SUO: Re: Sign Relations & Communication
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JA = Jon Awbrey
SR = Seth Russell
JA: The factorization example was designed to illustrate a particular theme
falling under the topic of "inter-communicability" ("inter-com"), namely,
how we might be able to accommodate, more or less roughly, several different
customs of speech and thought in regard to a commonly arising type of situation,
to wit, "general, multiple, plural reference" or "non-uniquely determined denotation".
The point of all that was to show how we might be able to rationalize the different
ways of speaking and thinking to each other. In the process, the precise meaning
of many of the points in the graph that I drew got stretched to cover a diversity
of alternative readings.
SR: Well that just goes to show how rare actual communication actually is.
I had though that an "intercom" was, as I had mentioned, just an intercom
between our minds and that we were testing the intercom with the example of
agreeing upon a way (a notation) to express the distinction between intension
and extension. I guess I should report back to reading comprehension class.
So you reified the process of communication,
that's how the intercom got its name in the
first place. Perhaps the "inter" is otiose.
Only perfect communication is all that rare.
JA: We started with a function f : X -> Y, interpreted
as a classification of the elements in X under the
elements in Y. Then we looked at a single section
of this function, one that associated the elements
x_1, x_2, x_3 in X with the element y in Y.
| f
| X ---> Y
|
| x_1 ~> y
| x_2 ~> y
| x_3 ~> y
JA: This piece of the function factored
through an "intermediate element" i.
| g h
| X ---> M -> Y
|
| x_1 ~> i ~> y
| x_2 ~> i ~> y
| x_3 ~> i ~> y
JA: The point of factoring f as g o h is seen
if you look at the whole functions g and h,
in that g is surjective and h is injective.
SR: Which probably explains why you didn't understand my diagram. I simply
assigned the symbol 'y' to be the name of a extensional set, and 'i'
to be the name of the corresponding intensional set.
I do not understand this way of talking here:
"extensional set" sounds redundant to my ear,
and "intensional set" I cannot fathom at all.
JA: No such notion. My aim at the moment is to describe the conduct of complex systems,
ones that are complex enough to do or to simulate what we ordinarily call "learning",
"looking", "reasoning", "talking", "thinking", "understanding", and so on. The first
bit of the descriptive work is to find or to make a descriptive language that is just
enough to do the job. I have been recommending the descriptive formalism that I hope
will be more and more commonly known as "sign relations" as the one that I have tried
and found, provisionally as always, the "minimum adequate resource kit" (MARK) for it.
So far Job_1 appears to be a purely descriptive task. But Job_0 is the conduct of the
object systems, and "conduct" to a pragmatic thinker is defined as "action or behavior
with regard to an object (= pragma)", and that is by any other nomen a normative form
of action or behavior. And Job_2 is the requiremnt that I would like all of this to
constitute a "good" description of the object systems, and so the whole production
is a piece of descriptive baloney between two slices of normative bread.
SR: Well, will you let me know when this this descriptive baloney
is going to be useful so I can go back and study it in detail?
Utility is a normative question. And there be sustenance in baloney.
The point is just the systems of which I speak are in the world, not
in the mind alone, not in some rarefied platonic heaven alone. I am
in the world, you are in the world, we are all in the world together.
QQQ-chu.
SR: I can put a specific record *in* a computer's memory ... those and only
those records I ~want~ to consider to be our beloved Interpertant for the
purposes of the computer. So then everything the agent knows of itself must
needs be a record in the computer's memory. This space inside the computer is
a real world natural space, it is not an ideal space. It seems to me that you
keep on trying to make it some kind of platonic ideal space. My question again
(recoded here) is: Can you in good conscience *agree* to do that with me or not?
And if not, why not? Specifically what fears beset you?
JA: In my better conscience I have to observe that when you speak of
putting records "in" a computer's memory you are using a popular
figure of speech, a metaphorical use of the word "in", among the
host of other tropes that go into that phrase. It is most often
a harmless figure, and even quite useful from time to time, but
no further analysis of the system or situation can come from it,
and it will block our understanding to persist in pursuing it.
SR: I disagree. Record-A is in a database-B, if the bit string called
database_B contains a substring called record-A. Now of course that
definition needs a little work such that we factor in the grammar of the
database so we can deal with quoting; but, really, given any set of honest
computer scientist, they will be able to agree to a very high extent whether
a given record is in a given database or not.
You have slid from talking about a "computer", abstractly enough,
to talking about a "database", a far remoter abstraction. Don't
look down, but it's you my friend who are in platonic heaven now.
