Quote:
Originally Posted by Buffy
That's an interesting and unsupported opinion. How do you define "weakness" in this case?
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.
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 |
The signifigance of a Halting machine that works for anything but itself is that the halting problem is generally solvable...
I don't have to change the theorem. The theorem assumes that the machine can operate on itself as part of it's proof by contradiciton. The assumption is non trivial because any Universal Touring machine in this situation would cease it's normal situation and go into an infinite regress if it attempted to trace it's own computation. Thus, by assuming the Halting machine can do what it does in the proof by contradiction, he is saying that it cannot trace the computations of the machine it is fed as input.
