SUO: Re: Sign Relations & Communication
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
JA = Jon Awbrey
SR = Seth Russell
Seth,
We are in danger of forgetting the purpose of these reductive examples,
which is to illustrate something bigger than themselves, so let us try
to remember what we're about and not get lost in the minor details.
I said at the beginning that we would not be able to get very far by using
just a single level of quote marks, and "dumb quotes" at that. The array
of operations that are usually indicated through the devices of quotation
marks is a very important family of functions, but quotation marks proper
are not the only way to carry them out, and very often far from the best
way to achieve the same effects.
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.
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
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
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.
Then we considered giving X and Y a sign relational interpretation,
letting the object domain O = X and the syntactic domain S = I = Y,
and we formed various sign relations L, L', L", L'" c OxSxI = XxYxY.
Nota Bene. When S = I, as is usually the case in this sort of study,
I will generally refer to this single set as the "syntactic domain".
The other details are not so important to worry about.
JA: In so far as any agent is acting as an interpreter of
a formal language M c A*, according to the dictates of
the sign relation L c OxSxI, where S = I = M, then signs
of M might be regarded as being "in the memory" of that
interpretive agent.
JA: But what that does really mean?
JA: We have a habit of saying that signs are "in" the memory
and that the memory is "in" the agent, but really it would
make more sense to say that the agent is "in" the memory and
that the memory is "in" a certain sign. Let me explain this.
SR: Oh I see ... you want to open up the whole 'Is the mind in the body or
the body in the mind?' Pandora's box here. Well I don't think we need
to open it. I like to think very simply and concretely ... i'm not as
comfortable with thinking in ideal abstract spaces as you are.
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: 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?
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: Ok, if that be it, then fine. Perhaps, then, could we peruse your way
of thinking in another train? (... and I would, ok ok ?) But, Jon, in
this train, whether the Interpretant column can be exactly represented
in a computer's database memory *is* of paramount importance. What is
important to this train is not that an object, x, is somehow a member
of each of the three ideal sets {O, S, I} and hence that the sets can
be somehow dealt with equivalently, but rather what relationships
*can be* reasonably depicted in the three different domains of
this ~new~ sign relationship which I am proposing. The ~newness~
coming exclusively from the idea that we are considering the
Interpertant column to be (and only be) that which we can
be effectively put in a computer's database and control
its behavior.
JA: I have read this paragraph 3 times and cannot tell
if I have yet answered the questions in it or not.
Please let me know.
SR: No, it appears to me that you are still avoiding answering my
specific question directly. My question goes to our intent and
purpose here in this dialogue. It is of the form: "Do you want
to go to New York with me or not?"
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
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}.
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?
"cat_1" denotes cat_1, etc. "x_1" denotes x_1, etc.
JA: 3. 'i intension of y'? and 'y extension of i'?
Should be that i is a common intension of x_1, x_2, x_3,
also that x_1, x_2, x_3 are in the extension of "i", y,
where the later are taken as terms or as concepts.
SR: I am a bit confused here as to why you think those
restraints are not explicit in my diagram.
SR: 'Should be that i is a common intension of x_1, x_2, x_3'
is expressed by the arrows labeled with 'hasProperty'
which is common to all of those.
The "hasProperty" arcs from x_1, x_2, x_3 to i look okay to me.
SR: Also 'that x_1, x_2, x_3 are in the extension of
[... intentional snip of "i"...] y' is similarly
represented in the mentograph by the arrows
labeled with 'isa'.
The "isa" arcs are wrong because they extend
from the objects x_1, x_2, x_3 to the sign y.
So these arcs are more like "is denoted by".
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.
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.
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. 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. 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.
JA: 4. 'x_j isa y'? Will need some concreteness:
x_j = cat_j, an object.
SR: Me thinks the equality copula here is quite out of place.
That was just a substitution, for the sake of concreteness in the game.
JA: y = "Cat", a string of char.
SR: True, look for signs (strings) in the domain appropriately labeled 'Signs'.
JA: 'x_j isa "Cat"' >>>--->>> syntax error.
SR: Agree. Where in the mentograph do you find such an arrow?
Where you say "x_1 isa y".
Var x is of type object.
Var y is of type sign.
JA: I think this is right -- could be tiredness, though.
JA: I will have to "jog my memory" about that augmented sign relation
and what all we were talking about on the "Factorization" thread:
SR: Please don't bother ... I kinda interloped on the Factorization thread ...
such a connection will probably not have much to do with this dialogue.
SR: In other words, ~cats~ are just a figment of the computer's
imagination, we'll never find ~cats~ in reality. So if we
want to talk about ~cats~, we had better look into the
computer's imagination.
JA: Don't know what "~cats~" means.
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.
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".
Jon Awbrey
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