1. Re: Identity & Teridentity
2. Re: Identity & Teridentity
3. Re: Identity & Teridentity
4. Re: Identity & Teridentity
5. Re: Identity & Teridentity
6. Re: Identity & Teridentity
7. Re: Identity & Teridentity
8. Re: Identity & Teridentity
9. Re: Identity & Teridentity
10. Re: Identity & Teridentity
11. Re: Identity & Teridentity
12. Re: Identity & Teridentity
13. Re: Identity & Teridentity
14. Re: Identity & Teridentity
15. Re: Identity & Teridentity
16. Re: Identity & Teridentity
17. Re: Identity & Teridentity (TO AVOID "BETWEEN")
18. Re: Identity & Teridentity
19. Re: Identity & Teridentity
20. Re: Identity & Teridentity
21. Re: logic's logic
22. Re: CSP QUOTES RE: GENUINE/DEGENERATE DISTINCTION
23. Re: Identity & Teridentity
24. Re: Identity & Teridentity
25. Re: CSP QUOTES RE: GENUINE/DEGENERATE DISTINCTION
26. Re: Identity & Teridentity
27. Re: Identity & Teridentity
28. Re: Identity & Teridentity
29. Re: Identity & Teridentity
30. Re: Identity & Teridentity
31. Re: Identity & Teridentity
32. Re: Identity & Teridentity
33. server problems
34. Re: Identity & Teridentity
35. Re: CSP QUOTES RE: GENUINE/DEGENERATE
DISTINCTION

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

Subject: Re: Identity & Teridentity
From: HGCALLAWAY[…]aol.com
Date: Sun, 24 Nov 2002 03:11:02 EST
X-Message-Number: 1

Gary, Joe & list,

You wrote, Gary,

----quote------------
I would like to echo Howard's thanks for your supplying the relevant
quotations, Joe; and to thank you Howard for your thoughtful response to my
post which, along with your most recent one to Joe--and the quotations
already mentioned--I'll be digesting most all of the free hours I have today
(which, unfortunately, aren't many).

Let me say that both your comments have already suggested to me that this is
a far more subtle matter than I had once imagined. I think you are quite
right about that, Joe. Also, I am beginning to follow more fully some parts
of the identity-teridentity
problematic which I had not previously, thanks to your recent comments,
Howard. (More on this after the rich meal of quotes and comments has been
digested.)
---end quote------

Thanks for your reply and generous comments, Gary. I am wondering if I can
add something to your readings regarding this thread of "Identity &
Teridentity." Part of what motivated me to start it was something I wrote in
a book review back in 1995
which appeared in the Transactions.

I mentioned this review, of Baltzer, in one of my previous postings, in
passing, and I have also sent out a few E-mail offprints privately. I think
that having the review more generally available to readers of the list might
help clarify some various elements of what is involved. So, I would like to
ask if Joe can make the review available from Arisbe. I'll send him a copy.

There is a complication, though, since we may want the publisher's permission
to
make the review available. Normally, this is no problem, since the Editor of
the Trans-actions has told me in the past, at the time when I was doing a lot
of reviews for the journal, that we need only state that such a review was
originally published in the Transactions of the C.S. Peirce Society.

In spite of that general policy, I think it best to ask permission to make
the review available from Arisbe, and this may take a bit of time. I do
think, though that having the review available to the readers of the list
might be helpful to this thread. What do you think, Joe? Is this something we
can do at Arisbe?

Howard

H.G. Callaway
(hgcallaway[…]aol.com)

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

Subject: Re: Identity & Teridentity
From: "Joseph Ransdell" <joseph.ransdell[…]yahoo.com>
Date: Sun, 24 Nov 2002 05:49:40 -0600
X-Message-Number: 2

Just let me know when you are ready to have the review made availablle at
Arisbe, Howard. I doubt if there is any need for further permission
than you already have from the Transactions editor, but I leave that to you.
Just include a description of where and when it originally appeared, or
provide the information to me and i'll type it in. As far as I know, Peter
is still editor. (You may be thinking of Randy Dipert replacing Dick Robin
as special Peirce editor.) They don't require my permission to give you
theirs. Bear in mind that it is your paper, not theirs, unlesss you
explicitly gave them copyright when you published it earlier.

Joe

----- Original Message -----
From: <HGCALLAWAY[…]aol.com>
To: "Peirce Discussion Forum" <peirce-l[…]lyris.acs.ttu.edu>
Sent: Saturday, November 23, 2002 11:45 AM
Subject: [peirce-l] Re: Identity & Teridentity

[TEXT OMITTED; SEE ABOVE]

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

Subject: Re: Identity & Teridentity
From: "Joseph Ransdell" <joseph.ransdell[…]yahoo.com>
Date: Sun, 24 Nov 2002 06:09:49 -0600
X-Message-Number: 3

I thought the basic claim is that representation is irreducibly triadic,
John. Peirce recogmizes any degree of adicity you like, if it is only a
matter of verbal form. So I understand you to be saying that you don't
regard representation as triadic, other than verbally so. I don't know what
you would have in mind in saying that Peirce convinced you of its
triadicity, though, since I don't recall him trying to make any claim for it
that wasn't a claim to its irreducibility to a complex of dyads.

Joe Ransdell



----- Original Message -----
From: "John Collier" <ag659[…]ncf.ca>
To: "Peirce Discussion Forum" <peirce-l[…]lyris.acs.ttu.edu>
Sent: Saturday, November 23, 2002 10:17 AM
Subject: [peirce-l] Re: Identity & Teridentity


> At 07:36 PM 22/11/2002, you wrote:
> >Thanks for the clarification, John. I find something baffling in the
> >following, though:
> >
> > > 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 you are persuaded of the first, why are you not persuaded ipso
facto
> >of the second? Is there some recondite sense of "reducible" involved in
> >this?
>
> Not at all, Joe. It is possible for a relation to be triadic and
> for it to be reducible. I gave examples in my post. There is
> nothing especially difficult or tricky in what I am saying.
> Quite the contrary. Between, as I mentioned, is a triadic
> relation, but it can be composed of dyadic relations. For example,
> if we say that the ham is between the upper and lower slices
> of bread, that is equivalent to saying that it is below the upper
> and above the lower. More formally Between(ham,upper,lower)
> iff Above(upper, lower) and Above(ham,lower) and Above(upper,
> ham). Between is clearly a triadic relation, and the location of the
> ham in this case involves it, but the relation can be analyzed fully
> into dyadic relations.
>
> John
>
>
> ---
> Message from peirce-l forum to subscriber joseph.ransdell[…]yahoo.com
> To unsubscribe send a blank email to: leave-peirce-l-3113A[…]lyris.ttu.edu


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

Subject: Re: Identity & Teridentity
From: "Charles Pyle" <pyle[…]modempool.com>
Date: Sun, 24 Nov 2002 09:27:36 -0500
X-Message-Number: 4

I have not been following this thread closely, but I haven't seen it pointed
out that someplace (I don't have access to Peirce texts just now) Peirce
explicitly discusses the example of 'between' in terms of the relation of
Philadelphia as between Washington and New York, arguing that 'between' is
not a relation of genuine thirdness, but is rather degenerate thirdness. In
other words, as I understand Peirce's thinking, 'between' is not a relation
of thirdness, but rather a relation of compounded secondesses.



-----Original Message-----
From: John Collier [mailto:ag659[…]ncf.ca]
Sent: Saturday, November 23, 2002 11:18 AM
To: Peirce Discussion Forum
Subject: [peirce-l] Re: Identity & Teridentity

At 07:36 PM 22/11/2002, you wrote:
>Thanks for the clarification, John. I find something baffling in the
>following, though:
>
> > 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 you are persuaded of the first, why are you not persuaded ipso facto
>of the second? Is there some recondite sense of "reducible" involved in
>this?

Not at all, Joe. It is possible for a relation to be triadic and
for it to be reducible. I gave examples in my post. There is
nothing especially difficult or tricky in what I am saying.
Quite the contrary. Between, as I mentioned, is a triadic
relation, but it can be composed of dyadic relations. For example,
if we say that the ham is between the upper and lower slices
of bread, that is equivalent to saying that it is below the upper
and above the lower. More formally Between(ham,upper,lower)
iff Above(upper, lower) and Above(ham,lower) and Above(upper,
ham). Between is clearly a triadic relation, and the location of the
ham in this case involves it, but the relation can be analyzed fully
into dyadic relations.

John


---
Message from peirce-l forum to subscriber pyle[…]modempool.com
To unsubscribe send a blank email to: leave-peirce-l-6640K[…]lyris.ttu.edu



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

Subject: Re: Identity & Teridentity
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Sun, 24 Nov 2002 08:54:14 -0500
X-Message-Number: 5

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

I&T. Note 19

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

JC: It is possible for a relation to be triadic and
for it to be reducible. I gave examples in my
post. There is nothing especially difficult or
tricky in what I am saying. Quite the contrary.
Between, as I mentioned, is a triadic relation, but
it can be composed of dyadic relations. For example,
if we say that the ham is between the upper and lower
slices of bread, that is equivalent to saying that it
is below the upper and above the lower. More formally
Between(ham, upper, lower) iff Above(upper, lower) and
Above(ham, lower) and Above(upper, ham). Between is
clearly a triadic relation, and the location of the
ham in this case involves it, but the relation can
be analyzed fully into dyadic relations.

JA: John Collier has provided us with a perfect example --
a perfect example of someone who does not know what
a relation is, does not know what the difference
between a relation and one of its instances is,
does not therefore know what either a 3-adic
or a 2-adic relation is, and does not know
what decomposition or reduction is.

JA: No wonder he buys Quine's brand of baloney.

John Collier has done us the yowman's service of exemplifying
almost all of the commonly known fallacies in a single short
paragraph. I have a bit more time now, so let us run through
these points in detail.

Zeroth, I will allow that there may be something that JC
is talking about under the heading of the word "relation",
but I have yet to see a coherent account of it, and I do
not hold out much hope for its consistency. I am pretty
sure that it bears no consistent relation to what Boole,
DeMorgan, Peirce, Schroeder, and omnes generationes of
logicians and mathematicians, before and after, meant
by the words "relation" or "relative term". Since
this crew got there first, even Plato and Aristotle
knew better, I suggest that others choose another
word, so as to avoid confusing the massess.

I analyzed the "betweensy" example in some detail for the
Standard/Ontology Lists last year and I will look up those
links for you later on. In the meantime, here is a summary,
far succincter than I have ever done before, of the pertinent
material, as the pertinent thinkers and tradition understand it:

Theory Of Relations

01. http://suo.ieee.org/ontology/msg04377.html
02. http://suo.ieee.org/ontology/msg04378.html
03. http://suo.ieee.org/ontology/msg04379.html
04. http://suo.ieee.org/ontology/msg04380.html
05. http://suo.ieee.org/ontology/msg04381.html
06. http://suo.ieee.org/ontology/msg04382.html

Before we start, let us dismiss JC's inane example, since his "analysis"
of it fails if the plane of the sandwich is vertical to the surface of
the nearest-by large planet, if the sandwich is flipped over, or if the
sandwich is floating in space "between" galaxies -- which incidentally
illustrates the fact that the English "between" is polymorphous, since
"among" would not substitute 'saliva verita' (sic joke), and I never
said anything about there being just two galaxies, but never mind
all that now.

A fairer example would be to pull the mathematician's
"without loss of generality" (WOLOG) gambit, and say
that we are discussing, say, real numbers a, x, b,
where we assume a < b, WOLOG, and then revert to
the 3-adic situs where "x is between a and b".

1. What a relation is.

So far we are still discussing relations in general,
and have not got as far as discussing sign relations,
which are a special case of 3-adic relations.

Where terms of the characters "abstract", "concrete", "general", "individual",
and so on, are distinguished relative to a particular context of discourse,
where we conventionally neglect the differences that are irrelevant to the
purposes of that discourse, relations are denoted by abstract general terms,
and not by concrete individual terms.

2. What the difference between a relation and one of its instances is.

This brings up the fallacy that DB professionals know as the
"one-row database" (ORD) fallacy. Any relation worth its salt
serves up a whole "table" of instances, and not just one like:

<this top slice, this baloney, this bottom slice>.

3. What decomposition or reduction is.

In this regard, JC commits what has long been known as the fallacy
of the "Alchemist's Dodge" or the "(Philosophers') Stone Soup".
It goes a bit like this:

You can make a hearty soup out of nothing but stones and hot water ...
if you add a pinch of salt ...
if you add a dash of pepper ...
if you add a few potatoes ...
if you add a carrot or two ...
if you add a hock of ham ...
if you add ...

And so it goes.

The moral of this particular telling of the story
is that a reduction is not a proper reduction if
it does not reduce something to something lower.

