Subject:
Re: SUO: Re: Effective Logical Formalism -- Literature Notes
From:
"John F. Sowa" <sowa@bestweb.net>
Date:
Fri, 17 Oct 2003 12:07:50 -0400
To:
Jon Awbrey <jawbrey@att.net>
CC:
Murray Altheim <m.altheim@open.ac.uk>, SUO <standard-upper-ontology@ieee.org>, Jack Park <jackpark@thinkalong.com>, Gary Richmond <garyrichmond@rcn.com>


Jon and Murray,

One point I'd like to emphasize is the title of Tarski's
original paper on model theory:

   Tarski, Alfred (1933) "Pojecie prawdy w jezykach nauk dedukcynych,"
   German trans. as "Der Wahrheitsbegriff in den formalisierten
   Sprachen," English trans. as "The concept of truth in formalized
   languages," in Tarski (1982) pp. 152-278.

Tarski explicitly said that he was not trying to represent
the concept of truth in natural languages, but he wavered on
that issue in many ways.  Following is a later paper (1944),
in which he elaborates the implications of his approach:

   http://www.jfsowa.com/logic/tarski.htm
   The Semantic Conception of Truth

Following is a quotation:

   The most natural and promising domain for the applications
   of theoretical semantics is clearly linguistics -- the empirical
   study of natural languages. Certain parts of this science are
   even referred to as "semantics," sometimes with an additional
   qualification. Thus, this name is occasionally given to that
   portion of grammar which attempts to classify all words of
   a language into parts of speech, according to what the words
   mean or designate. The study of the evolution of meanings in
   the historical development of a language is sometimes called
   "historical semantics." In general, the totality of investigations
   on semantic relations which occur in a natural language is
   referred to as "descriptive semantics." The relation between
   theoretical and descriptive semantics is analogous to that
   between pure and applied mathematics, or perhaps to that between
   theoretical and empirical physics; the role of formalized
   languages in semantics can be roughly compared to that of
   isolated systems in physics.

But one point that Tarski and most logicians, including Pat Hayes,
do not emphasize is the importance of a theory of reference as
a prerequisite for a theory of truth.  For the "formalized
languages" that Tarski addressed, the entities under discussion
were already collected into well defined sets:  a set of
individuals D and a set of relations R defined over D.

The questions that model theory addresses were well understood
by Aristotle, Ockham, and Peirce, among others.  They are
certainly important, but equally important, if not more so,
are the questions of how to identify, enumerate, and refer
to the entities and relations in the sets D and R.  What are
the entities and relations in D and R?  How many are there?
Which, if any, is designated by any particular symbol?

Although I think Quine's vision was rather limited in many
ways, I give him credit for recognizing the limitations
of model theory:

   The notion of possible world did indeed contribute to the
   semantics of modal logic, and it behooves us to recognize the
   nature of its contribution: it led to Kripke's precocious and
   significant theory of models of modal logic. Models afford
   consistency proofs; also they have heuristic value; but they
   do not constitute explication. Models, however clear they be
   in themselves, may leave us at a loss for the primary, intended
   interpretation.

Bottom line:  Model theory is important, but it only solves
one part of the problem.  The other parts are of the utmost
importance for ontoloy.

John Sowa