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

Subject: Re: Peircean Semiotic & Intelligence Augmentation
From: Bernard Morand <morand[…]iutc3.unicaen.fr>
Date: Mon, 02 Dec 2002 11:13:30 +0100
X-Message-Number: 1

At 11:28 01/12/02 -0500, Jon Awbrey wrote:

>JA: Its main thrust has been to present several models of "effective
>description",
> somewhat surprisingly discovering that all of those yet proposed have
> turned
> out to be equivalent in the class of computable functions that they
> capture.
>
>JA: Mathematical models do not say what they are about.
> People may see some image or likeness of reality in them,
> but all sensible people and especially all sensible math
> folk already recognize that reality is inexhaustible.
>
>JA: So computational models are meant to capture what mindful people do
> only in so far as mindful people do what is effectively describable.
> The model itself does not say, cannot say, how big a proportion of
> the whole human reality the effectively describable portion may be.
>
>JA: The notion of effective description is almost the same idea as that
> of the pragmatic maxim, and I do not think that it would be good to
> draw any hard and fast lines that might lend themselves to obscuring
> this connection.
>
>JA: The reason that any of this business has much importance to us is this:
> the relationship between the effectively describable and the teachable.
>
>JA: So the heart of the question is rather ancient: Whether virtue can be
>taught.

Jon, Joe, Peter and list,
I don't see the notion of effective description as the same idea as that of
the pragmatic maxim. I would tend to place the difference as something like
the difference between the efficient causes and the final cause. The first
one seems to me to refer to the possibility of a positive test here and
now. The second, as testable in the future (the famous "would be"), seems
to me something like a "negative possibility" : if nothing (no fact)
happens to contradict the conception (that is to say its foreseeable
effects), then it has to be taken for granted for the time being.
I think that this has consequences about how we see the matter of
intelligent / thinking machines. On the first side we have the intelligence
augmentation which I see as just another word for information augmentation
in semiosis, by means of men and machines. The growth of symbols is the
criteria for judging such an augmentation (and probably in order to account
for effective descriptions ...)

But on the second side, the problematic has to be reversed and I think that
it is the really logical scientific space for computer science. It should
have been the very program of the so called Artificial Intelligence (so
called because there is nothing "artificial" here). It seems to me that the
first article of this program was accurately stated by Peirce even if some
other ones are probably needed:

"Precisely how much of the business of thinking a machine could possibly be
made to perform, and what part of it must be left for the living mind is a
question not without of practical importance; the study of it can at any
rate not fail to throw needed light on the nature of the reasoning process"
(Logical Machines, W6, p. 65).

Making clearer the point of departure between machine thinking and living
thought would in turn further determine what I called the first side. As to
the second, computers and software play the role of study instruments for
logical thinking analysis. This amount to your concluding note : whether
virtue can be taught.

Hoping all of this is not trivial for the course of this discussion

Bernard



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

Subject: Re: Identity & Teridentity
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Mon, 02 Dec 2002 05:22:39 -0500
X-Message-Number: 2

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

I&T. Note 38

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

| I have also pointed out that in consequence of imperceptible variations no two
| individuals things could be perfectly alike, and that they must always differ
| more than numerically. This puts an end to the blank tablets of the soul,
| a soul without thought, a substance without action, empty space, atoms,
| and even to portions of matter which are not actually divided, and also
| to absolute rest, completely uniform parts of time or place or matter,
| perfect spheres of the second element which take their origin from
| perfect cubes, and hundreds of other fictions which have arisen
| from the incompleteness of philosophers' notions. They are
| something which the nature of things does not allow of.
| They escape challenge because of our ignorance and our
| neglect of the insensible; but nothing could make them
| acceptable, short of their being confined to abstractions
| of the mind, with a formal declaration that the mind is not
| denying what it sets aside as irrelevant to some present concern.
| On the other hand if we meant literally that things of which we are
| unaware exist neither in the soul nor in the body, then we would fail
| in philosophy as in politics, because we would be neglecting 'to mikron',
| imperceptible changes. Whereas abstraction is not an error as long as one
| knows that what one is pretending not to notice, is 'there'. This is what
| mathematicians are doing when they ask us to consider perfect lines and
| uniform motions and other regular effects, although matter (i.e. the
| jumble of effects of the surrounding infinity) always provides some
| exception. This is done so as to separate one circumstance from
| another and, as far as we can, to trace effects back to their
| causes and to foresee some of their results; the more care
| we take not to overlook any circumstance that we can control,
| the more closely practice corresponds to theory. But only the
| supreme Reason, who overlooks nothing, can distinctly grasp the
| entire infinite and see all the causes and all the results. All
| we can do with infinities is to know them confusedly and at least
| to know distinctly that they are there. Otherwise we shall not
| only judge quite wrongly as to the beauty and grandeur of the
| universe, but will be unable to have a sound natural science
| which explains the nature of things in general, still less
| a sound pneumatology, comprising knowledge of God, souls,
| and simple substances in general.
|
| Leibniz, 'New Essays', p. 57.
|
| G.W. Leibniz, 'New Essays on Human Understanding'
| Peter Remnant & Jonathan Bennet (trans. & ed.),
| Cambridge University Press, Cambridge, UK, 1996.

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

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

Subject: Re: Peircean Semiotic & Intelligence Augmentation
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Mon, 02 Dec 2002 06:22:35 -0500
X-Message-Number: 3

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

BM = Bernard Morand

BM: I don't see the notion of effective description as the same idea as that of
the pragmatic maxim. I would tend to place the difference as something like
the difference between the efficient causes and the final cause. The first
one seems to me to refer to the possibility of a positive test here and now.
The second, as testable in the future (the famous "would be"), seems to me
something like a "negative possibility": if nothing (no fact) happens to
contradict the conception (that is to say its foreseeable effects), then
it has to be taken for granted for the time being. I think that this has
consequences about how we see the matter of intelligent/thinking machines.
On the first side we have the intelligence augmentation which I see as
just another word for information augmentation in semiosis, by means
of men and machines. The growth of symbols is the criteria for
judging such an augmentation (and probably in order to account
for effective descriptions ...)

