SUO: Re: Re: Sign Relations & Communication
From: "Jon Awbrey" <jawbrey@oakland.edu>
>
> ¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
>
> JA = Jon Awbrey
> SR = Seth Russell
>
> 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.
Ok, I'm sorry if I may have deviated from acceptable nomenclature. But can
we not do this? There is, of course, just the one ideal set, yet there are
still two ways to define it. Is it too much to ask that we just imagine two
different sets?: the one set defined by criteria (by some program if_i )
and called by the sign "i", and the other set defined by pointing out
individual members and called by the sign "y". Then, of course, we can say
{i = y} in some ideal world. But it is, after all, the real world where
things go bump in the night, and the maze of cause and effect that
implements our program called "if_i" might fail of some particulars ... and
so in this real world, in this natural world in which I think I live and in
which I have faith that you also live and in which we find our computing
device, we might not be all that surprised if we actually do get a report
back that {i =/= y} .... would you not agree? Is this level of detail not
mandated by the exemplar at hand?
> 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.
What do you mean by 'Utility is a normative question' ?
> JA: 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.
Strange .... The systems of which I speak are in the real world, *and also
in* our minds, and perhaps *even in* some (abstract/normative?) ideal
world. But maybe we are operating on quite different ontologies and hence
our utter confusion.
> 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.
I don't get that a database is an abstraction. It is quite as tangible to
my way of thinking as any cat. And a computer, that machine which operates
on said databases, is just as tangible as Tabatha who is now munching of her
chow. I can find these things in time and space. But a circle .... that
you will never find ....nor will you find the number 3.
Regarding ...
> SR: [1] http://robustai.net/mentography/intensionExtension.gif
>
> 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?
You have run across my minor contrivance here. I put the i in the objects
because something did exist there for my program if_i to key upon.
> 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.
Why the need to guess, I labeled the Venn diagram circle with the word
"Interpertant".
> 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?
Yes certainly because they **are** distinct objects. Perhaps you should
look at these mentographs are depicting things at a level of detail that
that you have always known and talked about, and yet were not accustomed to
tease apart in your notations. The concept, the image of some particular
cat in your mind is certainly not the cat itself, nor is the word with which
you call such an object to your mind. Pierce's sign triad [1] helped us
tease these apart. The menograph clearly shows this, and is just an
expansion of Pierce's triad. But I don't know of any serialization notation
that is easily capable of this level of detail, do you?
[1] http://users.bestweb.net/~sowa/peirce/yojo.gif
Thanks to Sowa.
> 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.
Well perhaps that is your way ... but I am easily confused, and so am not
comfortable using it. When the Interpertant arrows are viewed as signs we
have changed the point of view of the diagram and must needs draw a
different one.
> JA: The "isa" arcs are wrong because they extend
> from the objects x_1, x_2, x_3 to the sign y.
>
> SR: 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.
Well it feels like we are getting somewhere .... sorry for my lack of
legending .. I have been drawing these graph for decades and almost forget
the processes by which they had evolved. These mentographs are nothing but
labeled directed graphs. The only things which really exists in them are
arrows and those arrows could be translated directly to records in some
database. Each of these arrows have four (or more) attributes {context,
subject, property, object}. From the ordered pair {subject, object} we get
the arrow which is labeled with some other node in the graph. The
{context} is a recent addition; it names the Venn circle in which the real
arrows exist. As such you can see that the nodes themselves don't really
exist, they supervene on the arrows which have the same subject attribute,
likewise the Venn circles supervene on those arrows with the same context
attribute. The labels I write *inside* the boxes that look like they are
nodes in the diagram are simply labels for you, so that you will be able to
grock what a node is called should we want to talk about it. To talk about
a particular node you must specify its context as well as the name that
appears inside the box.
It is also hoped that these graphs are an extension of RDF graphs [2] which
are arguably becoming the accepted method for exchanging metadata on the
Semantic Web [3]; this is what motivates my current interest in them. The
SUO ontology as well as anything expressed in KIF can be translated
directly into this graphic notation and round tripped back with no loss of
information.
[2] http://www.w3.org/TR/REC-rdf-syntax/
[3] http://www.w3.org/2000/01/sw/
> 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.
But why is one quoted and the other not?
> SR: 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.
Well I originally thought this was a typo, but now I guess it's actually a
variation between our different notations. I had though that when you put a
character between quotes in some string grammar that it means that you are
not using the character to symbolize something but rather are talking about
the character itself. So that it makes perfect sense to me to write
something like {"i" isa sign} which says to me that the mark "i" will be
used as a sign. But then, were that true, to also say that {y isa sign}
would look like a category error. The copula (the property arc) in those
statements cannot be the same copula for in the former it ranges over marks
and in the latter it ranges over nodes.
> Think of it this way:
>
> Var type declaration y : string.
> Assignment statement y := "cat".
Fine, but then how would you write in that same program the case for "i" and
be consistent?
> SR: {x_j isa "Cat"} ~=/=~ {x_j isa Cat}
>
> y =/= Cat. y = "Cat".
Ok that matches your assignment statement above ,{y := "cat"}, but how can
you assign {"i" := Cat} ... literals do not function that way in computer
programs.
> 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.
I agree. But I could not script (as you said above) it to you (nor you to
me) without some physical voicing of the sign designated here by the ASCII
string "cats".
> 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.
Well, me thinks, that is a bit of a conjecture on your part. Were you to
take me there, kicking and screaming no doubt, you would need to do much
more than merely wave at something off the edge of the paper.
> 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.
2-adic relations scale up to n-adic relations quite nicely. I have shown
this in several mentographs:
http://robustai.net/mentography/conceptualDependency.gif
http://robustai.net/mentography/represents4.gif
http://robustai.net/mentography/arity.gif
http://robustai.net/mentography/ConceptualDependency2.gif
Seth Russell