well, this discussion on lattice of theories seems to be missing a lot.
Perhaps we would see why it became part of the ONTAC discussion only if we
know about things happening behind the scenes. Micro-theories was something
that came up with Doug system, can all micro-theories by usefully mapped to
a single lattice? But somehow I feel that there is no fire behind this
smoke. (01)
John, the comparison to the integers seems very weak. As a historical fact,
the integers placed a key role in the development of modern civilizations.
(It is not clear that counting was universally recognized - not by Toltec
(indigenous Mexican) or by some indigenous peoples in Australia.) (02)
Lev Goldfarb develops a wonderful new approach on non-numeric models of
ontological realities - particularily relational models that do not borrow
heavily from the notion of quantification. (03)
He asks: "Is there a different mathematics, a mathematics of generatively
structured entities, that would explain the biological, or structural,
"measurement" processes?" (04)
http://www.cs.unb.ca/profs/goldfarb/ (05)
Ring theory is a Platonic form, why not suggest that we standardize around
ontological theories that form rings? Or perhaps we should talk about fiber
bundles of inferences. These are Platonic also. (06)
You said: (07)
"The reason why a lattice is better than the
integers is that the integers are linearly ordered,
but a lattice has a partial order, which allows more
options in the way one theory is related to any other." (08)
<end quote> (09)
But in both cases, the ordering relationship is a single formally defined
relationship. This is contrasted with the "classes" of relationships
between natural occuring concepts when experienced and communicated within
human communities. (010)
oh well, I give up on this discussion regarding a lattice of theories - it
just does not make sense and no one - John in particular - gives a reason
for talking about it. The hand waving just become a habit after a while. (011)
I am not sure what I want to suggest. The government goes its merry way
listening to high priests like Hendler and Berners-Lee (and John) and yet
the real work is done elsewhere. If it where not for peer review, the
community might actually get on to talking about real work. (012)
For those who might like to have serious discussions, please send me a
separate email. (013)
psp@xxxxxxxxxxxxxxxxxx (014)
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