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Re: [ontolog-forum] Intensional relation

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: sowa@xxxxxxxxxxx
Date: Fri, 4 Jan 2013 12:57:57 -0500 (EST)
Message-id: <c7e72503b75425bd56e9634173d65fc4.squirrel@xxxxxxxxxxxxxxxxxxxx>


> 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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