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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Every sufficiently competent C programmer knows --- Semantic
 Property of Finite String
Date: Fri, 14 Mar 2025 21:57:39 -0400
Organization: i2pn2 (i2pn.org)
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On 3/14/25 9:08 PM, olcott wrote:
> On 3/14/2025 6:09 PM, Andy Walker wrote:
>> On 14/03/2025 19:48, Keith Thompson wrote:
>>> [...] That would imply that [PO] could solve
>>> Goldbach's Conjecture, among other things, but I haven't seen him
>>> do so.
>>
>>      Perhaps [just about] worth noting that a sufficiently long
>> [but not "infinite"] brute force attack on the GC [and many other
>> similar conjectures] would resolve the issue. 
> 
> Not if GC is true and the proof cannot algorithmically
> compressed into a finite sequence of steps.

So, are you now admitting that it is possible for GC to be true, and no 
finite proof (the only kind of proof that exists) might exist, and thus 
that GC might be the instance that makes the system incomplete?

> 
>>  Basically, if you
>> have a program [eg, TM] of size N by some suitable measure [eg, TM
>> states] then within [eg] BB(N) steps it must find the counter-example
>> [if there is one] or else there isn't one [and the GC is proven true],
>> where BB is the Busy Beaver function.  Of course, BB is uncomputable,
>> but that doesn't mean specific individual values are uncomputable,
>> just that there is no TM that computes it /in general/.
>>
>>      [I have mentioned here before that BB gives us a much less
>> troublesome way of attacking the HP than the standard proofs.]
>>
> 
>