Re: SUO: Re: Semiotics Formalization
Jon,
You bring up some interesting issues. Someone who is more familiar than
I with Shannon's information theory may be able to help. However, I think
we can address the issues of Information and Signs without delving into how
to represent uncertainty in information and signs. If you agree, maybe you
could come up with an English definition for Sign to augment the few terms
I proposed earlier?
Adam
At 05:43 PM 9/14/2000 -0400, Jon Awbrey wrote:
>Adam Pease (in reply to an off-list messaage) wrote:
> >
> > Jon,
> >
> > I appreciate your comments but I'm not quite sure how they
> > add to the ontology. Are you proposing a Sign class which
> > is a subclass of Information and subclass of PhysicialThing?
> >
> > Adam
> >
><...>
>
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>
>Adam,
>
>I do not know how others understand the word "information",
>but for me it has its meaning in a particular kind of context.
>
>In the setting where this notion of information makes sense to me,
>we have, as a part of the overall background set-up, a measure of
>a quantity called "entropy" or "uncertainty". This is a measure on
>distributions ("frequency distributions" or "probability densities").
>
>The distribution F : X -> R is a function from a sample space X
>to the real numbers R, such that the real value F(x) € R can be
>interpreted as the probability that x will happen. (More carefully,
>this interpretation only works for discrete frequency distributions,
>but that is more or less the general idea.) (Also, it is traditional
>to use a capital omega for the sample space, for "outcomes" or perhaps
>for "occurrences", I think, but here I will have to sign it with an "X".)
>
>The entropy or uncertainty measure M is thus a function of the
>type M : (X -> R) -> R, and it satisfies some additional axioms
>that make it a decent formalization of our intuitive notions of
>doubt or uncertainty in the situations that are described by the
>distributions of type (X -> R).
>
>In this setting, if we can say what our measure of uncertainty
>would be both before and after receiving a particular sign, say,
>by way of making an observation or by way of some other courier,
>then we can define a quantity called the "information capacity"
>of the set of signs at issue. The information capacity is the
>"average uncertainty reduction on receiving each sign" (AURORES).
>Thus comes the dawn of information theory.
>
>The way I understand it, sign-tokens are physical things --
>they are actually another set of "outcomes" that "occur"
>in the real world, and so they have to have some sort of
>physical basis, but sign-types are classes of sign-tokens,
>what statistical folks called "events", that is, subsets
>of some sample space, and so they have an abstract quality
>to them. We "typically" intend the token as a representative
>of its class, and so there is almost always some ambiguity here.
>
>So when I hear people talking about a category of being that
>they call "information", I have to stop and say to myself:
>Okay, they mean a sign that is given in a setting where it
>posseses and potentially conveys a quantity of information.
>
>Anyway, this is how I understand these things. As I read over what
>I just wrote, however, I notice that it looks more like a personal
>attempt to come up with a rational -- and risky -- reconstruction
>of what I rememeber of classical information theory, but within the
>kind of sign-theoretic setting that I get from Peirce, and I now see
>that many of the details are looking kind of fuzzy.
>
>So, thanks for the chance to at least start on the work of clarification,
>and I will shift this back to on-list communication so as not to protect
>it from the criticism of others who might be able to help out here.
>
>Regards,
>
>Jon
>
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-----------------
Adam Pease
Teknowledge
(650) 424-0500 x571