On 10/29/23 10:30 AM, olcott wrote:
> *Everyone agrees that this is impossible*
> No computer program H can correctly predict what another computer
> program D will do when D has been programmed to do the opposite of
> whatever H says.
>
Good that you admit that.
> H(D) is functional notation that specifies the return value from H(D)
> Correct(H(D)==false) means that H(D) is correct that D does not halt
> Correct(H(D)==true) means that H(D) is correct that D does halt
Except that it should be H(D,D), since you need to give H the input that
D needs to be given.
So, your "Correct" function is false since H(D,D) will, as you just
agreed, never return the right answer for the D designed for it.
Note also, the FUNCTION Correct must return the value false if the H as
its input doesn't return a value in a finite number of steps, as that
makes H not actually a decider, so it is not a "correct decider".
>
> For all H ∈ TM there exists input D such that
> (Correct(H(D)==false) ∨ (Correct(H(D)==true))==false
Nope, try to give the case. You are just LYING here and showing your
ignorance.
Remember, each H above is a SPECIFIC Turing machine (and for each H
there will be a SPECIFC D, based on that SPECIFIC H, for which that
SPECIFIC H will get the answer wrong.
Remember, for EVERY actual SPECIFIC Turing Machine D (with input x) D(x)
will either Halt or Not.
For every actual SPECIFIC Turing Machine H, it will either give the
correct answer, so Correct will answer True, of H will either not answer
or give an incorrect answer, so Correct will answer False.
There is no case for a SPECIFIC H, and a SPECIFIC D that Correct(H(D))
doesn't have a True or False answer. Try to show the case.
Remember H is a SPECIFIC TM, (since H ∈ TM) not a "set" of Turing
Machines. Your "Correct" predicate doesn't take a "set" of Turing
Machines, but an individual Turing Machine, and the "Pathological" D
isn't built on a "Set" of Turing Machine, but an individual one.
The actual question is about a specific input, and that ALWAYS has a
correct answer, its just that some machihes won't get it right. And we
can show that for EVERY decider we can make, there WILL be some specific
input (depending on the specific decider we are looking at) that the
decider WILL get wrong.
Thus, non-computable valid problems exist, as shown by theory.
>
> *No one pays attention to what this impossibility means*
> The halting problem is defined as an unsatisfiable specification thus
> isomorphic to a question that has been defined to have no correct
> answer.
Nope, again your ignorance of the probem.
>
> What time is it (yes or no)?
> has no correct answer because there is something wrong with the
> question. In this case we know to blame the question and not the one
> answering it.
Right, THAT question has no correct answer.
Does D halt, HAS a correct answer, H just doesn't give it.
DIFFERENCE.
Shows you don't understand the problem.
>
> When we understand that there are some inputs to every TM H that
> contradict both Boolean return values that H could return then the
> question: Does your input halt? is essentially a self-contradictory
> (thus incorrect) question in these cases.
But there IS a "Correct Answer", so the QUESTION isn't actualy
self-contradictory.
You are showing your stupidity,
>
> The inability to correctly answer an incorrect question places no actual
> limit on anyone or anything.
Sure does, but you are too stupd to understand.
>
> This insight opens up an alternative treatment of these pathological
> inputs the same way that ZFC handled Russell's Paradox.
>
Nope. ZFC handled Russell's Paradox by deciding that we can't actually
logically talk about a truely "Unversal" set of all possible sets.
At best, your equivalence is just the admission that there IS a
limitation to computabilty, that there exist a class of properties of
Turing Machine that does exist and is valid (as the property is defined
for all Turing Machines) but can not be computed by another Turing
machine, given a proper description of the machine to be decided on.
That is EXACTLY the statement you have been trying to DISPROVE for all
these years, but seem to now be accepting, but still saying it doesn't
affect anything.
You are ADMITTING some things are not computable, and then saying this
fact doesn't limit what a computation can do.
That is like saying I know I can't get this car over 80 MPH, but there
is no limit to how fast this car can go.
Just a pitiful LIE.