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[ontac-forum] Theories, Models, Reasoning, Language, and Truth

To: ONTAC-WG General Discussion <ontac-forum@xxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Tue, 13 Dec 2005 22:23:21 -0500
Message-id: <439F9029.2000108@xxxxxxxxxxx>
There have been a number of discussions on this list
related to issues of logic, reasoning, and language.
To address these issues, I pulled together some excerpts
from some previous publications and assembled them in
a 13-page paper with the above title:    (01)

    http://www.jfsowa.com/logic/theories.htm
    Theories, Models, Reasoning, Language, and Truth    (02)

One of the topics I emphasized in this paper is the
lattice of theories, which I have discussed many times
before, but my writings on that topic were scattered
in several different publications.   I put the relevant
material from all of them in this short paper.    (03)

Following is the title, abstract, and first two
paragraphs of the paper.    (04)

John Sowa
_________________________________________________________    (05)

Theories, Models, Reasoning, Language, and Truth    (06)

John F. Sowa    (07)

One of the oldest controversies about Aristotle's categories was
whether they represent the kinds of things that exist or the way people 
perceive, think, and talk about things that exist.  Theophrastus, 
Aristotle's successor as head of the Lyceum, said that the categories 
were intended in all those ways  in modern terms, ontological, 
epistemological, and lexical. Today, the fragmented treatments of those 
subjects are scattered across the fields of philosophy, linguistics, and 
artificial intelligence, in each of which the researchers who work with 
formal representations or informal techniques tend to cluster in 
disjoint sets.  Yet natural languages are capable of expressing and 
reasoning about both kinds of information:  anything that can be 
expressed in the most precise formal logic ever invented can be 
paraphrased in any natural language; conversely, a three-year-old child 
has the ability to learn, imagine, and express ideas that are far beyond 
the most sophisticated computer systems available today.    (08)

The limitations of current systems have been discussed in the article on 
The Challenge of Knowledge Soup. As a companion piece, this article is a 
tutorial about formal theories and their relationships to language and 
the world. It has been assembled as a series of extracts from several 
published papers that have been modified and pieced together. The 
references can be found in the combined bibliography for this web site. 
There is also a PDF version for more convenient printing.    (09)

1. Relating Theories to the World    (010)

As an example of the controversies, Gangemi et al. (2003) maintain
that the terms vase and lump of clay have different identity criteria; 
therefore, they imply two distinct objects that happen to occupy the 
same location. Others maintain that the distribution of matter takes 
precedence over any method of describing it:  if two descriptions 
characterize the same matter, they must describe the same object. In 
terms of his theory of signs, Peirce would say that anything can be 
described in any number of ways from any perspective for any purpose. 
The particular choice of words or other signs depends on the intentions 
of some viewer who might choose one perspective rather than another. 
That choice is not purely subjective, since there are objective, but 
species-specific criteria for preferring one to another (Deely 2003). A 
bee, for example, might ignore the vase and focus on the flowers in the 
vase, while a dog might push the flowers aside and drink the water that 
some human had put there for a very different purpose. Each perspective 
depends on the intentions of some individual of some species, and any 
question about the priority of one perspective over another cannot be 
answered without considering the intentions of the questioner.    (011)

The problems of knowledge soup result from the difficulty of matching 
theories based on discrete concepts to the continuous physical world. 
Methods of fuzziness, probability, defaults, revisions, and relevance 
represent different ways of measuring, evaluating, or accommodating the 
inevitable mismatch. Each technique is a metalevel approach to the task 
of finding or constructing a theory and determining how well it 
approximates reality. To bridge the gap between theories and the world, 
models are Janus-like structures, with an engineering side facing the 
world and an abstract side facing the theories (Figure 1).    (012)


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