PEIRCE-L Digest for Friday, November 22, 2002.
NOTE: This record of what has been posted to PEIRCE-L
has been nodified by omission of redundant quotations in
the messages. both for legibility and to save space.
-- Joseph Ransdell, PEIRCE-L manager/owner]
1. Re: Apology
2. Re: logic's logic
3. Re: Jamesian Impasse
4. Re: History of American Thought - Featured Area
5. Re: Identity & Teridentity
6. Re: Jamesian Impasse
7. Re: logic's logic
8. Re: History of American Thought - Featured Area
9. Re: History of American Thought - Featured Area
10. Re: logic's logic
11. Re: Identity & Teridentity
12. re: logic's logic
13. Re: Identity & Teridentity
14. Re: logic's logic
15. Re: Identity & Teridentity
16. Re: logic's logic
17. Re: History of American Thought - Featured Area
18. Re: Identity & Teridentity
19. Re: Identity & Teridentity
20. Re: logic's logic
21. Re: Identity & Teridentity
22. Re: Identity & Teridentity
23. Re: New List & Classification of Signs
24. Re: Classification Of Signs
25. Re: Jamesian Impasse
26. Re: logic's logic
27. Re: logic's logic
28. Re: logic's logic
29. Re: Identity & Teridentity
30. Re: Identity & Teridentity
31. Re: Identity & Teridentity
32. Re: Identity & Teridentity
33. Classification Of Signs
34. Theory Of Relations
35. Re: Theory Of Relations
----------------------------------------------------------------------
Subject: Re: Apology
From:
----------------------------------------------------------------------
Subject: Re: logic's logic
From:
----------------------------------------------------------------------
Subject: Re: Jamesian Impasse
From: "Axel Schlotzhauer"
<
----------------------------------------------------------------------
Subject: Re: History of American Thought - Featured Area
From: "Joseph Ransdell" <
----------------------------------------------------------------------
Subject: Re: Identity & Teridentity
From: Jon Awbrey <
----------------------------------------------------------------------
Subject: Re: Jamesian Impasse
From: "Joseph Ransdell" <
[SEE MESSAGE ABOVE; NO NEED TO DUPLICATE AGAIN]
----------------------------------------------------------------------
Subject: Re: logic's logic
From: Bernard Morand <
----------------------------------------------------------------------
Subject: Re: History of American Thought - Featured Area
From: "Joseph Ransdell" <
----------------------------------------------------------------------
Subject: Re: logic's logic
From:
----------------------------------------------------------------------
Subject: Re: Identity & Teridentity
From: Jon Awbrey <
----------------------------------------------------------------------
Subject: re: logic's logic
From: Bernard Morand <
----------------------------------------------------------------------
Subject: Re: Identity & Teridentity
From:
----------------------------------------------------------------------
Subject: Re: logic's logic
From: Bernard Morand <
----------------------------------------------------------------------
Subject: Re: History of American Thought - Featured Area
From: Charles F Rudder <
[SEE EARLIER MESSAGE ABOVE]
----------------------------------------------------------------------
Subject: Re: logic's logic
From: Gary Richmond <garyrichmond[…]rcn.com>
Date: Fri, 22 Nov 2002 15:10:14 -0500
X-Message-Number: 26
Jon,
I knew you and Jack Park have been working on this for some time. Glad
to see it up and lookin' good. Now I can trash
most all my "Awbrey" files as they've become redundant One problem: I
wasn't able to open this:
>A work in progress on "Propostional Equation Reasoning Systems":
>
>http://www.nexist.org/wiki/Doc15368Document
>
Since it sounds most intriguing, I hope to be able to open it soon.
Congratulations to both you and Jack on getting so much of your work
together on this nexist/wiki site
Gary
Jon Awbrey wrote:
>o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
>
>Bernard,
>
>The Nexist site is back up again, though I can't say
>for how long, so here are some more detailed links:
>
>The main catalog of documents for the whole site is here:
>
>http://www.nexist.org/wiki/DocumentIndex
>
>A "Lite" Intro to the "Cactus Language" for Prop Calc:
>
>http://www.nexist.org/wiki/Doc3927Page
>
>A work in progress on "Propostional Equation Reasoning Systems":
>
>http://www.nexist.org/wiki/Doc15368Document
>
>Here is the hub for all of the Theme One program documentation:
>
>http://www.nexist.org/wiki/Doc5099Document
>
>NB. Some of the longer pages may take a few minutes to load.
