SUO: Re: Ontology, Epistemology, Semiotics
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Arun, Len,
The choice of a probability model is an abductive choice.
You cannot eliminate the riskiness of this choice by any
deductive or inductive means. Some people call this the
"reference class problem". I think I recall there being
a good discussion of it, perhaps under some other alias,
in Burks:
| Arthur W. Burks,
|'Chance, Cause, Reason: An Inquiry into the Nature of Scientific Evidence',
| University of Chicago Press, Chicago, IL, 1977.
It is analogous to the "system identification" problem, a good account for
AI applications being given by Arbib in the 2 'Metaphorical Brain' volumes.
You cannot avoid the circumstantial bias of looking under a priorly chosen
reference class (lamppost) and you will only identify the unknown system,
if at all, as falling in with those that are visible thereunder.
The problem of systematizing inquiry, which involves in part the
problem of "giving a rule to abduction", is a bit more like this:
Given a motley assortment of clues, gathered under a motley assortment of lampposts,
the clues entangling a mass of conflicting indictments with reguard to the identity
of the system that is susceptible to being rounded up among their respective gangs
of usual suspects, what lamppost should we look under next?
As long as we don't fall for the line and the sinker
of a risk-free method and a value-free science, then
all the rest of this stuff I think is just beautiful.
On a more timely topical note, we must not forget the possibility
of what might be called a "hypo-critical request for information".
More later, maybe, as I work through the note.
Jon Awbrey
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Arun Majumdar wrote:
>
> Hi,
>
> Okay - so after this email I have to get back to my day-job!
>
> Ronald A. Fisher put forth the idea that measurement principles are
> interactions with observable and that these themselves are determined
> by the locality principle (example, error of measurements are locally
> determined elements). It is also related to the idea (by Otto Rossler)
> of the "world as an interface" (Endophysics --- my correlation, not Fishers)
>
> REF (do not go here until readig the next bit of this email - it won't make sense!):
>
> http://www.mathbook.com/c/Chaos_Theory/Endophysics_The_World_As_an_Interface_9810227523.htm
>
> With Fisher info. you do NOT need a prior information as in Bayes theory.
> Instead, you can use the "bounds" priovided by the fisher infomation matrix
> to get the prior based on the errors in measures (i.e. a prior bayes probability
> usually is not qulaified by its relevance against error, so if I take a prior belief
> to be 10% but my error is 20%, then the error terms dominate the prior!).
>
> In the Bayesian frame we can get p(A|B) from p(B|A) and p(A) using Bayes relation but,
> this "A" and "B" are NOT functions. When they are functions (ie. for example, density
> or mass-evidence functions or intensity) then you will need to deal with "errors",
> measurables and observables to make the functions have a realistic meaning over
> data (example: the density and mass-evidence measures using of phone-call data
> in a terrorist search effort). Traditional Bayes would fail since you have no
> basis by which to get the prior. It is *unknowable* --- so here is where you
> use Fisher (and the Cramer-Rao inequality)!
>
> So you will need to develop some function of B,
> e(B) that provides you with a way to get to the
> prior (an estimator approach).
>
> So, e(B) is the thingy that is determined by locality
> (no globality as general thermodynamic laws, for example).
>
> Now, determining e(B) can be via a "conduit of observation" with certain
> "filters" (these filters could include beliefs etc.) and this could,
> imaginatively, be developed using mutable-interface based view of
> observation and measurement.
>
> Or, you could invent an e(B) somehow that you tink works!
>
> A great online work to see it in action (sans my personal input on the value
> of Endophysics) is: http://www.colorado.edu/isl/papers/info/paper.html
>
> It is *not* view-centric in the strict sense as I assume you to mean, but it
> is locale centric in terms of "mutual information" between the interacting
> parties using the matrix and the error to parameterize the bounds within
> which you can start to get to some interesting applications.
>
> You should find that a combination of E.T Jaynes work and this may be valuable in
> developing a more interesting picture of incomplete-information based processing.
>
> We are interested in Fisher information and many other variants that
> provide a higher-order way to get out of "beliefs-in-someones-head" or
> other "ad-hocery".
>
> Not easy.
>
> I hope this very quick and dirty note helps. I found the book great in parts,
> but really, really unreadable in others without significant secondary references
> (but, then again, I struggle constantly tryin to understand the mathematics as I am
> not a mathematician myself).
>
> I hope someone will pursue some of the ideas out there in the world more formally.
>
> And, I hope this helps. I am no expert and any corrections
> to my own thinking would be appreciated.
>
> Here is my interpretation of the relevance of this discussion to CGs:
>
> The value I see here is the Concepual Graphs are "graph" structures and
> that the functions on a graph (example, spectral graph theory) may have
> significant relevancy about the deeper meanings behinds patterns of graphs
> (CG's) of knowledge or knowing. CG's are images of dual spaces (the space
> in which you define the concepts, and, the space in which you define the
> relations). The mapping result from these two spaces is what a CG really
> is and the structures and type of mapping functions determines your views
> of reality.
>
> How these functions that map fro concepts and relations to a CG instance
> change between different observers that construct realities may be also
> called the "Thirdness" --- a mediating environment that constrains or
> shapes the way in which these mappings are actually locally done.
> IN this sense, we coul have local thirdness that is "secondly"
> related to a global "thirdness". A secondness of thirdness
> between the local and the global thirdness. These could
> be "contexts" in CG parlance.
>
> In this case, you could use Fisher Info. and related techniques to develop a
> federated model of the error perceptions about reality to get some "consensus"
> of the "ignorances" about some reality. In this sense, we could be using this
> to try to characterize the semantic concept of Thirdness using functions, not
> just logic (which are a special restricted form of functions (actually, functors)).
>
> Cheers,
>
> Arun
> VivoMind LLC.
>
> ----- Original Message -----
> From: "Bullard, Claude L (Len)" <clbullar@ingr.com>
> To: <cg@cs.uah.edu>; "John F. Sowa" <sowa@bestweb.net>
> Cc: "Jon Awbrey" <jawbrey@att.net>; "SUO"
> <standard-upper-ontology@ieee.org>; "Jay Halcomb" <jhalcomb8@attbi.com>
> Sent: Tuesday, September 09, 2003 9:07 AM
> Subject: CG: RE: Re: Re: Ontology, Epistemology, Semiotics
>
> > I may be simplistic here, but
> >
> > "The information principle is based upon a new theory of measurement, one
> > which incorporates the observer into the phenomenon that he/she observes.
> > The 'request' for data creates the law that, ultimately, gives rise to
> > the data. The observer creates his or her local reality."
> >
> > sounds a lot like a view-centric theory in which the actor interacts based
> > on the information queried, and this action changes the state of the queried
> > dataset. Not having the book at hand, is that the case?
> >
> > That doesn't seem to be new, so I must be missing
> > something of great importance in the author's work.
> >
> > len
> >
> > From: Arun Majumdar [mailto:arun@vivomind.com]
> >
> > Hi,
> >
> > You might want to look at Fisher Information theory (Fisher Entropy)
> > in which the observer is embedded withi nthe observed.
> >
> > You will find that this is not a metaphysical claim but a well developed
> > theory, with book publications in its support.
> >
> > http://books.cambridge.org/052163167X.htm
> >
> > Fisher information is, unfortunately, not well known.
> > Neither is Endophysics.
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