I guess I begin by seeing the spirit of the notion as being the same,
being an effort to clarify concepts. Pick any old problematic word --
intelligence, mind, thinking, whatever -- the chances are that it will
always be far too informally used in practice to clarify very much, so
we drop the impossible part of the problem and look to the possible:
Is there any portion of its meaning that is worth trying to clarify?
To me, that is all that Turing was doing, trying to tender a first
operational depiction of what we mean by intelligent functioning.
He is not trying to define the entirety of a human being -- the
whole purpose of the "telegraphic" or "teletypical" abstraction
that is made at the outset of the test is to take the 'ad hominem'
factors out of the game, that is, to ignore all of the features of
a real human being that would not be relevant to a judgment of mind.
Since we are not beginning with a general definition of intelligence,
but are trying to work toward one, and since we are not generalizing
from a large number of species, for instance, ignoring the diversity
of distinctive styles of intelligence among the Malacandrian 'hnau',
then we have no clue as to the "would be" variety of intelligence,
but we are trying to generalize from a single case, our species,
with regard to which we are making the rather rash assumption
to regard it as proto-typical. Hence, the need for caution.

BM: But on the second side, the problematic has to be reversed
and I think that it is the really logical scientific space
for computer science. It should have been the very program
of the so called Artificial Intelligence (so called because
there is nothing "artificial" here). It seems to me that the
first article of this program was accurately stated by Peirce
even if some other ones are probably needed:

BM, quoting CSP:

| Precisely how much of the business of thinking a machine could possibly
| be made to perform, and what part of it must be left for the living mind
| is a question not without conceivable practical importance; the study of
| it can at any rate not fail to throw needed light on the nature of the
| reasoning process. (Peirce, "Logical Machines", 'Writings' 6, p. 65).

Yes, exactly.

BM: Making clearer the point of departure between machine thinking and living thought
would in turn further determine what I called the first side. As to the second,
computers and software play the role of study instruments for logical thinking
analysis. This amount to your concluding note: whether virtue can be taught.

I've always found that half the problem with
the "mind =?= machine" question is with the
definition of "machine" that we mean to use.
Ashby suggested something like "law-governed
process", which would conceivably make the
whole universe a machine, only we don't
yet know all of the laws.

Jon Awbrey

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

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

Subject: Re: Peircean Semiotic & Intelligence Augmentation
From: Peter Skagestad <Peter_Skagestad[…]uml.edu>
Date: Mon, 02 Dec 2002 10:31:08 -0500
X-Message-Number: 4

Jon,

I think it is quite clear that our interests are simply divergent. Various individuals who
have contributed to the theory of recursive functions have held a variety of nuances of
opinion. As an historian of ideas I am primarily interested in those nuances, and less
interested in what the field in general is all about. But if you have the slightest
interest in Turing's views about intelligence, I strongly recommend re-reading his 1950
paper.

Cheers,
Peter

Subject: Re: Peircean Semiotic & Intelligence Augmentation
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Mon, 02 Dec 2002 10:56:38 -0500
X-Message-Number: 5

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

http://www.loebner.net/Prizef/TuringArticle.html

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

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

Subject: Re: Peircean Semiotic & Intelligence Augmentation
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Mon, 02 Dec 2002 11:16:27 -0500
X-Message-Number: 6

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

a slightly better facsimile, for those who are playing along at home:

http://www.cse.msu.edu/~cse841/papers/Turing.html

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

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

Subject: Re: Peircean Semiotic & IntelligenceAugmentation
From: Peter Skagestad <Peter_Skagestad[…]uml.edu>
Date: Mon, 02 Dec 2002 11:23:55 -0500
X-Message-Number: 7

Joe, Bernard, Joe, et al,

I may have been too hasty in agreeing with Jon here; I actually see both
similarities and differences between the pragmatic maxim and the notion of an
effective procedure. I think the similarities and the differences are both
important, and I go into the subject in some detail in my 1996 paper quoted by
Joe.

I found Joe's paper extremely interesting, although I was disappointed at the end
to find the concluding section omitted. What conclusion, I wondered, is Joe going
to draw? I hope you will satisfy my curiosity at some later date.

The presentation of my own ideas was fair, accurate, and perceptive in the
extreme - I doubt I could have done a better job myself. As for the unifying idea
of IA, I have simply adopted Engelbart's formula "external symbol manipulation".
While IA in this sense goes far beyond computer technology, and encompasses
language, writing, alphabets, numerals, moveable type, etc., Engelbart
characterizes his own research project as "automated external symbol
manipulation". It is interesting that Engelbart, who personally made such
groundbreaking contributions to the computer user interface as the mouse, did not
himself regard interactivity as basic to his program. But Joe is absolutely right
that interactivity and the related idea that computing should be fun were in the
forefront in J.C.R. Licklider's group at MIT; cf. on this subject Mitchell
Waldrop's wonderful Licklider biography The Dream Machine, published last year
and just issued in paperback.

Having programmed in Fortran and used a text editor in the dark ages before
personal computers were commercially available, I agree that word processing can
be regarded as a natural by-prtoduct of programming. But the attitude that
computers should be forbidding and difficult to use could have prevailed. What is
surprising is not that a few individuals got the idea that computers should be
easy and even fun to use; what is surprising is that these individuals prevailed
against a powerful establishment firmly opposed to this idea. Again, Waldrop
gives a fascinating account of the opposition Licklider and his colleagues
encountered.

Finally, I totally agree with Joe that Peirce's dictum "All thinking is in signs"
means, inter alia, that all thinking is communicational. I have thought so for as
long as I can remember, and I am not quite sure why this did not get down on
paper in my earlier papers; I hope to make this point abundantly clear in a
forthcoming paper.

Cheers,
Peter

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

Subject: Re: Peircean Semiotic & Intelligence Augmentation
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Mon, 02 Dec 2002 12:24:13 -0500
X-Message-Number: 8

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

Note 16

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

PS = Peter Skagestad

PS: I think it is quite clear that our interests are simply divergent.
Various individuals who have contributed to the theory of recursive
functions have held a variety of nuances of opinion. As an historian
of ideas I am primarily interested in those nuances, and less interested
in what the field in general is all about. But if you have the slightest
interest in Turing's views about intelligence, I strongly recommend
re-reading his 1950 paper.

