Re: Godel's Incompleteness and Nonmonotonic Logic

From: Herman Jurjus (h.jurjus_at_hetnet.nl)
Date: 08/28/04

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    Date: Sat, 28 Aug 2004 12:07:49 +0200

    Xee wrote:

    > hgtohybtml@mailinator.com (Student) wrote in
    > news:edc21089.0408201124.2850d5cb@posting.google.com:
    >
    >
    >>I have recently read a few papers, web pages, and parts of a text on
    >>nonmonotonic logic, Answer Set programming, and AnsProlog in
    >>particular. I find it interesting that nobody addresses the issue of
    >>Godel's incompleteness theorems because these "logics" force
    >>completeness by making any formula "A" or its negation "not A"
    >>provable. Does anybody have any information, links, references,
    >>comments on this topic? In most other aspects of computer science, it
    >>would be considered foolish to dismiss metamathematics issues
    >>(decidability, etc)... so why are modern logicians unconcerned about
    >>consistency and soundness of their logical system?
    >
    >
    > Indeed, such a requirement, that all formulae be provable, will help
    > greatly with decidability. There are several types of logic. The most
    > basic formal system, propositional logic (aka the predicate calculus),
    > assumes such a requirement.

    [etc. etc. snip]

    Isn't it amazing? A question about non-monotonic logic invites someone
    to reply a long explanation of classical (monotonic) logic, as far as he
    understood it, even giving references for further reading.
    All without the slightest indication of awareness of the existence of
    any non-monotonic logic.
    It makes you wonder if we ourselves also miss the real issues, and show
    the same blindness without ever realizing it, when we read, say,
    Aristotle or the Scholastic masters, with modern eyes.

    "The vanity of education makes us forget that we're stupid." 

    -- 
Cheers,
Herman Jurjus
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