JC's purported "analysis" goes like this:

| Between(ham, upper, lower)
|
| iff
|
| Above(upper, lower)
|
| and
|
| Above(ham, lower)
|
| and
|
| Above(upper, ham).

Each of the bits of connective tissue that are signified by the
uses of the word "and" invokes a 3-adic relation, in other words,
an operation that passes from two sentences to a conjoint sentence --
or from their truth values to the conjunction of their truth values,
according to your taste -- and so the putative "reduction" is really
the sort of "improper" reduction that reduces something to something
of the same complexity, in this case, more 3-adic relations.

All of these things were commonplace understandings well
before Boole, DeMorgan, Peirce, & Co. got into the act.

Jon Awbrey

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

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

Subject: Re: Identity & Teridentity
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Sun, 24 Nov 2002 09:06:25 -0500
X-Message-Number: 6

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

I&T. Note 19

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

JC: It is possible for a relation to be triadic and
for it to be reducible. I gave examples in my
post. There is nothing especially difficult or
tricky in what I am saying. Quite the contrary.
Between, as I mentioned, is a triadic relation, but
it can be composed of dyadic relations. For example,
if we say that the ham is between the upper and lower
slices of bread, that is equivalent to saying that it
is below the upper and above the lower. More formally
Between(ham, upper, lower) iff Above(upper, lower) and
Above(ham, lower) and Above(upper, ham). Between is
clearly a triadic relation, and the location of the
ham in this case involves it, but the relation can
be analyzed fully into dyadic relations.

JA: John Collier has provided us with a perfect example --
a perfect example of someone who does not know what
a relation is, does not know what the difference
between a relation and one of its instances is,
does not therefore know what either a 3-adic
or a 2-adic relation is, and does not know
what decomposition or reduction is.

JA: No wonder he buys Quine's brand of baloney.

John Collier has done us the yowman's service of exemplifying
almost all of the commonly known fallacies in a single short
paragraph. I have a bit more time now, so let us run through
these points in detail.

Zeroth, I will allow that there may be something that JC
is talking about under the heading of the word "relation",
but I have yet to see a coherent account of it, and I do
not hold out much hope for its consistency. I am pretty
sure that it bears no consistent relation to what Boole,
DeMorgan, Peirce, Schroeder, and omnes generationes of
logicians and mathematicians, before and after, meant
by the words "relation" or "relative term". Since
this crew got there first, even Plato and Aristotle
knew better, I suggest that others choose another
word, so as to avoid confusing the massess.

I analyzed the "betweensy" example in some detail for the
Standard/Ontology Lists last year and I will look up those
links for you later on. In the meantime, here is a summary,
far succincter than I have ever done before, of the pertinent
material, as the pertinent thinkers and tradition understand it:

Theory Of Relations

01. http://suo.ieee.org/ontology/msg04377.html
02. http://suo.ieee.org/ontology/msg04378.html
03. http://suo.ieee.org/ontology/msg04379.html
04. http://suo.ieee.org/ontology/msg04380.html
05. http://suo.ieee.org/ontology/msg04381.html
06. http://suo.ieee.org/ontology/msg04382.html

Before we start, let us dismiss JC's inane example, since his "analysis"
of it fails if the plane of the sandwich is vertical to the surface of
the nearest-by large planet, if the sandwich is flipped over, or if the
sandwich is floating in space "between" galaxies -- which incidentally
illustrates the fact that the English "between" is polymorphous, since
"among" would not substitute 'saliva verita' (sic joke), and I never
said anything about there being just two galaxies, but never mind
all that now.

A fairer example would be to pull the mathematician's
"without loss of generality" (WOLOG) gambit, and say
that we are discussing, say, real numbers a, x, b,
where we assume a < b, WOLOG, and then revert to
the 3-adic situs where "x is between a and b".

1. What a relation is.

So far we are still discussing relations in general,
and have not got as far as discussing sign relations,
which are a special case of 3-adic relations.

Where terms of the characters "abstract", "concrete", "general", "individual",
and so on, are distinguished relative to a particular context of discourse,
where we conventionally neglect the differences that are irrelevant to the
purposes of that discourse, relations are denoted by abstract general terms,
and not by concrete individual terms.

2. What the difference between a relation and one of its instances is.

This brings up the fallacy that DB professionals know as the
"one-row database" (ORD) fallacy. Any relation worth its salt
serves up a whole "table" of instances, and not just one like:

<this top slice, this baloney, this bottom slice>.

3. What decomposition or reduction is.

In this regard, JC commits what has long been known as the fallacy
of the "Alchemist's Dodge" or the "(Philosophers') Stone Soup".
It goes a bit like this:

You can make a hearty soup out of nothing but stones and hot water ...
if you add a pinch of salt ...
if you add a dash of pepper ...
if you add a few potatoes ...
if you add a carrot or two ...
if you add a hock of ham ...
if you add ...

And so it goes.

The moral of this particular telling of the story
is that a reduction is not a proper reduction if
it does not reduce something to something lower.

JC's purported "analysis" goes like this:

| Between(ham, upper, lower)
|
| iff
|
| Above(upper, lower)
|
| and
|
| Above(ham, lower)
|
| and
|
| Above(upper, ham).

Each of the bits of connective tissue that are signified by the
uses of the word "and" invokes a 3-adic relation, in other words,
an operation that passes from two sentences to a conjoint sentence --
or from their truth values to the conjunction of their truth values,
according to your taste -- and so the putative "reduction" is really
the sort of "improper" reduction that reduces something to something
of the same complexity, in this case, more 3-adic relations.

All of these things were commonplace understandings well
before Boole, DeMorgan, Peirce, & Co. got into the act.

Jon Awbrey

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

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

Subject: Re: Identity & Teridentity
From: "Armando Sercovich" <cispec[…]com4.com.ar>
Date: Sun, 24 Nov 2002 12:50:31 -0300
X-Message-Number: 7

John,

How would you analyse the relation between a sign, its object and its =
interpretant in dyadic relations? (avoiding that becomes a sandwich, of =
course).=20

Armando Sercovich
CISPEC




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

Subject: Re: Identity & Teridentity
From: "Peter Brawley" <peter.brawley[…]artfulsoftware.com>
Date: Sun, 24 Nov 2002 07:51:13 -0800
X-Message-Number: 8

> JC: It is possible for a relation to be triadic and
> for it to be reducible. I gave examples in my
> post. There is nothing especially difficult or
> tricky in what I am saying. Quite the contrary.
> Between, as I mentioned, is a triadic relation, but
> it can be composed of dyadic relations. For example,
> if we say that the ham is between the upper and lower
> slices of bread, that is equivalent to saying that it
> is below the upper and above the lower. More formally
> Between(ham,upper,lower) iff Above(upper, lower) and
> Above(ham,lower) and Above(upper, ham). Between is
> clearly a triadic relation, and the location of the
> ham in this case involves it, but the relation can
> be analyzed fully into dyadic relations.
>
> John Collier has provided us with a perfect example --
> a perfect example of someone who does not know what
> a relation is, does not know what the difference
> between a relation and one of its instances is,
> does not therefore know what either a 3-adic
> or a 2-adic relation is, and does not know
> what decomposition or reduction is.

Jon would you please point to where John shows he "does
not know what the difference between a relation and one of
its instances is" and "does not know what decomposition or
reduction is"? Thanks.

PB



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

Subject: Re: Identity & Teridentity
From: Gary Richmond <garyrichmond[…]rcn.com>
Date: Sun, 24 Nov 2002 13:15:44 -0500
X-Message-Number: 9


--------------050405020009090808080505
Content-Type: text/plain; charset=us-ascii; format=flowed
Content-Transfer-Encoding: 7bit

Joe,

As I had just posted a response to John Collier in which I approved of
his distinguishing (1) the representation of triadic
relations from (2) the triadic relations themselves, perhaps thinking of
the famous sunflower example.(and imagining it to
imply a kind of "existential triadicity," the triadic relations as such
apart from their representation), I was surprised when,
referring to the same passage of John's, you asked:

>JR: But if you are persuaded of the first, why are you not persuaded ipso facto
>of the second?
>
So I looked at the sunflower passage again:

> CP: A Sign is a Representamen with a mental Interpretant. Possibly
> there may be Representamens that are not Signs. Thus, if a sunflower,
> in turning towards the sun, becomes by that very act fully capable,
> without further condition, of reproducing a sunflower which turns in
> precisely corresponding ways toward the sun, and of doing so with the
> same reproductive power, the sunflower would become a Representamen of
> the sun. But thought is the chief, if not the only,
> mode of representation.

I had forgotten that even in the example quoted, "the sunflower would become a Representamen of the sun. And meanwhile,
for all our intents and purposes, the last sentence need hold.

> [T]hought is the chief, if not the only, mode of representation.

Now I see why you asked the question.

Gary



Joseph Ransdell wrote:

>Thanks for the clarification, John. I find something baffling in the
>following, though:
>
>>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 you are persuaded of the first, why are you not persuaded ipso facto
>of the second? Is there some recondite sense of "reducible" involved in
>this?
>
> Joe Ransdell
>


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

Subject: Re: Identity & Teridentity
From: Gary Richmond <garyrichmond[…]rcn.com>
Date: Sun, 24 Nov 2002 13:23:23 -0500
X-Message-Number: 10



(postscript to my last message) from the first of your quoted passages
(the segment I had omitted when posting it myself, incidentally)

>CP 1.345 I think even degenerate triadic
>relations involve something like thought.
>
In short, all triadic relations involve thought, so there is no need to
distinguish between them and their representations, right?

GR

Joseph Ransdell wrote:

>Howard:
>
>"Genuine" is a term of art in Peirce's philosophy, and is not equivalent to
>"real" as opposed to "apparent". I am distributing separately a
>collection of passages from the CP compiled some time ago. Bear in mind
>that they were acquired by a string search, and I have only minimally edited
>them for legibility. The first paragraph is the same as the one Gary
>quoted, but contains a little more, I believe..
>
>Joe Ransdell
>
>
>----- Original Message -----
>From: <HGCALLAWAY[…]aol.com>
>To: "Peirce Discussion Forum" <peirce-l[…]lyris.acs.ttu.edu>
>Sent: Saturday, November 23, 2002 5:10 AM
>Subject: [peirce-l] Re: Identity & Teridentity

Subject: Re: Identity & Teridentity
From: John Collier <ag659[…]ncf.ca>
Date: Sun, 24 Nov 2002 02:01:24 -0500
X-Message-Number: 11

At 07:09 AM 24/11/2002, you wrote:
>I thought the basic claim is that representation is irreducibly triadic,
>John.

No, I grant that representation is triadic. I don't yet grant that it is
irreducibly triadic. So far I have been able to get everything I
like from Peirce by assuming that representation is triadic without
assuming it is irreducibly triadic.

>Peirce recogmizes any degree of adicity you like, if it is only a
>matter of verbal form. So I understand you to be saying that you don't
>regard representation as triadic, other than verbally so. I don't know what
>you would have in mind in saying that Peirce convinced you of its
>triadicity, though, since I don't recall him trying to make any claim for it
>that wasn't a claim to its irreducibility to a complex of dyads.

I don't see that the irreducibility claim plays any role in Peirce's
arguments that triadicity that is not irreducible can play. Betweenness
is reducible to a complex of dyads: each instance can be so represented,
and the relation can be take to be the collection (set, if you wish)
of such cases. Betweenness is still triadic. This is not just a verbal
trick -- the ham is in the sandwich, between the pieces of bread.
If there is a problem, it is not that the triadic relation cannot be
expressed as a structure over dyadic relations; all of the
information is there in the components and (dyadic) relations.
The problem is that the parts of the reducing structure might
not be independent, so that the same information gets counted
more than once. This can be misleading. There is no formal
problem in dissecting n-adic relations into dyadic relations, however,
contrary to what Jon insists. if anything, it is too easy to do.

What I had in mind is that one cannot account for meaning, as in
classical semantics in logic, as a relation between word and object
alone, but one must also take into account the circumstances of
interpretation. One way of doing that, which I have criticized in
print, is to add together a sequence of dyadic functions, syntax
+ context to intension, and intension + selection of world to
extension (this is Montague's approach, taken up explicitly
by David Kaplan, and at one time by John Perry to deal
with indexicals and other context dependent aspects of language).
The problem with this method is that context and selection
of world are not independent within this scheme. So there is
something wrong with the scheme. Nonetheless, there is nothing
logically wrong with breaking up interpretation in this way,
even if the two parts have an interdependence. It is just
misleading. However, it does have an advantage, and this is
that the non-linear aspect of the analysis can be made
explicit, rather than hiding it in some obscure notion
of irreducible triadicity. What we are really talking about
here is non-linearity; the issue of non-analyzability
into dyads is, I submit, a red herring.

