Re: Can a regular Turing Machine provide Protected Memory?

From: Chris Menzel (cmenzel_at_remove-this.tamu.edu)
Date: 08/30/04 

Date: 30 Aug 2004 11:01:10 GMT

On 28 Aug 2004 11:30:37 -0700, George Greene <greeneg@cs.unc.edu> said:
>> (e.g., http://tinyurl.com/6ow6c),
> Well, that's not exactly wrong, but it is a matter of opinion. In may
> opinion, the cited proof is nowhere near simple or elegant ENOUGH.

No doubt there is room for improvement, but I think it's hard to do a lot
better *and* make all the necessary infrastructure explicit. A simpler
and/or more elegant, but equally explicit, proof would be welcome,
obviously.

>> the latter follows with complete certainty.
>>
>> That really is a simple piece of reasoning.
>
> It is important to talk about what is really going on
> here. First-order logic has a rule of inference commonly
> referred to as "universal generalization".

I'm sure you meant "universal instantiation" here.

> PO has never studied first-order logic and does not accept this rule.

I'm not completely sure of that, though I admit he seems to have said as
much. But another explanation is that he simply does not have the
mathematical competence to understand the proof that the Halting Problem
is unsolvable. Hence, since he thinks he can come up with a solution, he
infers (with considerable hubris) that there must be a fallacy in the
proof.

> Pedagogically, you are not going to make any progress until you can
> convince him that first-order logic Is Actually Important. Until then,
> he is just going to be using intuitive reasoning and he is going to
> insist that "proving a negative" (which is how HE views proving a
> universal generalization) "is hard" and that all the short simple
> proofs are dismissable purely for not being hard enough and not being
> clearly addressed to his favorite special case.

You are probably right. Olcott is pretty clearly a lost cause, but I
suspect others may be benefitting from the exercise.

Chris Menzel

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