Peter,

I have read this paper over again and find it pretty much as I remember.
Certainly, I can find nothing in it that would cause me to summarize it
under the rubric that you gave:

"Turing regarded the human being as essentially indistinguishable from a machine."

The only appearance of the word "indistinguishable" is here:

| The new problem has the advantage of drawing a fairly sharp line
| between the physical and the intellectual capacities of a man.
| No engineer or chemist claims to be able to produce a material
| which is indistinguishable from the human skin. It is possible
| that at some time this might be done, but even supposing this
| invention available we should feel there was little point in
| trying to make a 'thinking machine' more human by dressing it
| up in such artificial flesh. The form in which we have set the
| problem reflects this fact in the condition which prevents the
| interrogator from seeing or touching the other competitors, or
| hearing their voices.
|
| A.M. Turing, "Computing Machinery and Intelligence" (1950)
| http://www.cse.msu.edu/~cse841/papers/Turing.html

Everything about the set-up tells us that we are talking
about models of a yet to be formalized abstract property.

I understand that it's probably in the nature of the primate brain
to form up teams, appoint team captains, and pick a side, and once
the old football game gets rolling it will most likely drag itself
on and on through the mud'n'guts until the final whistle gets blown,
but I really think it's a big mistake to create another one of these
false dichotomies -- say, the "Algorithmics" vs. the "Associatives",
or whatever. In the physics library of my old university they used
to have a commercial prototype of a machine that was inspired by the
Memex idea, a cabinent full of microfilmed physics journals, a fancy
automated spooler and reader, with a copier that would generate hard
copy at the touch of a button. I think I was about the only person
who ever used it. The reason that we are talking about Memex again
is not because of advances in automated microfilm spooling over the
last half century! Everything that makes these new media usable in
any semio-reliable way at all is based on algorithms, however much
the free associations of the designers may have played a part in
their genesis.

Jon Awbrey

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

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

Subject: Re: Peircean Semiotic & Intelligence Augmentation
From: Peter Skagestad <Peter_Skagestad[…]uml.edu>
Date: Mon, 02 Dec 2002 12:47:44 -0500
X-Message-Number: 9

Jon,

The paper contains rebuttals of nine arguments for fundamental differences between
humans and machines, and includes statements such as the following (under Argument 8):

"For we believe that it is not only true that being regulated by laws of behaviour
implies being some sort of machine (though not necessarily a discrete-state machine),
but that conversely being such a
machine implies being regulated by such laws."

Cheers,
Peter

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

Subject: Re: Peircean Semiotic & Intelligence Augmentation
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Mon, 02 Dec 2002 13:44:42 -0500
X-Message-Number: 10

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

Note 17

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

PS: The paper contains rebuttals of nine arguments for fundamental
differences between humans and machines, and includes statements
such as the following (under Argument 8):

PS, quoting AT:

| For we believe that it is not only true that being regulated by
| laws of behaviour implies being some sort of machine (though not
| necessarily a discrete-state machine), but that conversely being
| such a machine implies being regulated by such laws.

The context is:

| 8) The Argument from Informality of Behaviour. It is not possible to produce
| a set of rules purporting to describe what a man should do in every conceivable
| set of circumstances. One might for instance have a rule that one is to stop
| when one sees a red traffic light, and to go if one sees a green one, but what
| if by some fault both appear together? One may perhaps decide that it is safest
| to stop. But some further difficulty may well arise from this decision later.
| To attempt to provide rules of conduct to cover every eventuality, even those
| arising from traffic lights, appears to be impossible. With all this I agree.
|
| From this it is argued that we cannot be machines. I shall try
| to reproduce the argument, but I fear I shall hardly do it justice.
| It seems to run something like this: 'If each man had a definite
| set of rules of conduct by which he regulated his life he would be
| no better than a machine. But there are no such rules, so men cannot
| be machines.' The undistributed middle is glaring. I do not think
| the argument is ever put quite like this, but I believe this is the
| argument used nevertheless. There may however be a certain confusion
| between 'rules of conduct' and 'laws of behaviour' to cloud the issue.
| By 'rules of conduct' I mean precepts such as 'Stop if you see red
| lights', on which one can act, and of which one can be conscious.
| By 'laws of behaviour' I mean laws of nature as applied to a man's
| body such as 'if you pinch him he will squeak'. If we substitute
| 'laws of behaviour which regulate his life' for 'laws of conduct by
| which he regulates his life' in the argument quoted the undistributed
| middle is no longer insuperable. For we believe that it is not only
| true that being regulated by laws of behaviour implies being some sort
| of machine (though not necessarily a discrete-state machine), but that
| conversely being such a machine implies being regulated by such laws.
| However, we cannot so easily convince ourselves of the absence of
| complete laws of behaviour as of complete rules of conduct. The
| only way we know of for finding such laws is scientific observation,
| and we certainly know of no circumstances under which we could say,
| "We have searched enough. There are no such laws."

The "we" here is clearly intended to be the Chorus,
or, at least the Chorus of scientific common sense.

Turing's paper also contains statements like this:

| The reader will have anticipated that I have no very convincing
| arguments of a positive nature to support my views. If I had
| I should not have taken such pains to point out the fallacies
| in contrary views. Such evidence as I have I shall now give.

The playful, experimental, intended-to-make-you-think character of
the paper is evident throughout. Serves him right for putting it
in a philosophy journal.

Jon Awbrey

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

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

Subject: Re: Peircean Semiotic & Intelligence Augmentation
From: "Joseph Ransdell" <joseph.ransdell[…]yahoo.com>
Date: Mon, 2 Dec 2002 13:13:18 -0600
X-Message-Number: 11


----- Original Message -----
From: "Jon Awbrey" <jawbrey[…]oakland.edu>
I don't get it, Jon. Peter says that Turing's view is that there is no
fundamental differences between human beings and machinces. You cite
passages in which he seems to be quite explictly identifies himself with
that view, and then instead of explaining why, nevertheless, Peter is
mistaken, you just walk away from it as if you have answered him.