>
>E-joy!
>
>Jon
>
>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: logic's logic
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Fri, 22 Nov 2002 15:38:54 -0500
X-Message-Number: 27
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
re:
http://www.nexist.org/wiki/Doc15368Document
hi gary, thanks for the click! that one is kinda large,
and on my old 56kb modem, i usually have to wait a couple
of minutes to load it, but when i think about it, i'm not
really sure that the bottleneck is r.o.c., but it might
be because these documents are assembled from separate
"addressable information resources" (air's) as jack
calls them -- but i don't really know.
cheers,
jon
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
GR: I knew you and Jack Park have been working on this for some time.
Glad to see it up and lookin' good. Now I can trash most all
my "Awbrey" files as they've become redundant. One problem:
I wasn't able to open this:
JA: A work in progress on "Propostional Equation Reasoning Systems":
JA: http://www.nexist.org/wiki/Doc15368Document
GR: Since it sounds most intriguing, I hope to be able to open it soon.
GR: Congratulations to both you and Jack on getting so
much of your work together on this nexist/wiki site.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
----------------------------------------------------------------------
Subject: Re: logic's logic
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Fri, 22 Nov 2002 16:54:50 -0500
X-Message-Number: 28
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
----------------------------------------------------------------------
Subject: Re: Identity & Teridentity
From: John Collier <ag659[…]ncf.ca>
Date: Fri, 22 Nov 2002 17:29:26 -0500
X-Message-Number: 29
I see: you pull relations up into mathematics in terms of some
representation thereof (ordered n-tuplets) and then map them onto
another representation. I still maintain that you are confusing properties
of the representation with the thing in your previous arguments.
The discussion of graphs does not help. Well, actually it does,
since any three terminal graph can be reduced to a convergence
of three two terminal graphs in which one terminus of each of the
three is shared (identical). Since identity is dyadic (or at least has
not yet been proven to be not dyadic, we haven't got anyplace.
As I said, we are being bombarded with red herrings. It is beginning
to stink.
John
At 11:30 AM 22/11/2002, you wrote:
>o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
>
>I&T. Note 16
>
>o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
>
>JC = John Collier
>
>JC: I think from the line of argument below, which is none
> to clear in itself, that we can see an appeal to the way
> things are represented (graphs) to their actual properties.
> This appears to me to be a pretty fundamental category error.
>
>It is not a category error. It is a morphism between categories,
>h : Relations -> Graphs, mapping relation arities to vertex degrees,
>preserving the pertinent properties under compositions on each side.
>This is helpful to some people, but it's not a proof. In any case,
>a proof is not required, since the fact at issue is a definition.
>
>JC: Relations and graphs are not the same.
> Graphs are representations.
> Relations are not.
>
>Graphs are a category of mathematical objects,
>not to be confused with their representations,
>whether you mean "representations" in the
>mathematical or the sign-theoretic sense.
>
>Representations in mathematics are just morphisms,
>typically from a space to a group of automorphisms,
>but that is only indirectly related to this issue.
>
>Jon Awbrey
>
>o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
>
>---
>Message from peirce-l forum to subscriber ag659[…]ncf.ca
>To unsubscribe send a blank email to: leave-peirce-l-7176J[…]lyris.ttu.edu
----------------------------------------------------------------------
Subject: Re: Identity & Teridentity
From: John Collier <ag659[…]ncf.ca>
Date: Fri, 22 Nov 2002 18:30:41 -0500
X-Message-Number: 30
At 12:54 PM 22/11/2002, you wrote:
>John Collier says:
>
> > I think from the line of argument below, which is none to clear
> > in itself, that we can see an appeal to the way things are represented
> > (graphs) to their actual properties.
>
>This appears to be something missing in the grammar of that sentence, John,
>and when I try to supply it I can't figure out what it is supposed to be. I
>don't suppose you mean to say that one cannot appeal to a true
>representation -- or what one takes to be such -- in referring to
>something's properties. You don't mean, surely, that one can only appeal to
>the Ding an sich. Could you clarify that, or correct my misunderstanding
>of the sentence?
What I meant was that Jon seems to be appealing to properties of
the representation to try to make his case about what is represented.
We have to abstract away from the from these, ignore them, or whatever.
basically, we have to forget that we are representing, or we get
our knickers in a knot.
