[SCL] two comments

[Murray Altheim]

John F. Sowa wrote:
> Murray,
> 
> This is not my definition.  It is McCarthy's definition,
> which was adopted by the formal specification community.
> It was developed and applied by a large community of
> people who know and understand logic, syntax, and formal
> specification.  Pat, Chris, and I have found it very useful.
[...]
 > This, however, is not an issue about reality.  It is a simple
 > point of mathematics.  Any branch of mathematics starts with
 > whatever axioms we please to use.  And this one very simple
 > choice of axioms that many eminent people from McCarthy on
 > down have very useful.

No, I didn't miss the point. I understand where mathematics
and logic fits into the grand schema of things, and how as a
system it has been refined over many years of study. My point
was that many communities have created definitions for things
that limited their ability to move past those definitions.
The field of mathematics is no different from any other in
this respect -- it's ultimately a form of communication. In
the end, mathematics is neither right nor wrong, it's simply
an agreement to communicate in a certain way.  I realize that
some mathematicians take a much more religious view of their
field. But all formalized systems of knowledge are evolutionary,
not final. At any given moment in time there are formal
definitions for things -- you choose to follow them in order to
communicate within the constraints of the system, or you question
those constraints. That's all I'm doing.

 > Before making pronouncements about turtles, you should do
 > your homework.  Until you have studied the subject, your
 > objections are meaningless.

Actually, this is not true. There've been many times in history
where someone operating without a thorough knowledge of a field
has created a breakthrough (TimBL is a recent example), or been
able to intuit a solution that those steeped in the domain have
missed (I'm not suggesting that I'm doing that here, just speaking
in the general case). I know you are prone to do so, but I've
learned not to judge someone's ability to make correct statements
based on their ostensible qualifications -- even children sometimes
see things that adults don't. We've also seen the history where
those who were otherwise highly qualified were also dead wrong;
there have been many cul de sacs, sometimes lasting for centuries.
And we've also seen that experts in a field must sometimes look
past the limitations declared by their forebearers in order to
create new ideas. The axioms we choose to use may be limiting our
ability to create the axioms we need.

But I also realize this is seriously off the beaten track of
where we're heading with SCL, so we can drop it, or at least take
it offline.

Murray

...........................................................................
Murray Altheim                         http://kmi.open.ac.uk/people/murray/
Knowledge Media Institute
The Open University, Milton Keynes, Bucks, MK7 6AA, UK                    .

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