \\\ / | |
| | \ \ | /\\\ / | |
| | \ \ | / \\\ / | |
| | \ \ | / \\\/ | |
| | \ \ | / \/\ | |
| | * \ \|/ /\\* | |
| X * Y o Y \* Z |
| \ * | | * / |
| \ G | | H / |
| \ | | / |
| \ | | / |
| \ | | / |
| \ | | / |
| \| |/ |
| o o |
| |
o-------------------------------------------------o
Figure 3. Tacit Extension of H to X x Y x Z

Finally, we can now supply a visual interpretation
that helps us to see the meaning of a formula like:

F(x, y, z) = G(x, y) & H(y, z).

The conjunction that is indicated by "&" corresponds as usual
to an intersection of two sets, however, in this case it is
the intersection of the tacit extensions TE(G) and TE(H).

o-------------------------------------------------o
| |
| o |
| /|\ |
| / | \ |
| / | \ |
| / | \ |
| / | \ |
| / | \ |
| / | \ |
| o o o |
| |\ / \ /| |
| | \ / F \ / | |
| | \ / * \ / | |
| | \ *** / | |
| | / \//*\\/ \ | |
| | / /\/ \/\ \ | |
| |/ ///\ /\\\ \| |
| o X /// Y \\\ Z o |
| |\ \/// | \\\/ /| |
| | \ /// | \\\ / | |
| | \ ///\ | /\\\ / | |
| | \ /// \ | / \\\ / | |
| | \/// \ | / \\\/ | |
| | /\/ \ | / \/\ | |
| | *//\ \|/ /\\* | |
| X */ Y o Y \* Z |
| \ * | | * / |
| \ G | | H / |
| \ | | / |
| \ | | / |
| \ | | / |
| \ | | / |
| \| |/ |
| o o |
| |
o-------------------------------------------------o
Figure 4. F as the Intersection of TE(G) and TE(H)

Jon Awbrey

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

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

Subject: Re: Identity & Teridentity
From: "Seth Sharpless" <seth.sharpless[…]colorado.edu>
Date: Tue, 26 Nov 2002 16:37:16 -0700
X-Message-Number: 16

Jon Awbrey wrote:
~~~~~~~~~~~~~~~~~~~~~~~~
A reader of Peirce's 1870 "Notation" who recognizes how much of
his technical language comes straight out of Leibniz would know
that the phrase "contained in", as used in the quotation at issue,
invokes a very different concept, that Peirce is here talking about
containment in the 'de inesse' or intensional sense, rather than the
extensional sense. Ignoring many niceties, this is more or less what
you are invoking with formulations of the form "F(x, y) & G(y, z)".
~~~~~~~~~~~~~~~~~~~~~~~~~
=20
I reply:

Jon, the "quotation at issue" was:

~~~~~~~~~~~~~~~~~~~
Now, identity is essentially a dual relation. That is, it requires two
subjects and no more. If three objects are identical, this fact is
entirely contained in the fact that the three pairs of objects are
identical. CP1.446 (1896)
~~~~~~~~~~~~~~~~~~~

As usual, Jon, you baffle me. What can you mean by "in the
'de inesse' or intensional sense, rather than the extensional
sense"? For Peirce, "de inesse" refers to the extensional=20
sense, in which the subjects are existing singulars and the
mode is that of the material conditional. In other words,=20
it is concerned with relations between individuals, not
between ideas. =20

Intensional refers to the relations between ideas, as of the
modal or "would-be" and "might-be" universe of discourse. =20

~~~~~~~~~~~~~~~~~~~~~~~~~
CP2.323. (1902) Indexical Dicisigns seem to have no important
varieties; but propositions are divisible, generally by dichotomy
primarily in various ways. In the first place, according to=20
Modality or Mode, a proposition is either de inesse (the
phrase used in the Summulae) or modal. A proposition
de inesse contemplates only the existing state of things--existing,
that is, in the logical universe of discourse. A modal proposition
takes account of a whole range of possibility. =20

CP4.376. A proposition de inesse relates to a single state of the
universe, like the present instant. Such a proposition is
altogether true or altogether false. (Baldwin's Dictionary, 1911?)
~~~~~~~~~~~~~~~~~~~~~~~~~~

