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Re: the RM and Godel

From: mountain man <hobbit_at_southern_seaweed.com.op>
Date: Sun, 26 Jun 2005 22:53:48 GMT
Message-ID: <0mGve.5248$oJ.4934@news-server.bigpond.net.au>


"Jan Hidders" <jan.hidders_at_REMOVETHIS.pandora.be> wrote in message news:vy9ve.129657$F62.7015496_at_phobos.telenet-ops.be...
> mountain man wrote:
>> I seem to recall there is no "solid ground" in mathematics
>> in that the formalisms of mathematics cannot lead to
>> anything resembling "absolute truth".
>
> That's a grave oversimplification and a very misleading statement. A
> slightly less oversimplified version would be that if you formalize the
> theory of natural numbers (or sets, for that matter) you cannot have "the
> truth, the whole truth, and nothing but the truth" because you have to
> choose between either "the whole truth" or "nothing but the truth". Most
> tend to choose the "nothing but the truth".

The article which supported the statement concerning lack of absolute truth in mathematics was provided as: http://www.cs.auckland.ac.nz/CDMTCS/chaitin/cmu.html

>> How do RM theorists view the work of Godel, Turing and
>> Chaitin? What are the implications of Godels theorem of
>> incompleteness, or Chaitin's random truth, to the RM?
>
> Practically zero. Note that there is Goedels *completeness* result for
> first-order logic (i.e., the flat relational model) that tells us that for
> uninterpreted predicates we in fact can and do have a complete
> axiomatization. So whether there is going to be a problem in this respect
> depends upon what you take as your domains, and that decision's not really
> part of the RM anyway. But even if the problem would occur, that would be
> practically meaningless in practice. Would it stop us from proving things?
> No. Would it stop us from being able to ask certain queries or reason
> correctly about them? No.

Thanks for the direct responses to these questions.

-- 
Pete Brown
IT Managers & Engineers
Falls Creek
Australia
www.mountainman.com.au
Received on Sun Jun 26 2005 - 17:53:48 CDT

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