This is one of the clearest examples of my earliest work that
derives my 2023-10-21 view:

*All undecidable decision problems are simply invalid because their*
*problem definition requires the logically impossible*

On 6/20/2004 4:17 PM, Peter Olcott wrote:
>> : PREMISES:
>> : (1) The Halting Problem was specified in such a way that a solution
>> : was defined to be impossible.
>>
>> That is false.
>> The problem has to do with the possible existence of something.
>> If it turns out that the something doesn't exist, that does NOT
>> mean that "the solution to the problem was defined to be impossible".
>
> Yet this is not the case with the solution to the Halting Problem
> (and square circles). In both these cases it is not merely that no
> solution has been found to satisfy the requirements of the problem.
> In BOTH these cases the problem is defined in such a way that
> no solutions are possible. The lack of solution is directly derived
> from the definition of the problem itself.
>
>
>

--
Copyright 2023 Olcott

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

On 10/21/23 11:20 AM, olcott wrote:
> This is one of the clearest examples of my earliest work that
> derives my 2023-10-21 view:
>
> *All undecidable decision problems are simply invalid because their*
> *problem definition requires the logically impossible*
>
> On 6/20/2004 4:17 PM, Peter Olcott wrote:
>>>   : PREMISES:
>>>   : (1) The Halting Problem was specified in  such a way that a solution
>>>   : was defined to be impossible.
>>>
>>> That is false.
>>> The problem has to do with the possible existence of something.
>>> If it turns out that the something doesn't exist, that does NOT
>>> mean that "the solution to the problem was defined to be impossible".
>>
>> Yet this is not the case with the solution to the Halting Problem
>> (and square circles). In both these cases it is not merely that no
>> solution has been found to satisfy the requirements of the problem.
>> In BOTH these cases the problem is defined in such a way that
>> no solutions are possible. The lack of solution is directly derived
>> from the definition of the problem itself.
>>
>>
>>
>

But it doesn't do that.

The halting problem is asking if a machine can compute the Halting Function.

The Halting Function exists, and is well defined, as every possible
machihe given every possible input will either Halt in finite time, or
run for an umbounded number of steps.

The asking if a given function is computable is a valid question, as
either a machine exist that does the computation or no such machine exists.

A decision problem is called "Undecidable" if there does not exist a
program that can compute the decision function.

So, your claim, in essence, is that since we can't compute the Halting
Function (in finite time), it does not logically exist.

SO, what point of the function doesn't exist to make the function not exist?

You are just proclaiming your stupidity.

You are claiming that something is a logical impossibility that actually
exists.

Thus, you are proven to be a LIAR and an IDIOT.

I guess you think square root of two and Pi do not exist as numbers.