Re: Every sufficiently competent C programmer knows --- Semantic Property of Finite String

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.]
>