> > This appears to me to be a
> > pretty fundamental category error. No it is true that we need a third
> > thing to represent a dyadic relation, but this is not to say that
> > the relation itself is triadic (let us hope not, or else the notion of a
> > dyadic relation is gibberish).
>
>It IS to say that we need a third thing, though -- in fact you just now said
>it -- and I thought that was the point to Jon's remark. The question isn't
>whether dyadic relations are really triads, but whether dyadic relations can
>be represented without recourse to a triadic relation in doing so, namely,
>the one which is the representation itself. It would appear that in
>supposing that the two elements composing the dyad constitute a dyad there
>IS an appeal to a third thing, namely the representation of the dyad as
>such, which is in addition to the representation of each of the elements of
>the dayd apart from their dyadicity. That adds up to three needful things to
>refer to, doesn't it? Which of them would you get rid of -- A or B or the
>dyad AB -- in expressing the proposition that one need only appeal to two
>things in representing a dyad as such?
It seems to me that we can have a dyadic relation that has its properties
independently of any way it is represented, and that all Jon has shown
is that a representation of a dyad is more complex than a dyad. I
don't think that is the sort of issue that Quine had in mind.
> > However, the argument below,
> > such as it is, does nothing to rule out the possibility that this
> > third element might also be dyadic in nature, . . .
>
>That is not to the point, so far as I can see.
>
> > and that the talk of
> > thirds cannot be embedded in a more complex construction
> > of dyadic relations.
>
>Well, I guess if you can re-express what you are saying without appealing to
>a third thing I would find your argument more persuasive.
The example I gave of the three pointed graphs constructed from
two pointed ones. In any case, Quine's reduction was on the table,
and it is mathematically of the same form as the version that I gave.
> > Relations and graphs are not the same. Graphs are representations.
> > Relations are not.
>
>I find it odd that you would say this when the claim is that some are and
>some are not. You can't just say that relations are not representations --
>unless, of course, this is just an a priori metaphysical dictum to the
>effect that there are only dyads and monads, in which case I should think
>you would actually want to hold that there are no such things as dyads
>either, just monads: so that A is one thing and B another, but the dyad AB
>is nothing at all but . . . but what? An illusion due to a notation that
>actually corresponds to nothing? Logical atomism, in short.
There is no need to go to atomism. All reality could be irreducibly
relational as far as I am concerned. The issue is whether the relations
can be analyzed into dyadic relations such that they can be seen
to be constructions of dyadic relations. It may require triadic relations
to do this, but that does not resolve the issue in itself (see below).
Actually, the problem is a slip that Jon makes between properties
of the thing represented and properties of the representation. There
are a number of ways to phrase my objection, but since the original
position is absurd, none of them will sound much better.
I come back to the basic problem that is Jon's line of argument
is correct, then dyadic relations are not dyadic, but triadic,
and that is absurd.
> > In the meantime, I share Seth's and Howard's frustration with this
> > discussion, which seems to me to be largely directed after red
> > herrings.
>
>Maybe, maybe not. Impatience in matters as subtle as these is sometimes a
>symptom of something other than correct judgment, particularly when appeal
>to a consensus opinion is being made.
There is no argument so far from Jon that talks about the properties
of relations and rather than the properties of representations
of relations to make its point. I don't think that the issues as they
have been discussed so far are subtle at all. The discussion has
been clumsy and heavy handed, and I responded in kind.
It may well be that one cannot represent relations without relying
on triadic relations. This is not the same issue as whether or not
all relations can be constructed from dyadic relations. Even if
a triadic relation can be constructed from dyadic relations,
it does not mean that it ceases to be triadic. So showing
that the representation of something requires triadic relations
does not show that the thing cannot be constructed from dyadic
relations. Neither does it show that the representation itself
cannot be constructed from dyadic relations. Basically,
the need for triadic relations does not show that triadic
relations cannot be constructed from dyadic relations.
Betweenness does not cease to be triadic because it can
be constructed from dyadic relations. Showing that there
is a triadic relation, betweenness, does not show that
betweenness cannot be constructed from dyadic relations.
Likewise, showing that dyadic relations cannot be represented
without using, at least implicitly, triadic relations does not
show that all relations cannot be constructed from dyadic
relations. It is beside the point. If it leads to the conclusion
that all dyadic relations are essentially triadic, then it is not
only beside the point (a red herring), but it is also hopelessly
confused, and it is best consigned to the bit bucket.