I have a lot more to say on this and its consequences, but
as long as the issue of the interdependence of the
parts of such an analysis is confused with the impossibility
of doing such an analysis, then what I have to say won't
really make a lot of sense. The issue depends on the fact
that there are two forms of model, which Robert Rosen,
in Life Itself, calls synthetic and analytic. Analytic models
are those that break something down into the components
and their relations. Synthetic models require that the analysis
be entirely into independent parts. If the two are confused,
the results can be confusing. Reduction can be taken to
be either form of modelling. Quine uses the analytic method.
From his other work (e.g., his brilliant drum metaphor) he
is quite aware that this does not imply independence, and
hence that analytic models are synthetic models. Jon
seems to be taking Quine to be saying that analyses of
n-adic relations into dyadic relations are synthetic models.
There is little reason to think that Quine would agree with
this. Now Rosen claims that only when analytic models
correspond to synthetic models do we have a reduction.
That is one way to use the word, but it is not the only usage,
by any means. Personally, I prefer to call the use of analytic
models a reductive methodology. I would suppose that
it is indispensable in science. When we get a synthetic
model (independence of the analytical units), we have
a reduction.

The independence is a matter of how the world is, not
a formal property of the relations. Jon complained that
I did not treat the relations as a whole, but just the
instances, but relations are defined as a set of instances
in all of the material Jon has presented to us about relations.
(At least I assume so; I am not prepared to read large
amounts of material indiscriminately posted, but the
few cases I looked at said nothing more or less.) So
treating an instance as an example of how each case
would be treated to get the members of the set should not
be a problem. The problem does not lie in the logic.
As far as logic is concerned, an analytic model is
a reduction, since logic has nothing to say about the
independence issue -- I would call an analytic model
of this sort a logical reduction, since logic is insensitive
to any problems that might arise in the real world
application of the model. The moral that I would
take from this is that logical reductions are not
all that useful, and may well be misleading. Far from
being impossible, they are far to easy to get.

I still maintain that even if the interpretation of dyadic
relations is triadic in the sense of there being no
synthetic dyadic models of the interpretation of dyadic
models (a point I am quite prepared to concede, though
my reasoning for it depends on the functionality of
meaning, the grounding of functionality in a property
I call autonomy, and the synthetic irreducibility of
autonomy), it still seems to me that there has been
a serious error made if it is concluded that because
of this dyadic relations are really triadic. That confuses
matters of interpretation with matters of content. That
is too idealist for me to accept. What I am objecting
to here is the move from "our understanding of
dyadic relations is synthetically irreducibly triadic"
to "dyadic relations are irreducibly triadic". If
a dyadic relation becomes triadic through our theory,
there is something wrong with the theory. As I said
before, it would be better to say that there are no
dyadic relations. Unfortunately for this position,
there are. Not only that, they can be quite useful,
but one should keep in mind that an analysis into
dyadic relations does not necessarily produce
a synthetic model (and if I read Quine's holism
about meaning correctly, it never does, on his
view). So I also think that Jon, in his attacks
on Quine and his recent unsupported claim
against me is attacking a straw man of his
own construction.

So, returning to the issue of what Peirce meant, my
best guess is that he means that interpretation
is non-linear and does not have a synthetic model.
He was mistaken in thinking that there are logically
irreducible triadic relations.

Given this, how could I have got something from
Peirce's insistence that interpretation is triadic,
and irreducibly so? Well, since I have been
puzzled by his claims about irreducible triadic
relations since about 1971 when I first encountered
them, I have spent a lot of time trying to make sense
of this, since it seems to be counter to standard methods
in logic, and it seems to lead much too easily to a
conclusion that is counter to common sense -- that
dyadic relations are really triadic. What I was led
to is that solely dyadic systems are not capable
of non-linearity, whereas triadic systems can be
non-linear. Further, non-linear systems can have
analytic models that are not synthetic, and can be such
that there are no analytic models that are synthetic.
(Incidentally, if the last is the case, then there will
be consequences of the model -- semantically
entailed -- that cannot be inferred from the model --
being charitable, this may be the basis of Jon's
complaint that dealing with instances of a relation
to construct the relation misses something important.)
If interpretation is like this, then there are no
synthetic models of interpretation. It is not coincidental
that my own model of interpretation requires this
through its grounding in autonomy. My main difference
from Peirce is that I do not put the non-linearity
into the logic, which cannot distinguish between
analytic and synthetic models, at least in its standard
form, but in the dynamics of interpretation, which
has causal non-linearities (an idea that I probably got
from reading Peirce -- interpretation is inherently
interactive). I also came into these ideas from
studying Quine and Kuhn, and their versions of holism
about meaning. My dissertation was on just these issues
in theory change in science. This is part of the reason
that I became impatient with Jon's misrepresentation
of Quine, and of what is at stake. Jon would have
Quine not be a holist about meaning, or else have him
be deeply inconsistent. Quine is, however, the arch holist.
He is also one of the most consistent philosophers since
David Hume. I knew that there had to be something deeply
wrong with Jon's objection. By distinguishing between
synthetic and analytic models, and between formal logic
and interpretation, one can make sense of Quine's
reductionism about relations (a logical matter), and his
holism about meaning, without contradiction. I should
note in passing that these distinctions do not require
independence :-) What we really have, and Joe you sort
of suggested this earlier, is two types of reduction. What
I disagreed with was your characterization of the one
required for the reduction of relations in Quine as unusual.

John



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

Subject: Re: Identity & Teridentity
From: John Collier <ag659[…]ncf.ca>
Date: Sun, 24 Nov 2002 02:12:26 -0500
X-Message-Number: 12

At 08:54 AM 24/11/2002, Jon wrote:

>Each of the bits of connective tissue that are signified by the
>uses of the word "and" invokes a 3-adic relation, in other words,
>an operation that passes from two sentences to a conjoint sentence --
>or from their truth values to the conjunction of their truth values,
>according to your taste -- and so the putative "reduction" is really
>the sort of "improper" reduction that reduces something to something
>of the same complexity, in this case, more 3-adic relations.

This commits the fallacy of assuming that there is some third
over and above the conjunction operation on the two parts
that is somehow different from the operation on the parts.
There are the related things. There is no third thing.

The rest of Jon's post is full of red herrings. This one
is just wrong, as it begs the question at issue. Again, Jon
is confusing the form with the content: the form is a relation
between two parts and a whole. The content is that the whole
is identical to the conjunction of the parts, and there is
no additional thing, the conjunct. It is identical to the conjunction
of the parts. Again, Jon seems to be assuming the irreducibility
of teridentity, which was, as I recall from the subject line,
exactly the point that was at issue.

John


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

Subject: Re: Identity & Teridentity
From: John Collier <ag659[…]ncf.ca>
Date: Sun, 24 Nov 2002 02:17:12 -0500
X-Message-Number: 13

At 09:27 AM 24/11/2002, you wrote:
>I have not been following this thread closely, but I haven't seen it pointed
>out that someplace (I don't have access to Peirce texts just now) Peirce
>explicitly discusses the example of 'between' in terms of the relation of
>Philadelphia as between Washington and New York, arguing that 'between' is
>not a relation of genuine thirdness, but is rather degenerate thirdness. In
>other words, as I understand Peirce's thinking, 'between' is not a relation
>of thirdness, but rather a relation of compounded secondesses.

Thank you Charles. This is why I used betweenness, but I could
not recall the passage. Whatever else is the case about
triadic relations, teridentity and their reducibility or not, Jon's
recent discussion, and his objection to my ham sandwich example,
cannot be a defense of Peirce's position, unless Peirce himself
was confused on the betweenness case in the same way that
Jon accuses Quine (or at least me) of being confused.

John



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

Subject: Re: Identity & Teridentity
From: John Collier <ag659[…]ncf.ca>
Date: Sun, 24 Nov 2002 02:19:42 -0500
X-Message-Number: 14

At 10:50 AM 24/11/2002, you wrote:
>John,
>
>How would you analyse the relation between a sign, its object and its
>interpretant in dyadic relations? (avoiding that becomes a sandwich, of
>course).

See my response to Joe today. I do argue that the resulting analysis is not
adequate, however. My diagnosis, however, is not the same as either Jon's
or Peirce's own. I have been trying to avoid putting my positive views
forward on this list.

John




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

Subject: Re: Identity & Teridentity
From: Gary Richmond <garyrichmond[…]rcn.com>
Date: Sun, 24 Nov 2002 14:13:49 -0500
X-Message-Number: 15


--------------040208010405070001060305
Content-Type: text/plain; charset=us-ascii; format=flowed
Content-Transfer-Encoding: 7bit

HGCALLAWAY[…]aol.com wrote:

>We need only consider identity itself. In logic identity is generally
>considered to be a binary or dyadic relation. It is written as a two-placed
>prdicate, certainly, and so employed.
>
Certainly this is the position of Peirce in such passages as this:

> Now identity is a relation which cannot be implied by a general
> description of the identical things; and the descriptions of the sets,
> so far as they leave out the individual things, are general. Hence, it
> follows that the only purpose in indicating the units in the
> representation of the set, is in order that each of them may signify
> its identity with an individual of another set. The identity of
> different units of the same set might be similarly represented. Hence,
> passing from the representation of the set, to the set itself, as it
> is logically conceived, the only function of the units in it is to
> establish possible identities with the units of other sets. A unit,
> therefore, is something essential to a set whose existence consists in
> its possible identity with another unit of the same or another set.
> 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. Hence a unit is something whose existence consists in a
> possible dyad of which it is the subject. [emphasis added by me]

You continue, getting right to the heart of the matter under discussion:

>But Peirce recommends the concept of
>teridentity, in which the identity predicate is not so limited. So, to put
>the matter directly, we have been asking, in part, in this thread whether
>identity is or is properly considered a dyadic or binary relation or instead
>in some other way akin to Peirce's conception of teridentity.
>
Perhaps we can get a handle on the putative need for the teridentity
conception by considering the passage I recently quoted concerning the
"other
premiss of the argument that genuine triadic relations can never be
built of dyadic relations and of qualities" (CP 1.346, which I've reproduced
near the end of this message for convenience); keeping in mind the
example of the man seen on Monday, Tuesday, and Wednesday,
in relation to a discussion of existential graphs. Commenting on the
Beta graphs:

> CP 2.21611. Any indefinitely small dot may be a spot replica called a
> spot of teridentity, and three lines of identity may be attached to
> such a spot.

And shortly after:

> Peirce: CP 4.417
> Permission No. 9. It is permitted to scribe an unattached line of
> identity on the sheet of assertion, and to join such unattached lines
> in any number by spots of teridentity. This is to be understood as
> permitting a line of identity, whether within or without a cut, to be
> extended to the cut, although such extremity is to be understood to be
> on both sides of the cut.

Later, commenting on the tinctured, modal graphs:

> Peirce: CP 4.561
> A heavy line shall be considered as a continuum of contiguous dots;
> and since contiguous dots denote a single individual, such a line
> without any point of branching will signify the identity of the
> individuals denoted by its extremities, and the type of such
> unbranching line shall be the Graph of Identity, any instance of which
> (on one area, as every Graph-instance must be) shall be called a Line
> of Identity. The type of a three-way point of such a line shall be
> the Graph of Teridentity; and it shall be considered as composed of
> three contiguous Pegs of a Spot of Identity.

Finally, Peirce makes his claim regarding teridentity quite clear in
this passage (which follows shortly after the one just quoted)

> . . .A heavy line, whether confined to one area or not (and therefore
> not generally being a Graph-instance) of which two extremities abut
> upon pegs of spots shall be called a Ligature. Two lines cannot abut
> upon the same peg other than a point of teridentity. (The purpose of
> this rule is to force the recognition of the demonstrable logical
> truth that the concept of teridentity is not mere identity. It is
> identity and identity, but this "and" is a distinct concept, and is
> precisely that of teridentity.)

So, identity in the way it's been traditionally seen in logic is hardly
denied, but added to this is the concept of teridenity, which "is not
mere identity. It is identity and identity" in the very sense of the man
seen on consecutive days.

> Peirce: CP 1.346
> The other premiss of the argument that genuine triadic relations can
> never be built of dyadic relations and of qualities is easily shown.
> In existential graphs, a spot with one tail -- X represents a quality,
> a spot with two tails -- R -- a dyadic relation.+1 Joining the ends of
> two tails is also a dyadic relation. But you can never by such joining
> make a graph with three tails. You may think that a node connecting
> three lines of identity Y is not a triadic idea. But analysis will
> show that it is so. I see a man on Monday. On Tuesday I see a man, and
> I exclaim, "Why, that is the very man I saw on Monday." We may say,
> with sufficient accuracy, that I directly experienced the identity. On
> Wednesday I see a man and I say, "That is the same man I saw on
> Tuesday, and consequently is the same I saw on Monday." There is a
> recognition of triadic identity; but it is only brought about as a
> conclusion from two premisses, which is itself a triadic relation. If
> I see two men at once, I cannot by any such direct experience identify
> both of them with a man I saw before. I can only identify them if I
> regard them, not as the very same, but as two different manifestations
> of the same man. But the idea of manifestation is the idea of a sign.
> Now a sign is something, A, which denotes some fact or object, B, to
> some interpretant thought, C.

