John Sowa wrote (01)
"If you consider Euclid's first four postulates by themselves, you get a
primitive, underspecified version of geometry, which is neutral with
respect to issues about parallel lines. One might reasonably claim that
this simple geometry is sufficient to capture the basic meaning of the
word 'point" and its relationships to other words, such as 'line'." (02)
This exactly illustrates the nub of the argument. What ever you intend
to mean by "point" and "line", it does not necessarily mean what you
think it means, at least in formal mathematical theories. In my course on
geometry, virtually every theorem
started with the assumption "If two is not equal to zero", which is quite a
different concept of geometry to Euclid's.
I later worked on a geometry for computation where points were ill defined
splodges, since if you
formaly specify computational geometry over the real numbers, the code
does not always work as specified. (03)
A.P. Herbert, in his "Misleading cases" had great fun interpreting legal
terms, so that a cow had to be accepted by a bank as a cheque (check for
the US) and a snail was a "wild and savage beast" - in the same category
as a lion. (04)
Yes there are intended meanings, but actually tying them down is very
tricky. If you are going to let a computer reason about terms, then
those intended meanings must be precisely constrained. If you are not
going to let it reason, then use a data exchange standard. If you are
going to let it do only a little bit of reasoning, so it doesn't go off
at a tangent, then that might work, if only you can define "a little bit
of reasoning". (05)
Sean Barker
Bristol, (06)
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
> [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F.
> Sowa
> Sent: 02 March 2010 13:59
> To: [ontolog-forum]
> Subject: Re: [ontolog-forum] Foundation ontology, CYC, and Mapping
>
>
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> Dear Matthew, Chris, Pat, Pat, and Gary,
>
> ... (07)
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