Quote:
Originally Posted by Kriminal99
The fact that the H in the proof is "Touring Complete" means the result is extremely weak.
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That's an interesting and unsupported opinion. How do you define "weakness" in this case?
Quote:
Originally Posted by Kriminal99
There could still be a halting machine that is "Touring - {H} Complete" where H is the halting machine itself.
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There could, indeed, there's no reason to believe there is not. This is the fourth time you've been asked to distinguish why this is a special case.
Quote:
Originally Posted by Kriminal99
Encompassing any Universal machine in a larger machine that also contains a machine capable of copying input causes an infinite regress if that Universal machine attempts to trace the computations of the machine encoding it recieves as input. Why? When it traced the computations it would just start the whole process over again, and make a new copy of the input for the next level of recursion. This is done in the proof.
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Well, no it's not done in the proof: You've fallen into the trap that both Craig and I described previously. There's no requirement--although no reason it cannot be done--for the machine itself to be implemented as a level of indirection. That is not implied or necessary in the proof.
But more importantly it does *not* require the machine to do--again as I stated in an earlier post--an infinite recursion on the the inputs to the data, and to say so is to misunderstand what the theorem is saying.
If you want to change the theorem so that it fails, that's not a disproof of the theorem, something that I think that would be obvious to anyone with philosophical training even if they did not understand computer science.
Machines take me by surprise with great frequency,
Buffy