I am no expert in the EG's, but connecting this example with the
discussion of identity/teridenity above ought at least to provide some
basis for discussion.

Gary

>Opinions differ
>on the question. So, there is at least the possibility here that we will find
>out that some conceptions of identity are defective, or limited, specifically
>with regard to their valency. (Say, that we do better not to regard identity
>as a dyadic or binary relation.) That is to suggest the possibility that what
>seems to be a dyadic (or triadic) relation has been misconstrued or
>misunderstood and is better understood in the alternative way. Whether this
>is thought of as a matter of "genuine" (meaning "really" triadic of dyadic
>relations) or in some other way is less important than the possibility that
>we may be able to decide, only after some considerable inquiry, to construe
>identity in one way or the other. If this is a possible result and course of
>inquiry in the case of identity, then we have little reason to think that it
>would not also turn out similarly with other relations.
>
>Let's see what we come up with from the passages you supply. Thanks for your
>interest in this and related threads.
>
>Howard
>
>H.G. Callaway
>(hgcallaway[…]aol.com)
>
>H.G. Callaway
>(hgcallaway[…]aol.com)
>
>---
>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
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Sun, 24 Nov 2002 14:51:05 -0500
X-Message-Number: 16

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

I sent this message out early this morming,
but it seems to have fallen victim to one
of the server's random acts of moderation.

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

JC: It is possible for a relation to be triadic and
for it to be reducible. I gave examples in my
post. There is nothing especially difficult or
tricky in what I am saying. Quite the contrary.
Between, as I mentioned, is a triadic relation, but
it can be composed of dyadic relations. For example,
if we say that the ham is between the upper and lower
slices of bread, that is equivalent to saying that it
is below the upper and above the lower. More formally
Between(ham, upper, lower) iff Above(upper, lower) and
Above(ham, lower) and Above(upper, ham). Between is
clearly a triadic relation, and the location of the
ham in this case involves it, but the relation can
be analyzed fully into dyadic relations.

JA: John Collier has provided us with a perfect example --
a perfect example of someone who does not know what
a relation is, does not know what the difference
between a relation and one of its instances is,
does not therefore know what either a 3-adic
or a 2-adic relation is, and does not know
what decomposition or reduction is.

JA: No wonder he buys Quine's brand of baloney.

John Collier has done us the yowman's service of exemplifying
almost all of the commonly known fallacies in a single short
paragraph. I have a bit more time now, so let us run through
these points in detail.

Zeroth, I will allow that there may be something that JC
is talking about under the heading of the word "relation",
but I have yet to see a coherent account of it, and I do
not hold out much hope for its consistency. I am pretty
sure that it bears no consistent relation to what Boole,
DeMorgan, Peirce, Schroeder, and omnes generationes of
logicians and mathematicians, before and after, meant
by the words "relation" or "relative term". Since
this crew got there first, even Plato and Aristotle
knew better, I suggest that others choose another
word, so as to avoid confusing the massess.

I analyzed the "betweensy" example in some detail for the
Standard/Ontology Lists last year and I will look up those
links for you later on. In the meantime, here is a summary,
far succincter than I have ever done before, of the pertinent
material, as the pertinent thinkers and tradition understand it:

Theory Of Relations

01. http://suo.ieee.org/ontology/msg04377.html
02. http://suo.ieee.org/ontology/msg04378.html
03. http://suo.ieee.org/ontology/msg04379.html
04. http://suo.ieee.org/ontology/msg04380.html
05. http://suo.ieee.org/ontology/msg04381.html
06. http://suo.ieee.org/ontology/msg04382.html

Before we start, let us dismiss JC's inane example, since his "analysis"
of it fails if the plane of the sandwich is vertical to the surface of
the nearest-by large planet, if the sandwich is flipped over, or if the
sandwich is floating in space "between" galaxies -- which incidentally
illustrates the fact that the English "between" is polymorphous, since
"among" would not substitute 'saliva verita' (sic joke), and I never
said anything about there being just two galaxies, but never mind
all that now.

A fairer example would be to pull the mathematician's
"without loss of generality" (WOLOG) gambit, and say
that we are discussing, say, real numbers a, x, b,
where we assume a < b, WOLOG, and then revert to
the 3-adic situs where "x is between a and b".

1. What a relation is.

So far we are still discussing relations in general,
and have not got as far as discussing sign relations,
which are a special case of 3-adic relations.

Where terms of the characters "abstract", "concrete", "general", "individual",
and so on, are distinguished relative to a particular context of discourse,
where we conventionally neglect the differences that are irrelevant to the
purposes of that discourse, relations are denoted by abstract general terms,
and not by concrete individual terms.

2. What the difference between a relation and one of its instances is.

This brings up the fallacy that DB professionals know as the
"one-row database" (ORD) fallacy. Any relation worth its salt
serves up a whole "table" of instances, and not just one like:

<this top slice, this baloney, this bottom slice>.

3. What decomposition or reduction is.

In this regard, JC commits what has long been known as the fallacy
of the "Alchemist's Dodge" or the "(Philosophers') Stone Soup".
It goes a bit like this:

You can make a hearty soup out of nothing but stones and hot water ...
if you add a pinch of salt ...
if you add a dash of pepper ...
if you add a few potatoes ...
if you add a carrot or two ...
if you add a hock of ham ...
if you add ...

And so it goes.

The moral of this particular telling of the story
is that a reduction is not a proper reduction if
it does not reduce something to something lower.

JC's purported "analysis" goes like this:

| Between(ham, upper, lower)
|
| iff
|
| Above(upper, lower)
|
| and
|
| Above(ham, lower)
|
| and
|
| Above(upper, ham).

Each of the bits of connective tissue that are signified by the
uses of the word "and" invokes a 3-adic relation, in other words,
an operation that passes from two sentences to a conjoint sentence --
or from their truth values to the conjunction of their truth values,
according to your taste -- and so the putative "reduction" is really
the sort of "improper" reduction that reduces something to something
of the same complexity, in this case, more 3-adic relations.

All of these things were commonplace understandings well
before Boole, DeMorgan, Peirce, & Co. got into the act.

Jon Awbrey

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

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

Subject: Re: Identity & Teridentity (TO AVOID "BETWEEN")
From: "Armando Sercovich" <cispec[…]com4.com.ar>
Date: Sun, 24 Nov 2002 17:34:00 -0300
X-Message-Number: 17

CORRECTON TO AVOID "BETWEEN"=20

John,

How would you analyse the genuine relation sign-object-interpretant in =
dyadic relations? (avoiding that that becomes a sandwich, of course).=20

Armando Sercovich
CISPEC



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

Subject: Re: Identity & Teridentity
From: "Joseph Ransdell" <joseph.ransdell[…]yahoo.com>
Date: Sun, 24 Nov 2002 15:52:09 -0600
X-Message-Number: 18

Armando:

Your messages are being distributed to the list but perhaps there is
something not working right as regards its delivery to you. I will check it
out and see what i can figure out.

Joe



----- Original Message -----
From: "Armando Sercovich" <cispec[…]com4.com.ar>
To: "Peirce Discussion Forum" <peirce-l[…]lyris.acs.ttu.edu>
Sent: Sunday, November 24, 2002 9:50 AM
Subject: [peirce-l] Re: Identity & Teridentity


John,

How would you analyse the relation between a sign, its object and its
interpretant in dyadic relations? (avoiding that becomes a sandwich, of
course).

Armando Sercovich
CISPEC




---
Message from peirce-l forum to subscriber joseph.ransdell[…]yahoo.com
To unsubscribe send a blank email to: leave-peirce-l-3113A[…]lyris.ttu.edu



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

Subject: Re: Identity & Teridentity
From: Gary Richmond <garyrichmond[…]rcn.com>
Date: Sun, 24 Nov 2002 17:46:36 -0500
X-Message-Number: 19

Caro Armando,

It's good to see Socratic method employed on the list!

Warmest regards,

Gary

Joseph Ransdell wrote:

>Armando:
>
>Your messages are being distributed to the list but perhaps there is
>something not working right as regards its delivery to you. I will check it
>out and see what i can figure out.
>
>Joe
>
>
>
>----- Original Message -----
>From: "Armando Sercovich" <cispec[…]com4.com.ar>
>To: "Peirce Discussion Forum" <peirce-l[…]lyris.acs.ttu.edu>
>Sent: Sunday, November 24, 2002 9:50 AM
>Subject: [peirce-l] Re: Identity & Teridentity
>
>
>John,
>
>How would you analyse the relation between a sign, its object and its
>interpretant in dyadic relations? (avoiding that becomes a sandwich, of
>course).
>
>Armando Sercovich
>CISPEC
>
>
>
>
>---
>Message from peirce-l forum to subscriber joseph.ransdell[…]yahoo.com
>To unsubscribe send a blank email to: leave-peirce-l-9178T[…]lyris.ttu.edu
>
>
>
>---
>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
From: "Armando Sercovich" <cispec[…]com4.com.ar>
Date: Sun, 24 Nov 2002 19:49:23 -0300
X-Message-Number: 20

Joe: =20
=20
Thank you very much. I have already received my two messages.

Armando =20
=20
----- Original Message -----=20
From: "Joseph Ransdell" <joseph.ransdell[…]yahoo.com>
To: "Peirce Discussion Forum" <peirce-l[…]lyris.ttu.edu>
Sent: Sunday, November 24, 2002 6:52 PM
Subject: [peirce-l] Re: Identity & Teridentity


> Armando:
>=20
> Your messages are being distributed to the list but perhaps there is
> something not working right as regards its delivery to you. I will =
check it
> out and see what i can figure out.
>=20
> Joe



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

Subject: Re: logic's logic
From: Gary Richmond <garyrichmond[…]rcn.com>
Date: Sun, 24 Nov 2002 17:52:43 -0500
X-Message-Number: 21

Jon,

I have been thinking about this post, but find I have nothing to say in
reply as it does
not fall within my field of interest. Meanwhile, I benefit from that of
your work which
is within my purview.

Best regards,

Gary

Jon Awbrey wrote:

>o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
>
>Bernard, Gary, & All,
>
>A cut-&-paste error between last year's draft
>and the current web page messed up the proof
>of the "double negation theorem", so here
>is the correct version, I think.
>
> o-----------------------------------------------------------o
> | C1. Double Negation Theorem. Proof. |
> o-----------------------------------------------------------o
> | |
> | a o |
> | \ |
> | \ |
> | o |
> | \ |
> | \ |
> | @ |
> | |
> o=============================< I2. Unfold "(())" >=========o
> | |
> | a o o |
> | \ / |
> | \ / |
> | o o |
> | \ / |
> | \ / |
> | @ |
> | |
> o=============================< J1. Insert "(a)" >==========o
> | |
> | a o |
> | / |
> | / |
> | a o a o o |
> | \ \ / |
> | \ \ / |
> | o o |
> | \ / |
> | \ / |
> | @ |
> | |
> o=============================< J2. Distribute "((a))" >====o
> | |
> | a o a o |
> | \ \ |
> | \ \ |
> | o o a o |
> | \ \ / |
> | \ \ / |
> | a o o |
> | \ / |
> | \ / |
> | o |
> | / |
> | / |
> | @ |
> | |
> o=============================< J1. Delete "(a)" >==========o
> | |
> | a o |
> | \ |
> | \ |
> | o o |
> | \ \ |
> | \ \ |
> | a o o |
> | \ / |
> | \ / |
> | o |
> | / |
> | / |
> | @ |
> | |
> o=============================< J1. Insert "a" >============o
> | |
> | a o |
> | \ |
> | \ |
> | o o a |
> | \ \ |
> | \ \ |
> | a o o a |
> | \ / |
> | \ / |
> | o |
> | / |
> | / |
> | @ |
> | |
> o=============================< J2. Collect "a" >===========o
> | |
> | a o |
> | \ |
> | \ |
> | o o a |
> | \ \ |
> | \ \ |
> | o o |
> | \ / |
> | \ / |
> | o |
> | / |
> | / |
> | a @ |
> | |
> o=============================< J1. Delete "((a))" >========o
> | |
> | o |
> | \ |
> | \ |
> | o |
> | / |
> | / |
> | a @ |
> | |
> o=============================< I2. Refold "(())" >=========o
> | |
> | a |
> | @ |
> | |
> o=============================< QED >=======================o
>
>o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
>
>---
>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: CSP QUOTES RE: GENUINE/DEGENERATE DISTINCTION
From: John Collier <ag659[…]ncf.ca>
Date: Sun, 24 Nov 2002 04:20:05 -0500
X-Message-Number: 22

At 09:36 AM 23/11/2002, Joe wrote:
>QUOTES RELEVANT TO "GENUINE/DEGENERATE" DISTINCTION
>FROM CHARLES PEIRCES COLLECTED PAPERS

These are very interesting quotes, but there is only one that
seems to me to really address the issue of the existence of non-
degenerate triads, other than to assume there existence and
to describe various degenerate cases. (I ignore the claim that
all representation is triadic, since I have already argued that
this claim is ambiguous.) My comments are interspersed.

