Re: Halting Problem is wrong two different ways

Am Wed, 05 Jun 2024 12:09:18 -0500 schrieb olcott:

On 6/5/2024 12:03 PM, John Smith wrote:

On 5/06/24 04:16, olcott wrote:

On 6/4/2024 9:12 PM, John Smith wrote:

On 5/06/24 04:05, olcott wrote:

On 6/4/2024 8:48 PM, Richard Damon wrote:

(6) Can Carol correctly answer “no” to this question?
Let's ask Carol. If she says “yes”, she's saying that “no” is the
correct answer for her, so “yes” is incorrect. If she says “no”, she's
saying that she cannot correctly answer “no”, which is her answer. We
are assuming for this and all subsequent questions that the only
acceptable answers are “yes” and “no”, and in this case, both answers
are incorrect. Carol cannot answer the question correctly. Now let's ask
Dave. He says “no”, and he is correct because Carol cannot correctly
answer “no”. So (6) is subjective because it is a consistent,
satisfiable specification for some agent (anyone other than Carol), and
an inconsistent, unsatisfiable specification for some agent (Carol).

But that's like running a different machine. That's not interesting.
We wanted to see a machine that can answer ALL questions. This one was
specifically constructed to be unanswerable by this machine. The
equivalent translation would be "Can YOU answer No?".

--
joes