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JA = Jon Awbrey
KBL = Kathryn Blackmond Laskey (02)
Re: Phenomena and Formalizations
http://ontolog.cim3.net/forum/ontolog-forum/2007-08/msg00090.html (03)
Continuing from where I left off ... (04)
KBL: Formal models enable engineering to take place. They allow
people to communicate precisely about a phenomenon in which
they have a compelling interest. They enable other people to
understand exactly what is being said about the phenomenon of
interest. (05)
Yes, formalizations can add exactness and precision to the developing
discussion of the phenomenal domain of interest. There is, of course,
nothing automatic about this -- it all depends on whether the formal
model is "apt", whether it captures just the right aspects of a domain
of interest. The history of science is littered with cases of sterile
formalizations -- formalization for the sake of formalization alone --
and not for the sake of the object phenomena. And "precision", precisely
speaking, is typically purchased in a trade-off for accuracy, completeness,
and concreteness. In other words, a formal model involves abstraction and
approximation. (06)
KBL: They enable automated reasoning engines to process descriptions
of the phenomenon of interest to derive logical consequences of
the descriptions that were not immediately obvious to those who
formulated the descriptions. (07)
Yes, this is the never-ending dream that many of us have been dreaming
for decades, but the actaul fact at present is that automated reasoning
as we know it seldom delivers any news that we did not work out the hard
way years before. Still, it doesn't hurt to dream -- when the sun is not
shining, anyway. (08)
Speaking of dreamland, I'm oftuit ... (09)
Jon Awbrey (010)
KBL: Sometimes this identifies weaknesses in the descriptions that can be
repaired to yield improved descriptions. Other times, the consequences
of the descriptions elicit great surprise and consternation, but when
checked against the world, they turn out to be correct! Historically,
this has been one of the most powerful features of the scienfific method.
One constructs a precise formal theory of a phenomenon. The formal theory
explains empirical observations that have been obtained, but also entails
some highly-counter-intuitive consequeces that -- amazingly -- turn out
upon investigation to be correct! (011)
KBL: There are people who care more about formal models per se than
they do about the phenomena being modeled. Such people tend to
become pure mathematicians or logicians. (012)
KBL: There are people who care about the phenomenon and dislike
mathematics and logic. Because they find mathematics difficult
and unpleasant, they tend to balk at the intellectual effort required
to apply math and logic to the phenomena in which they have an intrinsic
interest. However, when they encounter a truly gifted teacher who can
explain the relevance, they usually do come to understand why formal
models are necessary and important. (013)
KBL: There also are people who have an affinity both for the formal models
and for some particular phenomenon to which formal models can be
applied. Such people are the ones who make the breakthrough advances. (014)
KBL: None of this is intended to disparage in any way other modes of
inquiry and understanding, such as analogy, informal case studies,
experiential learning, and the like. Formal models are not the ONLY
way to understand a phenomenon. They do not replace other ways of
thinking about a phenomenon. Nevertheless, they can be extremely
useful. And they are essential for engineering and information
technology. (015)
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