If Jon were arguing that there are no dyadic relations,
and Quine's mistake was to suppose that there are,
I might find his line of argument a bit more reasonable.
It would be a heroic thing to argue, but at least it would
be coherent.
I hope this is reasonably clear, because I feel I am wasting
my time stating the obvious.
I do think there are interesting and subtle issues about whether
or not there are irreducible triadic relations. I would like
to see discussion of these.
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.
Jon's arguments have addressed the first issue. Perhaps
he can show why the first issue is related to the second,
but so far he has not, at least not clearly enough for me
to see that he has. I am getting a bit tired of repetition
of the same point that I find non-controversial as if it
addressed the point that I find controversial. That is
why I am impatient. I grant that representation is triadic
(at least). Let's get on with the second issue.
Incidentally, I appreciate the way you play your role
as moderator, Joe.
John
----------------------------------------------------------------------
Subject: Re: Identity & Teridentity
From: "Joseph Ransdell" <joseph.ransdell[…]yahoo.com>
Date: Fri, 22 Nov 2002 18:36:58 -0600
X-Message-Number: 31
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: Fri, 22 Nov 2002 20:35:33 -0500
X-Message-Number: 32
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John Collier wrote:
> Showing that there is a triadic relation, betweenness, does not show that
> betweenness cannot be constructed from dyadic relations.
> Likewise, showing that dyadic relations cannot be represented
> without using, at least implicitly, triadic relations does not
> show that all relations cannot be constructed from dyadic
> relations.
For people steeped in peircean logic, trying to improve on Peirce's
several argumentations--that triadic relations cannot be
constructed from dyadic ones--seems a fool's task. The irreducibility of
thirdness to secondness in "constructing
a world" has been so eloquently and, to my mind, convincingly argued by
Peirce, that it seems futile to attempt to argue it better.
I would imagine that if you are not going to be convinced by Peirce's
arguments in the matter, there
is little--if any chance--that you'd be convinced by, say, Jon's or mine.
Still, the matter is subtle, as Joe noted, and I would maintain that
you've contributed
something very important towards the explication of the subtle
problematic in this comment:
You wrote:
> JC: 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.
I would tend to agree with you that Jon's recent comments may have
placed an emphasis on the representation of dyadic
relations. But he has also argued here (and elsewhere) for the
irreducibility of triadic relations themselves, something which
Peirce--and I would imagine, most Peirceans--insist on. (Of course that
doesn't make it true; still, for me, the burden
of proof remains yours while a) a consensus seems to exists in relation
to b) Peirce's numerous solid arguments in the matter.)
I cannot say that I've found arguments to the contrary convincing. And I
must admit that for me it appears downright odd to see them
being offered here (not that they shouldn't be!)
Now, John, I'm no logician. However, I would appreciate having a strong
one, such as yourself, show me the unsoundness
of these arguments regarding the irreducibility of triadic
relations.What error, for example, do you find in the logic underlying
the following
snippet? Here Peirce succinctly touches upon both the issues you've
identified When he comes to speak of "handedness" here,
he not only does not hold that authentic dyadic relations do not exist,
but notes a most fundamental one in nature, chirality.
All he does insist on is that if you "[t]ake any fact in physics of the
triadic kind, by which I mean a fact which can only be defined by
simultaneous reference to three things, and you will find there is ample
evidence that it never was produced by the action of forces
on mere dyadic conditions."
> CP 1.345. I will sketch a proof that the idea of meaning is
> irreducible to those of quality and reaction. It depends on two main
> premisses. The first is that every genuine triadic relation involves
> meaning, as meaning is obviously a triadic relation. The second is
> that a triadic relation is inexpressible by means of dyadic relations
> alone. Considerable reflexion may be required to convince yourself of
> the first of these premisses, that every triadic relation involves
> meaning. There will be two lines of inquiry. First, all physical
> forces appear to subsist between pairs of particles. This was assumed
> by Helmholtz in his original paper, On the Conservation of Forces.+1
> Take any fact in physics of the triadic kind, by which I mean a fact
> which can only be defined by simultaneous reference to three things,
> and you will find there is ample evidence that it never was produced
> by the action of forces on mere dyadic conditions. Thus, your right
> hand is that hand which is toward the east, when you face the north
> with your head toward the zenith. Three things, east, west, and up,
> are required to define the difference between right and left.
