Ken, (01)
I agree that the authors should have stated the following
point more clearly: (02)
> However, it is the thesis of this paper that none of this
> goes far enough. In addition, we must consider the dynamic
> evolution of the underlying formalism in which the knowledge
> is represented. (03)
What they meant is that any given formalism may be revised,
and when it is revised, it becomes a different formalism.
But that is what happened when dinosaurs evolved into birds:
no individual dinosaur became a bird, but some individuals
in the sequence were more bird-like than their ancestors. (04)
That is the same clarification that must be made about sets:
The members of a set S cannot change because any change to S
causes it to become a different set. But change can occur
by generating a sequence of sets, each of which differs from
its predecessor by a minor modification. (In fact, that's
why it's better to talk about *types* in ontology: the
definition of the type Dinosaur remains constant, even though
the number of dinosaurs may change or become zero.) (05)
> Did Newton's formalism's evolve or change when Einstein
> introduced relativity? ... (06)
No, of course not. That is why I prefer to talk about the lattice
of all possible theories. Instead of saying that revision causes
a theory to "change", I say that the process of revision involves
moving through the lattice from the old theory to the new theory. (07)
However, I have discovered that this terminology, although precise,
causes confusion because some people think I'm advocating that we
implement an infinite lattice. Instead, I only said we should
"think" about the theories as a lattice, but implement (or record)
only those theories that we actually need to work with. (08)
In any case, Bundy knows mathematics and logic very well, and he
would be the first to acknowledge that evolution of formalism does
not cause any particular formalism to change, but that the people
(or computers) who use the formalism may need to replace an old one
with a new one that differs in certain respects. (09)
The most important points are the recognition that (1) such revisions
are inevitable, and (2) they may involve modification of the formalism
as well as modification of the contents expressed in that formalism. (010)
John (011)
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