If you could bring yourself to back off of the claim that the=20
"containment" at issue is in the "intensional" sense (but I know=20
you can't; your tender ego and _ad hominem_ mode of argument
won't allow you to admit a mistake), we might be able to make
some progress in understanding the significance of the following
quotes, which were at issue in connection with the principle of=20
indiscernibility of identicals. =20

~~~~~~~~~~~~~~~~~~~
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)
~~~~~~~~~~~~~~~~~~~~

From a _de inesse_ point of view, the merged drops or optical
images, at the instant of their merger, are indeed not discernable.
But if we take account of their future courses, during which they
may separate and interact, which we can only do by abandoning
the _de inesse_ view and adopting an intensional view in which we
consider the range of possibilities, they are distinct. The universe of
discourses, intensional or extensional, are relevant. =20

This also bears on teridentity. For Peirce's examples of teridentity in
CP always involve entities that persist in time, a gift that _becomes_
the possession of another, or a person met on Monday, Tuesday and
Wednesday. It would seem that one is not entitled to conjoin=20
extensional binary identity claims made at different times with an
AND to yield a triadic identity, without appealing to intensional
criteria
of identity. If this is correct, teridentity statements would always be

intensional claims.

Unfortunately, I don't think this entirely clears things up.

I am still troubled by a sense that for Peirce, it seems that the
subjects of those rain-drop or optical-image quotes are somehow
directly indexed, so that identification would be a matter of=20
secondness rather than thirdness, as would be the case if the
reference were to future possibilities.

For my part, I am still confused, but I am trying to understand and
would welcome (non ad-hominem) explanations, hopefully translated
into the vernacular. =20
Seth
=20


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

Subject: Triadic relation without mind ?
From: Christophe Menant <crmenant[…]free.fr>
Date: Tue, 26 Nov 2002 22:06:38 +0100 (CET)
X-Message-Number: 17


Thanks Joe for having made available the quotes relevant
to "genuine/degenerate" distinction.
When going thru them, another point came up. It is about the field
of application of Peirce triadic approach.
I have been again under the impression that Peirce introduces the
triadic relation as being essentially linked to a human mind.
Despite the "Sunflower example", it looks like Peirce may not have
been really willing to consider explicitly cases of lower levels of
organization, like non human life.
Some quotes:
CP 1.345: very genuine triadic relations involves thought or meaning.
CP 1.372: there is a triple connection of sign, thing, signified,
cognition produced in the mind.
CP 2. 274: a Sign is a Representamen with a mental Interpretant.
CP 3.360: a sign is a conjoint relation to the thing denoted and to
the mind....the sign is related to its object only in consequence
of a mental assocation.
CP 8.331: the inadequacy of Secondness to cover all that is in our
minds.

Of course, these quotes are only a very small sampling of Peirce's
writings. But the triadic relation is clearly referred there to
thought, mental and mind.

Could it be possible to know if Peirce has explicited somewhere
the applicability of his triadic approach to non human life ?

Regards
Christophe Menant (crmenant[…]free.fr)

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

Subject: =?ISO-8859-1?Q?Peirce=27s?= philosophy of logical notation
From: Gary Richmond <garyrichmond[…]rcn.com>
Date: Tue, 26 Nov 2002 18:58:10 -0500
X-Message-Number: 18




Paraphrase of Liu-hua Zhang's summing up of his abstract:

Summing up: Peirce's philosophy of logical notation contains many
illuminating suggestions as well [as being an] original and extensive
[contribution. to logic] If [we were to ] examine [the] philosophy of
notation [in relation to current developments in] linguistics, computer
science and philosophy, then we [might conclude]:: logical notation is
not [a] trivial matter, so how to achieve [an optimal weaving] of
icons, indexes and symbols, is [essentialas regards] the progress of
logic, [it is] no longer only a question of arbitrary formal arrangement.

