Re: [ontolog-forum] Intensional relation

[sowa@xxxxxxxxxxx]

> I disagree, John. The point of using mathematical (or
logical) notation is
> to make your statement precise and
unambiguous.
> 
> You can't have it both ways: 1) avoiding
terminology wars by using precise
> logical statements (witness
the recent discussion here on "individual"),
> and 2)
avoiding logical and  mathematical notation by using supposedly
>
clearer natural language.
> 
> One reason for the success
of ontological engineering in general, as for
> formal ontology in
philosophy, is that one can write logical axioms,
> thereby
curtailing somewhat the endless argumentation in English and other
> natural languages that has gone on in philosophy for generations
(and
> often goes on here).
> 
> Logic and
mathematics are formal tools that ontologists and computer
>
scientists need to use, so they can express their ontological analysis
in
> logical expressions that they can then share/compare.
Ontological analysis
> does not reduce to logical analysis, but
uses logic as a way to formalize
> what it wants to say.
>
> I do think that you need to use simple but precise English for
neophytes,
> but at some point ontologists (and ontological
engineers) need to learn
> logic and at least some mathematics.
One can use good English and formal
> definition together.
> 
> Thanks,
> Leo
> 
>>-----Original Message-----
>>From:
ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
>>bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F Sowa
>>Sent: Thursday, January 03, 2013 6:36 AM
>>To:
ontolog-forum@xxxxxxxxxxxxxxxx
>>Subject: Re: [ontolog-forum]
Intensional relation
>>
>>On 1/3/2013 12:19 AM,
Hassan Aït-Kaci wrote:
>>> The notation "2^S" for
a set S denotes the set of all subsets of S -
>>> i.e., it
powerset (also written P(S) sometimes). It is because its
>>> cardinality |S| is equal to 2^|S| that this notation has
been used.
>>
>>I agree.
>>
>>But that is no excuse for writing statements like:
>>
>>> "An intensional relation (or conceptual
relation) Ï?^n of arity n
>>> on <D,W> is a total
function Ï?n : W â?? 2^D^n from the set W into
>>> the set
of all n-ary (extensional) relations on D"
>>
>>Mathematicians don't think like that.  They only use such
language
>>when they are deliberately trying to frighten the
unwashed.
>>
>>Following is a quotation by Paul
Halmos, whose books were used to
>>teach the mathematicians who
talk that way.  But thankfully, he
>>never wrote that way.  If
he had, nobody would have ever read
>>his books.
>>
>>As Halmos said, the intuition is fundamental. 
After you understand
>>the fundamental ideas, writing the
formalism is trivial:  "it is more
>>the draftsmanâ??s
work not the architectâ??s."
>>
>>Teaching
ontology by burying the fundamental insights under
>>the
trivial notation is pedagogical malpractice.
>>
>>John
>>___________________________________________________________
>>_____________
>>
>>Paul Halmos:
>>
>>â??Mathematics â?? this may surprise or shock some
â?? is never
>> deductive
>>in its creation. The
mathematician at work makes vague guesses,
>>visualizes broad
generalizations, and jumps to unwarranted conclusions.
>>He
arranges and rearranges his ideas, and becomes convinced of their
>>truth long before he can write down a logical proof... the
deductive
>>stage, writing the results down, and writing its
rigorous proof are
>>relatively trivial once the real insight
arrives; it is more the
>>draftsmanâ??s work not the
architectâ??s.â??
>>
>>___________________________________________________________
>>______
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> 
>
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