>Collected Papers 6.322
> 322. For forty years, that is, since the beginning of the year 1867, I have
>been constantly on the alert to find a genuine triadic relation -- that is,
>one that does not consist in a mere collocation of dyadic relations, or the
>negative of such, etc. (I prefer not to attempt a perfectly definite
>definition) -- which is not either an intellectual relation or a relation
>concerned with the less comprehensible phenomena of life. I have not met
>with one which could not reasonably be supposed to belong to one or other of
>these two classes. As a case as nearly brute and inorganic as any, I may
>mention the form of relationship involved in any screw-form which is
>definitely of the right-hand, or occidental, mode, or is definitely of the
>Japanese, or left-handed, mode. Such a relation exists in every carbon-atom
>whose four valencies are saturated by combination with four atoms of as many
>different kinds. But where the action of chance determines whether the screw
>be a right-handed or a left-handed one, the two forms will, in the long run,
>be produced in equal proportions, and the general result will not be
>definitely, or decisively, of either kind. We know no case of a definitely
>right-handed or left-handed screw-phenomenon, where the decision is not
>certainly due to the intervention of a definitely one-sided screw in the
>conditions of that decision, except in cases where the choice of a living
>being determines it; as when Pasteur picked out under the microscope the two
>kinds of crystals of a tartrate, and shoved those of one kind to the right
>and those of the other kind to the left. We do not know the mechanism of
>such choice, and cannot say whether it be determined by an antecedent
>separation of left-handed screws from right-handed screws or not. No doubt,
>all that chance is competent to destroy, it may, once in a long, long time,
>produce; but it is a question whether absolute chance -- pure tychism --
>ought not to be regarded as a product of freedom, and therefore of life, not
>necessarily physiological. It could not be caused, apparently, by the
>inorganic action of dynamical law. For the only way in which the laws of
>dynamics involve triadic relations is by their reference to second
>differentials of positions. But though a second differential generally
>involves a triadic relation, yet owing to the law of the conservation of
>energy, which has been sufficiently proved for purely inorganic phenomena,
>the dynamic laws for such phenomena are expressible in terms of first
>differentials. It is, therefore, a non-genuine, or, as I phrase it, a
>"degenerate" form of triadic relationship which is involved in such case. In
>short, the problem of how genuine triadic relationships first arose in the
>world is a better, because more definite, formulation of the problem of how
>life first came about; and no explanation has ever been offered except that
>of pure chance, which we must suspect to be no explanation, owing to the
>suspicion that pure chance may itself be a vital phenomenon. In that case,
>life in the physiological sense would be due to life in the metaphysical
>sense. Of course, the fact that a given individual has been persuaded of the
>truth of a proposition is the very slenderest possible argument for its
>truth; nevertheless, the fact that I, a person of the strongest possible
>physicistic prejudices, should, as the result of forty years of
>questionings, have been brought to the deep conviction that there is some
>essentially and irreducibly other element in the universe than pure dynamism
>may have sufficient interest to excuse my devoting a single sentence to its
>expression. For you may be sure that I had reasons that withstood severe,
>not to say hostile criticism; and if I live to do it, I shall embody them in
>a volume.

I want to note here that chirality (handedness) is a dynamical phenomenon.
We can convert a left handed screw to a right handed screw (and vice versa)
if we can operate on it in non-dynamical ways, e.g., by reflection. This gives
some credence to the claim that I made in my previous post to Joe, in
presenting my own views, that irreducible triadicity is of dynamical, not
logical,
origin. That is, the distinction between right and left handedness is a
dynamical
phenomenon. I don't have the time to go into this more right now, as it is
a very complex issue. I note only that it is connected to the issue of the
direction
of time through the issue of the failure of CPT symmetry by some mesons,
and that this is not yet fully understood. Of course, Kant thought that time
was essential to thought, but not space. The connection that is implied here
of dynamics to a case of irreducible triadicity and it connection to time
asymmetry, essential to mind, is a curiosity that may well be very deeply
significant. This is especially so with when the following is considered,
which may seem to contradict the "brute" example above. I do note the
irony, though, that from the point of view of mental operations alone,
right-handedness and left-handedness can be seen as symmetrical
and not fundamentally distinct. There is more going on here than
Peirce understands.

...

> 331. I now come to Thirdness. To me, who have for forty years considered
>the matter from every point of view that I could discover, the inadequacy of
>Secondness to cover all that is in our minds is so evident that I scarce
>know how to begin to persuade any person of it who is not already convinced
>of it. Yet I see a great many thinkers who are trying to construct a system
>without putting any thirdness into it. Among them are some of my best
>friends who acknowledge themselves indebted to me for ideas but have never
>learned the principal lesson. Very well. It is highly proper that Secondness
>should be searched to its very bottom. Thus only can the indispensableness
>and irreducibility of thirdness be made out, although for him who has the
>mind to grasp it, it is sufficient to say that no branching of a line can
>result from putting one line on the end of another. My friend Schroeder fell
>in love with my algebra of dyadic relations. The few pages I gave to it in
>my Note B in the 'Studies in Logic by Members of the Johns Hopkins
>University' were proportionate to its importance. His book is profound, but
>its profundity only makes it more clear that Secondness cannot compass
>Thirdness. (He is careful to avoid ever saying that it can, but he does go
>so far as to say that Secondness is the more important. So it is,
>considering that Thirdness cannot be understood without Secondness. But as
>to its application, it is so inferior to Thirdness as to be in that aspect
>quite in a different world.) Even in the most degenerate form of Thirdness,
>and thirdness has two grades of degeneracy, something may be detected which
>is not mere secondness. If you take any ordinary triadic relation, you will
>always find a mental element in it. Brute action is secondness, any
>mentality involves thirdness. Analyze for instance the relation involved in
>'A gives B to C.' Now what is giving? It does not consist [in] A's putting B
>away from him and C's subsequently taking B up. It is not necessary that any
>material transfer should take place. It consists in A's making C the
>possessor according to Law. There must be some kind of law before there can
>be any kind of giving, -- be it but the law of the strongest. But now
>suppose that giving did consist merely in A's laying down the B which C
>subsequently picks up. That would be a degenerate form of Thirdness in which
>the thirdness is externally appended. In A's putting away B, there is no
>thirdness. In C's taking B, there is no thirdness. But if you say that these
>two acts constitute a single operation by virtue of the identity of the B,
>you transcend the mere brute fact, you introduce a mental element . . . .

I find it strange that the identity of B with itself is described as a mental
element. I don't see how this could derive from anything but a strangely
(for Peirce) nominalist view of identity. Any suggestions would be most
welcome.-

>The criticism which I make on [my] algebra of dyadic relations, with which I
>am by no means in love, though I think it is a pretty thing, is that the
>very triadic relations which it does not recognize, it does itself employ.
>For every combination of relatives to make a new relative is a triadic
>relation irreducible to dyadic relations. Its inadequacy is shown in other
>ways, but in this way it is in a conflict with itself if it be regarded, as
>I never did regard it, as sufficient for the expression of all relations. My
>universal algebra of relations, with the subjacent indices and d and c, is
>susceptible of being enlarged so as to comprise everything; and so, still
>better, though not to ideal perfection, is the system of existential graphs.

This also seems to me to invoke a triadic view of identity. I see no reason,
as I said in my response to Jon's claim that conjunction relates two things
to a third, to suppose that the "new relative" is anything but identical to
the combination. If the identity is irreducibly triadic (teridentity), then
the argument goes through, but this is the very issue that is to be shown.
it also has the unfortunate consequence that all relations are triadic,
even dyadic ones. This is not a very elegant consequence, as I have
tried to explain in previous posts. I think we should want to find a
satisfactory
way to avid this conclusion if we can.

> 332. I have not sufficiently applied myself to the study of the degenerate
>forms of Thirdness, though I think I see that it has two distinct grades of
>degeneracy. In its genuine form, Thirdness is the triadic relation existing
>between a sign, its object, and the interpreting thought, itself a sign,
>considered as constituting the mode of being of a sign. A sign mediates
>between the interpretant sign and its object. Taking sign in its broadest
>sense, its interpretant is not necessarily a sign. Any concept is a sign, of
>course. Ockham, Hobbes, and Leibniz have sufficiently said that. But we may
>take a sign in so broad a sense that the interpretant of it is not a
>thought, but an action or experience, or we may even so enlarge the meaning
>of sign that its interpretant is a mere quality of feeling. A Third is
>something which brings a First into relation to a Second. A sign is a sort
>of Third. How shall we characterize it? Shall we say that a Sign brings a
>Second, its Object, into cognitive relation to a Third? That a Sign brings a
>Second into the same relation to a first in which it stands itself to that
>First? If we insist on consciousness, we must say what we mean by
>consciousness of an object. Shall we say we mean Feeling? Shall we say we
>mean association, or Habit? These are, on the face of them, psychological
>distinctions, which I am particular to avoid. What is the essential
>difference between a sign that is communicated to a mind, and one that is
>not so communicated? If the question were simply what we do mean by a sign,
>it might soon be resolved. But that is not the point. We are in the
>situation of a zologist who wants to know what ought to be the meaning of
>"fish" in order to make fishes one of the great classes of vertebrates. It
>appears to me that the essential function of a sign is to render inefficient
>relations efficient, -- not to set them into action, but to establish a
>habit or general rule whereby they will act on occasion. According to the
>physical doctrine, nothing ever happens but the continued rectilinear
>velocities with the accelerations that accompany different relative
>positions of the particles. All other relations, of which we know so many,
>are inefficient. Knowledge in some way renders them efficient; and a sign is
>something by knowing which we know something more. With the exception of
>knowledge, in the present instant, of the contents of consciousness in that
>instant (the existence of which knowledge is open to doubt) all our thought
>and knowledge is by signs. A sign therefore is an object which is in
>relation to its object on the one hand and to an interpretant on the other,
>in such a way as to bring the interpretant into a relation to the object,
>corresponding to its own relation to the object. I might say 'similar to its
>own' for a correspondence consists in a similarity; but perhaps
>correspondence is narrower.

It is clear from this that Peirce means by a genuine Third a non-degenerate
one. I think that it is also clear that he means by this a Third that is not
constructible from Seconds. It is also clear that he thinks that representation
has this property. However the argument invokes the triadicity
of a sign, but there is no argument that this triadicity is not reducible
to Seconds.

From the combination of the first part of this and the second, I suggest
that the non-reducibility of genuine triads is a dynamical and not
a logical property


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

Subject: Re: Identity & Teridentity
From: "Armando Sercovich" <cispec[…]com4.com.ar>
Date: Sun, 24 Nov 2002 20:45:18 -0300
X-Message-Number: 23

Dear Gary,

It's good to hear you! Holderlin said poetically (maybe thinking on =
Socrate): "Wir--die Menschen--sind ein Gesprach" /Us, the men, are a =
dialogue.

Best wishes,

Armando
---=20

You wrote:

> Caro Armando,
>=20
> It's good to see Socratic method employed on the list!
>=20
> Warmest regards,
>=20
> Gary
>=20
> Joseph Ransdell wrote:
>=20
> >Armando:
> >
> >Your messages are being distributed to the list but perhaps there is
> >something not working right as regards its delivery to you. I will =
check it
> >out and see what i can figure out.
> >
> >Joe
> >
> >
> >
> >----- Original Message -----
> >From: "Armando Sercovich" <cispec[…]com4.com.ar>
> >To: "Peirce Discussion Forum" <peirce-l[…]lyris.acs.ttu.edu>
> >Sent: Sunday, November 24, 2002 9:50 AM
> >Subject: [peirce-l] Re: Identity & Teridentity
> >
> >
> >John,
> >
> >How would you analyse the relation between a sign, its object and its
> >interpretant in dyadic relations? (avoiding that becomes a sandwich, =
of
> >course).
> >
> >Armando Sercovich
> >CISPEC
> >
> >
> >
> >
> >---
> >Message from peirce-l forum to subscriber joseph.ransdell[…]yahoo.com
> >To unsubscribe send a blank email to: =
leave-peirce-l-34459I[…]lyris.ttu.edu
> >
> >
> >
> >---
> >Message from peirce-l forum to subscriber garyrichmond[…]rcn.com
> >To unsubscribe send a blank email to: =
leave-peirce-l-34459I[…]lyris.ttu.edu
> >
>=20
>=20
>=20
>=20
> ---
> Message from peirce-l forum to subscriber cispec[…]com4.com.ar
> To unsubscribe send a blank email to: =
leave-peirce-l-34459I[…]lyris.ttu.edu
>=20


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

Subject: Re: Identity & Teridentity
From: Gary Richmond <garyrichmond[…]rcn.com>
Date: Sun, 24 Nov 2002 21:29:57 -0500
X-Message-Number: 24


--------------050000090106090905090904
Content-Type: text/plain; charset=us-ascii; format=flowed
Content-Transfer-Encoding: 7bit

A very Peircean quotation of Holderlin. Thanks, Armando!
That was uplifting.

