SUO: Re: Semiotics Formalization
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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