. For we believe that it is not only
> | true that being regulated by laws of behaviour implies being some sort
> | of machine (though not necessarily a discrete-state machine), but that
> | conversely being such a machine implies being regulated by such laws.
> | However, we cannot so easily convince ourselves of the absence of
> | complete laws of behaviour as of complete rules of conduct. The
> | only way we know of for finding such laws is scientific observation,
> | and we certainly know of no circumstances under which we could say,
> | "We have searched enough. There are no such laws."
>
> The "we" here is clearly intended to be the Chorus,
> or, at least the Chorus of scientific common sense.

Well, the "we" explicitly identifies with the view that Peter imputes to
Turing. I don't get it, Jon.

> Turing's paper also contains statements like this:
>
> | The reader will have anticipated that I have no very convincing
> | arguments of a positive nature to support my views. If I had
> | I should not have taken such pains to point out the fallacies
> | in contrary views. Such evidence as I have I shall now give.
>
> The playful, experimental, intended-to-make-you-think character of
> the paper is evident throughout. Serves him right for putting it
> in a philosophy journal.

The question is not whether his responses are "playful, experimental,
intended-to-make -you-think" but what his view is,and he seems to be quite
clearly identifying himself with the view that people anre not fundamentally
different from machines, which he is defending against objections, though,
as he recognizes, there is no way to prove a priori that there is a
determining law for everything. He is certainly identifying himself with
SOME view in defending against objections to it, whatever it is, so what is
it if it is not the view that Peter imputes to him?

Joe Ransdell




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

Subject: Re: Peircean Semiotic & Intelligence Augmentation
From: "R. Jeffrey Grace" <rjgrace[…]yahoo.com>
Date: Mon, 2 Dec 2002 11:45:00 -0800
X-Message-Number: 12



Joe and Peter,

If I may, I have a question regarding Joe's paper where you discuss
Peter's understanding of Peirce's dictum "All thought is in signs". It
looks like to me that a move is made from "All thought is in
signs"(point A) to "All thought IS signs" (point B) by Peter and I'm
wondering if you offer any argument for from moving from point A to B?

I ask because this move seems to be a reductive one! My pardon if this
has been broached already in your discussion!

Pax...

---
R. Jeffrey Grace
rjgrace[…]pobox.com
http://www.rjgrace.com <http://www.rjgrace.com/>




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

Subject: Re: Peircean Semiotic & Intelligence Augmentation
From: Peter Skagestad <Peter_Skagestad[…]uml.edu>
Date: Mon, 02 Dec 2002 15:05:53 -0500
X-Message-Number: 13



Jeffrey,

Off the top of my head I think Peirce also said that thoughts are signs,
but I'll have to look it up, and I also do not recall by what exact
means he arrived at this. Nor, at the moment, am I sure what is at stake
here - what turns on the distinction. I hope to revisit the question.

Cheers,
Peter

"R. Jeffrey Grace" wrote:

> Joe and Peter, If I may, I have a question regarding Joe's paper
> where you discuss Peter's understanding of Peirce's dictum "All
> thought is in signs". It looks like to me that a move is made from
> "All thought is in signs"(point A) to "All thought IS signs" (point B)
> by Peter and I'm wondering if you offer any argument for from moving
> from point A to B? I ask because this move seems to be a reductive
> one! My pardon if this has been broached already in your
> discussion! Pax...

--- R. Jeffrey Grace rjgrace[…]pobox.com
> http://www.rjgrace.com

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

Subject: Re: Peircean Semiotic & Intelligence Augmentation
From: Peter Skagestad <Peter_Skagestad[…]uml.edu>
Date: Mon, 02 Dec 2002 15:07:02 -0500
X-Message-Number: 14

Jon,

I did understand that Turing was joking, but I do not believe he was simply joking.

Cheers,
Peter

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

Subject: Re: Identity & Teridentity
From: Kenneth Ketner <b9oky[…]TTACS.TTU.EDU>
Date: Mon, 02 Dec 2002 14:44:07 -0600
X-Message-Number: 15

Howard and Jon: All this nonreduction of triads stuff and the wrongness
of Quine's supposed reduction to a dyadic predicate is laid out with the
highest mathematical rigor in Robert Burch's A PEIRCEAN REDUCTION
THESIS: THE FOUNDATIONS OF TOPOLOGICAL LOGIC. Arisbebooks has some
copies (search via google). This volume is an absolute essential in any
literature review for persons working this area.

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




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

Subject: Re: Peircean Semiotic & Intelligence Augmentation
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Mon, 02 Dec 2002 16:00:14 -0500
X-Message-Number: 16

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

Note 18

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

JR: I don't get it, Jon. Peter says that Turing's view
is that there is no fundamental differences between
human beings and machines. You cite passages in which
he seems to be quite explictly identifies himself with
that view, and then instead of explaining why, nevertheless,
Peter is mistaken, you just walk away from it as if you have
answered him.

Joe,

Please read this statement:

"Turing regarded the human being as essentially indistinguishable from a machine."

Let us abstract its content as follows:

Thesis 1. A human being is essentially indistinguishable from a machine.

I see nowhere that Turing says this.

Thesis 1 contains three big wiggle words:

A. "human being"
B. "essentially"
C. "machine"

A phrase like "no fundamental differences between human beings and machines"
merely substitutes the indefinite qualifier "fundamental" for "essentially".

Turing discusses several different possibilities for pinning down the meanings
of the terms A, B, C to the point of having an well-posed significant question.
Under some definitions of A, B, C, Thesis 1 is true but trivial, for instance,
if your definition of "machine" is "law-governed process" or "natural process".
At any rate, the Chorus in Objection 8 would probably take it for granted that
everything that goes on in the universe is by definition "natural". But that
is an obvious sop, and Turing picks a more restrictive definition of "machine"
for his own model. Under other definitions of A, B, C, Thesis 1 is obviously
false, but for reasons that have nothing to do with intelligence or reasoning.