SR: [1] http://robustai.net/mentography/intensionExtension.gif
JA: This picture still looks off to me.
JA: 1. What are the red boxes with x_1 written over i in them?
SR: Well they are certainly in the Venn Diagram circle labeled Objects ...
so they are objects. I put labels on them so that you could pick
them out ... as far as I know that would be all that I can do with
such objects when I have identified the domain as being of the o
in our sign relation {s, i, o}.
JA: I still don't understand this part.
JA: 2. '"x_j" connotes x_j' seems wrong.
JA: Signs connnote other signs, roughly.
SR: I will be glad to use whatever term you prefer ...
you know the literature on the subject far better than I ...
since I have found no consensus in my reading, I am at a loss to
choose a term. You had used the term previously (I forget where) in
a way that I though I knew that at least the blunt end of the reference
would need to be in the Interpertant domain ... consequently I had thought
you would understand me. But whatever word we do use to label it, there is
such an arrow of which we can speak that has its blunt end in the Interpertant
domain and its sharp end on a corresponding object in the Object domain. So,
what label would you prefer for that arrow?
JA: "cat_1" denotes cat_1, etc. "x_1" denotes x_1, etc.
SR: Yes, that matches my diagram exactly.
Not exactly:
1. You have "x_1" denotes [x_1, i] (= red box with x_1 over i).
2. You have x_1 represents [x_1, i] (= same red box).
3. You have "x_1" connotes x_1.
SR: Of course in my diagram there are two sets with objects labeled with x_1,
the set named Interpertant and the set named Objects. I had labeled the
arrow from the sign "x_1" to the object x_1 with 'denotes' ... which
matches your sentence above.
But what is the i in the red box for?
SR: The question is what is the label on the arrow from the sign "x_1"
to the Interpertant x_1? We obviously cannot call that arrow (that
relationship) denotes. Agreeing on this term, would for me, mean that
we have made some small progress in communicating.
Okay, I see now that you mean for the x_1, x_2, x_3 in the Interpretant circle
to be Interpretants. This is possible, I suppose, but I am guessing that this
is not what you mean. Remember that x_1, x_2, x_3 are already cast as objects.
I am guessing that you mean for the x_1, x_2, x_3 in the Interpretant circle
to be distinct entities from the objects x_1, x_2, x_3. Or not? Remember
that interpretants are just signs, even if they are concepts, concepts are
just signs, since they satisfy the definition of signs, and so you have
the option of using quoted strings to talk about them.
JA: The "isa" arcs are wrong because they extend
from the objects x_1, x_2, x_3 to the sign y.
There are no such arcs, please report to the optometrist. The nodes labeled
x_1 in the set called Interpertant have arcs labeled "isa" extending to the
node labeled "y" in that set. Nothing in the set of objects has any arc
extending anywhere.
I have been considering x_1, x_2, x_3 to be the same things
no matter where that they happen to be placed in the figure.
Only confusion will come from violating that convention.
If you want graphic elements like little boxes to act
as quotation operators then you have to blazon that
in a legend that goes with the figure. But it's
better just to use quotation marks.
JA: So these arcs are more like "is denoted by".
The 'denotes' arcs do extend from the signs to the objects ...
'is denoted by' would be the inverse arcs which could be inferred.
JA needs to refer to his maps:
o-----------------------------o
| Sign Relation L'" |
o---------o---------o---------o
| Object | Sign | Interp |
o---------o---------o---------o
| i | "i" | ... |
| x_1 | "i" | ... |
| x_2 | "i" | ... |
| x_3 | "i" | ... |
o---------o---------o---------o
| i | y | ... |
| x_1 | y | ... |
| x_2 | y | ... |
| x_3 | y | ... |
o---------o---------o---------o
o-----------------------------o
| Denotative Component of L'" |
o--------------o--------------o
| Objects | Signs |
o--------------o--------------o
| |
| i |
| /|\ * |
| / | \ * |
| / | \ * |
| o o o >>>>>>>>>>>> y |
| . . . ' |
| . . . ' |
| ... ' |
| . ' |
| "i" |
| |
o-----------------------------o
JA: You can tell that "i" and y are both signs
because I put them both in the Sign column
of the above Table and on the Signy side
of the above Figure.
I did substantially the same thing .. from my point of view more
consistently. You will find both "i" and "y" in the set of signs
in the mentograph, you will find nodes labeled with those signs in
the set of Interpertant nodes.
