On 10/15/2025 4:15 AM, Mikko wrote:A problem does not entail anything, semantically or otherwise.On 2025-10-15 02:17:50 +0000, olcott said:It semantically entails U(p)
5. In shortThe halting problem does not pretend anything about U(p). It does not
The halting problem as usually formalized is syntactically consistent only because it pretends that U(p) is well-defined for every p.
even mention U(p).
The words "ptoblem" and "entail" are semantically incompatible.
It requires every decider H to report on the behaviorNo, it does not. But a decider that does not answer as required
of UTM(p). When p calls H then the behavior of UTM(p)
is outside of the domain of H.
by the halting problem is not a nalting decider.
When in fact they are not, thus a break from reality.That does not make sense. What "they" and what they are not?
The halting problem stipulates that they are in theThe halting problem does not stipulate. It asks for a method to
same domain. Correct semantic entailment proves that
they are not.
answer all questions that ask about a Turing machine and an
input that can be given to it whether the Turing machine halts.
HHH(DD)==0 and HHH1(DD)==1 proves this when the ultimateNo, it does not. It only proves that one of them gives the wrong
measure of the behavior that the input specifies is
the simulation of its input by its decider according to
the semantics of its language.
answer and the other the right one.
--
Mikko
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