But Holderlin also said (maybe referring to the agonizing pain of modern
life)
"Aber Weh! Es wandelt in Nacht. Es wohnt wie in Orkus, unser Geschlecht."\
(This is from memory, so forgive any errors. I first read this passage
in an essay by Martin Buber.)

Best to you,

Gary

Armando Sercovich wrote:

>Dear Gary,
>
>It's good to hear you! Holderlin said poetically (maybe thinking on Socrate): "Wir--die Menschen--sind ein Gesprach" /Us, the men, are a dialogue.
>
>Best wishes,
>
>Armando


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

Subject: Re: CSP QUOTES RE: GENUINE/DEGENERATE DISTINCTION
From: Inna Semetsky <innasense[…]mac.com>
Date: Sun, 24 Nov 2002 18:50:37 -0800 (PST)
X-Message-Number: 25

John: why is reflection non-dynamical? because it is not a function of time? Does it mean that all mathematical transformations are non-dynamical? there seems to be some fallacy here that i cannot yret articulate.
Personally i think that reflection is dynamical--so i would appreciate your explanation. thanks. inna

On Sunday, Nov 24, 2002, at 08:20PM, John Collier <ag659[…]ncf.ca> wrote:

>At 09:36 AM 23/11/2002, Joe wrote:
>>QUOTES RELEVANT TO "GENUINE/DEGENERATE" DISTINCTION
>>FROM CHARLES PEIRCES COLLECTED PAPERS
>
>These are very interesting quotes, but there is only one that
>seems to me to really address the issue of the existence of non-
>degenerate triads, other than to assume there existence and
>to describe various degenerate cases. (I ignore the claim that
>all representation is triadic, since I have already argued that
>this claim is ambiguous.) My comments are interspersed.
>
>>Collected Papers 6.322
>> 322. For forty years, that is, since the beginning of the year 1867, I have
>>been constantly on the alert to find a genuine triadic relation -- that is,
>>one that does not consist in a mere collocation of dyadic relations, or the
>>negative of such, etc. (I prefer not to attempt a perfectly definite
>>definition) -- which is not either an intellectual relation or a relation
>>concerned with the less comprehensible phenomena of life. I have not met
>>with one which could not reasonably be supposed to belong to one or other of
>>these two classes. As a case as nearly brute and inorganic as any, I may
>>mention the form of relationship involved in any screw-form which is
>>definitely of the right-hand, or occidental, mode, or is definitely of the
>>Japanese, or left-handed, mode. Such a relation exists in every carbon-atom
>>whose four valencies are saturated by combination with four atoms of as many
>>different kinds. But where the action of chance determines whether the screw
>>be a right-handed or a left-handed one, the two forms will, in the long run,
>>be produced in equal proportions, and the general result will not be
>>definitely, or decisively, of either kind. We know no case of a definitely
>>right-handed or left-handed screw-phenomenon, where the decision is not
>>certainly due to the intervention of a definitely one-sided screw in the
>>conditions of that decision, except in cases where the choice of a living
>>being determines it; as when Pasteur picked out under the microscope the two
>>kinds of crystals of a tartrate, and shoved those of one kind to the right
>>and those of the other kind to the left. We do not know the mechanism of
>>such choice, and cannot say whether it be determined by an antecedent
>>separation of left-handed screws from right-handed screws or not. No doubt,
>>all that chance is competent to destroy, it may, once in a long, long time,
>>produce; but it is a question whether absolute chance -- pure tychism --
>>ought not to be regarded as a product of freedom, and therefore of life, not
>>necessarily physiological. It could not be caused, apparently, by the
>>inorganic action of dynamical law. For the only way in which the laws of
>>dynamics involve triadic relations is by their reference to second
>>differentials of positions. But though a second differential generally
>>involves a triadic relation, yet owing to the law of the conservation of
>>energy, which has been sufficiently proved for purely inorganic phenomena,
>>the dynamic laws for such phenomena are expressible in terms of first
>>differentials. It is, therefore, a non-genuine, or, as I phrase it, a
>>"degenerate" form of triadic relationship which is involved in such case. In
>>short, the problem of how genuine triadic relationships first arose in the
>>world is a better, because more definite, formulation of the problem of how
>>life first came about; and no explanation has ever been offered except that
>>of pure chance, which we must suspect to be no explanation, owing to the
>>suspicion that pure chance may itself be a vital phenomenon. In that case,
>>life in the physiological sense would be due to life in the metaphysical
>>sense. Of course, the fact that a given individual has been persuaded of the
>>truth of a proposition is the very slenderest possible argument for its
>>truth; nevertheless, the fact that I, a person of the strongest possible
>>physicistic prejudices, should, as the result of forty years of
>>questionings, have been brought to the deep conviction that there is some
>>essentially and irreducibly other element in the universe than pure dynamism
>>may have sufficient interest to excuse my devoting a single sentence to its
>>expression. For you may be sure that I had reasons that withstood severe,
>>not to say hostile criticism; and if I live to do it, I shall embody them in
>>a volume.
>
>I want to note here that chirality (handedness) is a dynamical phenomenon.
>We can convert a left handed screw to a right handed screw (and vice versa)
>if we can operate on it in non-dynamical ways, e.g., by reflection. This gives
>some credence to the claim that I made in my previous post to Joe, in
>presenting my own views, that irreducible triadicity is of dynamical, not
>logical,
>origin. That is, the distinction between right and left handedness is a
>dynamical
>phenomenon. I don't have the time to go into this more right now, as it is
>a very complex issue. I note only that it is connected to the issue of the
>direction
>of time through the issue of the failure of CPT symmetry by some mesons,
>and that this is not yet fully understood. Of course, Kant thought that time
>was essential to thought, but not space. The connection that is implied here
>of dynamics to a case of irreducible triadicity and it connection to time
>asymmetry, essential to mind, is a curiosity that may well be very deeply
>significant. This is especially so with when the following is considered,
>which may seem to contradict the "brute" example above. I do note the
>irony, though, that from the point of view of mental operations alone,
>right-handedness and left-handedness can be seen as symmetrical
>and not fundamentally distinct. There is more going on here than
>Peirce understands.
>
>...
>
>> 331. I now come to Thirdness. To me, who have for forty years considered
>>the matter from every point of view that I could discover, the inadequacy of
>>Secondness to cover all that is in our minds is so evident that I scarce
>>know how to begin to persuade any person of it who is not already convinced
>>of it. Yet I see a great many thinkers who are trying to construct a system
>>without putting any thirdness into it. Among them are some of my best
>>friends who acknowledge themselves indebted to me for ideas but have never
>>learned the principal lesson. Very well. It is highly proper that Secondness
>>should be searched to its very bottom. Thus only can the indispensableness
>>and irreducibility of thirdness be made out, although for him who has the
>>mind to grasp it, it is sufficient to say that no branching of a line can
>>result from putting one line on the end of another. My friend Schroeder fell
>>in love with my algebra of dyadic relations. The few pages I gave to it in
>>my Note B in the 'Studies in Logic by Members of the Johns Hopkins
>>University' were proportionate to its importance. His book is profound, but
>>its profundity only makes it more clear that Secondness cannot compass
>>Thirdness. (He is careful to avoid ever saying that it can, but he does go
>>so far as to say that Secondness is the more important. So it is,
>>considering that Thirdness cannot be understood without Secondness. But as
>>to its application, it is so inferior to Thirdness as to be in that aspect
>>quite in a different world.) Even in the most degenerate form of Thirdness,
>>and thirdness has two grades of degeneracy, something may be detected which
>>is not mere secondness. If you take any ordinary triadic relation, you will
>>always find a mental element in it. Brute action is secondness, any
>>mentality involves thirdness. Analyze for instance the relation involved in
>>'A gives B to C.' Now what is giving? It does not consist [in] A's putting B
>>away from him and C's subsequently taking B up. It is not necessary that any
>>material transfer should take place. It consists in A's making C the
>>possessor according to Law. There must be some kind of law before there can
>>be any kind of giving, -- be it but the law of the strongest. But now
>>suppose that giving did consist merely in A's laying down the B which C
>>subsequently picks up. That would be a degenerate form of Thirdness in which
>>the thirdness is externally appended. In A's putting away B, there is no
>>thirdness. In C's taking B, there is no thirdness. But if you say that these
>>two acts constitute a single operation by virtue of the identity of the B,
>>you transcend the mere brute fact, you introduce a mental element . . . .
>
>I find it strange that the identity of B with itself is described as a mental
>element. I don't see how this could derive from anything but a strangely
>(for Peirce) nominalist view of identity. Any suggestions would be most
>welcome.-
>
>>The criticism which I make on [my] algebra of dyadic relations, with which I
>>am by no means in love, though I think it is a pretty thing, is that the
>>very triadic relations which it does not recognize, it does itself employ.
>>For every combination of relatives to make a new relative is a triadic
>>relation irreducible to dyadic relations. Its inadequacy is shown in other
>>ways, but in this way it is in a conflict with itself if it be regarded, as
>>I never did regard it, as sufficient for the expression of all relations. My
>>universal algebra of relations, with the subjacent indices and d and c, is
>>susceptible of being enlarged so as to comprise everything; and so, still
>>better, though not to ideal perfection, is the system of existential graphs.
>
>This also seems to me to invoke a triadic view of identity. I see no reason,
>as I said in my response to Jon's claim that conjunction relates two things
>to a third, to suppose that the "new relative" is anything but identical to
>the combination. If the identity is irreducibly triadic (teridentity), then
>the argument goes through, but this is the very issue that is to be shown.
>it also has the unfortunate consequence that all relations are triadic,
>even dyadic ones. This is not a very elegant consequence, as I have
>tried to explain in previous posts. I think we should want to find a
>satisfactory
>way to avid this conclusion if we can.
>
>> 332. I have not sufficiently applied myself to the study of the degenerate
>>forms of Thirdness, though I think I see that it has two distinct grades of
>>degeneracy. In its genuine form, Thirdness is the triadic relation existing
>>between a sign, its object, and the interpreting thought, itself a sign,
>>considered as constituting the mode of being of a sign. A sign mediates
>>between the interpretant sign and its object. Taking sign in its broadest
>>sense, its interpretant is not necessarily a sign. Any concept is a sign, of
>>course. Ockham, Hobbes, and Leibniz have sufficiently said that. But we may
>>take a sign in so broad a sense that the interpretant of it is not a
>>thought, but an action or experience, or we may even so enlarge the meaning
>>of sign that its interpretant is a mere quality of feeling. A Third is
>>something which brings a First into relation to a Second. A sign is a sort
>>of Third. How shall we characterize it? Shall we say that a Sign brings a
>>Second, its Object, into cognitive relation to a Third? That a Sign brings a
>>Second into the same relation to a first in which it stands itself to that
>>First? If we insist on consciousness, we must say what we mean by
>>consciousness of an object. Shall we say we mean Feeling? Shall we say we
>>mean association, or Habit? These are, on the face of them, psychological
>>distinctions, which I am particular to avoid. What is the essential
>>difference between a sign that is communicated to a mind, and one that is
>>not so communicated? If the question were simply what we do mean by a sign,
>>it might soon be resolved. But that is not the point. We are in the
>>situation of a zologist who wants to know what ought to be the meaning of
>>"fish" in order to make fishes one of the great classes of vertebrates. It
>>appears to me that the essential function of a sign is to render inefficient
>>relations efficient, -- not to set them into action, but to establish a
>>habit or general rule whereby they will act on occasion. According to the
>>physical doctrine, nothing ever happens but the continued rectilinear
>>velocities with the accelerations that accompany different relative
>>positions of the particles. All other relations, of which we know so many,
>>are inefficient. Knowledge in some way renders them efficient; and a sign is
>>something by knowing which we know something more. With the exception of
>>knowledge, in the present instant, of the contents of consciousness in that
>>instant (the existence of which knowledge is open to doubt) all our thought
>>and knowledge is by signs. A sign therefore is an object which is in
>>relation to its object on the one hand and to an interpretant on the other,
>>in such a way as to bring the interpretant into a relation to the object,
>>corresponding to its own relation to the object. I might say 'similar to its
>>own' for a correspondence consists in a similarity; but perhaps
>>correspondence is narrower.
>
>It is clear from this that Peirce means by a genuine Third a non-degenerate
>one. I think that it is also clear that he means by this a Third that is not
>constructible from Seconds. It is also clear that he thinks that representation
>has this property. However the argument invokes the triadicity
>of a sign, but there is no argument that this triadicity is not reducible
>to Seconds.
>
> From the combination of the first part of this and the second, I suggest
>that the non-reducibility of genuine triads is a dynamical and not
>a logical property
>
>
>---
>Message from peirce-l forum to subscriber irs5[…]columbia.edu
>To unsubscribe send a blank email to: leave-peirce-l-36948S[…]lyris.ttu.edu
>
>


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

Subject: Re: Identity & Teridentity
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Sun, 24 Nov 2002 20:52:49 -0500
X-Message-Number: 26

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

For those who are keeping tabs:

1. What a relation is.
1.1. Fallacy. the "I lied about the set" puzzle.

2. What the difference between a relation and a relation instance is.
2.1. Fallacy. the "one row datbase" (ORD) illusion.

