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Subject: Re: Alan Turing's Halting Problem is incorrectly formed
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On 6/9/2004 8:10 AM, Daryl McCullough wrote:
> 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

The questions are incorrect like:
What time is it (yes or no)?

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


-- 
Copyright 2024 Olcott

"Talent hits a target no one else can hit;
  Genius hits a target no one else can see."
  Arthur Schopenhauer