http://ewisdom.myetang.com/abstract-en.htm

Peirce's philosophy of logical notation

by Zhang Liu-hua <mailto:liuhwazhang[…]21cn.com>


Abstract
In some measure, logic, or at least modern logic, can be perceived as
"notation of reasoning". It is known that logic treats reasoning (and
argumentation) as the central subject. However, logic consists in not
only study of reasoning, but in a crucial sense it consists in the study
of reasoning by convenient notation, which tell you how to represent
reasoning in some suitable notation and make reasoning efficiently by
the notation. Many facts in history of logic make it clear that logical
notation, making much sense, should be regarded as an important matter.

Logic and notation is not a new topic, but in the past it often behaves
as relation between sign and inference. As mathematical notation played
a revolutionary role in the development of algebra and geometry in the
abstract, the new logical notation mainly illuminated by the algebraic
notation brought on the birth of modern logic in a more direct sense.
American logician C.S.Peirce, one of the founders of modern logic, shows
greater zeal for exploration and research in logical notation than his
many contemporaries. He, for the first time in history of logic, made an
inviting exposition and discussion on the profound significance of
logical notation, and advanced "philosophy of notation" in his
terminology. The dissertation titled "Peirce's philosophy of logical
notation", concentrates on discussing the methodological bearing of
Peirce's notation on his elementary logic, Peirce's logical thoughts on
types of signs, and Peirce's quest for an ideal logical notation, trying
to touch into and reveal Peirce's comprehensive and original
contribution through his investigation on logical notation on one hand
and attach more importance than people commonly would to logical
notation on the other hand.

Firstly, the article expounded that Peirce's unique semiotics offered
the widest context and frame for investigating logical notation,
particularly from points of view of sign revealing the inherent links
between notation and logic: semiotics as logic. In general, logical
notation is sign or sign system. Logicians all through the history
concerned studies of signs. Peirce, a distinguish logic historian,
grounding on his irreductive triadic relation between Sign, Object and
Iinterpretant, developed his Semieotic which is distinct from Saussure's
Semiology, and then used the semiotic as the comprehensive context for
investigating logical notation and all his logic theory. Having
synthesized and abstracted types of signs in the logic history, he
classified signs into icons, indices and symbols. Subsequently, this
notable classification of signs was adopted by many logicians,
linguists, philosophers and cognitive scientists. Next, he pointed out
that each of icon, index and symbol is essential for a perfect logical
notation, as becomes a foundational idea of Peirce's philosophy of
logical notation in some degree. In the whole, Peirce's investigation on
signs is always along with his logical research. He said, "Logic, in its
general sense, is, as I believe I have shown, only another name for
semiotic".

Secondly, the article, via a few instances of logical notation in modern
logic, analyzed the refinement and profoundness of Peirce's algebraic
notation, mirrored some important contribution in his early logical
research, and indicated Peirce's algebraic notation as a source of
standard logical notation today. Inclusive disjunction "+", limited
discourse of universe "1", material implication"--<" and universal and
particular quantifiers (in a sense of modern logic) "? " " ?" not only
spread out Peirce's great improvement on notation of Boolean algebra,
but also took on severe logical significance in Peirce. In practice,
Peirce's various thoughts of algebraic notation directly speeded up
maturing propositional logic and predicate logic in initial stages of
modern logic.

