John F. Sowa wrote: (01)
> Following are the points I would emphasize:
>
> 1. The immense size and complexity of the universe and its
> continuous variability in time and space make it impossible
> for any discrete, finite set of labels (words or predicates)
> to have a perfect, one-to-one mapping to all aspects of the
> universe or even to some small chunk we are familiar with.
>
> 2. Human systems for perception, action, and mental imagery
> enable us to interact with the world more accurately than
> we can characterize it in discrete words or predicates.
> ...
>
> 3. Therefore, anything we can express in a discrete string of
> symbols (in logic or natural language) will inevitably be
> an approximation to some limited part of the universe for
> the purpose of fulfilling some particular narrow goal. (02)
Unsurprisingly, we are all in violent agreement. And the apparent
discord was a consequence of the language used to express the model.
Who would have thunk it? ;-) (03)
> 4. Natural languages have evolved under those constraints for
> thousands of years, and they have proved to be amazingly
> successful and flexible in adapting to an open-ended variety
> of situations while enabling us to communicate enough of our
> thoughts with sufficient accuracy to achieve specific goals. (04)
Or with sufficient ambiguity to confuse our peers, as John managed to do
with his earlier email. (05)
As to the rest of John's posting, I refuse to be drawn into a discussion
of the power of either mathematics or logic. I am an engineer. "By
their fruits shall ye know them." (06)
-Ed (07)
--
Edward J. Barkmeyer Email: edbark@xxxxxxxx
National Institute of Standards & Technology
Manufacturing Systems Integration Division
100 Bureau Drive, Stop 8263 Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263 FAX: +1 301-975-4694 (08)
"The opinions expressed above do not reflect consensus of NIST,
and have not been reviewed by any Government authority." (09)
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