: 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.
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.
*These are the words that are perfectly aligned with my current view*
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.
On 10/21/2023 1:24 PM, 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.
*These are the words that are perfectly aligned with my current view*
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.
The halting problem is defined such that it is unsatisfiable
with a single algorithm that correctly determines the halt
status of the behavior of the direct execution of every input.
An unsatisfiable decision problem means that the decision
problem is requiring the logically impossible.
People that can think outside-the-box of the view that
they have memorized by rote can see that requiring the
logically impossible is an invalid requirement.
People that cannot-think-outside-the-box can only
parrot what they have learned by rote this memorized
pattern is the full extent of their understanding.
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