> Consequently chemists find that those substances which rotate the
> plane of polarization to the right or left can only be produced from
> such [similar] active substances. They are all of such complex
> constitution that they cannot have existed when the earth was very
> hot, and how the first one was produced is a puzzle. It cannot have
> been by the action of brute forces. For the second branch of the
> inquiry, you must train yourself to the analysis of relations,
> beginning with such as are very markedly triadic,
Of course this is just the beginning of an argumentation. But perhaps
you would like to critique some other Peircean text
relating to the "other" issue?
Regards,
Gary
> At 12:54 PM 22/11/2002, you wrote:
>
>> John Collier says:
>>
>> > I think from the line of argument below, which is none to clear
>> > in itself, that we can see an appeal to the way things are represented
>> > (graphs) to their actual properties.
>>
>> This appears to be something missing in the grammar of that sentence,
>> John,
>> and when I try to supply it I can't figure out what it is supposed to
>> be. I
>> don't suppose you mean to say that one cannot appeal to a true
>> representation -- or what one takes to be such -- in referring to
>> something's properties. You don't mean, surely, that one can only
>> appeal to
>> the Ding an sich. Could you clarify that, or correct my
>> misunderstanding
>> of the sentence?
>
>
> What I meant was that Jon seems to be appealing to properties of
> the representation to try to make his case about what is represented.
> We have to abstract away from the from these, ignore them, or whatever.
> basically, we have to forget that we are representing, or we get
> our knickers in a knot.
>
>> > This appears to me to be a
>> > pretty fundamental category error. No it is true that we need a third
>> > thing to represent a dyadic relation, but this is not to say that
>> > the relation itself is triadic (let us hope not, or else the notion
>> of a
>> > dyadic relation is gibberish).
>>
>> It IS to say that we need a third thing, though -- in fact you just
>> now said
>> it -- and I thought that was the point to Jon's remark. The question
>> isn't
>> whether dyadic relations are really triads, but whether dyadic
>> relations can
>> be represented without recourse to a triadic relation in doing so,
>> namely,
>> the one which is the representation itself. It would appear that in
>> supposing that the two elements composing the dyad constitute a dyad
>> there
>> IS an appeal to a third thing, namely the representation of the dyad as
>> such, which is in addition to the representation of each of the
>> elements of
>> the dayd apart from their dyadicity. That adds up to three needful
>> things to
>> refer to, doesn't it? Which of them would you get rid of -- A or B
>> or the
>> dyad AB -- in expressing the proposition that one need only appeal to
>> two
>> things in representing a dyad as such?
>
>
> It seems to me that we can have a dyadic relation that has its properties
> independently of any way it is represented, and that all Jon has shown
> is that a representation of a dyad is more complex than a dyad. I
> don't think that is the sort of issue that Quine had in mind.
>
>> > However, the argument below,
>> > such as it is, does nothing to rule out the possibility that this
>> > third element might also be dyadic in nature, . . .
>>
>> That is not to the point, so far as I can see.
>>
>> > and that the talk of
>> > thirds cannot be embedded in a more complex construction
>> > of dyadic relations.
>>
>> Well, I guess if you can re-express what you are saying without
>> appealing to
>> a third thing I would find your argument more persuasive.
>
>
> The example I gave of the three pointed graphs constructed from
> two pointed ones. In any case, Quine's reduction was on the table,
> and it is mathematically of the same form as the version that I gave.
>
>> > Relations and graphs are not the same. Graphs are representations.
>> > Relations are not.
>>
>> I find it odd that you would say this when the claim is that some are
>> and
>> some are not. You can't just say that relations are not
>> representations --
>> unless, of course, this is just an a priori metaphysical dictum to the
>> effect that there are only dyads and monads, in which case I should
>> think
>> you would actually want to hold that there are no such things as dyads
>> either, just monads: so that A is one thing and B another, but the
>> dyad AB
>> is nothing at all but . . . but what? An illusion due to a notation
>> that
>> actually corresponds to nothing? Logical atomism, in short.
>
>
> There is no need to go to atomism. All reality could be irreducibly
> relational as far as I am concerned. The issue is whether the relations
> can be analyzed into dyadic relations such that they can be seen
> to be constructions of dyadic relations. It may require triadic relations
> to do this, but that does not resolve the issue in itself (see below).
>
> Actually, the problem is a slip that Jon makes between properties
> of the thing represented and properties of the representation. There
> are a number of ways to phrase my objection, but since the original
> position is absurd, none of them will sound much better.
