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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