John, (01)
It seems we agree. You only argue with the novelty of the idea
("birth".) That's good. I also agree we can trace this kind of
thinking far back. Indeed it can be seen as central to Taoism as Rick
points out. (02)
So, given that we are agree, the interesting question becomes how do
we apply these ideas practically. (03)
For a long time you advocated having some kind of network of theories,
simply itemizing theories and selecting between them according to
need/purpose, without necessarily going into where these theories come
from or attempting to model them more fundamentally. (04)
In contrast your "pursuing" presentation
(http://www.jfsowa.com/talks/pursuing.pdf) mentioned what you call
"continuous" theories which should be seen as underlying discrete
categories. (05)
Is that a change? Are you moving from a "network of theories" model to
an underlying "continuous" model? (06)
I don't recall if you actually called these "continuous" theories
geometric. Geometric theories have been quite successful at modeling
this kind of variability, notably in physics, but more recently also
in mathematics. For instance General Relativity might be seen as a way
of dealing with "uncertainty/indefiniteness" in the measurement of
(concepts of) space and time (and separately gauge theories as ways of
dealing with "uncertainty/indefiniteness" in the measurement of
position, momentum etc. in quantum mechanics.) So there are some very
nice parallels there at the philosophical core of all these subjects. (07)
Once the commonality is identified it opens up all kinds of
interesting ways to look at the problem. Personally I find the
"many-body system" model very powerful. I referenced once before here
Giuseppe Vitiello's lecture on a basis for concepts in the dynamics of
many-body systems. Perhaps it bears repeating: (08)
http://www.archive.org/details/Redwood_Center_2007_01_23_Giuseppe_Vitiello (09)
For good measure I hope you don't mind if I throw in the references I
sent you in a private mail some months back: (010)
<<<
I recently found some more "chaos in cognition" refs. which brought
you to mind. They were sitting around, waiting for some kind of
critical mass before I posted them somewhere. Perhaps now is as good a
time as any. (011)
Here's a taster... (012)
Firstly, did you know one Ben Goerztel wrote a book entitled "Chaotic
Logic - Language, Thought and Reality From the Perspective of Complex
Systems Science" back in 1994?
(http://www.chaoticlanguage.com/node/35) (013)
Then, even more interesting, poking around Ben Goertzel's associates,
something called "Vector Symbolic Architecture" for cognitive
representation. E.g. Simon Levy presents VSA's in the context of "The
Need for New Representational Principles"
(http://www.chaoticlanguage.com/node/37.) (014)
Then the idea of holographic representation comes up: (015)
Jones, M. N., & Mewhort,D. J. K. (2007). Representing word meaning and
order information in a composite holographic lexicon. Psychological
Review, 114, 1-37. (016)
http://psyc.queensu.ca/~hiplab/LAB_PUBS/Jones_Mewhort_PR.pdf (017)
Remember how holograms came up also in our Ontolog discussion. It's a
wonderfully close parallel. It turns out a guy named Tony Plate has a
formalism he calls HRR, or Holographic Reduced Representation. That
was what inspired VSA's (due to Ross Gayler.) (018)
VSA's are especially good. They seem to present (compositional)
representation as a vector product in much the way I've been
advocating. (019)
Broadly speaking all these people are in the perception/psychology
community. Quite a different world once again from both the
linguistics and ontology communities. (020)
>From my point of view all we need to do is mix the idea of a vector
product giving a compositional character (VSA's), with
example/usage-based ideas already current in linguistics. Perhaps the
initiative will come from the perception/psychology community.
<<< (021)
-Rob (022)
On Wed, Sep 17, 2008 at 4:28 AM, John F. Sowa <sowa@xxxxxxxxxxx> wrote:
> Rick and Rob,
>
> RF>> I don't think this indicates an "End of Theory" so much as
> >> "the birth of the theory that there can be lots more theories
> >> buried in a set of data than we've ever imagined we needed to
> >> look for before."
>
> My only quarrel with that statement is over the word 'birth'.
> Some logicians I admire (among them, Peirce, Whitehead, and the
> later Wittgenstein) have said or implied something similar. In
> fact they would agree that the number of possible theories and
> even theories that are reasonably accurate for useful applications
> is either infinite or far beyond our practical ability to count.
>
> At the end of this note are some of my favorite quotations from
> Whitehead, Peirce, and Robert Frost. If you do a global change
> of Frost's word 'poem' to 'theory', you would get a statement
> that Peirce, Whitehead, and Wittgenstein would have agreed with.
>
> Actually, they would have agreed with Robert Frost's original
> with the word 'poetry' in it. That attitude should be contrasted
> with Rudolf Carnap, whose favorite phrase for denouncing some
> idea was "That's poetry!"
>
> John
> ___________________________________________________________________
>
> Alfred North Whitehead:
>
> Human knowledge is a process of approximation. In the focus of
> experience, there is comparative clarity. But the discrimination
> of this clarity leads into the penumbral background. There are
> always questions left over. The problem is to discriminate exactly
> what we know vaguely.
>
> Charles Sanders Peirce:
>
> It is easy to speak with precision upon a general theme. Only,
> one must commonly surrender all ambition to be certain. It is
> equally easy to be certain. One has only to be sufficiently vague.
> It is not so difficult to be pretty precise and fairly certain at
> once about a very narrow subject.
>
> Robert Frost:
>
> I've often said that every poem solves something for me in life.
> I go so far as to say that every poem is a momentary stay against
> the confusion of the world.... We rise out of disorder into order.
> And the poems I make are little bits of order.
>
> Alfred North Whitehead:
>
> We must be systematic, but we should keep our systems open. (023)
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