SUO: Re: Re: Sign Relations & Communication
From: "Jon Awbrey" <jawbrey@oakland.edu>
> 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.
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.
> 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.
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.
> 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.
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 ?
> 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.
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.
> 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.
Yes, that matches my diagram exactly. 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. 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.
> 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.
> 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.
> 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.
> 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.
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.
>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.
Woops! I don't think so ... at least in my diagram that clearly is not the
case :)
>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.
Yes that does sound confusing.
> 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".
{x_ j isa "Cat"} ~=/=~ {x_j isa 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.
>
> 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".
Yep, if I voiced it out loud ... if I get your drift.
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:
http://robustai.net/mentography/semiosis2.jpg
Seth Russell