Simplified Halting Problem Proof Rebuttal

[PeteOlcott]

A PhD computer science professor came up with a way to show that Turing's halting problem proof is erroneous. I have simplified it for people that know nothing about computer programming.

One thing that I found in my 20 year long quest is that self-contradictory expressions are not true. “This sentence is not true.” is not true and that does not make it true. As a corollary to this self-contradictory questions are incorrect.

Linguistics understands that when the context of [who is asked] changes the meaning of this question, this context cannot be correctly ignored. When Carol's question is posed to Carol it has no correct answer.

Can Carol correctly answer “no” to this [yes/no] question?

Carol's question when posed to Carol meets the definition of an incorrect question in that both answers from the solution set of {yes, no} are the wrong answer.

Simplified Halting Problem Proof
Likewise no computer program H can say what another computer program D will do when D does the opposite of whatever H says.

[Skepdick]

A PhD computer science professor came up with a way to show that Turing's halting problem proof is erroneous. I have simplified it for people that know nothing about computer programming.

One thing that I found in my 20 year long quest is that self-contradictory expressions are not true. “This sentence is not true.” is not true and that does not make it true. As a corollary to this self-contradictory questions are incorrect.

Linguistics understands that when the context of [who is asked] changes the meaning of this question, this context cannot be correctly ignored. When Carol's question is posed to Carol it has no correct answer.

Can Carol correctly answer “no” to this [yes/no] question?

Carol's question when posed to Carol meets the definition of an incorrect question in that both answers from the solution set of {yes, no} are the wrong answer.

Simplified Halting Problem Proof
Likewise no computer program H can say what another computer program D will do when D does the opposite of whatever H says.

Nothing prevents Carol from answering yes/no to your question.

You have not defined what it means for the answer to be "correct". Define your terms; or formalize your question.

Here's your code.

Code: Select all

In [1]: def ask():
   ...:     answer = carol('Can Carol correctly answer “no” to this [yes/no] question?')
   ...:     print(f'Carol answered {answer}')
   ...:     print(f'The answer was {is_correct(answer)}')
   ...:

In [2]: def carol(question):
   ...:     from random import choice
   ...:     return choice(["Yes", "No"])
   ...:

In [3]: ask()
Carol answered No
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[3], line 1
----> 1 ask()

Cell In[1], line 4, in ask()
      2 answer = carol("Can you answer this question correctly?")
      3 print(f'Carol answered {answer}')
----> 4 print(f'The answer was {is_correct(answer)}')

NameError: name 'is_correct' is not defined

[PeteOlcott]

Can Carol correctly answer “no” to this [yes/no] question?

The computer scientist that wrote Carol's question said:
If she says “yes”, she's saying that “no” is the correct answer for her, so “yes”
is incorrect. If she says “no”, she's saying that she cannot correctly answer “no”,
which is her answer. So both answers are incorrect.

[Skepdick]

Can Carol correctly answer “no” to this [yes/no] question?

The computer scientist that wrote Carol's question said:
If she says “yes”, she's saying that “no” is the correct answer for her, so “yes”
is incorrect. If she says “no”, she's saying that she cannot correctly answer “no”,
which is her answer. So both answers are incorrect.

The person who is stating the question determines what the question means.

It's not Carol's problem that you've only given her two choices (yes/no). She's just flipping a coin...

It's on you to explain why the answer is "correct" or "incorrect".

[PeteOlcott]

Words stipulate their own meaning.
"I am going to the store to buy some cake"
does not mean
{I am going to vaccumn my carpet}.

[Skepdick]

Words stipulate their own meaning.
"I am going to the store to buy some cake does not mean"
{I am going to vaccumn my carpet}.

Nonsense. Undefined terms are meaningless in a computational setting.

Carol's just flipping a coin.

Code: Select all

random.choice(["Yes", "No"])

It's on you to explain why either choice is correct; or incorrect.

[PeteOlcott]

Carol's question is not a computational setting.

[Skepdick]

Carol's question is not a computational setting.

Then you can't constrain Carol to a yes/no answer.

Carol rebuts with "Sorry, I don't understand what you are asking me. Define 'correct'"

[Skepdick]

Can Carol correctly answer “no” to this [yes/no] question?

How's this not a computational setting?

[PeteOlcott]

The words already have meanings that need not be redundantly specified.

[Skepdick]

The words already have meanings that need not be redundantly specified.

If it was redundant Carol wouldn't ask you to elaborate; or even paraphrase the question.

If it was redundant I wouldn't be asking you to formalize your question as a decision procedure.

[PeteOlcott]

Your name says your motives.
Your primary goal has always been to thwart any honest dialogue.

[Skepdick]

Your name says your motives.
Your primary goal has always been to thwart any honest dialogue.

My primary goal has always been definability.

Define your terms.

[PeteOlcott]

You are shooting for infinite regress.
Whatever definition is provided is infinitely not good enough.
Prove that I am wrong by providing a definition that you would accept.

[Skepdick]

You are shooting for infinite regress.
Whatever definition is provided is infinitely not good enough.
Prove that I am wrong by providing a definition that you would accept.

You want me to define the terms in your question?!?

How am I supposed to figure out what you mean? Read your mind?