5/22/2004 9:03
AM
On the generality of the particular
Key questions on Common Upper
Ontology -> .
(new
beads are edited for a few days until the grammar is correct)
Liane,
I am forwarding your note to a wider group and hope that others will find time to help in this discussion. I believe that the concepts should be made available in a K-12 curriculum in the knowledge sciences.. (as the BCNGroup is proposing in the National Project).
You mentioned:
It has been proven that the mathematical description of intrinsically contextual situations--that is, wherein our lack of knowledge lies not with respect to the state of the entity itself but with respect to how it interacts with a context---introduces a non-Kolmogorovian probability distribution, and a classical formalism such as selection theory cannot be used. I wont go into the details of the formalism we have been using (its in our papers) but that is the gist of the rationale for NOT using selection theory.
As someone with mathematics training (PhD) I am very interested in how this mathematical description was derived. It seems right, in the context of explaining the need to have ontology defined locally. Ontological relativity can then be talked about as a principle that must be taken into account in these standards discussion over common controlled vocabularies in the Semantic Web.
For a discussion on local and upper ontologies see: { bead }
Of course, the Kolmogorovian statement on conditional probabilities makes an assumption that two things have no possibility of causing something new. Another way of saying this is that the Kolmogorovian space is Laplacian in nature.
A Goggle search will show that quantum mechanics finds speculations about non-Kolmogorovian spaces useful, but I have not worked into the details. I would love to have the time to sort this out. My intuition is that a lot of the formalism is still not allowing an openness to change axioms and inference rules as part of a shift from a specific ontology to another ontology.
The Kolmogorovian statement on conditional probabilities does not go to the issue of origin. Where do new features come from in the first place? The formalism remains closed, and the assumption remains that the "universe" is likewise closed. In parallel to special relativity, ontological relativity allows for a conversion, of things, from a holonomic set of constraints (energy) to a localized (mass) in the simply equation E = mc^2. But, of course relativity depends strongly on the distribution of things locally and does not lead to a unified theory. The dependency on location, and point of view, is also why one should not expect to find a standard ontology for some enterprise, such as a large corporation.
Clearly Kolmogorovian conditional probabilities is not what one wants if one is looking at the nature of thought.
You mentioned also:
Creative thought is more a
matter of honing in on a vague idea through redescribing successive iterations
of it from different real or imagined perspectives; in other words, of
manifesting some portion or aspect of what the mind is capable of manifesting,
through its interaction with a particular situation or context.
And in this search amongst several possible contextual settings, one sees the immediacy of a selection process like what Edelman talks about in his book Neural Darwinism.
So selection can become Larmarian if there is an anticipatory mechanism that guides this iterative review of contextual possibilities. One can look ahead and make changes in the “meme” so that the meme expresses differently that it would otherwise, thus introducing a new feature because of the anticipation. Anticipation is associated with the ecological affordances as discussed in ecological psychology. A personal discussion with Robert Shaw (Univ of Conn) in 1998 led us to understand that that anticipation is often “over” a fiber bundle of potential paths to the future, and these fibers are reflecting what the environment allows. There is an underconstrainted casual framework that is forced into a specific outcome by the conservational laws in real time. (Anyway, this is how the discussion went.)
How does Edelman address indeterminacy? I think that ultimately that he does not. But his notion of response degeneracy is similar to your "honing in on a vague idea".
My own work on formative ontology very much needs additional language for both a more complex notion of selectionism as well as some additional language on the origins of novelty.
I recently reedited the following as an introduction to anticipatory technology.
http://www.bcngroup.org/area3/pprueitt/kmbook/Chapter4.htm
Paul Prueitt
From: fmb-majordomo@mmu.ac.uk [mailto:fmb-majordomo@mmu.ac.uk]
On Behalf Of Liane Gabora
Natural selection is but one form of evolution, construed
as it was before Darwin in its broadest sense as the change of state of an
entity through ongoing interaction with an external world or context. The
mathematics of selection theory requires multiple, distinct, simultaneously-actualized
states. In cognition, however, each thought or cognitive state changes the
selection pressure against which the next is evaluated; they are not
simultaneously selected amongst. Creative thought is more a matter of honing in
on a vague idea through redescribing successive iterations of it from different
real or imagined perspectives; in other words, of manifesting some portion or
aspect of what the mind is capable of manifesting, through its interaction with
a particular situation or context. It has been proven that the
mathematical description of intrinsically contextual situations--that is,
wherein our lack of knowledge lies not with respect to the state of the entity
itself but with respect to how it interacts with a context---introduces a
non-Kolmogorovian probability distribution, and a classical formalism such as
selection theory cannot be used. I wont go into the details of the formalism we
have been using (its in our papers) but that is the gist of the rationale for
NOT using selection theory.
Liane