https://en.wikipedia.org/wiki/Russell%27s_paradox
ZFC axiomatic set theory simply rejects that sets can be members of themselves. This is the same as simply saying there is no such barber.
For the halting problem proofs this would be the same as rejecting the pathological input as semantically unsound.
On 1/2/2024 11:44 PM, olcott wrote:
https://en.wikipedia.org/wiki/Russell%27s_paradox
ZFC axiomatic set theory simply rejects that sets can be members of
themselves. This is the same as simply saying there is no such barber.
For the halting problem proofs this would be the same as rejecting the
pathological input as semantically unsound.
The question: Does the barber shave himself?
has no correct answer from [yes/no] so ZFC rejects the question.
When we apply the same reasoning to H(D,D) because H has
no [0/1] return value corresponding to the direct execution
of D(D) we reject the input just like ZFC rejects the question.
The Halting paradox can be solved in the same way that ZFC
solved Russell's Paradox. ZFC establishes the precedent
that self-referential paradox can be solved.
In the same way that a set is no longer allowed to contain
itself as a member an input is not allowed to call its own
termination analyzer. These inputs are recognized and rejected.
https://en.wikipedia.org/wiki/Russell%27s_paradox
ZFC axiomatic set theory simply rejects that sets can be members of themselves. This is the same as simply saying there is no such barber.
For the halting problem proofs this would be the same as rejecting the pathological input as semantically unsound.
The question: Does the barber shave himself?
has no correct answer from [yes/no] so ZFC rejects the question.
On 1/4/2024 2:58 PM, immibis wrote:
On 1/3/24 16:31, olcott wrote:
The question: Does the barber shave himself?
has no correct answer from [yes/no] so ZFC rejects the question.
Ridiculous. The correct answer is yes if the barber shaves himself, or
no if he doesn't.
Ignoramus.
https://en.wikipedia.org/wiki/Russell%27s_paradox
On 1/4/2024 2:58 PM, immibis wrote:
On 1/3/24 16:31, olcott wrote:
The question: Does the barber shave himself?
has no correct answer from [yes/no] so ZFC rejects the question.
Ridiculous. The correct answer is yes if the barber shaves himself, or
no if he doesn't.
Ignoramus.
https://en.wikipedia.org/wiki/Russell%27s_paradox
https://en.wikipedia.org/wiki/Russell%27s_paradox
ZFC axiomatic set theory simply rejects that sets can be members of themselves. This is the same as simply saying there is no such barber.
For the halting problem proofs this would be the same as rejecting the pathological input as semantically unsound.
On 1/6/2024 9:46 AM, immibis wrote:
On 1/3/24 06:44, olcott wrote:
You never answered my question.
https://en.wikipedia.org/wiki/Russell%27s_paradox
ZFC axiomatic set theory simply rejects that sets can be members of
themselves. This is the same as simply saying there is no such barber.
For the halting problem proofs this would be the same as rejecting the
pathological input as semantically unsound.
"This is the same as simply saying there is no such barber."
This is the same as simply saying there is no such halting problem
solution.
So you agree there is no such halting problem solution?
The termination analyzer must reject the input that targets itself
as invalid input thus permitting a termination analyzer for other
inputs.
Does the Barber shave himself?
Rejected as an incorrect question.
Does the directly executed D(D) halt?
Rejected as an incorrect question when posed to H.
On 1/6/2024 9:46 AM, immibis wrote:
On 1/3/24 06:44, olcott wrote:
You never answered my question.
https://en.wikipedia.org/wiki/Russell%27s_paradox
ZFC axiomatic set theory simply rejects that sets can be members of
themselves. This is the same as simply saying there is no such barber.
For the halting problem proofs this would be the same as rejecting the
pathological input as semantically unsound.
"This is the same as simply saying there is no such barber."
This is the same as simply saying there is no such halting problem
solution.
So you agree there is no such halting problem solution?
The termination analyzer must reject the input that targets itself
as invalid input thus permitting a termination analyzer for other
inputs.
Does the Barber shave himself?
Rejected as an incorrect question.
Does the directly executed D(D) halt?
Rejected as an incorrect question when posed to H.
On 1/6/2024 2:15 PM, immibis wrote:
On 1/6/24 17:18, olcott wrote:
On 1/6/2024 9:46 AM, immibis wrote:
On 1/3/24 06:44, olcott wrote:
You never answered my question.
https://en.wikipedia.org/wiki/Russell%27s_paradox
ZFC axiomatic set theory simply rejects that sets can be members of
themselves. This is the same as simply saying there is no such barber. >>>>>
For the halting problem proofs this would be the same as rejecting the >>>>> pathological input as semantically unsound.
"This is the same as simply saying there is no such barber."
This is the same as simply saying there is no such halting problem
solution.
So you agree there is no such halting problem solution?
The termination analyzer must reject the input that targets itself
as invalid input thus permitting a termination analyzer for other
inputs.
Does the Barber shave himself?
Rejected as an incorrect question.
Does the directly executed D(D) halt?
Rejected as an incorrect question when posed to H.
If a termination analyzer rejects any input, it's not a termination
analyzer, so no termination analyzer exists.
The domain of deciders does not include invalid inputs.
On 1/6/2024 2:59 PM, immibis wrote:
On 1/6/24 21:55, olcott wrote:
On 1/6/2024 2:15 PM, immibis wrote:Invalid rebuttal.
On 1/6/24 17:18, olcott wrote:
On 1/6/2024 9:46 AM, immibis wrote:
On 1/3/24 06:44, olcott wrote:
You never answered my question.
https://en.wikipedia.org/wiki/Russell%27s_paradox
ZFC axiomatic set theory simply rejects that sets can be members of >>>>>>> themselves. This is the same as simply saying there is no such
barber.
For the halting problem proofs this would be the same as
rejecting the
pathological input as semantically unsound.
"This is the same as simply saying there is no such barber."
This is the same as simply saying there is no such halting problem >>>>>> solution.
So you agree there is no such halting problem solution?
The termination analyzer must reject the input that targets itself
as invalid input thus permitting a termination analyzer for other
inputs.
Does the Barber shave himself?
Rejected as an incorrect question.
Does the directly executed D(D) halt?
Rejected as an incorrect question when posed to H.
If a termination analyzer rejects any input, it's not a termination
analyzer, so no termination analyzer exists.
The domain of deciders does not include invalid inputs.
What is the square root of an orange?
On 1/6/2024 2:59 PM, immibis wrote:
On 1/6/24 21:55, olcott wrote:
On 1/6/2024 2:15 PM, immibis wrote:Invalid rebuttal.
On 1/6/24 17:18, olcott wrote:
On 1/6/2024 9:46 AM, immibis wrote:
On 1/3/24 06:44, olcott wrote:
You never answered my question.
https://en.wikipedia.org/wiki/Russell%27s_paradox
ZFC axiomatic set theory simply rejects that sets can be members of >>>>>>> themselves. This is the same as simply saying there is no such
barber.
For the halting problem proofs this would be the same as
rejecting the
pathological input as semantically unsound.
"This is the same as simply saying there is no such barber."
This is the same as simply saying there is no such halting problem >>>>>> solution.
So you agree there is no such halting problem solution?
The termination analyzer must reject the input that targets itself
as invalid input thus permitting a termination analyzer for other
inputs.
Does the Barber shave himself?
Rejected as an incorrect question.
Does the directly executed D(D) halt?
Rejected as an incorrect question when posed to H.
If a termination analyzer rejects any input, it's not a termination
analyzer, so no termination analyzer exists.
The domain of deciders does not include invalid inputs.
What is the square root of an orange?
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