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Re: [ontolog-forum] Language and logic

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Sun, 13 Dec 2009 09:35:37 -0500
Message-id: <4B24FBB9.1030303@xxxxxxxxxxx>
Pat and Ferenc,    (01)

PC> Concerning the possibility of a finite number of conceptual
 > primitives...    (02)

That depends on what you mean by "primitive" and what you plan
to do with whatever "primitives" you select.    (03)

I acknowledge the possibility of having a vocabulary of *vague*
primitives, such as Anna Wierzbicka's or Longman's, which can be
adapted to give *vague* definitions along the lines of typical
dictionaries designed for human readers.    (04)

And I also believe that the cross-cultural studies by linguists
such as Wierzbicka, Talmy, and others provide valuable guidelines
for the selection of terms to be formalized in an ontology.  In
fact, I not only believe that, I have strongly advocated that
in publications since my 1984 book.    (05)

But when you use a vague term or definition as a guideline for
a formal definition, you are creating a totally new formal term
that is somewhere in the same region or ballpark as the vague
term.  That is a useful methodology for many purposes, and I
strongly endorse it.    (06)

But please note the following point by Peirce, which I often quote:    (07)

CSP> It is easy to speak with precision upon a general theme.  Only,
 > one must commonly surrender all ambition to be certain.  It is
 > equally easy to be certain.  One has only to be sufficiently vague.
 > It is not so difficult to be pretty precise and fairly certain at
 > once about a very narrow subject.  (CP 4.237, 1902)    (08)

In summary, you can use vague terms to cover a broad field -- as
Wierzbicka and Longman's did.  But if you want a formal ontology
that is sufficiently precise for computer interoperability, you
can only cover a "very narrow subject" or microtheory.  And for
each microtheory, the formal axioms that make those vague terms
sufficiently precise for one application will be different from
and *incompatible* with the definitions for other microtheories
that use the same terms.    (09)

JFS>> The world is a continuum (at least as far as human perception is
 >> concerned) and languages consist of discrete worlds.  That implies
 >> that the number of potential percepts and concepts is immensely
 >> greater than any human language can designate.    (010)

PC> The conclusion does not follow from the premise:  if the world is
 > continuous in quantitative terms, then a small number of arithmetic
 > primitives will still suffice to allow division of some dimension
 > into an infinite number of different regions, each of which can be
 > labeled by some word in a human language, and which may overlap,
 > giving ambiguity to the linguistic terms.    (011)

I agree.  That's fine for developing a collection of vague terms.
But note the qualifications above.    (012)

PC> It should be clear that an infinite number of objects or terms
 > can be represented by combinations of a small finite number of
 > primitive concepts (objects, relations, functions).    (013)

That is also true.  Mathematicians do that all the time.  But they
don't start with vague terms.  They start with very narrow, but
precise terms and build up a collection of equally precise compound
terms that cover a highly specialized microtheory.    (014)

PC> Whether or not human language can be mapped to a set of fixed
 > concepts based on such a finite set of primitives is still an
 > empirical question.  The continuity of reality does not preclude
 > finding primitives that can specify the boundary points for useful
 > concepts lexicalized in human languages.    (015)

That is a very useful procedure, which humans use all the time.
They start with the vague terms of their natural language, and
they carry on a dialog to make them sufficiently precise for
whatever topic (or language game) they are engaged in.    (016)

But note that for each dialog that makes those terms precise,
the participants are focusing on a very narrow topic.  That is
a useful method for designing microtheories (or language games).
The totality of all those microtheories (in some arrangement,
such as a lattice) will give you many useful special cases.
But they won't give you a single fixed, universal ontology
of everything.    (017)

PC> The fact that terms in human languages can change their meaning
 > does not mean that the terms in an ontology must change meaning,
 > because the terms in the ontology can (at least in theory) be
 > grounded in procedures that assure their unchanging meaning.    (018)

I certainly agree.  But when you fix the meanings, you are stuck
with a very specialized microtheory.  If you want universality,
you need to adopt the procedure that people use:  take your vague
terms as the basis for a *methodology* for developing microtheories.    (019)

PC> To be easily usable, a good mapping of any foundation ontology
 > to human language will probably be necessary.  The **mapping** of
 > the ontology to the human language will need to be updated frequently.    (020)

You have it backwards.  The universal primitives are extracted from
human languages, and they are already adapted to human languages.
The cause of frequent changes is *not* in the human languages, but
in the technology.  Technology changes at a much faster rate than
any human language.  That is why human languages become ambiguous.    (021)

The word 'car' for example was used in the 19th century for a simple
horse-drawn carriage.  But today, it applies to a computerized metal
box.  Just look at the detailed maintenance manuals for every model
of every car produced in the last century.  There are many common
terms from one manual to the next, but the details of each object
to which those terms are applied are very, very different.    (022)

If you want to look at computer technology, take the series of
manuals for MS DOS in 1981 up to MS Windows System 7 today.
They use many of the same words, but with very different *and*
incompatible definitions.  Microsoft tried to be upward compatible,
but every release and bug fix forced many programs to be revised
or completely rewritten.    (023)

FK> To see what standard contemporary linguists have to say on the
 > subject check out semantics as seen by David Crystal. But do not
 > read anything from Steve Pinker who is deemed to be the number
 > one linguist today (he was a psychologist originally) unless you
 > want to have a good laugh. Especially I refer to his The stuff
 > of thought, which is a long story made up in metaphors without
 > ONE definition in the whole "product" that makes sense.    (024)

I agree that Pinker is not a reliable guide to the foundational
issues of language and cognition.  I often cite linguistic research,
but I have never found anything to cite in any of Pinker's writings.    (025)

John    (026)

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