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Re: the RM and Godel

From: Jan Hidders <jan.hidders_at_REMOVETHIS.pandora.be>
Date: Sat, 25 Jun 2005 09:34:19 GMT
Message-ID: <vy9ve.129657$F62.7015496@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".

> 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.

Received on Sat Jun 25 2005 - 04:34:19 CDT

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