Lastly, the article, introducing Peirce's Existential Graphs on the
backgrounds of logical diagrams in history, analyzed and assessed
Peirce's Existential Graphs and its superiority and developmental
perspectives, trying to claim that Peirce's graphic notation not only
radically improves on logical diagrams in history but also shows to
logicians in right of its tremendous logical expressive power that,
besides traditionally algebraic notation, there is an independent
diagrammatical logical notation. Existential Graphs, which Peirce
dedicated his later life to, is a two-dimensional notation which is
different from his early linear algebraic notation, as is called by
Peirce "my chef d'oeuvre". His finished "Alpha" and "Beta" portions of
Existential Graphs correspond respectively to propositional logic and
predicate logic we commonly use today, and have proved to be consistent
and complete by some peircians and logicians. Moreover the "Gamma"
portion of Existential Graphs which Peirce himself hadn't finished in
his life covers evidently the thoughts of modal logic and higher-order
logic. This notation is a natural deduction system in inferring rules,
and its visual features are higher than algebraically natural deduction
system, which was created thereafter by Gentzen. Peirce's work on the
graphic notation is continued by Barwise, Sowa and other logicians and
computer scientists of the day.

Summing up, Peirce's philosophy of logical notation contains many
illuminating suggestions as well as much original and extensive logical
contribution. If examine philosophy of notation with the development
nowadays of linguistics, computer science and philosophy, then we would
have a conclusion: logical notation is not trivial matter, so how to
achieve a optimizing weaving of icons, indexes and symbols, is of
essential issues which is referred to the progress of logic, no longer
only a question of arbitrary formal arrangement.




KEY WORDS

C.S.Peirce; logical notation; philosophy of notation; semiotics;
algebraic notation; graphic notation; Existential Graphs



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

Subject: Re: Identity & Teridentity
From: Cathy Legg <clegg[…]cyc.com>
Date: Tue, 26 Nov 2002 18:05:36 -0600 (CST)
X-Message-Number: 19

On Fri, 22 Nov 2002, John Collier wrote:

> I almost remarked on a previous post that Jon seemed to be saying,
> in his account of (instances of) dyadic relations as ordered pairs,
> that dyadic relations were really triadic. This seems to me to be a
> reduction of his position. So where has he gone wrong?
>
> I think from the line of argument below, which is none to clear
> in itself, that we can see an appeal to the way things are represented
> (graphs) to their actual properties. This appears to me to be a
> pretty fundamental category error. No it is true that we need a third
> thing to represent a dyadic relation, but this is not to say that
> the relation itself is triadic (let us hope not, or else the notion of a
> dyadic relation is gibberish). However, the argument below,
> such as it is, does nothing to rule out the possibility that this
> third element might also be dyadic in nature, and that the talk of
> thirds cannot be embedded in a more complex construction
> of dyadic relations. I remain unimpressed with the supposed
> proofs I have seen of the irreducible need for triadic logic, however
> interesting it and suggestive it is, and however interesting it would
> be if it could be shown to be required. I do not think that Quine's
> position has been refuted, since his arguments do not depend
> on the specific means of representation, which plays a crucial role
> in what is presented below.

John (/anyone) does Quine's proof admit of summarising for the list in
natural language?

Regards,
Cathy.

--------------------------------------------------------------------------
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: Identity & Teridentity
From: Cathy Legg <clegg[…]cyc.com>
Date: Tue, 26 Nov 2002 18:13:01 -0600 (CST)
X-Message-Number: 20

On Fri, 22 Nov 2002, John Collier wrote:

> As I see it, there are two issues. One is whether representation
> and some other things involve triadic relations. The other
> is whether there are irreducibly triadic relations. They
> are not the same issue. So far, I find in Peirce the first
> issue made quite convincingly in the affirmative. I have not
> found the second case to be made convincingly at all
> by either side.

But if one were to establish that representation involves *irreducibly*
triadic relations, wouldn't one have established the second point, since
representational relations (to state the obvious) are relations?

Regards,
Cathy.

--------------------------------------------------------------------------
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: Identity & Teridentity
From: Gary Richmond <garyrichmond[…]rcn.com>
Date: Tue, 26 Nov 2002 19:19:52 -0500
X-Message-Number: 21




Cathy Legg wrote:


But if one were to establish that representation involves *irreducibly*
triadic relations, wouldn't one have established the second point, since
representational relations (to state the obvious) are relations?