3. What decomposition or reducibility is.
3.1. Fallacy. the "2-ped dog" (2PD) dogma.
3.2. Fallacy. the "alechemist's dodge" (AD).
3.3. Fallacy. the "stone soup" (SS) parable.
3.4. Fallacy. the "who's on third" (WOT) joke.
AKA. "truth-functions compute themselves".

Peter,

I continue from where I left off last time.

I gather that you have some computer science background, so I will
take the liberty of expressing some of my arguments in those terms.

Let us consider the informal notion of "computational work" as
a measure of the presence of an "information-theoretic reality".

For instance, consider JC's statement to the effect that there
is no "third" involved in the formation of the truth-functional
conjunction 'and' : B x B -> B.

I wish! Sadly, though, truth-functions do not compute themselves,
and even if they did, they would need to do computational work in
order to do the job. This should clue us in to the informational
realities of the situation, and it tells what a practical fallacy
JC has e-mitted in this connection. Like my old algebra book said:
"A binary operation is a ternary relation" -- so any truth-function
of the type f : B x B -> B is also 3-adic relation F c B x B x B.
Being functional from its first two domains to its third, it is
of course a very special type of 3-adic relation, but it remains
a 3-adic relation for all that. And we both know that there is
a gap between the indicated operation and the functional result
that doesn't get crossed without doing some computational work.

Let us imagine a generic venn diagram with circle A and circle B.
Then the intersection A |^| B is a third thing, distinct from both.
For another third thing, there is the union A |_| B, also distinct
from A, B, and A |^| B. Now maybe in our fantasy the intersection
and the union just appear as if by magic, but how, even in fantasy,
do you know which of the 16 possible third things is the right one?
And of course, you know and I know that, no matter how you compute
the intersection or the union or any other truth function, whether
by bit-maps or by object equations, its just gonna take some work.

To be continued

Jon Awbrey

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

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

Subject: Re: Identity & Teridentity
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Sun, 24 Nov 2002 19:50:10 -0500
X-Message-Number: 27

PB = Peter Brawley

PB: Jon would you please point to where John shows
he "does not know what the difference between a
relation and one of its instances is" and "does
not know what decomposition or reduction is"?

Peter,

I explained these points more fully in the next post that I sent --
I got a message from Lyris saying that it was rejected, now I see
two copies at the Archive, but I still don't know for sure if it
got distributed or not. Anyway, here's an expansion of that.

JA: John Collier has done us the yowman's service of exemplifying
almost all of the commonly known fallacies in a single short
paragraph. I have a bit more time now, so let us run through
these points in detail.

| Of JC's statements the multitude of fallacies is so terrific
| that I have usually shrunk from the task of enumerating them ...

The more that JC writes on this issue, the more his logical and practical
fallacies pile up, and the more I realize that he has never really taken
an interest in reading what Peirce actually wrote on any of these topics.

JA: Zeroth, I will allow that there may be something that JC
is talking about under the heading of the word "relation",
but I have yet to see a coherent account of it, and I do
not hold out much hope for its consistency. I am pretty
sure that it bears no consistent relation to what Boole,
DeMorgan, Peirce, Schroeder, and omnes generationes of
logicians and mathematicians, before and after, meant
by the words "relation" or "relative term". Since
this crew got there first, even Plato and Aristotle
knew better, I suggest that others choose another
word, so as to avoid confusing the massess.

I am vety serious about this. JC is perfectly free to exposit his idea of
what a relation is, or to exposit his interpretation of what Rosen's idea
of a relation is, and "ethics of terminology" notwithstanding he is free
to use any terms that he fancies to do so. But I would be amiss in my
responsibilities if I did not continue to point out, what I can say
with a great deal of confidence from having read everything in CP
once or twice of three times, often after a decade or two of
reflection and acquired perspective, that whatever he is
talking about has very little to do, thank goodness,
with what Peirce and that whole army of logicians
and mathematicians are talking about under the
headings of "relations", "relative terms",
"reducibility", "generic vs. degenerate",
and all those other words in play.

What Peirce was talking about under the headings of relations,
relative terms, relative and non-relative operations on relations,
strong and weak types of reducibility with respect to these operations,
genericity, degeneracy, identity, teridentity, and so on, is very clear
and immediately recognizable to readers with the minimal mathematical
background, was published in the premier mathematical journals of his
day and ours, is subject to definition, formalization, and the whole
discipline of theorem and proof, for those who accept those rigors.

JA: I analyzed the "betweenness" example in some detail for the
Standard/Ontology Lists last year and I will look up those
links for you later on. In the meantime, here is a summary,
far succincter than I have ever done before, of the pertinent
material, as the pertinent thinkers and tradition understand it:

Theory Of Relations

01. http://suo.ieee.org/ontology/msg04377.html
02. http://suo.ieee.org/ontology/msg04378.html
03. http://suo.ieee.org/ontology/msg04379.html
04. http://suo.ieee.org/ontology/msg04380.html
05. http://suo.ieee.org/ontology/msg04381.html
06. http://suo.ieee.org/ontology/msg04382.html

Betweenness is an example of a 3-adic relation, which makes it by the
definition of relational composition, irreducible to a composition of
2-adic relations. That is the "strong" notion of reducibility, to put
it in a more contemporary idiom. However, once that is understood, it
is possible to weaken the notion of reducibility, saying to the wannabe
reducer, as it were: Okay, now that you have conceded that this 3-adic
is irreducible to 2-adics in the primary sense, suppose that I give you
gratis to use in your composition some simple 3-adic relations, oh, say,
like 'and' : B x B -> B, or things of that ilk -- could you then compose
me this 3-adic out of nothing but 2-adics and those gratuitous 3-adics?

That game is about the "weak" notion of reducibility,
but it's a consolation game, and only begins when the
reducer has acknowledged futility on the first score.

Have to take a time out here, back later ...

Jon Awbrey

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

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

Subject: Re: Identity & Teridentity
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Sun, 24 Nov 2002 19:40:13 -0500
X-Message-Number: 28

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

PB = Peter Brawley

PB: Jon would you please point to where John shows
he "does not know what the difference between a
relation and one of its instances is" and "does
not know what decomposition or reduction is"?

Peter,

I explained these points more fully in the next post that I sent --
I got a message from Lyris saying that it was rejected, now I see
two copies at the Archive, but I still don't know for sure if it
got distributed or not. Anyway, here's an expansion of that.

JA: John Collier has done us the yowman's service of exemplifying
almost all of the commonly known fallacies in a single short
paragraph. I have a bit more time now, so let us run through
these points in detail.

| Of JC's statements the multitude of fallacies is so terrific
| that I have usually shrunk from the task of enumerating them ...

The more that JC writes on this issue, the more his logical and practical
fallacies pile up, and the more I realize that he has never really taken
an interest in reading what Peirce actually wrote on any of these topics.

JA: Zeroth, I will allow that there may be something that JC
is talking about under the heading of the word "relation",
but I have yet to see a coherent account of it, and I do
not hold out much hope for its consistency. I am pretty
sure that it bears no consistent relation to what Boole,
DeMorgan, Peirce, Schroeder, and omnes generationes of
logicians and mathematicians, before and after, meant
by the words "relation" or "relative term". Since
this crew got there first, even Plato and Aristotle
knew better, I suggest that others choose another
word, so as to avoid confusing the massess.

I am vety serious about this. JC is perfectly free to exposit his idea of
what a relation is, or to exposit his interpretation of what Rosen's idea
of a relation is, and "ethics of terminology" notwithstanding he is free
to use any terms that he fancies to do so. But I would be amiss in my
responsibilities if I did not continue to point out, what I can say
with a great deal of confidence from having read everything in CP
once or twice of three times, often after a decade or two of
reflection and acquired perspective, that whatever he is
talking about has very little to do, thank goodness,
with what Peirce and that whole army of logicians
and mathematicians are talking about under the
headings of "relations", "relative terms",
"reducibility", "generic vs. degenerate",
and all those other words in play.

What Peirce was talking about under the headings of relations,
relative terms, relative and non-relative operations on relations,
strong and weak types of reducibility with respect to these operations,
genericity, degeneracy, identity, teridentity, and so on, is very clear
and immediately recognizable to readers with the minimal mathematical
background, was published in the premier mathematical journals of his
day and ours, is subject to definition, formalization, and the whole
discipline of theorem and proof, for those who accept those rigors.

JA: I analyzed the "betweenness" example in some detail for the
Standard/Ontology Lists last year and I will look up those
links for you later on. In the meantime, here is a summary,
far succincter than I have ever done before, of the pertinent
material, as the pertinent thinkers and tradition understand it:

Theory Of Relations

01. http://suo.ieee.org/ontology/msg04377.html
02. http://suo.ieee.org/ontology/msg04378.html
03. http://suo.ieee.org/ontology/msg04379.html
04. http://suo.ieee.org/ontology/msg04380.html
05. http://suo.ieee.org/ontology/msg04381.html
06. http://suo.ieee.org/ontology/msg04382.html

Betweenness is an example of a 3-adic relation, which makes it by the
definition of relational composition, irreducible to a composition of
2-adic relations. That is the "strong" notion of reducibility, to put
it in a more contemporary idiom. However, once that is understood, it
is possible to weaken the notion of reducibility, saying to the wannabe
reducer, as it were: Okay, now that you have conceded that this 3-adic
is irreducible to 2-adics in the primary sense, suppose that I give you
gratis to use in your composition some simple 3-adic relations, oh, say,
like 'and' : B x B -> B, or things of that ilk -- could you then compose
me this 3-adic out of nothing but 2-adics and those gratuitous 3-adics?

That game is about the "weak" notion of reducibility,
but it's a consolation game, and only begins when the
reducer has acknowledged futility on the first score.

Have to take a time out here, back later ...

Jon Awbrey

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

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

Subject: Re: Identity & Teridentity
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Sun, 24 Nov 2002 22:30:58 -0500
X-Message-Number: 29

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

Second try on this one, so they will be out of sequence.

PB = Peter Brawley

PB: Jon would you please point to where John shows
he "does not know what the difference between a
relation and one of its instances is" and "does
not know what decomposition or reduction is"?

Peter,

I explained these points more fully in the next post that I sent --
I got a message from Lyris saying that it was rejected, now I see
two copies at the Archive, but I still don't know for sure if it
got distributed or not. Anyway, here's an expansion of that.

JA: John Collier has done us the yowman's service of exemplifying
almost all of the commonly known fallacies in a single short
paragraph. I have a bit more time now, so let us run through
these points in detail.

| Of JC's statements the multitude of fallacies is so terrific
| that I have usually shrunk from the task of enumerating them ...

The more that JC writes on this issue, the more his logical and practical
fallacies pile up, and the more I realize that he has never really taken
an interest in reading what Peirce actually wrote on any of these topics.

JA: Zeroth, I will allow that there may be something that JC
is talking about under the heading of the word "relation",
but I have yet to see a coherent account of it, and I do
not hold out much hope for its consistency. I am pretty
sure that it bears no consistent relation to what Boole,
DeMorgan, Peirce, Schroeder, and omnes generationes of
logicians and mathematicians, before and after, meant
by the words "relation" or "relative term". Since
this crew got there first, even Plato and Aristotle
knew better, I suggest that others choose another
word, so as to avoid confusing the massess.