>
> I come back to the basic problem that is Jon's line of argument
> is correct, then dyadic relations are not dyadic, but triadic,
> and that is absurd.
>
>> > In the meantime, I share Seth's and Howard's frustration with this
>> > discussion, which seems to me to be largely directed after red
>> > herrings.
>>
>> Maybe, maybe not. Impatience in matters as subtle as these is
>> sometimes a
>> symptom of something other than correct judgment, particularly when
>> appeal
>> to a consensus opinion is being made.
>
>
> There is no argument so far from Jon that talks about the properties
> of relations and rather than the properties of representations
> of relations to make its point. I don't think that the issues as they
> have been discussed so far are subtle at all. The discussion has
> been clumsy and heavy handed, and I responded in kind.
>
> It may well be that one cannot represent relations without relying
> on triadic relations. This is not the same issue as whether or not
> all relations can be constructed from dyadic relations. Even if
> a triadic relation can be constructed from dyadic relations,
> it does not mean that it ceases to be triadic. So showing
> that the representation of something requires triadic relations
> does not show that the thing cannot be constructed from dyadic
> relations. Neither does it show that the representation itself
> cannot be constructed from dyadic relations. Basically,
> the need for triadic relations does not show that triadic
> relations cannot be constructed from dyadic relations.
>
> Betweenness does not cease to be triadic because it can
> be constructed from dyadic relations. Showing that there
> is a triadic relation, betweenness, does not show that
> betweenness cannot be constructed from dyadic relations.
> Likewise, showing that dyadic relations cannot be represented
> without using, at least implicitly, triadic relations does not
> show that all relations cannot be constructed from dyadic
> relations. It is beside the point. If it leads to the conclusion
> that all dyadic relations are essentially triadic, then it is not
> only beside the point (a red herring), but it is also hopelessly
> confused, and it is best consigned to the bit bucket.
>
> If Jon were arguing that there are no dyadic relations,
> and Quine's mistake was to suppose that there are,
> I might find his line of argument a bit more reasonable.
> It would be a heroic thing to argue, but at least it would
> be coherent.
>
> I hope this is reasonably clear, because I feel I am wasting
> my time stating the obvious.
>
> I do think there are interesting and subtle issues about whether
> or not there are irreducible triadic relations. I would like
> to see discussion of these.
>
> 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.
>
> Jon's arguments have addressed the first issue. Perhaps
> he can show why the first issue is related to the second,
> but so far he has not, at least not clearly enough for me
> to see that he has. I am getting a bit tired of repetition
> of the same point that I find non-controversial as if it
> addressed the point that I find controversial. That is
> why I am impatient. I grant that representation is triadic
> (at least). Let's get on with the second issue.
>
> Incidentally, I appreciate the way you play your role
> as moderator, Joe.
>
> John
>
>
> ---
----------------------------------------------------------------------
Subject: Classification Of Signs
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Fri, 22 Nov 2002 21:16:44 -0500
X-Message-Number: 33
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COS. Note 1
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ML = Martin Lefebvre
ML: I have an exegetical question regarding the "New List" and
in particular M.G. Murphey's reading of it. In chapter 15 of
his book on Peirce ('The Development of Peirce's Philosophy'),
Murphey makes a big deal out of Peirce moving from predicate
logic to the logic of relatives to discuss the categories.
He goes so far as to claim that from 1885 Peirce operated
"substantial changes in the definitions of [the] categories",
and that "these changes are sufficiently great so that Peirce
ought to have adopted new names for them to prevent confusion
with his earlier papers". Murphey's analysis of the situation
rests in good measure on the index. His claim is that in the
New List, the index does not refer directly to an individual,
but rather to a concept. "The use of the term 'index' to mean a
sign which refers not to a concept but to an individual directly
does not appear until 1885 [...]". Now it is possible that I
have been misreading the New List for some time (projecting on
it, as it were, later notions), yet I find Murphey's take hard
to reconciliate with the idea, which we find in the New List,
according to which indices are not general signs. Peirce
defines indices as representations "whose relation to their
object consists in a correspondence in fact". Moreover,
the absence of generality in likenesses and indices is why
the rules of logic "have no immediate application" to them
(according to the 1867 view). Now isn't it the case that the
exclusion of indices from the rules of logic stems directly
from the fact that they do not refer to concepts (unlike what
Murphey is saying)? Doesn't correspondence in fact already
imply haecceity? Am I missing something here? What the final
section of the New List makes clear, I believe, is that Peirce
is unwilling in 1867 to fully consider the icon and the index
semeiotically, since he is confining his view to propositions
and arguments. And in that sense the logic of relatives,
by offering a view of the categories not subordinated to
propositional logic, may be what makes possible the
famous 1903 classification.