Bravo!

Gary

>On Fri, 22 Nov 2002, John Collier wrote:
>
>>As I see it, there are two issues. One is whether representation
>>and some other things involve triadic relations. The other
>>is whether there are irreducibly triadic relations. They
>>are not the same issue. So far, I find in Peirce the first
>>issue made quite convincingly in the affirmative. I have not
>>found the second case to be made convincingly at all
>>by either side.
>>
>
>But if one were to establish that representation involves *irreducibly*
>triadic relations, wouldn't one have established the second point, since
>representational relations (to state the obvious) are relations?
>
>Regards,
>Cathy.
>
>--------------------------------------------------------------------------
>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
>--------------------------------------------------------------------------
>
>
>
>---
>Message from peirce-l forum to subscriber garyrichmond[…]rcn.com
>To unsubscribe send a blank email to: leave-peirce-l-9178T[…]lyris.ttu.edu
>


--



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

Subject: Re: Identity & Teridentity: to Howard
From: Cathy Legg <clegg[…]cyc.com>
Date: Tue, 26 Nov 2002 18:22:44 -0600 (CST)
X-Message-Number: 22

On Tue, 26 Nov 2002 HGCALLAWAY[…]aol.com wrote:

[...]>
> The idea here, I take it, is to emphasize thirdness as law, and surely the
> concept of natural law plays an important role in Peirce's anti-nominalism.
> So, we might expect that looking at the difference between teridentity and
> identity (in standard contem-porary treatments) in terms of some relation to
> law would help to resolve the appa-rent reduction of teridentity to standard
> binary identity in contemporary logic. In a private message, Seth suggested
> some similar ideas to me.
>
> Let me repeat, though, the simple idea of the reduction of teridentity. If
> the following
> can be regarded as a formulation of teridentity,
>
> Ixyz,
>
> Then the idea is that we don't need teridentity, in standard logic, since we
> can always just substitute "x=y & y=z" for "Ixyz."

These two instances of 'y' above - who is to say they refer to the same
object? I submit that the reader's mind (trained in certain algebraic
habits) is supplying an enthymematic triadic relation. If the reader is
not trained in certain algebraic habits they may misinterpret what is
being stated above.

Thus I would suggest that this is still a logical issue and not one of
physical law, as you explore below, Howard.

Regards,
Cathy.

> So, the question would seem to be, does the idea of reference to law force us
> to accept teridentity in contrast to the proposed alternative? If there is
> some law involved in our coming to state or derive a claim making use of
> "Ixyz," then it seems that we may employ the same law in deriving a
> corresponding claim making use of something on the order of "x=y & y=z."
>
> Consider again my suggestion about how folks may have come to identify the
> morning star and the evening star. The idea is that we have some law or
> observed regularity governing the movements or orbits of the planets (planets
> being, perhaps,
> just those heavenly bodies which move against the background of the fixed
> stars,
> whose relations to each other do not change from night to night). So, the
> planets are found to move in particular sorts of orbits, and an orbit has
> been calculated, say, for the evening star. On calculating an orbit for the
> morning star it is found that the orbits of the morning star and the vening
> star fit the same pattern. So, we identify the morning star and the evening
> star. In some sense laws or law-like regularities
> govern our conclusion that the morning star is the evening star.
>
> But if we have the laws of planetary motion stated in our theory, do we also
> need the concept of teridentity in order to identify the morning star and the
> evening star? Actually, I don't see how it would help. Though we are guided
> by some laws or law-like regularities in coming to identify the morning star
> with the evening star, still that identification is a kind of hypotheses
> intended to explain the congruence of the orbits of the morning star and the
> evening star. It is a kind of hypothesis, in relation to the evidence
> accumulated before the identification is made, and it is a kind of hypothesis
> which might call for further checking. While accepting some role for law or
> prior accepted generalization in the acceptance of the identity statement, it
> remains unclear how the concept of teridentity might help make that
> connection. If x is the morning star and y is the evening star, then what
> could z be in the statement "Ixyz"? It is surely not the law or
> generalization which may have rendered the identi-fication of the morning
> star and the evening star plausible. So, whatever z may be, if "Ixyz" is
> true, then so is "x=y & y=z."
>
> So, I do not see how thirdness as law could be brought in here to argue for
> teri-dentity in contrast to the proposed or apparent reduction of it. I
> continue to think that the notion of teridentity may be connected with some
> particularities of Peirce's system of graphs which we are yet to explore in
> sufficient detail.
>
> Howard
>
> H.G. Callaway
> (hgcallaway[…]aol.com)
>
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Subject: Re: Identity & Teridentity
From: Gary Richmond <garyrichmond[…]rcn.com>
Date: Tue, 26 Nov 2002 19:26:58 -0500
X-Message-Number: 23




