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Re: [ontolog-forum] PROF Swartz ON DEFINITIONS

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Wed, 22 Sep 2010 18:17:33 -0400
Message-id: <4C9A807D.7020504@xxxxxxxxxxx>
Chris and Patrick,    (01)

On 9/22/2010 12:47 PM, Christopher Menzel wrote:
> This is just not true, John.  In many branches of mathematics -- set
> theory and computability theory especially spring to mind -- it is often
> important to represent a complex mathematical notion as a class of
> well-defined mathematical*objects*  for which one can define properties
> and on which one can define operations. Representing the separate
> components of a complex notion by means of n-tuples is a very clear and
> convenient way of doing so.    (02)

I wasn't objecting to the definition, but to the writing style.    (03)

> -- indeed, I can't think of any other way of
> doing it that wouldn't amount to the same thing.    (04)

My recommendation is to do "the same thing" in a more readable way:    (05)

  1. Start by explaining the problem to be solved without using any
     formalism.    (06)

  2. Give an intuitive explanation of what is being defined,
     preferably with a diagram.    (07)

  3. Name and describe each component of the structure as it is
     introduced, instead of the end.    (08)

For example, translate the example I gave    (09)

    A whatchamacallit is an n-tuple (A, B, C, D, E)...    (010)

Into an equivalent form:    (011)

A whatchamacallit is a structure with five components:    (012)

  1. A set A, whose elements are called apples,    (013)

  2. A function B, which maps A to...    (014)

That's the point I was trying to make.    (015)

And by the way, I have no objection to talking about n-tuples
when those n-tuples are going to be organized in a matrix or table
of some kind.  But if there aren't going to be any operations on
those tuples, the word 'n-tuple' is misleading jargon for saying
that the structure has n components.    (016)

On 9/22/2010 5:04 PM, Patrick Durusau wrote:
> Isn't the turning to the blackboard episode been attributed to several
> people?    (017)

Yes.  But the conclusion is usually different.  I don't know how many
of them are true, but I suspect that quite a few are.    (018)

One version is about Norbert Wiener, and it is so characteristic of him
that it should be true, even if it isn't:    (019)

During a lecture, Wiener was filling several blackboards full of formula
after formula.  Then he said "From this it is obvious that..." and
wrote down another formula.  Then he stood back and stared at the
board for a very long pause, went to the side of the board, and
started writing something.    (020)

For several minutes, he hid what he was writing with his very large
body while the chalk was going clickety clack.  Then he erased what
he had written, turned around, and declared triumphantly    (021)

    I was right!  It is obvious!    (022)

John    (023)

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