Re: Reductive Paraphrase again
Rich and John B.,
Children (and adults) learn words by associating them with
images, feelings, actions, and other experiences. There are
very few basic words that can be adequately defined by
reductive paraphrases -- and most of those are found in science
and engineering.
Mathematics is the primary source of examples of reductive
paraphrases that are precise and reliable -- but only because
the people who invented those ideas deliberately designed them
(or chose them) to be reducible by formal methods.
Unlike some people who try to set up artificial barriers
between common sense and logical and/or mathematical reasoning,
I believe there is a continuity. Logic and mathematics are
based on perfectly natural human abilities, but they have been
developed to a high degree of skill. I would compare them to
gymnastics and other atheletic skills, which require a very
high degree of professionalism. Another example would be the
musical skills of professional musicians.
All those skills -- mathematics, gymnastics, and music -- are
"natural" in the sense that everybody can do them to some
extent, but doing them at a professional level requires an
enormous amount of dedication and practice.
Summary: I would say that reductive paraphrase is possible for
a small percentage of the words that people use -- primarily
words in science and engineering that have been deliberately
designed for reducibility. It may be possible to develop
approximate definitions for others, but those approximations
would always be highly specialized for some specific purpose.
For more detail on these and related issues, I would recommend
my article on the Challenge of Knowledge Soup:
http://www.jfsowa.com/pubs/challenge.pdf
John