PS But I do believe that John is correct in maintaining that triadicity
in representation is effect rather than (empirical)
cause. Certainly, the thrust of Peirce's 1903 Lecture series, especially
the "Whetstone" part, to demonstrate that
triadicity occurs in nature. It is then represented.

Gary



Cathy Legg wrote:

>On Fri, 22 Nov 2002, John Collier wrote:
>
>>As I see it, there are two issues. One is whether representation
>>and some other things involve triadic relations. The other
>>is whether there are irreducibly triadic relations. They
>>are not the same issue. So far, I find in Peirce the first
>>issue made quite convincingly in the affirmative. I have not
>>found the second case to be made convincingly at all
>>by either side.
>>
>
>But if one were to establish that representation involves *irreducibly*
>triadic relations, wouldn't one have established the second point, since
>representational relations (to state the obvious) are relations?
>
>Regards,
>Cathy.
>
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Subject: Peirce, Leibniz and neoPlatonism
From: Clark Goble <Clark.Goble[…]attbi.com>
Date: Tue, 26 Nov 2002 18:16:43 -0700
X-Message-Number: 24

Hi, I've been away from the list for a few months, but thought I'd
broach a new topic.

I've been studying Leibniz rather heavily the past month, trying to
come to grips with exactly how his monads function. I'd always noted
some parallels with Peirce, especially in how the mind-matter line went.

I've just read one essay though that made a more formal neoPlatonic tie
to both Peirce and perhaps to Leibniz.

http://agora.phi.gvsu.edu/kap/Neoplatonism/csp-plot.html

I'm not sure I'm comfortable calling Leibniz a neoPlatonist, as the
author in the above does. However the overall scheme is rather
interesting for understanding Leibniz in terms of both Peirce and
Plotinus. Further many have pointed out that Bruno's form of
neoPlatonism in the Renaissance was likely influential on both Spinoza
and Leibniz. Especially their panpsychism as well as the way in which
matter was viewed.

Basically the Peircean application goes as follows:

Firstness is equivalent to the Leibniz monad. This is firstness proper
as an ontological category. I'd note though that for Leibniz the
relationship from a view from matter and mechanics leads to a
correspondence, but not causal relationship to what goes on inside the
monad. Thus whether one views the system in a more idealistic
perspective ala Berkeley or a more Newtonian scheme is simply a choice
of perspective. Leibniz accounts for this via his prearranged dynamics.

Secondness is basically external monads appearing in the monad's
perception. It is the dualism in which more than one monad exists. I
believe that this would also count as perception or representation for
Leibniz. Leibniz' theory of representation seems very much akin to
Peirce's iconic sign.

Thirdness is the "meaning" we give things. Really there are just
monads but because of our apprehension (to use Leibniz' term) we are
conscious of bodies and not individual monads. Note how for Peirce, as
Leibniz, there are infinite number of monads under a class.


What I am curious about is if this is a well noted view in Peirce and
if anyone knows of a good study on it.

