Re: Alan Turing's Halting Problem is incorrectly formed

Sander Bruggink says...

>
Peter Olcott wrote:

 

Its not syntactically similar its semantically analogous. The {Halting
Problem} merely forms an absurd question, just as the above three
questions are absurd.

>
Why is it an absurd question?

 Here's my psychological analysis of why Peter thinks
it is absurd.
 What Peter is doing is "anthropomorphising" the Halting program. He's
putting himself in the position of Halt, and he's imagining that Halt
is asked his opinion on whether this or that program halts. Then the
particular program that Halt is asked to pass judgement on is felt
by Peter to be an "unfair question". There is no way for Halt
to answer the question---it isn't a matter of lack of intelligence,
it is that answering the question correctly is analytically impossible.
So Peter thinks that this is an unfair thing to hold against our poor
Halt program.
 It's exactly as if Peter himself were being asked a series of yes-no
questions, and he is punished if he answers a question incorrectly.
Then questioner's first question is:
        Will your answer to my first question be "no"?
 Peter cannot possibly answer that question correctly, but it's
not because Peter is stupid, or because he lacks some key piece
of knowledge. It doesn't matter *how* smart Peter is, he can
never answer that question correctly.
 So, I think that Peter's objection to impossibility proofs
(including Godel's theorem and Turing's proof of the unsolvability
of the halting problem) is that they don't intuitively demonstrate
a limitation on the *intelligence* or *power* of the systems
(Peano Arithmetic in the one case or the Halt program in the other
case) to say that they can't correctly answer a particular question.
So Peter thinks these proofs are somehow unfair.
 But the bottom line, of course, is that it doesn't matter whether
the questions are unfair or not, it is provable that there are

well-defined questions that Peano Arithmetic or a purported Halt
program cannot answer correctly.
--
Daryl McCullough
Ithaca, NY