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Re: [ontolog-forum] Editor COE view of a new list of categories

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Mon, 16 Jul 2007 17:27:36 -0400
Message-id: <469BE2C8.9050006@xxxxxxxxxxx>
Pat,    (01)

Some responses:    (02)

PH> Nothing useful is served by throwing around vaguely insulting remarks...    (03)

I apologize.  There are many very useful subsets of FOL, and I agree
that DLs (and even smaller subsets, such as Aristotle's syllogisms)
have abundantly proved their value.    (04)

JFS>> But I believe that making an explicit distinction between the
 >> model and reality is important for any application of formal
 >> languages...    (05)

PH> And for the record, I believe that this is a basic mistake.
 > The 'model' here (ie in Tarski's sense) can *be* a part of reality.    (06)

I agree, but the word I would emphasize is *part*.  There is an
open-ended number of selections and subdivisions that can be made.
The choice of the domain D and relations R is always done for some
purpose, and what is ignored may be as significant or even more
significant than what is selected.    (07)

PH> Tarski himself seems to have taken his view by his choice
 > of example:  "Snow is white" is true when snow, in fact, is white.
 > No "model" there: he is talking about (real) snow and (really being)
 > white.    (08)

Many people have pointed out that his choice of example was
unfortunate, since that sentence raises two thorny issues that
Tarski did not intend to represent in his introductory paper:
snow as a continuous substance, and the use of a singular noun
for making a generic statement about all snow.    (09)

JFS>> The mapping of D and R to reality is often unstated, and
 >> for any important application, it's usually far from obvious.    (010)

PH> I disagree. It's often blindingly obvious...    (011)

We'd need a corpus of data to settle the question about which
kinds occur usually or often.  For starters, Tarski's actual
example about snow is definitely not obvious.    (012)

JFS>> I agree that formal model theorists tend to talk that way, but
 >> that is not how scientists work.  The model comes first, and
 >> the axioms are derived from the model.    (013)

PH> First, I wonder how you can possibly know this.    (014)

 From reading what scientists actually report about how they do science.    (015)

PH> Isn't one way that scientists work the simple noting of
 > observational facts in lab journals? Aren't such notations sentences.
 > and don't they describe reality?    (016)

They certainly do.  But note that observational reports require
*only* the operators of conjunction and the existential quantifier.
(Any other operators that may occur in such reports must always
be suitably restricted -- e.g., "Every sample tested was..." --
and they can always be replaced by a list of ex-con statements.)    (017)

Those statements can be, as you correctly noted, directly mapped
to some part of reality that may be regarded as the model.    (018)

 > But more seriously, HOW does one 'derive' axioms from a model?    (019)

By induction (introducing universal quantifiers and implications),
abduction (guessing, which may introduce any logical operators
that seem "reasonable"), and further testing of any predictions
derivable by deduction.    (020)

This procedure provides a way to guarantee that the axioms are
consistent:  just check that every hypothesis derived by induction
or abduction is consistent with the observational reports (i.e.,
those that describe a suitable model).    (021)

John    (022)

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