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

Subject: Re: Identity & Teridentity
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Tue, 26 Nov 2002 22:10:03 -0500
X-Message-Number: 25

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

I&T. Note 34

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

Actually, Seth, since I recited this out of remembered
impressions formed a quarter of a century ago, and not
myself being a mental power on the order of Peirce,
I would consider it very likely that I need to
check almost anything like that over again,
so let me bring some materials together:

| Leibniz, "Elements of a Calculus" (1679)
|
| 7. To make evident the use of symbolic numbers in propositions, it is
| necessary to consider the fact that every true universal affirmative
| categorical proposition simply shows ['significat'] some connexion
| between predicate and subject (a 'direct' connexion, which is what
| is always meant here). This connexion is, that the predicate is
| said to be in the subject, or to be contained in the subject;
|
| [Example:]
|
| ... so when I say "All gold is metal"
| I simply mean that in the concept
| of gold the concept of metal is
| contained directly, since gold
| is the heaviest metal.

So "Gold => Metal" is read "The predicate Metal is 'contained in' the subject Gold".

| Now, identity is essentially a dual relation.
| That is, it requires two subjects and no more.
| If three objects are identical, this fact is
| entirely contained in the fact that the three
| pairs of objects are identical. CP1.446 (1896).

A. The fact that i, j, k are identical
is contained in
B. The fact that i = j, i = k, j = k.

According to my interpretation, a statement of the
form "predicate A is contained in subject B" would
decode as the implication "B => A" or "All B is A".

That still accords with the way that I read the original statement.

Jon Awbrey

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

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

Subject: Re: Identity & Teridentity
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Wed, 27 Nov 2002 00:16:01 -0500
X-Message-Number: 26

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

I&T. Note 35

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

Seth,

I had this vague sense of familiarity about your second indiscernibility
quote from Peirce, but you had so ripped it out of context that I never
became quite aware of it till now. As it happens, I wrote my senior
thesis "Complications of the Simplest Mathematics" (1976) on this
locus in Peirce's studies, and I can tell you exactly what he was
talking about here. He was talking about the "conjugacy classes"
of group elements in the symmetric group on three letters Sym(3)
and in group theory generally.

I constantly get the feeling that various people are trying to get
something out of Peirce's work that he did not put into it, because
he had a differnt sense of what were the truly inportant questions
than they do -- especially in these places where some people act as
if they are trying squeeze ontological blood out of logical turnips.

I gave my best maxim at the beginning of this discussion:
Tease apart as much as possible the ontological objects
from the logical signs -- then the apt answers to the
questions of identity will look very different from
one side of the Object/Sign ledger to the other.

On the ontological side, identity tends away from being a 3-adic relation
and even away from being a 2-adic relation towards being a 1-adic relation --
things just are, and there is no real need to put them besides themselves
for ontology's sake. I am not myself all that teribly interisted in those
sorts of questions.

On the logical (formal semiotic) side, the interesting and useful questions
involve sign relations, whereby a sign relates to another sign in respect
of an object, and the sensible identity question is just a special case
of that type, whereby a sign is equivalent to another in identifying
an object. These are the sorts of things that are handled in math
by means of different sorts of equivalence classes of signs, and
one of the more interesting semiotic phenomena that arises here
is that these equivalence classes interpenetrate, overlap, and
superpose each other, "like raindrops", to pursue the metaphor,
which is probably all that it is.

| Let us now glance at the permutations of three things.
| To say that there are six permutations of three things
| is the same as to say the two sets of three things may
| correspond, one to one, in six ways. The ways are here
| shown:
|
| o-----------o-----------o-----------o-----------o-----------o-----------o
| | | | | | | |
| | r s t | r s t | r s t | r s t | r s t | r s t |
| | | | | | | \/ | \__\/ | \/ | | \/__/ | \|/ |
| | | | | | | /\ | /\ \ | /\ | | / /\ | /|\ |
| | o p q | o p q | o p q | o p q | o p q | o p q |
| | | | | | | |
| o-----------o-----------o-----------o-----------o-----------o-----------o
|
| No one of these has any properties different from those of any other.
| They are like two ideal raindrops, 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).