So the interesting cases reside with a very restrictive definition of "machine"
and a very abstract definition of "essential", indeed, the "rational" without
the "animal", which Scholastics might regard as more an argument about angels
than real human beings, but never mind that now.

I have already emphasized that it is impossible to understand Turing's paper,
or any other thesis that makes use of effective descriptions and formal models
without understanding the way that these descriptions and models are intended
to be used by those who use them. The fundamental rule is not to confuse the
model with the reality, and I see no evidence, here or elsewhere, that Turing
is confused about that. Observing this rule means that all arguments in favor
of a model have to be understood as arguments that the model is "good", and
that always means "good" in some limited and relevant sense.

| For we believe that it is not only true that being regulated by
| laws of behaviour implies being some sort of machine (though not
| necessarily a discrete-state machine), but that conversely being
| such a machine implies being regulated by such laws. However, we
| cannot so easily convince ourselves of the absence of complete laws
| of behaviour as of complete rules of conduct. The only way we know
| of for finding such laws is scientific observation, and we certainly
| know of no circumstances under which we could say, "We have searched
| enough. There are no such laws."

JA: The "we" here is clearly intended to be the Chorus,
or, at least the Chorus of scientific common sense.

JR: Well, the "we" explicitly identifies with the view
that Peter imputes to Turing. I don't get it, Jon.

Turing is engaged here in reconstructing the argument for the Objection.
He concedes the point of it under the "rules of conduct" interpretation,
then considers its possible clarification under the "laws of behavior"
interpretation, where he imagines that his interlocutors would agree
with this natural scientific point of view about laws. But this is
back under the trivial definition of "machine", and Turing himself
is considering a harder case.

JA: Turing's paper also contains statements like this:

| The reader will have anticipated that I have no very convincing
| arguments of a positive nature to support my views. If I had
| I should not have taken such pains to point out the fallacies
| in contrary views. Such evidence as I have I shall now give.

JA: The playful, experimental, intended-to-make-you-think character of
the paper is evident throughout. Serves him right for putting it
in a philosophy journal.

JR: The question is not whether his responses are "playful,
experimental, intended-to-make-you-think" but what his
view is, and he seems to be quite clearly identifying
himself with the view that people are not fundamentally
different from machines, which he is defending against
objections, though, as he recognizes, there is no way
to prove a priori that there is a determining law for
everything. He is certainly identifying himself with
SOME view in defending against objections to it,
whatever it is, so what is it if it is not the
view that Peter imputes to him?

His view, I am guessing, is that mathematical models and
effective descriptions are useful for some purposes and
not for others, and sensing the attitude of experiment,
play, and thought-provocation is very much a part of
understanding this view.

If Peter imputes to Turing the view that:

"A human being is essentially indistinguishable from a machine",

then my view would be that Peter is exaggerating just a little bit.

Jon Awbrey

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

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

Subject: Re: Peircean Semiotic & Intelligence Augmentation
From: Peter Skagestad <Peter_Skagestad[…]uml.edu>
Date: Mon, 02 Dec 2002 16:53:37 -0500
X-Message-Number: 17

Jon,

I never presented Thesis 1 as a quotation from Turing; it is a summary of what I
believe to be a fair and careful exegesis of Turing's views, together with a
comparison of his views with those of Bush. The word "essentially" may function as a
"wiggle word"; it may also function more or less as a placeholder for what I have
already said earlier in the paper.

I want the record to show that I have never remotely suggested that Turing was
confused about anything. Finally, I still do not understand what view you think Turing
was advancing in 'Computing Machinery and Intelligence'.

Cheers,
Peter


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

Subject: Re: Peircean Semiotic & Intelligence Augmentation
From: "Joseph Ransdell" <joseph.ransdell[…]yahoo.com>
Date: Mon, 2 Dec 2002 15:56:00 -0600
X-Message-Number: 18

There is material in the first volume of the Writings -- thus from his
earliest years of publication -- that makes it clear that what Peirce
originally had in mind in saying that thought is in signs was tp
establlish that there is a public subject-matter for logic, and thus it
means that thought is literally in the public manifestations of its
expression, such as, for example, in signs like those before you which
you are currently reading if you are working from your screen. My
thought is presently on your screen. (It is on my screen, too, and
elsewhere as well.) Why was this important to him? Because logic
could not lay claim to being a science if it had no subject-matter that
is publicly available, and his basic and standing aim in his
philosophical work from beginning to end was to establish that logic is
a genuine science.

Thought is in signs in the sense in which any relation -- any relational
property -- is in its relata. This doesn't mean that it is not in the
mind but rather that it is not in the head, hidden away either in a
mysterious domain in there called "the mind", or even inside the skull.
Note that it would seem, then, that at that time he did not mean that
thought is in neurons, that is, that is not what it meant as used in the
context of logic, at least. We do not open skulls and examine neurons
in order to find our public subject matter if we are practicioners of
the science of logic.

I take it that this is always the bottom meaning of that dictum, as it
were, but as it occurs in a number of different contexts across his
whole career it seems to mean a number of different things, as e.g. I
understand it in certain contexts to mean also that thought is
dialogical (because it must be interpreted -- sign and interpretant are
dialogically related). In other words I take it to have multiple
mutually consistent meanings in his work.

I don't think the dictum ever means that thought is in neurons; however,
he may have had other reasons to regard neurons as bearers of thought.
Still, I don't think it could be in the same sense in which, say,
word-signs are bearers of thought.

As regards whether thought IS signs, that seems an awkward way of
expressing it and I would have to see some place where he says that to
figure out why he would have put it that way. But he might have. I
just don't recall that usage myself.

Joe Ransdell




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

Subject: Re: Identity & Teridentity
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Mon, 02 Dec 2002 17:02:32 -0500
X-Message-Number: 19

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

HC = Howard Callaway
JA = Jon Awbrey
KK = Kenneth Ketner

KK: Howard and Jon: All this nonreduction of triads stuff and the wrongness
of Quine's supposed reduction to a dyadic predicate is laid out with the
highest mathematical rigor in Robert Burch's A PEIRCEAN REDUCTION THESIS:
THE FOUNDATIONS OF TOPOLOGICAL LOGIC. Arisbebooks has some copies (search
via google). This volume is an absolute essential in any literature review
for persons working this area.