I am vety serious about this. JC is perfectly free to exposit his idea of
what a relation is, or to exposit his interpretation of what Rosen's idea
of a relation is, and "ethics of terminology" notwithstanding he is free
to use any terms that he fancies to do so. But I would be amiss in my
responsibilities if I did not continue to point out, what I can say
with a great deal of confidence from having read everything in CP
once or twice of three times, often after a decade or two of
reflection and acquired perspective, that whatever he is
talking about has very little to do, thank goodness,
with what Peirce and that whole army of logicians
and mathematicians are talking about under the
headings of "relations", "relative terms",
"reducibility", "generic vs. degenerate",
and all those other words in play.

What Peirce was talking about under the headings of relations,
relative terms, relative and non-relative operations on relations,
strong and weak types of reducibility with respect to these operations,
genericity, degeneracy, identity, teridentity, and so on, is very clear
and immediately recognizable to readers with the minimal mathematical
background, was published in the premier mathematical journals of his
day and ours, is subject to definition, formalization, and the whole
discipline of theorem and proof, for those who accept those rigors.

JA: I analyzed the "betweenness" example in some detail for the
Standard/Ontology Lists last year and I will look up those
links for you later on. In the meantime, here is a summary,
far succincter than I have ever done before, of the pertinent
material, as the pertinent thinkers and tradition understand it:

Theory Of Relations

01. http://suo.ieee.org/ontology/msg04377.html
02. http://suo.ieee.org/ontology/msg04378.html
03. http://suo.ieee.org/ontology/msg04379.html
04. http://suo.ieee.org/ontology/msg04380.html
05. http://suo.ieee.org/ontology/msg04381.html
06. http://suo.ieee.org/ontology/msg04382.html

Betweenness is an example of a 3-adic relation, which makes it by the
definition of relational composition, irreducible to a composition of
2-adic relations. That is the "strong" notion of reducibility, to put
it in a more contemporary idiom. However, once that is understood, it
is possible to weaken the notion of reducibility, saying to the wannabe
reducer, as it were: Okay, now that you have conceded that this 3-adic
is irreducible to 2-adics in the primary sense, suppose that I give you
gratis to use in your composition some simple 3-adic relations, oh, say,
like 'and' : B x B -> B, or things of that ilk -- could you then compose
me this 3-adic out of nothing but 2-adics and those gratuitous 3-adics?

That game is about the "weak" notion of reducibility,
but it's a consolation game, and only begins when the
reducer has acknowledged futility on the first score.

Have to take a time out here ...

Jon Awbrey

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

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

Subject: Re: Identity & Teridentity
From: "Peter Brawley" <peter.brawley[…]artfulsoftware.com>
Date: Sun, 24 Nov 2002 19:57:14 -0800
X-Message-Number: 30

Jon,

John Collier's ham sandwich looks to my (undoubtedly insufficiently
untutored) eyes like "standard issue" relational analysis, (eg
http://www.hum.auc.dk/cg/Module_I/1034.html, in an online course that
acknowledges Peirce). Could you give an example of a "non-degenerate"
triadic relation?

PB

-----

> JC: It is possible for a relation to be triadic and
> for it to be reducible. I gave examples in my
> post. There is nothing especially difficult or
> tricky in what I am saying. Quite the contrary.
> Between, as I mentioned, is a triadic relation, but
> it can be composed of dyadic relations. For example,
> if we say that the ham is between the upper and lower
> slices of bread, that is equivalent to saying that it
> is below the upper and above the lower. More formally
> Between(ham, upper, lower) iff Above(upper, lower) and
> Above(ham, lower) and Above(upper, ham). Between is
> clearly a triadic relation, and the location of the
> ham in this case involves it, but the relation can
> be analyzed fully into dyadic relations.

Subject: Re: Identity & Teridentity
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Sun, 24 Nov 2002 23:50:54 -0500
X-Message-Number: 31

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

You Can't Tell the Topics from the Fallacies without a Programme:

1. Topic. What is a relation?

1.1. Fallacy. The "I lied about the set" (ILATS) puzzle.

2. Topic. What is the difference between a relation and one of its instances?

2.1. Fallacy. The "one row database" (ORD) illusion.

3. Topic. What is decomposition or reducibility?

3.1. Fallacy. The "2-ped dog" (2PD) dogma.
3.2. Fallacy. The "alchemist's dodge" (AD).
3.3. Fallacy. The "stone soup" (SS) parable.
3.4. Fallacy. The "who's on third" (WOT) joke.
AKA. "Truth-functions compute themselves".

JA: Before we start, let us dismiss JC's inane example, since his "analysis"
of it fails if the plane of the sandwich is vertical to the surface of
the nearest-by large planet, if the sandwich is flipped over, or if the
sandwich is floating in space "between" galaxies -- which incidentally
illustrates the fact that the English "between" is polymorphous, since
"among" would not substitute 'saliva verita' (sic joke), and I never
said anything about there being just two galaxies, but never mind
all that now.

The point of my light objection is just this, that JC's example,
in the form that he gave it, does not serve his purpose, since
the 2-adic relation that he uses, "Above(x, y)", requires and
external orientation or reference direction to make sense.
So I supply him with a better example on my own:

A fairer example to JC's case, if I have to supply it myself, would be
to pull the mathematician's"without loss of generality" (WOLOG) gambit,
and stipulate that we are discussing, say, real numbers a, x, b, where
we assume a < b, WOLOG, and then revert to the 3-adic situs specified
by the statement "x is between a and b".

JA: 1. What a relation is.

JA: So far we are still discussing relations in general,
and have not got as far as discussing sign relations,
which are a special case of 3-adic relations.

JA: Where terms of the characters "abstract", "concrete", "general", "individual",
and so on, are distinguished relative to a particular context of discourse,
where we conventionally neglect the differences that are irrelevant to the
purposes of that discourse, relations are denoted by abstract general terms,
and not by concrete individual terms.

Let me now explain to you the "I lied about the set" (ILATS) fallacy.
I have already discussed this fallacy early on in connection with the
loco classico from Quine's 'Math Logic'. Very often you find people
who have learned to 'say' the correct thing, namely, that a relation
is a SET of relation instances, also called "elementary relations"
or "tuples", but when it comes to drawing even the most immediate
consequences of this definition, they constantly slip up, most
likely on account of the examined assumption that what you can
say about an instance will automatically "lift up" to a closely
analogous statement about the set, in this case, the relation.
Anyone who reflects on this assumption would find ample reason
to question it. And indeed, it is a very rare property that
can be "lifted" from elements to sets in such a facile manner.
One of the principal symptoms of this unconscious fantasy is
that the afflicted one will compulsively, repetitively regress
to the level of a single primal instance, the "one row database".
They will do their perfunctory analytic dance on that pinhead,
and then wave their arms about while chanting the incantation:
"As Below, So Above" or perhaps some Greco-Latin equivalent.

For example, "Being uniquely determined by its projections" is
NOT one of those properties that lifts from elements to sets.

To express the point in computer science terms, as in Lisp or any
other moderately "functional" language, complex elements like tuples
are formalized in terms of their "constructors" and their "selectors".
In category theory these are called "injections" and "projections",
respectively.

Now a single point, here, a tuple, is determined by its projections,
but a set of points, here, a relation, is not in general determined
by its projections. For example a solid ball and a hollow sphere
with the same center and radius have indiscernible projections
on the XY, XZ, YZ planes.

So we get the follwing breakdown:

a. All 3-adic relations are irreducible to compositions of 2-adic relations.

b. If one allows the use of one 3-adic relation, namely, 'and' : B x B -> B,
this corresponds to a weaker form of reducibility, that may be called the
"projective reducibility" of relations. Even so, even with this assist,
some 3-adics are projectively reducible to 2-adics -- these are bodies
in XYZ-space that can be reconstructed uniquely from their shadows on
the XY, XZ, YZ planes, and some are not.

To be continued ...

Jon Awbrey

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

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

Subject: Re: Identity & Teridentity
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Mon, 25 Nov 2002 00:20:02 -0500
X-Message-Number: 32

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

PB: John Collier's ham sandwich looks to my (undoubtedly
insufficiently untutored) eyes like "standard issue"
relational analysis, (e.g.:

http://www.hum.auc.dk/cg/Module_I/1034.html

in an online course that acknowledges Peirce).

PB: Could you give an example of a "non-degenerate" triadic relation?

Peter,

That website crashes my browser. Maybe you could give us
a relevant excerpt? So far I am still just going on what
seemed "obvious" to me when I first, or maybe second read
this stuff some time ago, but so far the distances example
seems to confirm my first impression. If what Peirce means
by a "non-degenerate" 3-adic really does turn out to be what
I have called a "non-reconstructible" 3-adic, in other words,
a "projectively irreducible" 3-adic, then they always come in
bunches of two or more projectively indiscernible relations at
a time, and so the solid/hollow ball is one example, and there
many, many others. I will go look up the discrete example that
I gave on the Standard/Ontology List last year.

Jon

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

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Subject: server problems
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Mon, 25 Nov 2002 00:28:55 -0500
X-Message-Number: 33

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Joe, & All,

I don't know if this is a superstitious induction or not,
but I seem to notice a pattern on the messages that have
trouble getting through Lyris -- whenever the roster of
previous messsage references gets up to about 20 or so,
the distribution time seesm to bog down and then start
to fail, so maybe that is hypothesis to check out.

Jon

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Subject: Re: Identity & Teridentity
From: HGCALLAWAY[…]aol.com
Date: Mon, 25 Nov 2002 00:38:51 EST
X-Message-Number: 34

Joe,

Well, perhaps you are right, explicit permission for each piece is not
needed, I hold the copyright, the Editor would not be intersted in whether
you are willing to take the trouble to put the review up at Arisbe, etc.
Still policies do change over time, and I thought it simply a courtesy to
check with the Editor. Moreover, I haven't spoken with Peter for quite some
time and I wasn't even sure that he still was the Editor of the Transactions.
So, in any case, let's see what the policy is now.

I'll get back to you.

Howard

H.G. Callaway
(hgcallaway[…]aol.com)

<< Just let me know when you are ready to have the review made availablle at
Arisbe, Howard. I doubt if there is any need for further permission
than you already have from the Transactions editor, but I leave that to you.
Just include a description of where and when it originally appeared, or
provide the information to me and i'll type it in. As far as I know, Peter
is still editor. (You may be thinking of Randy Dipert replacing Dick Robin
as special Peirce editor.) They don't require my permission to give you
theirs. Bear in mind that it is your paper, not theirs, unlesss you
explicitly gave them copyright when you published it earlier.

Joe
>>


H.G. Callaway
(hgcallaway[…]aol.com)

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Subject: Re: CSP QUOTES RE: GENUINE/DEGENERATE
DISTINCTION
From: John Collier <ag659[…]ncf.ca>
Date: Sun, 24 Nov 2002 23:24:09 -0500
X-Message-Number: 35

At 09:50 PM 24/11/2002, Inna wrote:
> John: why is reflection non-dynamical? because it is not a function of
> time? Does it mean that all mathematical transformations are
> non-dynamical? there seems to be some fallacy here that i cannot yret
> articulate.
>Personally i think that reflection is dynamical--so i would appreciate
>your explanation. thanks. inna

I was talking about the context of chirality. Reflection is the name of a
mathematical relation that preserves the symmetry of handedness. I wasn't
talking about the process of making a mirror image, but of the transform of
a system into itself that reverses the handedness. The idea is that
handedness is not a fundamental property if it is not invariant under
transformation. One can't transform a handed object through three space by
any dynamically possible process to get the effect of a reflection.
Therefore, reflection is a non-dynamical transformation. However we can
imagine it, so we can imagine that handedness is not an intrinsic property.
The interesting thing about the quote from Peirce is that he asserts that
it is intrinsic ("brute"), so it cannot be merely a logical property that
he is talking about. I am assuming that Peirce would hold that a genuine
Third is intrinsic in something like this sense. If handedness were a
purely relational property, then we could define it relative to whatever we
wanted, and get different answers for the appropriate choice of reference.
In this case it would be a purely relative property, like "to the right
of", and "above". This sort of property can be reduced, if any relational
properties can be reduced. In a similar way, I would assume that Pierce
thinks that representation is intrinsically triadic, not just relative to
some perspective on it. There is no way to transform the triadicity away
that preserves the character of representation. So an analysis of the
Montague sort, that I gave as an example, would have to loose something
essential to representation.

I suspect that you are concerned that whether right-handed or left-handed,
a handed object is still handed one way or another with respect to each
perspective, even if reflection were possible. This really just puts the
issue out one step, with the handedness now in the full context. But then
we can transform this away, and so on. So I think for a property to be real
enough to ground genuine triadicity it will have to be intrinsic. It is
worth reading carefully what Peirce says in the passage I was commenting on
abut the origins of chirality. There is a lot about causes, and not a word
about logic.

John






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END OF DIGEST 11-24-02