Re: Peter Olcott's Source of Confusion

From: Daryl McCullough (daryl_at_atc-nycorp.com)
Date: 07/03/04 

Date: 3 Jul 2004 08:42:59 -0700

Peter Olcott says...

>"Daryl McCullough" <daryl@atc-nycorp.com> wrote

>> Well, that's false, for one thing. What you have shown is
>> that for any entity, there is a hypothetical situation in
>> which that entity will be unable to correctly answer such
>> a question.
>
>That's cool, you say that what I am saying is not true

No, I'm saying that you are confusing two different claims,
one of which is true, and one of which is false. You keep
saying the false version, and I keep correcting you.

Let me make your scenario more explicit. A person, call him
"Jack" is sitting before a computer. The computer
running a program P gives Jack the following information:

    I'm going to ask you a yes/no question. If you answer "yes"
    I will enter an infinite loop. If you answer "no" I will
    halt immediately. The question is: "Will I halt?" (Please
    answer "yes" or "no".

It is impossible for *Jack* to answer the question "Will P halt?"
But Jill, looking over Jack's shoulder can perfectly well answer
that question. For instance, maybe she knows that Jack answers
"no" to every question asked of him, whether that's the correct
answer or not. In that case, the correct answer to the question
is "yes", and Jill can perfectly well give that correct answer.

The question "Will P halt?" is not a well-defined question until
you specify *who* will be giving P inputs. If it's Jack, then
the full question is "Will P halt when Jack is the one giving
inputs?" That fully-specified question has a correct answer,
it is just that it is impossible for Jack to give that answer
if he is the one giving the inputs.

The question "Will P halt when Jack is the one giving inputs?"
is a perfectly well-defined question, and it has a perfectly
well-defined answer. It *isnt'* an "incorrect question", it's
just one that *Jack* can't answer.

>The set that my program applies to includes the set that Turing
>was concerned with. (It includes people, and programs which
>include Turing Machines). Also the most important point is that
>my counter-example program uses exactly the same gimmick
>that Turing used in the counter-example program.

Yes, it's similar. The general conclusion is that for
every entity there is a well-formed question that that entity
cannot correctly answer. 

--
Daryl McCullough
Ithaca, NY

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