JA: Ergo, all notions of analysis, composition, reduction, synthesis, whatever,
contain a notion of triadic relations as a part of their very constitution.

HC: I find the related arguments very slippery. Certainly I am no fan of reductionism,
but it seems the the presuppositions involved in the proofs offered of the reduction
or non-reduction of "genuine" triadic relations (Correct me if I am wrong, but I think
Peirce uses the term "genuine" triadic relations, so that there is some distinction
between genuinely triadic relations and those which may just appear to be so, and
are open to some analysis) -- the various presuppositions -- seem not so obvious.

HC: So, please be aware that I do not have in mind to defend Quine's proof of
reduction to non-triadic relations. But that he gives a proof or apparent
proof seems a chief point of interest. On the other hand, Peirce's contrary
arguments to the effect that triadic relations cannot be reduced, seems to
involve presuppositions connected with his use of teridentity, in contrast
to the usual versions we see in logic books.

HC: I have my serious doubts that we actually need the concept of teridentity for
logical purposes generally. The cross-reference and possible cross-reference
of the variables seems to take the place of teridentity as things are usually
formulated.

HC: If you can clarify this matter, then I think you will
provide a benefit to readers of the list, myself included.

Howard, Ken, & All,

I apparently failed to receive this earlier message from Howard.
I will put Burch's book on my wish list, but the basic facts have
long been beyond question in the necks of the mathematical woods
that I was once accustomed to frequent. We had long battles over
this on SUO, and even when I got one of the reviewers who panned
Burch's book in print to concede off-list -- they always do it by
saying that it was always already trivial in the first place --
he/she never would fess up in public. So I have little hope.

There are at least three levels to the irreducibility half of it,
and I have seen all the relevant Peirce quotes already pass under
the bridge several times here with not so much cognizance of what
they say.

At level one, the argument is over before it starts. The very idea
of reducing 1 thing to 1 thing plus 1 other thing is a triadic idea.

At level two, there is ordinary relational composition, or as Peirce
called it "relative multiplication", and it defines the composition
of two 2-adic relations to be a 2-adic relation, which means that
you can never ever get a 3-adic relation as the composition of
two 2-adic relations. Peirce just takes this much as given
from the start, as it is already clear in his first papers.

At level three, which a player reaches in an orderly way
only by conceding the issue of irreducibility on the first
two scores, and this is where, as I currently understand it,
the whole business about "genuineness" comes into play, one is
given a single 3-adic relation, say, the one that corresponds to
logical conjunction, in terms of truth values 'and' : B x B -> B,
along with the whole stock of 2-adic relations previously granted.
Then one tries to see what other 3-adics can be generated from these
augmented resources. The ones that can be so produced are reducible
over this resource base; the ones that can't be so constructed are
then called "irreducible" in a stronger sense, the genuine 3-adics.
At any rate, this seems to fit the examples that Peirce provides.

I am putting a detailed "work in progress" on these issues here:

http://www.nexist.org/wiki/Doc16596Document
http://www.nexist.org/wiki/Doc16600Document

It can take a couple of minutes to load the pages, though.

Jon Awbrey

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

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

Subject: Re: Identity & Teridentity
From: HGCALLAWAY[…]aol.com
Date: Mon, 2 Dec 2002 17:31:02 EST
X-Message-Number: 20

Ken & list,

You wrote, Ken:

----quote----------
Howard and Jon: All this nonreduction of triads stuff and the wrongness of
Quine's supposed reduction to a dyadic predicate is laid out with the highest
mathematical rigor in Robert Burch's A PEIRCEAN REDUCTION THESIS: THE
FOUNDATIONS OF TOPOLOGICAL LOGIC. Arisbebooks has some copies (search via
google). This volume is an absolute essential in any literature review for
persons working this area.
----end quote----

As I believe I mentioned when Burch's book was last mentioned in connection
with related themes, I have not read this book. In consequence I have offered
no criticism of it. I have however asked, on occasion, whether anyone on the
list could explain or evaluate the argument of the book. That would be
interesting to see. I have not found the arguments so far advanced very
compelling --and as I think you know, Ken, I am not exactly noted for my
excesses of scepticism.

I wonder if any reviews of the volume have appeared in print. I would
certainly be interested in having a look. As I wrote in one posting or other,
I tend to think that Quine's argument is simply a mathematical model of
reduction to a dyadic predicate and one that would not be thought of as
finding compelling applications in many cases of interest. It is more like
saying that what we express by means of triadic predicates can in some sense
be simulated or paraphrased without them. It is of some interest in this
connection to reflect that Quine makes no synonym claims for his practice of
paraphrase. It is more a matter of having a suitable substitute for some
purpose or other, and it is not at all clear to me what the general purpose
would be in paraphrasing out of all triadic and higher predicates. So, I do
think that the general claim of reduction is better thought of as some
general model of para-phrase, (possibly) useful. That the purpose involved is
a limited, or possibly even purely theoretical one, seems evident in that
Quine wrote of reformulating any theory making use not simply of dyadic
predicates, but making use of a single dyadic predicate. Thus his opening:

----quote Quine---------
Consider any interpreted theory [T], formulated in the notation of
quantification theory (or lower predicate calculus) with interpreted
predicate letters. It will be proved that [T] is translatable into a theory,
likewise formulated in the notation of quantifica-tion theory, in which there
is only one predicate letter, and it is a dyadic one (Quine, _Selected Logic
Papers_, p. 224).
----end quote-------------

At the same time, I am not convinced that we need teridentity as contrasted
with the normal or standard version.

So, I would be glad to hear more about Burch's book. Thanks for the reminder.