You keep misreading this.
y is a sign. "i" is a sign.
I am not that bad a typist.
Think of it this way:
Var type declaration y : string.
Assignment statement y := "cat".
SR: Putting "i" in that sentence as you did would for my graph
break the rules ... and I don't know why you did it. The
whole point of the arrows labeled with 'intension of' and
'extension of' was to distinguish the Interpertant nodes
labeled respectively with i and with y. Since the whole
graph is named "intensionExtension.gif" and its purpose
was to illuminate the distinction between intension and
extension, I felt it was absolutely necessary that I
distinguish the concepts. To distinguish concepts
requires that some arrow between them exists and
screams for us to label it.
JA: Look, y came in as a sign that denotes all three of x_1, x_2, x_3.
That's just what a "plural reference" is. Later, we introduced the
intermediate object i, which we had the option to interpret either as
an intension or as a set.
SR: Perhaps this is where we used "i" differently.
For me there was no ~intermediacy~ involved in this symbol.
I simply labeled the intensional set with the sign "i". Then
I showed what the difference was between the extensional set y
which has the same members as the intensional set i. Apparently
we have had different intentions as to the purpose of the example.
One has to remember how the story began
in order to get the sense of the ending.
JA: Case 1. Let i be an intension. Now we have
even more ambiguity to y, as it still denotes
x_1, x_2, x_3, and can now be interpreted as
denoting the intension i.
SR: Woops! I don't think so ... at least in my diagram
that clearly is not the case :)
JA: Sounds confusing, but you can see it happening all the time
if you actually take the trouble to notice how people actually
use language. So we're stuck with it. Now, nothing prevents
us from tossing in the name "i" to name i in the usual way,
and so there it is.
SR: Yes that does sound confusing.
Happens all the time. See the metonymy example.
JA: 'x_j isa "Cat"' >>>--->>> syntax error.
SR: Agree. Where in the mentograph do you find such an arrow?
JA: Where you say "x_1 isa y".
SR: {x_j isa "Cat"} ~=/=~ {x_j isa Cat}
y =/= Cat. y = "Cat".
SR: Well If I had said, "Cats are just a figment of your imagination",
you would have held me crazy and have pointed at the tabby on your
lap screaming "Foul". Cats like the node labeled y in our discussion
and in my mentograph resides *exclusively* in the computer's memory
(also in a human's memory) as a concept ... this concept can not be
found in the natural world where your Tabby lives out it's life of
comfort. Now, please don't take my saying this here as indicating
that I thought you didn't know it ... in fact I'm sure you have
pointed out such distinctions frequently ... and your epistles
of such have helped me clarify this distinction in my mind.
I have just quoted this understanding here so that we might
know explicitidly of what we mutually speak. Point being
that this concept ~cats~ must needs be put exclusively
in the Interpertant column ... you assertion that S=I=M
notwithstanding.
JA: In the pragmatic conception of a "concept", a concept is just a symbol,
a mental symbol, I think, but there may be "quasi-concepts", too, that
do not have be pinned down in minds. Not sure, though. And so, yes,
concepts, as signs, can be cast in the role of interpretant signs,
just as they can be cast in the role of signs simpliciter, and,
since we are talking and thinking about them, they are clearly
also castable as objects of other signs. So, for my part,
you could script ~cats~ as "cats".
SR: Yep, if I voiced it out loud ... if I get your drift.
Even if you were only thinking to yourself, the thought would still be a sign.
SR: To me an arrow (an arc, an ordered pair) is a mathematical object that
represents abstractly (yet visually) what any sign (in any role) actually
does. As such, then the arrow would always be drawn from itself existing
in some context (blunt end) to that object to which it refers (sharp end).
But then Peirce tells us that we need some mind to interpret that mark as
meaningful, hence a sign (our beloved arrow) must needs an Interpertant.
An arrow without a mind to interpret it, is just a mark. Once we understand
this (as I had though I did), then we can use that same mathematical arrow
to analyze further the very process of signing in relationship to mind.
I tried to do that in this mentograph:
SR: http://robustai.net/mentography/semiosis2.jpg
Minds are just one example of how sign relations come to life.
But the formal structure of sign relations is something that
we can appreciate whether it is carved in carbon, or marble,
or silicon, or even just sketched on paper in pen and ink.
But you are trying to capture the forms of irreducibly
3-adic relations in the materials of 2-adic relations
that just cannot take the requisite impressions or
convey the articulations of their anatomy.
Jon Awbrey
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