ML: I'll appreciate any help with this.
Some questions have been asked about Peirce's conception of signs,
especially indices, in the light of Murphey's reading of the role
of indices in Peirce's quantification theory. This brings up the
question of so-called "individual terms", whether they are purely
conventional and discourse-relative as such, or whether there may
be some sense in which they genuinely "denote" individual objects,
properly speaking, in a suitable domain of quantification that is
made of up of individuals, properly speaking. Assorted questions
about identity and teridentity also raised their Cerberean heads.
Having studied, developed, and applied the work of C.S. Peirce
for some 35 years now, mostly within the sorts of mathematical
contexts within which he himself first began to develop and to
publish them, although with ample respect to the traditions of
philosophy that preceded him, I think that I have some idea of
what C.S. Peirce meant by the various terms and ideas at issue,
and I think that I can speak to these issues with some hope of
clarifying them to anyone who would like to see them clarified.
The problems that certain representatives of certain schools of philosophy
have with grasping Peirce's very clear concepts, much less the basic facts
of the scientific context in which they found their origin and their first
significant bearings, the troubles that they have working up a desire just
to give a careful reading to what is evidently worth learning about within
C.S. Peirce's work -- that is where I see the red herrings in this sea.
Jon Awbrey
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
----------------------------------------------------------------------
Subject: Theory Of Relations
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Fri, 22 Nov 2002 22:24:18 -0500
X-Message-Number: 34
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
TOR. Note 1
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
Let's see if we can build up a working theory of relations,
starting out as simply as we possibly can, forgetting most
of the finer subtleties of Peirce's distinctions, and yet
trying to build a system that will be roughly compatible
with the sorts of concepts that Peirce appeared to have
in mind, as it appears, that is, from reading what he
wrote, and from what we may know about the generic
mathematical background of his day.
If it were me, I would begin with a toy universe
like X = {i, j, k}, where the signs "i", "j", "k"
are taken to denote the distinct objects i, j, k,
repectively. It's not much, but it's enough for
a start.
Here are some relations that immediatedly,
if not exactly unmediatedly, come to mind:
The "2-identity relation" I_2 on X is the following set of ordered pairs:
I_2 = {(i, i), (j, j), (k, k)}
I will probably call it "I", not to be confused with me,
and bowing to convention call it the "identity relation".
For ease of expression, I will write relations in one
of the styles that Peirce was accustomed to write them,
in which the identity relation would be written like so:
I = i:i + j:j + k:k
He often called sets by the name of "aggregates" or "logical sums",
and so the plus sign here only signifies the aggregation of these
ordered pairs into a logical sum, or a "set" to us.
In this vein, the 3-identity relation over X would take the form:
I_3 = i:i:i + j:j:j + k:k:k
In general, a term of the form "x:y:z" denotes the
ordered triple that by any other name is (x, y, z).
To be continued ...
Jon Awbrey
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
----------------------------------------------------------------------
Subject: Re: Theory Of Relations
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Fri, 22 Nov 2002 22:56:29 -0500
X-Message-Number: 35
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
TOR. Note 2
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In view of the fact that X = {i, j, k} is a finite universe,
indeed, such a tiny universe, we can easily figure out how
many relations over X there are for any finite arity n
that you might care to name.
n = 1. A 1-adic relation is a subset of X^1 = X.
There are exactly 2^3 = 8 subsets of X.
So there are 8 1-adic relations over X.
n = 2. A 2-adic relation is a subset of X^2 = X x X.
There are 3 x 3 = 3^2 = 9 ordered 2-tuples in X^2.
So there are just 2^9 = 512 2-adic relations over X
n = 3. A 3-adic relation is a subset of X^3 = X x X x X.
There are 3 x 3 x 3 = 3^3 = 27 ordered 3-tuples in X^3.
So there are just 2^27 = 134217728 3-adic relations over X.
Like the man said:
| Of triadic Being the multitude of forms is so terrific that
| I have usually shrunk from the task of enumerating them ...
To be continued ...
Jon Awbrey
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END OF DIGEST 11-22-02
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