Howard

H.G. Callaway
(hgcallaway[…]aol.com)

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

Subject: Re: Peircean Semiotic & Intelligence Augmentation
From: "Joseph Ransdell" <joseph.ransdell[…]yahoo.com>
Date: Mon, 2 Dec 2002 16:38:02 -0600
X-Message-Number: 21

i don't see any need to press the issue further myself because I don't see
anything of importance that hinges on it other than the question whether
Peter misrepresented what Turing says. Now, one could grant your
interpretation as being okay considered as an extraordinarily charitable one
as regards Turing, presumably based on some collateral information about
Turing; but it is still true that, given what Turing actually said, Peter
was not misrepresenting Turing, who should have been more careful if he
really intended to hold to the more subtle and restrained thesis you impute
to him.

Joe Ransdell



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

Subject: Re: Identity & Teridentity
From: HGCALLAWAY[…]aol.com
Date: Mon, 2 Dec 2002 18:29:44 EST
X-Message-Number: 22

Peirce-l,

If anyone on the list can kindly translate the following out of Jon-ese for
me, I would be much obliged. I tend to think that if I ask Jon for
explanations, I will get so many explanations, equally unclear (to me at
least), that I will not come one step forward. So, I call upon the collective
wisdom of the list!

Good evening, Jon

It is getting late here. But have a look at my reply to Ken.

Howard

H.G. Callaway
(hgcallaway[…]aol.com)

----Jon wrote---------
<< Howard, Ken, & All,

I apparently failed to receive this earlier message from Howard.
I will put Burch's book on my wish list, but the basic facts have
long been beyond question in the necks of the mathematical woods
that I was once accustomed to frequent. We had long battles over
this on SUO, and even when I got one of the reviewers who panned
Burch's book in print to concede off-list -- they always do it by
saying that it was always already trivial in the first place --
he/she never would fess up in public. So I have little hope.

There are at least three levels to the irreducibility half of it,
and I have seen all the relevant Peirce quotes already pass under
the bridge several times here with not so much cognizance of what
they say.

At level one, the argument is over before it starts. The very idea
of reducing 1 thing to 1 thing plus 1 other thing is a triadic idea.

At level two, there is ordinary relational composition, or as Peirce
called it "relative multiplication", and it defines the composition
of two 2-adic relations to be a 2-adic relation, which means that
you can never ever get a 3-adic relation as the composition of
two 2-adic relations. Peirce just takes this much as given
from the start, as it is already clear in his first papers.

At level three, which a player reaches in an orderly way
only by conceding the issue of irreducibility on the first
two scores, and this is where, as I currently understand it,
the whole business about "genuineness" comes into play, one is
given a single 3-adic relation, say, the one that corresponds to
logical conjunction, in terms of truth values 'and' : B x B -> B,
along with the whole stock of 2-adic relations previously granted.
Then one tries to see what other 3-adics can be generated from these
augmented resources. The ones that can be so produced are reducible
over this resource base; the ones that can't be so constructed are
then called "irreducible" in a stronger sense, the genuine 3-adics.
At any rate, this seems to fit the examples that Peirce provides.

I am putting a detailed "work in progress" on these issues here:

http://www.nexist.org/wiki/Doc16596Document
http://www.nexist.org/wiki/Doc16600Document

It can take a couple of minutes to load the pages, though.

Jon Awbrey
>>

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

Subject: Re: Identity & Teridentity
From: John Collier <ag659[…]ncf.ca>
Date: Mon, 02 Dec 2002 19:12:16 -0500
X-Message-Number: 23

At 05:02 PM 02/12/2002, Jon wrote:

>At level one, the argument is over before it starts. The very idea
>of reducing 1 thing to 1 thing plus 1 other thing is a triadic idea.

If it is this simple, I doubt very much that it is what Pierce was
talking about. In any case, since ideas are taken by Peirce
to be triadic, I think you are begging the question by talking
about ideas of relations here rather than of relations. I have
said this before. Perice, as Howard says, distinguishes
between genuine triadic relations and the other kind of
three place relations. Numerous texts in which Peirce
makes this distinction have been cited. You are barking up the
wrong tree, Jon.

John

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

Subject: Re: Peircean Semiotic & Intelligence Augmentation
From: "R. Jeffrey Grace" <rjgrace[…]yahoo.com>
Date: Mon, 2 Dec 2002 16:13:12 -0800
X-Message-Number: 24



Peter,

Thanks! I think the distinction ultimately has to do with the reduction
of the mental to the physical, unless it's also maintained that signs
aren't reducible to the thing acting as a sign (written word, etc.).

---
R. Jeffrey Grace
rjgrace[…]pobox.com
http://www.rjgrace.com <http://www.rjgrace.com/>

-----Original Message-----
From: Peter Skagestad [mailto:Peter_Skagestad[…]uml.edu]
Sent: Monday, December 02, 2002 12:06 PM
To: Peirce Discussion Forum
Subject: [peirce-l] Re: Peircean Semiotic & Intelligence Augmentation



Jeffrey,

Off the top of my head I think Peirce also said that thoughts are signs,
but I'll have to look it up, and I also do not recall by what exact
means he arrived at this. Nor, at the moment, am I sure what is at stake
here - what turns on the distinction. I hope to revisit the question.


Cheers,
Peter



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

Subject: Re: Peircean Semiotic & Intelligence Augmentation
From: "R. Jeffrey Grace" <rjgrace[…]yahoo.com>
Date: Mon, 2 Dec 2002 16:13:12 -0800
X-Message-Number: 25



Joe, I'm formatting what you wrote in italics and grey font:

There is material in the first volume of the Writings -- thus from his
earliest years of publication -- that makes it clear that what Peirce
originally had in mind in saying that thought is in signs was tp
establlish that there is a public subject-matter for logic, and thus it
means that thought is literally in the public manifestations of its
expression, such as, for example, in signs like those before you which
you are currently reading if you are working from your screen. My
thought is presently on your screen. (It is on my screen, too, and
elsewhere as well.) Why was this important to him? Because logic
could not lay claim to being a science if it had no subject-matter that
is publicly available, and his basic and standing aim in his
philosophical work from beginning to end was to establish that logic is
a genuine science.

