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Re: circular paradox gizmo

From: Jos De_Roo <jos.deroo.jd@belgium.agfa.com>
Date: Fri, 3 May 2002 14:32:05 +0200
To: pfps@research.bell-labs.com
Cc: www-webont-wg@w3.org
Message-ID: <OF48F75EF2.B075F60F-ONC1256BAE.0027BDB1@agfa.be>

Peter,

[I really appreciate your efforts and wasn't
really intentending to criticize you]

[...]

>>   I find one of the most important characteristics
>>   of a model that it captures the *correspondence*
>>   between the-name-of-the-thing that we have in the
>>   assertional language and the-named-thing expressed
>>   in the object language (using e.g. URI decoupling)
>>   I just can't find such correpondence for a paradox
>>   so how could they exist in every model ???
>
>I don't understand this.  Where do names come in here?  If by names you
>include things like ``the set that consists of all sets that are not
>elements of themselves'', then I've been trying to define the
>correspondence.  If by names you mean atomic names, then to devise an
>expressive formalism you need much more in your model to give meaning to
>the other entities in the domain of discourse, if you by into the RDF
>vision, or you need to have syntactic constructs that do not correspond to
>entities in the domain of discourse, if you don't buy into the RDF vision.

I meant that in the mathematical language we *name*
an expression-in-the-object-language and give its
iff-truth-condition-for-the-*object*-language
in the *mathematical* language
is all

>> or
>>   one wants to prove a paradox by assertion of its
>>   negation and finding a contradiction
>>   which is succeeding here, so the paradox is proved
>>   of course it is, you have *asserted* an inconsistency
>>   and one should not do that

> I haven't asserted anything.  I've just pointed out a flaw in the
> definitions of OWL interpretations.

I see, I was just arguing that one should not *assert*
the negation of the consequent (too early)

>>   --
>>   I would make the claim that one cannot prove nor
>>   disprove a paradox, we just have incompleteness
>>   (no evidence/correspondence)
>
>Generally, paradoxes are paradoxes because you can (or should be able to)
>both prove and disprove them (at least in one way of thinking about
>paradoxes).

I'm just curious to see a SOUND PROOF ARGUMENT for your latest paradox
I mean an ARGUMENT as a pair of things:
  a set of sentences, the PREMISES;
  a sentence, the CONCLUSION.
  An argument is VALID if and only if it is necessary that
    if all its premises are true, its conclusion is true.
  An argument is SOUND if and only if it is valid and all
    its premises are true.
  A sound argument can be the premis of another sound argument.

  so
      { true-statements } log:implies { conclusion-statement } .
    is actually
      conclusion-statement .

If we can't soundly prove a paradox, then we should maybe live with them

--
Jos
Received on Friday, 3 May 2002 08:32:54 GMT

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