Peirce is making a point about operational structure that is closely
related to the pragmatic maxim. In themselves, as monadic elements
of a group, all of the group elements are in the first instance alike.
Still, in the second instance, they can be recognized as distinct from
one another "by their effects", that is to say, by the way that they
act on one another. This refers to the "regular representations" of
group elemnts acting on the group itself. See the following etude:

http://www.altheim.com/cs/difflogic.html

The version of Leibniz's principle of indiscernibility to
which Peirce is alluding in this connection, I am guessing,
is the one that says: "No two monads can be exactly alike".
And the objection that Peirce is really making is to the
logical necessity for it. So, my guess is that Peirce
is talking about a symmetry principle, something akin
to an equivalence or an invariance principle, say,
like all reference frames or POV's are alike,
but that does not diminish the diversity
of phenomena or the potential for truth
one little bit.

Jon Awbrey

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

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

Subject: Re: Peirce, Leibniz and neoPlatonism
From: martin lefebvre <lefebvre[…]vax2.concordia.ca>
Date: Wed, 27 Nov 2002 00:32:42 -0500
X-Message-Number: 27



Let me try a brief answer to your question with regards to Peirce and
Neo-Platonism. I need to specify first that I'm not sufficently
familiar with Leibniz to make sense of the way you "apply" Peirce to
him -- however, I must say for starters that I don't recognize
Peirce's categories in what you present.

In any case this is not what I have in mind. I think we can justify
the idea that, in the West, there has been two basic models with
which to understand representation. To summarize with broad (almost
carricatural) strokes we could say: image and word or, in
non-Peircean terms -- terms closer to Hegel's in his Esthetics --
symbol and sign. Whereas Western rationality has been on the side of
the sign, Neo-Platonist thought was on the side of the image or the
symbol. This seems to be the case, in fact, for all forms of hermetic
thinking (Eco has written on this in Interpretation and
Overinterpretation and in The Limits of Interpretation) whether
Kabbalah, the doctrine of signatures (see Foucault's the Order of
Things -- first chapter), artes memoriae (Bruno, Camillo -- see the
works of F. Yates, M. Carruthers, L. Bolzoni, P. Rossi on memory and
mnemonic systems), the medical theories of Paracelsus, etc etc. What
they seem to have in common with what, at one point, was also called
sensual or primitive thinking is the breaking down of the principle
of non contradiction: there is no difference between the symbol and
what it stands for. The symbol is also the thing it stands for (they
are identical). The Catholic dogma of transubstantiation is another
example: the host is both a piece of bread and the body of Christ.
For Port-Royal logicians (see the work of Louis Marin on this) this
was untenable (Jansenists were the closest Catholic thing to
Protestants Catholics had to offer) as it was for Protestants, who
prefered to see the host as a sign. Now Peirce is not a hermetic
thinker. He's a rationalist (in the broad sense of the term). And
yet, he offers what, to my knowledge, is the only model of
representation able to bridge the gap between the two great
traditions of representation. For in firstness there can be no
principle of non contradiction; and although signs and representation
belongs to thirdness there is an element of firstness in them, which
has to do with feeling, quality, possibility. This, in fact, is the
bedrock for representation. Of iconicity, Joe Ransdell wrote: "the
relationship of the icon proper and its object, just insofar as it is
its object, must be one of identity; for the iconic relationship is
grounded in a property identity of sign and object, and we are, ex
hypothesi, prescinding from every logically extraneous property in
considering them simply as icon proper and object. This peculiar
sign-object identity has far-reaching implications" (On Peirce's
Conception of the Iconic Sign). Far-reaching implications indeed,
especially if you consider that every complete sign must involve some
icon.

Martin Lefebvre

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