[RJG] You said "My thought is presently on your screen" but I'm
wondering if it isn't more accurate to say "My thought is present on
your screen through written words acting as signs" ? (Sounds like you
agree). In other words, what I'm seeing on my screen are words acting
as signs bringing me your thoughts. I think the distinction is
important, for if Peirce maintained ( and we agree with him) that
thoughts are signs rather than being in signs, then the next question
that arises for me is: are signs reducible to words, or anything else
that acts as a sign? I would guess that they aren't!

Thought is in signs in the sense in which any relation -- any relational
property -- is in its relata. This doesn't mean that it is not in the
mind but rather that it is not in the head, hidden away either in a
mysterious domain in there called "the mind", or even inside the skull.
Note that it would seem, then, that at that time he did not mean that
thought is in neurons, that is, that is not what it meant as used in the
context of logic, at least. We do not open skulls and examine neurons
in order to find our public subject matter if we are practicioners of
the science of logic.

I take it that this is always the bottom meaning of that dictum, as it
were, but as it occurs in a number of different contexts across his
whole career it seems to mean a number of different things, as e.g. I
understand it in certain contexts to mean also that thought is
dialogical (because it must be interpreted -- sign and interpretant are
dialogically related). In other words I take it to have multiple
mutually consistent meanings in his work.

I don't think the dictum ever means that thought is in neurons; however,
he may have had other reasons to regard neurons as bearers of thought.
Still, I don't think it could be in the same sense in which, say,
word-signs are bearers of thought.

As regards whether thought IS signs, that seems an awkward way of
expressing it and I would have to see some place where he says that to
figure out why he would have put it that way. But he might have. I
just don't recall that usage myself.

[RJG] That's the real issue for me I think. If he did say that or
something equivalent, it would be something I'd like to get to the
bottom of! On the other hand, the idea of thoughts being dependant on
neurons isn't too troubling for my thinking. :>


---
R. Jeffrey Grace
rjgrace[…]pobox.com
http://www.rjgrace.com <http://www.rjgrace.com/>





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

Subject: Re: Identity & Teridentity
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Mon, 02 Dec 2002 22:32:38 -0500
X-Message-Number: 26

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

Howard, by way of translation, let us return to the orginal.
What Peirce says in the following quote, that Joe posted on
23 Nov 2002 08:36:18 -0600, covers the same facts that I am
indicating under my rubric of level 1 and level 2. This is
all still terating of relations as sets of tuples, before
we even get as far as mentioning sign relations, per se.

| 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'.
|
| C.S. Peirce, 'Collected Papers', CP 8.331

JA: There are at least three levels to the irreducibility half of it,
and I have seen all the relevant Peirce quotes already pass under
the bridge several times here with not so much cognizance of what
they say.

JA: At level one, the argument is over before it starts. The very idea
of reducing 1 thing to 1 thing plus 1 other thing is a triadic idea.

JA: At level two, there is ordinary relational composition, or as Peirce
called it "relative multiplication", and it defines the composition
of two 2-adic relations to be a 2-adic relation, which means that
you can never ever get a 3-adic relation as the composition of
two 2-adic relations. Peirce just takes this much as given
from the start, as it is already clear in his first papers.

JA: At level three, which a player reaches in an orderly way
only by conceding the issue of irreducibility on the first
two scores, and this is where, as I currently understand it,
the whole business about "genuineness" comes into play, one is
given a single 3-adic relation, say, the one that corresponds to
logical conjunction, in terms of truth values 'and' : B x B -> B,
along with the whole stock of 2-adic relations previously granted.
Then one tries to see what other 3-adics can be generated from these
augmented resources. The ones that can be so produced are reducible
over this resource base; the ones that can't be so constructed are
then called "irreducible" in a stronger sense, the genuine 3-adics.
At any rate, this seems to fit the examples that Peirce provides.

JA: I am putting a detailed "work in progress" on these issues here:

JA: http://www.nexist.org/wiki/Doc16596Document
http://www.nexist.org/wiki/Doc16600Document

JA: It can take a couple of minutes to load the pages, though.

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

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

Subject: Re: Identity & Teridentity
From: Jon Awbrey <jawbrey[…]oakland.edu>
Date: Mon, 02 Dec 2002 22:40:41 -0500
X-Message-Number: 27

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

Howard,

Instead of translation, perhaps we can return to the orginal.
What Peirce says in the following quote, that Joe posted on
23 Nov 2002 08:36:18 -0600, covers the same facts that I am
indicating under my rubric of level 1 and level 2. This is
all still terating of relations as sets of tuples, before
we even get as far as mentioning sign relations, per se.

| 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'.
|
| C.S. Peirce, 'Collected Papers', CP 8.331

JA: There are at least three levels to the irreducibility half of it,
and I have seen all the relevant Peirce quotes already pass under
the bridge several times here with not so much cognizance of what
they say.

JA: At level one, the argument is over before it starts. The very idea
of reducing 1 thing to 1 thing plus 1 other thing is a triadic idea.

JA: At level two, there is ordinary relational composition, or as Peirce
called it "relative multiplication", and it defines the composition
of two 2-adic relations to be a 2-adic relation, which means that
you can never ever get a 3-adic relation as the composition of
two 2-adic relations. Peirce just takes this much as given
from the start, as it is already clear in his first papers.

JA: At level three, which a player reaches in an orderly way
only by conceding the issue of irreducibility on the first
two scores, and this is where, as I currently understand it,
the whole business about "genuineness" comes into play, one is
given a single 3-adic relation, say, the one that corresponds to
logical conjunction, in terms of truth values 'and' : B x B -> B,
along with the whole stock of 2-adic relations previously granted.
Then one tries to see what other 3-adics can be generated from these
augmented resources. The ones that can be so produced are reducible
over this resource base; the ones that can't be so constructed are
then called "irreducible" in a stronger sense, the genuine 3-adics.
At any rate, this seems to fit the examples that Peirce provides.

JA: I am putting a detailed "work in progress" on these issues here:

JA: http://www.nexist.org/wiki/Doc16596Document
http://www.nexist.org/wiki/Doc16600Document

JA: It can take a couple of minutes to load the pages, though.

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



---

END OF DIGEST 12-02-02