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Re: [ontolog-forum] Terminology Question concerning WebArchitecture and

To: paola.dimaio@xxxxxxxxx
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Chris Menzel <cmenzel@xxxxxxxx>
Date: Thu, 26 Jul 2007 05:42:36 -0500
Message-id: <20070726104236.GC10264@xxxxxxxx>
On Thu, Jul 26, 2007 at 04:00:45PM +0700, paola.dimaio@xxxxxxxxx wrote:
> Please tell me more
> I have not researched 'nothing' systematically in scientific
> representation (rather in a philosophical and liberal arts context)
> and now I am really thirsty for this stuff,    (01)

Great.  See below.    (02)

> I will start a studying 'nothing' from the point of scientific
> representation and  modelling 'nothingness' (how exciting, just my
> thing)
> but -
>> ...
>>> PDM  In classical western thinking there is no place for [nothing].
>> CM To the contrary, classical western thinking has accommodated the
>> concept quite robustly.
> Is there an ontological category called nothing?    (03)

Well, there are ontologies in which there is a class/category NOTHING or
NULL which is the complement of the class/category THING or ENTITY.  The
extension of the latter class, of course, includes everything, and that
of the former, of course, includes nothing, i.e., it is empty.  (Which,
I assume, is why Azamat has said that "nothing" could be "modeled" by
the empty set.)  But there are also ontologies in which there is no such
distinguished class NULL.  To express "nothingness" one simply uses
logical negation to say such things as, e.g., "There are no unicorns".
AFAICS, whether or not to introduce an honest-to-goodness NULL class is
a purely pragmatic question determined by such matters as theoretical
elegance and computational efficiency.    (04)

> If Ontology is rooted in Aristotelian 'Categories', could you please
> point me to the Category or equivalent artifact that represents
> 'nothing' for the purpose of scientific reasoning.    (05)

The only notion of "nothing" that is necessary for scientific reasoning
is the logical concept of negation.  So instead of getting bogged down
in complex historical studies of dubious relevance, I'd suggest you
focus instead simply on a rigorous course of study in mathematical
logic.  A fine (and inexpensive) basic intro text is Wilfrid Hodges'
_Logic_.  Good, more advanced texts include _Metalogic_ by Geoffrey
Hunter (also inexpensive), Enderton's _A Mathematical Introduction to
Logic_, and Mendelson's _Introduction to Mathematical Logic_.  John Sowa
has recommended Tarski's classic _Introduction to Logic and to the
Methodology of the Deductive Sciences_, and John himself has a nice
overview of basic logic, set theory, and abstract algebra on his web
site: http://www.jfsowa.com/logic/math.htm .    (06)

-chris    (07)

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