X-Message-Number: 23927
Date: Sun, 18 Apr 2004 23:17:31 -0700
From: Mike Perry <>
Subject: Re: Goedelian problems

Robert Ettinger, #23916:

>Mike Perry writes in part:
> >expanding the formal system to remove one [Goedelian] "problem"
> >does not at all remove another, similar problem in the expanded system.
>The first "problem" is (say) of the type: "Sentence number one is
>unprovable," while giving that sentence the label "number one."
>The new "problem" in the different system might be of the type: "Sentence
>number two is unprovable," while giving that sentence the label "number two."
>Are these "different" problems, and does either have any significance beyond
>quirks of language?

The two problems are different in detail though basically similar. I think 
they have significance well beyond quirks of language, since, for instance, 
they demonstrate limitations in our ability to predict the behavior of 
computers. We'd like to know if a certain program is in an infinite loop. 
Maybe the computer is working on something important, whose outcome we must 
forfeit if we terminate execution too soon. Or maybe it will never find the 
answer so the sooner we stop the less we waste precious resources. (This 
assumes too that its thrashing, in absence of the successful outcome, will 
not be worth the cost, which will arguably hold sometimes.) This strikes me 
as a very practical concern. Goedel's result has a direct bearing on it, 
telling us we can't tell in general, in advance of "what happens, happens," 
and will have to trust our luck. One might have suspected this, yes, but 
having a formal argument is something more than speculation. This is not to 
deny there are other weaknesses in formal systems--which still can be quite 

Goedel's result also tells us that a mathematical theory of everything, 
along the lines mathematicians generally like to use (2-valued or n-valued 
logic, for instance), is impossible. No such theory can be comprehensive 
enough to do even the basic theory of integer arithmetic, and also complete 
and consistent. That's quite an accomplishment

Mike Perry

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