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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/msg00066.html#nid03 (03)
Correcting a mess of typos in my pre-caffeinated message from this morning: (04)
JA: The ways things go in the real world, people begin with a compelling
interest
in some phenomenon, and they keep their eyes on prizing out some explanation
of that, at least, until something else distracts them or they give up the
quest for understanding that particular thing. (05)
JA: There are numerous fields of interest where people use concepts and models
of things called "attitudes", from market research to operations research
to philosophy to various shades of psychology. (06)
JA: When the research in a particular field has been going on long enough,
and the field has passed the gauntlet of many grueling animadversions
about the "construct validities" and the "operational definitions" of
this, that, and the other thing, people will naturally turn to formal
and mathematical models of the theoretical constructs of interest. (07)
JA: By this time, they will have been talking about sets and functions
and relations (oh my), or categories and morphisms and functors (OMG),
whether they are fully conscious of it or not. (08)
JA: But none of this very modern model of mediate representation is intended
to pose a terminal distraction from the initial phenomenon of interest. (09)
KBL: Absolutely! (010)
KBL: Formal models enable engineering to take place. (011)
I still owe this Forum an explanation of what I mean by "formal",
so I've been using the phrase "formal and mathematical" by way of
averting a host of conceivable but unintended interpretations --
does that work? does it ever? -- at any rate, I think it's clear,
especially from a "Community Of Reflective Practitioners (CORPs)
vantage point, that phenomena still tend to sprout their first
formalizations in the form of mathematical models described in
the mathematical vernacular, and not in the sorts of FOL talk
of which one community of knowledge engineers is so fond. (012)
Not that it's a bad idea to translate the mathematical lingua franca
into first order logical latin later on, and in which translation one
will find that many of the mathematical chunks and modules already have
standard translations that can be copied out of phrase books whole hog.
I'm just saying the order of things that I observe in typical practice.
(You'll find John and Pat arguing different sides of this egg-hen question
till the cows come home, so it's not for me to say any more than I have.) (013)
Have to break here till later ... (014)
Jon Awbrey (015)
KBL: 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. 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. 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! (016)
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. (017)
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. (018)
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. (019)
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. (020)
KBL: Kathy (021)
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