Simplified Halting Problem Proof Rebuttal

[Skepdick]

Making her wrong.

Yes, but she's right about that!

"This sentence is not true." is not true because it is not a truth bearer.

The same thing applies to Carol. Anything that Carol can say is
incorrect because her question is self-contradictory thus incorrect.

It's not her question. It's your question to her.

If it's "self-contradictory" which self is it contradicting? You or Carol?

Mutual recursion...

[PeteOlcott]

It's not her question. It's your question to her.

If it's "self-contradictory" which self is it contradicting? You or Carol?

Mutual recursion...

It is a question that contradicts any element of {yes, no}
that Carol can provide.

When D is defined to do the opposite of whatever H says
then it contradicts any element of {True, False} that H can
provide.

[Skepdick]

It is a question that contradicts any element of {yes, no}
that Carol can provide.

When D is defined to do the opposite of whatever H says
then it contradicts any element of {True, False} that H can
provide.

You are still confused.

H doesn't contradict itself.
D is contradicting H.

Different context.

[PeteOlcott]

It is a question that contradicts any element of {yes, no}
that Carol can provide.

When D is defined to do the opposite of whatever H says
then it contradicts any element of {True, False} that H can
provide.

You are still confused.

H doesn't contradict itself.
D is contradicting H.

When D does the opposite of whatever Boolean value
that H returns then D is contradicting H.

It is like I smash a Boston Cream pie in your face and you
deny that the pie exists while it drips from your face.

[Skepdick]

When D does the opposite of whatever Boolean value
that H returns then D is contradicting H.

D contradicting H is not the same thing as H contradicting itself.

D is the problem.
Not H.

It is like I smash a Boston Cream pie in your face and you
deny that the pie exists while it drips from your face.

You throwing a pie in my face is not the same thing as me throwing a pie in my own face.

You are the problem.
Not me.

[PeteOlcott]

When D does the opposite of whatever Boolean value
that H returns then D is contradicting H.

D contradicting H is not the same thing as H contradicting itself.

D is the problem.
Not H.

OK great this is close enough. When D does the opposite of
whatever H says then it is D that makes this question:
Does your input halt on its input? have no correct return
value from H. So D derives the incorrect question for H.

An incorrect question is any question that lacks a correct
answer because there is something wrong with the question.

There really is self-contradiction in there somewhere
because it has the same pattern as the Liar Paradox.

A self contradictory yes/no question is any question that
contradicts both answers.

A contradictory question differs from a self-contradictory
question find an integer N such that N > 5 and N < 2.

[Skepdick]

A contradictory question differs from a self-contradictory
question find an integer N such that N > 5 and N < 2.

Sure. Similar to "find a number which is equal to √-1"

Let x be the number you are looking for.

[PeteOlcott]

A contradictory question differs from a self-contradictory
question find an integer N such that N > 5 and N < 2.

Sure. Similar to "find a number which is equal to √-1"

Let x be the number you are looking for.

There is a whole branch of math that pretends there is such a number.

So can you see how Carol's question is self-contradictory for Carol
such that when posed to Carol both answers from the solution set
of {yes, no} are contradicted by the question?

Can you see how this is isomorphic to input D that does the
opposite of whatever Boolean value that program H returns?

[Skepdick]

A contradictory question differs from a self-contradictory
question find an integer N such that N > 5 and N < 2.

Sure. Similar to "find a number which is equal to √-1"

Let x be the number you are looking for.

There is a whole branch of math that pretends there is such a number.

So can you see how Carol's question is self-contradictory for Carol
such that when posed to Carol both answers from the solution set
of {yes, no} are contradicted by the question?

Can you see how this is isomorphic to input D that does the
opposite of whatever Boolean value that program H returns?

So the question's not a boolean. It's mis-typed. And then?

[PeteOlcott]

So can you see how Carol's question is self-contradictory for Carol
such that when posed to Carol both answers from the solution set
of {yes, no} are contradicted by the question?

Can you see how this is isomorphic to input D that does the
opposite of whatever Boolean value that program H returns?

So the question's not a boolean. It's mis-typed. And then?

Carol's question is yes/no The question posed to H:
Does your input D halt on its input? is Boolean and Boolean
is semantically equivalent to yes/no.

[Skepdick]

Carol's question is yes/no The question posed to H:
Does your input D halt on its input? is Boolean and Boolean
is semantically equivalent to yes/no.

The correct answer is Maybe Boolean.
So not a Boolean.

https://en.wikipedia.org/wiki/Monad_(fu ... ple:_Maybe

[PeteOlcott]

Carol's question is yes/no The question posed to H:
Does your input D halt on its input? is Boolean and Boolean
is semantically equivalent to yes/no.

The correct answer is Maybe Boolean.
So not a Boolean.

https://en.wikipedia.org/wiki/Monad_(fu ... ple:_Maybe

Computer science deciders are only allowed to take actions that
are equivalent to a Boolean return value. Every other action is
stipulated to be incorrect.

Likewise for Carol's question anything besides {yes, no} is not
a correct answer.

[Skepdick]

Computer science deciders are only allowed to take actions that
are equivalent to a Boolean return value. Every other action is
stipulated to be incorrect.

Nowhere does it stipulate that I can't encapsulate a Boolean in a Maybe monad.

It's a 2nd order computation.

Likewise for Carol's question anything besides {yes, no} is not
a correct answer.

And I can wrap that in a Maybe

Something like this makes perfect sense to me..

Code: Select all

data True = True 
data False = False
data MaybeTrueFalse a = Either True False | Nothing

In fact, the simplest thing for Carol to do when she realises you are entrapping her is to say "Hmmm, let me think about this for a while. I'll get back to you...". And then ignore you for infinity.

[PeteOlcott]

deleted

[PeteOlcott]

Computer science deciders are only allowed to take actions that
are equivalent to a Boolean return value. Every other action is
stipulated to be incorrect.

Nowhere does it stipulate that I can't encapsulate a Boolean in a Maybe monad.

It seems that you have reverted back to being a Troll
You know that deciders can only do the equivalent of returning a Boolean.