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Re: Madonna / Data + Application Semantics

From: Henry Story <henry.story@bblfish.net>
Date: Fri, 15 Apr 2005 10:49:34 +0200
Message-Id: <9deed1be82802754e071781574148a23@bblfish.net>
Cc: 'SWIG' <semantic-web@w3.org>
To: "Bill Kent" <billkent@bkent.net>


On 14 Apr 2005, at 22:51, Bill Kent wrote:
> Hi-
>
> I don't know if this dialog is still going on, but I never did get any
> response to my email of 2/10/05, which is appended at the very end.
>
> In the meantime, I've run across an interesting passage in an article 
> by Jim
> Holt entitled "Time Bandits", about Einstein and Godel, in the 
> February 28,
> 2005 issue of The New Yorker. On page 83, he writes:
>
> <beginning of quote>
>
> It had been an article of faith that, armed with logic, mathematicians 
> could
> in principle resolve any conundrum at all-that in mathematics, as it 
> had
> been famously declared, there was no ignorabimus. Godel's theorems 
> seemed to
> have shattered this ideal of complete knowledge.
>
> That was not the way Godel saw it. He believed he had shown that 
> mathematics
> has a robust reality that transcends any system of logic. But logic, 
> he was
> convinced, is not the only route to knowledge of this reality; we also 
> have
> something like an extrasensory perception of it, which he called
> "mathematical intuition." It is this faculty of intuition that allows 
> us to
> see, for example, that the formula saying "I am not provable" must be 
> true,
> even though it defies proof within the system where it lives. Some 
> thinkers
> (like the physicist Roger Penrose) have taken this theme further,
> maintaining that Godel's incompleteness theorems have profound 
> implications
> for the nature of the human mind. Our mental powers, it is argued, must
> outstrip those of any computer, since a computer is just a logical 
> system
> running on hardware, and our minds can arrive at truths that are 
> beyond the
> reach of a logical system.
>
> <end of quote>

I can't answer this point in a short time, though it is a very 
interesting
one, and would be more appropriately discussed on a philosophy forum. A 
more
elaborate answer would involve the following points:
   - restrictions have been placed on more recent formal systems that 
have
     taken Gödel's work into account
   - Even though Logic can't solve all problems, that does not mean that 
it
    is not an excellent tool to solve a huge number of them
   - fuzzy logics and modal logics need not be thought of as different 
logics
     but can well be seen as specialization of logics to certain domains 
of
     discourse. See David Lewis' "Counterfactuals" where he shows how 
modal
     logic can be expressed in simple first order logical terms. You 
just need
     to add quantification over possible worlds, introduce the notion of 
possible
     world similarity, and cross world identity. He also shows how to 
deal with
     problems of fuzziness in language, by defining the notion of a 
mathematically
     precise language and then defining natural languages as sets of 
sets of such
     languages. You can use that trick to deal with a huge range of 
fuzziness issues.
   - logic does not deny intuition in the least. Good 
logicians/philosophers are
     constantly calling upon our intuitions on various conceptual 
issues. Their
     aim is to help refine our concepts which at a certain level may 
seem contradictory
     in order to create more powerful conceptual structures. Not unlike 
Einstein
     reworking our notions of space time, thereby opening up worlds of 
possibilities
     unimaginable before.
   - the logic of emotions has been a major preoccupation of analytical 
philosophers
    in the 1990ies. You may find it odd that emotions have a structure 
or logic but
    think about the following example:
        you are walking down a dark alley. You hear some footsteps at a 
certain distance
        behind you, and you are worried. The steps get faster and you, 
not being a
        martial arts expert, feel defenseless and fearful. Suddenly a 
voice shouts out
        "coucou" and you realize it is your brother. The fear 
disappears, and you turn around
        with a smile.
    This story illustrates very well how your knowledge about the 
environment and your skills
    shape your emotions. A martial arts expert would not have had fear 
as he would have felt
    comfortable that even at the last moment he would have been able to 
turn the situation
    to his advantage. He may even have been able to hear better the non 
aggressive nature
    of the steps.
       The terms "would" "could" "knowledge" "skill" are all analyzable 
using
    modal logic. Understanding the nature of thought, its relation to 
logic, and intuition
    are all very important elements in correctly understanding the 
behavior of people around
    you.

>>>>>>
[snip]
>>>>>> Just a point of clarification about identity. (I thought the 
>>>>>> example
>>>>>> is fun enough that it may be of interest)
>>>>>>
>>>>>> As we all know Madonna is a material girl, and she lives in a
>>>>>> material [snip]
>
> My curiosity has been aroused. What came after the [snip]?

Please check the semweb archive. [1] I have proposed a simple solution 
[2]
and will provide a N3 formalization when I get time to do so. The trick
is simple to read up on mereology [3] and translate the mereological 
rules into
N3.

In any case the madonna problem has some very good solutions.

>
> Thank you all for keeping me in the loop.
>
> Bill
>
>
> BTW: The Help Wanted notice on my web site is still open.

[1] http://lists.w3.org/Archives/Public/semantic-web/2005Feb/0062
[2] http://lists.w3.org/Archives/Public/semantic-web/2005Feb/0073
[3] http://plato.stanford.edu/entries/mereology/
Received on Monday, 18 April 2005 09:00:40 UTC

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